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Variable Pressure Scanning Electron Microscopy

  • Bradley ThielEmail author
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

This chapter outlines the basic design modifications and operational considerations of variable-pressure SEM's relative to their high-vacuum counterparts. As the physics of electron–solid interactions are central to understanding the operation of these instruments and optimal selection of operating parameters, an introduction to that topic is provided. That section is divided into high-energy interactions, covering scattering of electrons from the primary beam, and low-energy interactions, regarding the interactions of secondary electrons with gas molecules. The latter topic leads into the discussion of the gas ionization cascade, which is the process by which secondary electron emissions can be amplified for detection. The background in this section forms the basis for a discussion of the wide variety of secondary electron signal detection strategies that have been developed. The operational principles and signal composition of several detector classes are discussed.

The gas ionization cascade also generates positive gaseous ions, which enable uncoated insulators to be imaged without resorting to the use of conductive coatings or low-voltage imaging. The principle of charge neutralization will be discussed, along with some of the imaging artifacts that can result from the positive ions. As a consequence of the charge neutralization process, some dynamic contrast mechanisms can be observed in some dielectric specimens. These effects will be described using a model for time-dependent charge decay.

Another primary use case for the VPSEM is in the examination of hydrated specimens in their native state, or more generally, water-containing specimens. The considerations for conducting experiments under humid conditions are discussed, along with the principles governing dynamic experiments such as hydration and dehydration. Particular attention is paid to the role of dissolved species in determining the thermodynamic activity of water in solutions.

Finally, the considerations for performing electron beam microanalysis under variable-pressure conditions are presented, along with various strategies for minimizing the uncertainties for quantification.

Keywords

variable pressure environmental SEM water vapor ions skirt electron scattering ionizing collisions gas cascade insulating specimens charging 

The addition of variable-pressure operation to a scanning electron microscope significantly increases both the capabilities and complexity of the . In addition to removing the constraint that specimens must be rendered vacuum compatible, the availability of a gaseous environment around the specimen considerably expands the range of analyses and in situ experiments that are possible, and transforms the SEM from an imaging and microanalysis tool to an experimental chamber that is equipped with imaging and analysis facilities. The introduction of a gas into the specimen chamber complicates operation of the instruments as not only are there more experimental parameters to be considered (e. g., gas pressure and composition) but the values of conventional parameters (e. g., working distance and beam energy) have additional implications. Finally, most secondary electron detectors used in high-vacuum scanning electron microscopes are not suitable for low-vacuum operation, necessitating a new generation of signal detection strategies.

The aim of this chapter is to educate microscopists about the principles underlying VPSEM operation, optimization of operating parameters, and experimental design. There is an unfortunate tendency for challenges in operating these instruments to be downplayed, and this often leads to frustration on the part of users, poorly designed experiments, and incorrectly interpreted results. In fact, the potential of these instruments has not yet been fully realized. Consider that the user has an experimental chamber with full control over thermodynamic variables such as substrate temperature, gas composition and gas pressure, and that also provides the ability to provide real-time, high-resolution image and spectroscopic data. Combined with the fact that the specimen chambers of these instruments readily accommodate nonvacuum-compatible experimental apparatus, these instruments offer tremendous opportunities for creative experiments.

The essential aspect that distinguishes variable-pressure from high-vacuum scanning electron microscopes is, of course, the presence of a significant amount of gas in the specimen chamber, typically less than \({\mathrm{1}}\,{\mathrm{kPa}}\). This gas can act as an electrical agent, a thermodynamic agent, or both. The former behavior is invoked most frequently for the examination of poorly conducting specimens, whereas the most common use of the latter is to keep wet specimens hydrated. These two functions are by no means mutually exclusive, and frequently the gas performs both functions simultaneously. In both cases, however, the presence of the gas gives rise to a number of considerations. Some of these are detrimental to the performance of the instrument under certain conditions, while others simply need to be taken into account when determining optimal operating conditions and performing analysis of data. Certainly, the addition of gas pressure and composition as user-selected variables increases the complexity of operating these instruments. Additionally, familiar operating parameters such as working distance, primary beam energy and detector bias have influences beyond determining electron-optical characteristics. Because of the complicated interdependence of the operating parameters, the image and information quality rapidly degrades if suboptimal conditions are chosen, leading to much frustration among inexperienced users. It is the aim of this chapter to elucidate those relationships and help users identify appropriate analysis conditions. In the end, more operating parameters translate to the possibility of designing more sophisticated experiments. An excellent book by Stokes provides more detailed discussions of most of the topics presented here, along with extensive references to the original papers that document the development of the field [6.1]. The range of specimens that can be examined and the types of experiments that can be performed in a variable-pressure scanning electron microscope ( ) as compared to their high-vacuum counterparts more than offsets the added complexity.

A brief note on terminology is appropriate here: this class of instruments has been described by a variety of terms, including low-vacuum SEM, environmental SEM, wet SEM, and leaky sem. While no formal designation exists, the user community has generally adopted variable pressure as the preferred overarching term. If a practical distinction is desired, most application papers invoking the low-vacuum term tend to involve the gas as an electrical agent, typically using the charge neutralization capability to image uncoated dielectrics. Environmental SEM is frequently used to describe applications where the specimen is interacting with the gas in the thermodynamic sense, described above.

Fig. 6.1

Unique attributes and phenomena of variable-pressure scanning electron microscopy. Gas molecules in the specimen chamber (spheres) scatter a fraction of the electrons out of the primary beam into a skirt of low intensity that surrounds the probe impact point. A short sleeve termed a bullet can be attached to the bottom of the final lens in order to extend the high-vacuum environment of the column further into the chamber to reduce skirt scattering. A positively biased electrode attracts and accelerates secondary electrons. Collisions between the accelerated secondary electrons and gas molecules produces positive ions (+-spheres) which can reduce the effects of specimen charging

The presence of a gas results in four primary phenomena, illustrated in Fig. 6.1, that are responsible for the imaging and analytic capabilities and considerations unique to a VPSEM. The detailed description, dependencies, and implications of each phenomenon will be covered in subsequent sections, but a brief introduction to these core concepts facilitates the flow of the discussion:
  1. 1.

    Skirt formation : Some fraction of the electrons in the primary beam are scattered by gas molecules such that they arrive at the sample some distance from the nominal probe impact point. This results in a low-intensity skirt of primary electron flux surrounding the focused probe. It is important not to think of this as a broadened probe, but rather two separate distributions of electron flux striking the specimen surface.

     
  2. 2.

    Gas ionization cascade : Low-energy, free electrons in the chamber are accelerated by electric fields. Once their kinetic energy exceeds the ionization threshold of the gas, collisions with gas molecules can liberate additional low-energy electrons. If the potential drop creating the electric field is several times the ionization potential of the gas, this process can repeat multiple times, acting as a current amplifier and generating a significant ionization cascade current flowing in the field. The cascade can also be treated as a weak plasma consisting of excited and ionized gas species.

     
  3. 3.

    Ion flux : The ionization cascade also produces positively charged gas ions. These ions can flow to ameliorate the effects of negative charging in poorly conducting specimens.

     
  4. 4.

    Thermodynamic equilibrium with the sample: The gas can have thermodynamic interactions with the specimen. A prime example is stabilization of hydrated specimens with a suitable pressure of water vapor. Surface and chemical reactions can be driven by suitable partial pressures of reactive species.

     

6.1 Variable-Pressure Vacuum Systems

Most of the major system components are common between high-vacuum and variable-pressure microscope platforms. The primary differences lie in the engineering of the vacuum system and in the design of the secondary electron detectors. Danilatos has provided a detailed description of the engineering and design considerations of these systems, so this chapter will concentrate on those aspects which the operator must consider when designing experiments or optimizing imaging and analysis conditions [6.2, 6.3, 6.4].

Conventional electron microscopes require a high vacuum for three main reasons. First, most electron guns use thermionic emitters, operating at temperatures in excess of \({\mathrm{1000}}\,{\mathrm{K}}\). As the filament materials are typically tungsten metal or a ceramic such as \(\mathrm{LaB_{6}}\) or \(\mathrm{CeB_{6}}\), the presence of a gas would lead to rapid deterioration of the filament, such as oxidation if air were present. Furthermore, with both thermionic emitters and field emitters arcing between the filament and anode would destroy the gun. The second consideration is scattering of the primary beam electrons by the gas. In the electron-optical column, this scattering would degrade both the spatial coherency and energy spread of the beam, compromising the ability of the instrument to form a useful electron probe. Finally, most electron detectors cannot operate well in the presence of gas. The popular Everhart–Thornley secondary electron ( ) detector uses a high potential (\(\approx{\mathrm{12}}\,{\mathrm{kV}}\)) anode screened from the specimen chamber by a Faraday cage. As with the electron gun, the high field created by this potential would result in arcing breakdown in the gas. Solid-state and scintillation detectors for backscattered electrons ( ), can be used with up to several hundred Pascals of gas, but are ultimately limited by scattering of the signal electrons at higher pressures. Thus, there are two technical challenges to designing an SEM that will operate outside of the high-vacuum regime: the gun and electron optics must be kept below an acceptable gas pressure, and suitable means must be employed for detecting electron signals.

Separating the electron-optical column from the environment of the specimen chamber can be accomplished by using pressure-limiting apertures ( s) along the optic axis and a differential pumping system. If an aperture is comparable to or smaller than the mean free path ( ) of a gas molecule, a significant pressure differential can be maintained. The mean free path of a gas molecule is determined by the gas pressure, as shown in Fig. 6.2. For gas pressures in the range of a few hundred Pa, apertures of a few hundred micrometers are adequate. Fortunately, apertures in this size range are quite compatible with the requirements of the electron-optical column, and do not interfere significantly with its operation. The most apparent effect for users is that the maximum field of view is somewhat limited, as compared to high-vacuum microscopes. At the lowest useable magnification, the field of view is often a millimeter wide or less. PLAs can be used to separate the microscope into pressure zones that can be differentially pumped. A field emission source requires an extremely good vacuum, so ion pumps are typically used here as well as for the upper column. The greatest pressure gradient occurs at the bottom of the column, just before the beam enters the specimen chamber. An assembly sometimes termed a bullet is inserted in the column just at the bottom of the objective lens (Fig. 6.1). The bullet houses two PLAs with the intermediate portion having large baffles that open to either a diffusion or turbo-molecular pump. For applications that require a long working distance, such as x-ray microanalysis or electron backscattered pattern analysis, an elongated bullet can be used, which extends the high-vacuum region further into the chamber below the pole-piece. Extended bullets can severely limit the field of view.

Fig. 6.2

The mean free path between collisions of gas molecules derived from kinetic theory. The specific values shown are calculated for water vapor, but the significant point is the order of magnitude scaling with pressure. In the typical operating range of the VPSEM, the mfp values range from \(\mathrm{10^{1}}\) to \({\mathrm{10^{2}}}\,{\mathrm{\upmu{}m}}\)

Unlike a conventional SEM, a means needs to be provided to maintain a small pressure of the desired atmosphere in the vicinity of the specimen. Most gases can be delivered from a high-pressure gas cylinder with a suitable arrangement of valves and regulators. Water vapor is more challenging, as it cannot be supplied in this way. A sealed and evacuated flask, partially filled with water, will automatically maintain an equilibrium pressure of water vapor over the surface of the liquid. At room temperature, this pressure is around \({\mathrm{4000}}\,{\mathrm{Pa}}\). Provided the specimen chamber pressure is lower than this, water vapor will flow into the chamber upon opening a valve.

6.2 Electron–Gas Interactions

All aspects of signal generation, amplification and detection, as well as charge stabilization and imaging artifacts that are unique to VPSEM originate with electron–gas interactions. This section provides a brief introduction to that topic, and serves as a basis for subsequent discussion.

For the present purposes, scattering events between ballistic electrons and gas molecules can be classified into three processes:
  1. 1.

    Elastic

     
  2. 2.

    Ionization

     
  3. 3.

    Excitation.

     
Each of these is important in the operation of the microscope, both in terms of scattering of the primary electrons and the emitted species. Scattering events are statistical processes, and the cross sections are used as weighting factors for the various possible events. For a given gas, the magnitude of the scattering cross section is a function of the kinetic energy of the electrons, which raises a subtle but important difference between high- and low-vacuum operation: nearly all secondary electron signal detectors in variable-pressure mode invoke a positively biased electrode somewhere in the specimen chamber to drive an ionization cascade (discussed in detail in Sect. 6.3.4). The bias on the anode \(V_{\mathrm{a}}\) can be several \({\mathrm{100}}\,{\mathrm{V}}\). In addition to the high-energy backscattered electrons (comparable to the landing energy) and low-energy secondary electrons (a few eV), electrons in the gas can have kinetic energy values that range from near thermal up to \(eV_{\mathrm{a}}\). These three energy regimes correspond to very different scattering behaviors, which underpin and enable operation of the VPSEM. Broadly, the scattering cross sections for primary beam and backscattered electrons are one to three orders of magnitude smaller than for the low-energy electrons. As the scattering probabilities are exponentially dependent on the cross section, emitted secondary electrons and cascade electrons interact far stronger with the gas molecules than the probe electrons: primary electrons are largely unaffected by the gas whereas the gas ionization cascade is based on a high probability of scattering.
A simplistic scattering model is presented here, sufficient to understand and describe the relevant processes occurring in a low-vacuum environment. The probability \(\varphi\) of a given type of collision event occurring as the electron traverses a distance \(z\) through the gas is given as
$$\phi(z)=1-\mathrm{e}^{-\frac{z}{\lambda}}\;,$$
(6.1)
where \(\lambda\) is the mfp between collisions of that type. The mfp is a function of molecular species, gas pressure, and electron energy \(\varepsilon\). It is obtained from the relation
$$\lambda^{-1}=\sigma(\varepsilon)\frac{P}{k_{\mathrm{B}}T}\;,$$
(6.2)
where \(\sigma\) is the electron scattering cross section for the given collision type, \(P\) is the gas pressure, \(k_{\mathrm{B}}\) is Boltzmann's constant, and \(T\) is the gas temperature. Accordingly, the mfp between collisions decreases as pressure, or more specifically the number density of molecules, is increased. Combining (6.1) and (6.2) gives the following expression for the fraction \(f\) of electrons scattered from a beam traveling through a gas
$$f(\varepsilon,P,z,T)=1-\mathrm{e}^{-\frac{\sigma(\varepsilon)Pz}{k_{\mathrm{B}}T}}\;.$$
(6.3)
The efficiency of a given scattering process as a function of the kinetic energy of the incident particle is described by the collision cross section. As the name implies, cross section is analogous to the area of a target as presented to the projectile. Accordingly, scattering cross sections have units of length squared. The form of the collision cross section, its energy dependency, and overall magnitude are specific to the type of collision and molecular species involved. Collision cross sections for water vapor are shown in Fig. 6.3 to provide a guide as to the general forms and magnitudes. The defining characteristics and processes pertaining to each type of collision are discussed below.
Fig. 6.3

Electron impact cross sections for water vapor. The excitation cross section contains electronic excitations only. Very low energy resonance and momentum transfer processes that do not play a significant role in VPSEM have been omitted for clarity. Values used are those compiled for the work in [6.5]

6.2.1 Elastic Collisions

In an elastic collision, momentum is conserved in the system, but the trajectories of the participating particles are altered. For electrons with kinetic energies greater than approximately \({\mathrm{1}}\,{\mathrm{keV}}\) (i. e., primary beam and backscattered electrons), the partial differential cross section for an electron to be scattered through an angle of \(\theta\) can be estimated using the Rutherford scattering model , where \(\Omega\) is the solid angle. This model considers the electrostatic interaction between the electron and the potential field of the nucleus (or nuclei) of the gas molecule, and is useful for highlighting the dependencies of experimental parameters
$$\frac{\partial\sigma}{\partial\Omega}\propto\frac{Z^{2}}{\varepsilon^{2}}\text{csc}^{4}\frac{\theta}{2}\;.$$
(6.4)
From this relationship, two important conclusions can be deduced: The probability of scattering through large angles decreases as the kinetic energy of the electrons increases, and the total elastic scattering cross section scales roughly as the square of the effective atomic number of the gas \(Z\).

For molecular gases, the electronic charges can partially screen the potential field of the nucleus, reducing its scattering strength. A very relevant example of this is water vapor. While the two hydrogen nuclei contribute little to elastic scattering, the electrons they contribute to the charge cloud around the oxygen atom have a significant impact. Because oxygen only has eight electrons to begin with, the addition of two more is a large percentage increase, providing very strong screening. In fact, the effective atomic number for a water molecule is around \(\mathrm{7.5}\)—less than an oxygen atom on its own.

In the context of VPSEM, the primary manifestation of elastic scattering is the loss of electrons from the focused primary beam into a low intensity skirt surrounding the nominal probe impact point on the specimen surface. The ramifications for skirt scattering on imaging and microanalysis are discussed in subsequent sections.

Low-energy electrons, such as secondary electrons or hot electrons in an ionized gas, also undergo elastic scattering, but the effects are less obvious to the user. A simple model for low-energy scattering behavior cannot be developed, as the details of the molecular orbital structure can have a significant influence on the exact shape of the cross section. Resonant states in molecules such as \(\mathrm{N_{2}}\) and \(\mathrm{O_{2}}\) can give rise to very elaborate fine structure, for example.

6.2.2 Ionizing Collisions

Ionizing collisions occur when the impact results in the gas molecule ejecting an electron and forming a positive ion. The total ionization cross section comprise the individual cross sections for each electron in the molecule. Thus, while the general shape of the ionization cross section is very similar for all molecules, the magnitude is directly proportional to the number of electrons present. The outermost (valence) electrons are the most easily ionized and therefore dominate the cross section at all energies. The valence electrons also determine the threshold, or first ionization potential for the molecule—that is, the amount of energy required to remove one electron. For the light gases used in low-vacuum microscopes, the first ionization potentials fall in the range of \(10{-}15\,{\mathrm{eV}}\). Water vapor, for example, has a threshold of \({\mathrm{12.6}}\,{\mathrm{eV}}\), whereas helium has an unusually high value of \({\mathrm{24.5}}\,{\mathrm{eV}}\). Table 6.1 lists the first ionization potential for several common gases. Above the threshold, the valence cross section increases rapidly to a maximum value around \({\mathrm{150}}\,{\mathrm{eV}}\), followed by a monotonic decay. For all gases, there are two aspects of the ionization cross section relevant to our purposes. First is that at low incident electron energies (i. e., energies present in cascade amplification) the ionization probability increases with energy above the threshold. Second, at high energies such as those of primary and backscattered electrons, ionization probability decreases with energy. The implications of these two facts are central to the operation and design of the VPSEM and will be explored in later sections. It should be noted that the trajectory of the incident electron can be altered as a result of excess momentum transfer in an ionizing collision.

Table 6.1

Electronic properties of common gases. First ionization potentials from [6.6]. Gas capacitor coefficients from [6.7]

 

Ionization potential

(eV)

Gas capacitor coefficient \(A\)

(\(\mathrm{mm^{-1}{\,}kPa^{-1}}\))

Gas capacitor coefficient \(B\)

(\(\mathrm{V{\,}mm^{-1}{\,}kPa^{-1}}\))

Ar

\(\mathrm{15.76}\)

\(\mathrm{9.0}\)

\(\mathrm{135.0}\)

\(\mathrm{CH_{4}}\)

\(\mathrm{12.6}\)

\(\mathrm{6.0}\)

\(\mathrm{156.8}\)

\(\mathrm{CO_{2}}\)

\(\mathrm{13.78}\)

\(\mathrm{15.0}\)

\(\mathrm{350.0}\)

\(\mathrm{H_{2}}\)

\(\mathrm{15.4}\)

\(\mathrm{3.75}\)

\(\mathrm{97.5}\)

\(\mathrm{H_{2}O}\)

\(\mathrm{12.62}\)

\(\mathrm{9.75}\)

\(\mathrm{218.0}\)

He

\(\mathrm{24.59}\)

\(\mathrm{2.25}\)

\(\mathrm{25.5}\)

\(\mathrm{N_{2}}\)

\(\mathrm{15.58}\)

\(\mathrm{9.0}\)

\(\mathrm{256.5}\)

\(\mathrm{N_{2}O}\)

\(\mathrm{12.89}\)

\(\mathrm{9.0}\)

\(\mathrm{267.8}\)

\(\mathrm{O_{2}}\)

\(\mathrm{12.07}\)

\(\mathrm{9.15}\)

\(\mathrm{200.0}\)

6.2.3 Excitation Collisions

In an excitation collision, the incident electron loses energy by transforming the target atom into an excited (but neutral) electronic or vibrionic state. The latter involves exciting vibrational and rotational modes of polyatomic molecules. These interactions tend to dominate in the extremely low energy regime, where the kinetic energy of the incident electron is less than a couple of eV. Although the cross sections can be extremely large and complex for these low-energy electrons, they drop off very rapidly with increasing incident energy, and can be ignored for our purposes.

Electronic excitations are more relevant for the processes involved in low-vacuum SEM. These include promotion of bound electrons into higher energy bound orbitals as well as occasional dissociation of molecules into neutral excited species. Each possible electronic transition has a unique cross section, with a threshold corresponding to the transition energy. No additional momentum is lost from the incident electron beyond the amount required for the electronic transition. As a result, excitation collisions do not produce angular deflection of the incident electron.

6.2.4 Inelastic Scattering

The ionization and excitation cross sections together comprise the inelastic scattering cross section. That is, the cross section for scattering events that result in significant loss of momentum by the incident electron. A closely related concept is the stopping power of the gas, the rate at which ballistic electrons lose energy per unit length when traveling through the gas. Briefly, stopping power is the probability of an inelastic collision per unit length, multiplied by the average energy loss per collision. It follows that the stopping power itself is a function of the instantaneous kinetic energy of the ballistic electron. The stopping power can be used to estimate the penetration depth of a ballistic electron into a medium, by calculating the distance required to absorb all of the incident kinetic energy.

An important difference exists between the stopping powers of gaseous versus condensed phases of a given substance, such as water vapor compared to liquid water. In condensed phases, the primary mechanism by which charged particles lose kinetic energy is plasmon generation; collective oscillations of valence electrons. This is the basis for the Bethe stopping power and range equations, which are implicitly used in many Monte Carlo simulations based on the continuous slowing down approximation, developed for modeling electron–solid interactions. That algorithm assumes that the path of an electron is determined through the distribution of elastic scattering events. Energy loss takes place continuously via plasmon excitation between the elastic events. In a gas, collective oscillations are not present and energy loss takes place via discrete ionization and excitation collisions. Additionally, ionization events can also result in deflection of the incident electron and therefore contribute to determining the electron trajectory. It is therefore critical when performing calculations and simulations that the models used be appropriate for electron–gas interactions.

6.3 Imaging Considerations in a Low-Vacuum Environment

Issues associated with obtaining images in a low-vacuum environment can be divided into two categories: Interactions of the primary beam with the gas before it impacts the specimen and interactions of emitted signal electrons with charged and neutral gas molecules. Whereas scattering of the primary beam by gas molecules is generally detrimental to imaging as well as microanalysis, interaction of secondary electrons with gas molecules is essential to the operation of most of these instruments.

6.3.1 Skirt Formation

The skirt around the primary beam is a consequence of high-energy scattering processes. Although the scattering cross sections for electrons in the keV range are much smaller than for those in the eV range, the primary beam must travel at least a few millimeters through gas at the chamber pressure as it traverses the gap from the final PLA to the specimen. For the present discussion, this pathlength is defined as \(l\) for use as the \(z\) variable in (6.1)–(6.3). This distance is a few millimeters less than the working distance by some fixed amount depending on the configuration of the instrument and whether a bullet is used. Figure 6.4a,b shows (6.2) plotted as a function of pressure for several gases at various electron energies. It is apparent that except for excessively high pressures or sub-keV electron energies, the mean free path is always several millimeters. Provided that \(l\) is only a few millimeters (typically in the range of \(2{-}5\)), most electrons in the primary beam never encounter a gas molecule before impinging on the specimen. Those that do experience collisions are scattered out of the focused probe and land on the specimen some distance away from the nominal focal point, depending on the height above the specimen surface at which the event occurred and the resulting angular deflection. Because the electron mass is much smaller than that of any gas molecule, and since the velocities of primary electrons are much greater than that of the gas molecules, momentum and energy conservation indicate that the electrons are strongly forward-scattered. However, to provide a point of reference, an electron scattered through a \(10^{\circ}\) angle one millimeter above the specimen surface will land \({\mathrm{173}}\,{\mathrm{\upmu{}m}}\) away from the unscattered probe impact point.

Fig. 6.4a,b

Mean free path for angular scattering of electrons as a function of pressure. (a) MFP of electrons in water vapor for various energies. (b) MFP of \({\mathrm{20}}\,{\mathrm{keV}}\) electrons in various gases

Equation (6.3) can be used to predict the fraction of the beam that is scattered into the skirt as a function of operating conditions. An important attribute of (6.3) is the reciprocity of pressure and pathlength. Changing either of them has the same effect of the fraction of electrons scattered. Treating the link between pressure and working distance in this way allows the operator to make intelligent choices when determining operating conditions for a given experiment. In particular, it is the \(Pl\) product that determines the fraction of the primary beam that contributes to the skirt, as well as the level of background in cascade-amplified secondary electron signals. Figure 6.5a,b shows the portion of electrons in the primary beam that are scattered into the skirt by water vapor as a function of the pressure–distance product for a range of energies. Figure 6.5a,b also provides a comparison between several gases at a specific electron energy in order to illustrate the relative impact of molecular weight.

Fig. 6.5a,b

Fraction of probe electrons scattered into the skirt as a function of the pressure–distance product. (a) Water vapor at various primary electron energies. (b) Other gases compared at \({\mathrm{10}}\,{\mathrm{keV}}\). Scattering probability scales with molecular weight

Both elastic and ionization collisions contribute to the skirt, but give rise to different spatial distributions of primary electrons. Although the scattering angles tend not to be as large as those resulting from elastic collisions, the ionization cross section is around double the elastic cross section for collisions in the \({\mathrm{10^{4}}}\,{\mathrm{eV}}\) range, so predictions that only account for elastic scattering severely underestimate the fraction of the beam lost to the skirt. Furthermore, the distributions and their relative contributions to the skirt intensity do not vary in a simple manner with operating conditions. As discussed, the mean free paths for both types of scattering are dependent on the \(Pl\) product.

Within the limit of the single scattering approximation, the magnitude of the skirt changes with \(Pl\), but its shape does not. However, the ratio of the elastic and ionization cross sections is a function of electron energy, as are their respective angular scattering distribution functions. Accordingly, both the shape and magnitude of the skirt change with beam energy. When the \(Pl\) value becomes sufficiently large, electrons scattered out of the primary beam have a non-negligible probability of undergoing additional scattering events, further randomizing the flux distribution at the sample surface. The probability of an electron undergoing multiple scattering events is described by Poisson statistics, as shown in Fig. 6.6a-c. Only under conditions of large \(Pl\) and low beam energy does double scattering become a concern.

Fig. 6.6a-c

Probability of primary electrons undergoing \(N\) scattering events before impacting the specimen as a function of the pressure–distance product in water vapor. \(N\geq 1\) correspond to electrons comprising the skirt. (a\({\mathrm{5}}\,{\mathrm{keV}}\); (b\({\mathrm{10}}\,{\mathrm{keV}}\); (c\({\mathrm{30}}\,{\mathrm{keV}}\)

Clearly, the intensity distribution in the skirt is complicated, and arriving at either a quantitative description or experimental measurement of it has been one of the primary challenges of researchers in the field. One factor that hampers efforts to obtain experimental data is that while an appreciable fraction of the probe current may scatter into the skirt, those electrons are distributed over an area many orders of magnitude larger than the nominal spot size, even factoring in the interaction volume in the specimen. The flux of electrons in the unscattered probe can be more than 10 orders of magnitude greater than in the skirt just a few \(\mathrm{\upmu{}m}\) away from the probe. Developing an analytic description would be useful, however, as the skirt has significant implications for imaging and microanalysis. One approach to estimating the skirt magnitude and shape is through Monte Carlo simulations . While in principle this approach can provide great insights, the caveats regarding the use of discrete scattering models versus continuous slowing down algorithms as described in Sect. 6.2.4 should be observed.

6.3.2 Resolution

One of the most enduring misconceptions surrounding low-vacuum and environmental SEM concerns the effect of the gas and skirt on secondary electron image resolution. Anyone experienced with conventional scanning electron microscopy could be forgiven for assuming that introducing gas into the specimen chamber will broaden the primary beam, thereby degrading resolution. In practice, this is not necessarily true. Figure 6.5a,b shows the mean free path of electrons of various energies in water vapor as a function of pressure. Even at the relatively high pressure of \({\mathrm{600}}\,{\mathrm{Pa}}\) (around the minimum pressure of water vapor necessary to stabilize a hydrated specimen) the mfp is \({\mathrm{7.5}}\,{\mathrm{mm}}\) for a \({\mathrm{20}}\,{\mathrm{keV}}\) electron. This is \(2-3\times\) greater than the typical gas path of the primary beam, meaning that the average electron is not scattered, as discussed in the preceding section. This condition is sometimes referred to as the oligo-scattering regime. It follows that there are two populations of primary electrons landing on the specimen surface: those that have been scattered into the skirt and those that remain unscattered in the primary probe, whose distribution is still defined by the electron optics. We have seen that the skirt is very large in comparison to the scanned area, especially at the high magnifications where ultimate resolution becomes a factor. The secondary electron signal generated by skirt electrons is therefore essentially constant throughout the raster frame. The net result is that the total secondary electron signal emitted from the specimen consists of the highly spatially resolved signal deriving from the unscattered portion of the probe superimposed on a flat background deriving from the skirt flux. Thus, the skirt makes a uniform contribution to the overall image brightness and does not significantly affect image resolution of typical instruments. However, the combined electron current of the skirt and probe is a constant for all gas paths. As pressure (or working distance) is increased, the signal-to-background ratio decreases, resulting in noisier images as brightness and contrast are adjusted. Eventually, of course, as the \(Pl\) product is increased, single and multiple scattering events become dominant (Fig. 6.6a-c) and resolution is compromised.

6.3.3 The Gas Ionization Cascade

The gas ionization cascade is one of the primary phenomena that distinguish variable-pressure from high-vacuum scanning electron microscopy. In most configurations the secondary electron imaging signal derives from the cascade, and in all cases, it is the source of the positive ion flux that allows imaging of uncoated insulators. The principle and relevant phenomena of the gas ionization cascade are easily understood with the simple model of a gas-filled (Townsend) capacitor, as depicted in Fig 6.7 [6.7]. The conceptual structure consists of two parallel plate electrodes separated by a gap \(d\). If a bias voltage \(V_{\mathrm{a}}\) is placed on the upper electrode (anode) while the bottom electrode is held at ground, a constant electric field \(E=V_{\mathrm{a}}/d\) is created in the gap. Secondary electrons injected into the space between the electrodes (for example through secondary electron emission from the bottom electrode) are accelerated by the electric field. When the electron gains enough kinetic energy to exceed the ionization potential of the gas, an ionizing collision can occur which will produce another low-energy electron and a positive ion. The two electrons will now be accelerated and can cause further ionizing collisions. Through this process, a substantial number of electrons can arrive at the anode, resulting in a current that effectively is an amplification of the secondary electron emission current. An equal flux of positive ions moves in the opposite direction.

Fig. 6.7

Schematic of a gas ionization cascade in a Townsend gas capacitor . A constant electric field \(E\) is created by placing a potential difference \(V_{\mathrm{a}}\) between the plates of the capacitor separated by a distance \(d\). Low-energy electrons emitted from the cathode are accelerated and undergo ionizing collisions with gas molecules, amplifying the emission current. Electron paths are represented by the arced lines with collisions occurring at the bifurcation points. Positive ions drift in the opposite direction in the field

The amplification mechanism can be considered as follows: If \(N\) electrons move through an incremental distance \(\mathrm{d}z\) through an electric field \(\varepsilon_{z}\), the incremental change in the number of electrons \(\mathrm{d}N\) is given by
$$\mathrm{d}N=\alpha N_{z}\mathrm{d}z\;,$$
(6.5)
where \(\alpha\) is the average number of ionization events per unit length, also known as Townsend's first ionization coefficient . For \(N_{0}\) electrons emitted into the gap at \(z=0\), the cascade amplification gain \(g\) over distance \(d\) is found by integrating (6.5a,b), thus
$$g=\frac{N_{d}}{N_{0}}=\mathrm{e}^{\alpha d}\;.$$
(6.6)
Townsend's first ionization coefficient is a function of the gas species, gas pressure, and electric field strength. A phenomenological expression for \(\alpha\) is given by
$$\alpha=AP\mathrm{e}^{\frac{-BPd}{V_{\mathrm{a}}}}\;,$$
(6.7)
where \(A\) and \(B\) are tabulated gas-specific factors. \(A\) is related to the ionization cross section of the gas, whereas the exponential term is related to the kinetic energy distribution of the electrons in the cascade. The \(B\) coefficient represents the energy losses per unit length through inelastic collisions in the gas, that is, the average stopping power for the ensemble of cascade electrons. Representative values of \(A\) and \(B\) for some common gases under VPSEM conditions are given in Table 6.1. These are empirical values for comparison and are only valid over a limited range of pressure and field strength.

In the field strength range relevant to VPSEM, the stopping power of the gas increases as the kinetic energy of the electrons increases. Accordingly, the average kinetic energy of electrons in the cascade quickly reaches an equilibrium value where the stopping power loss per unit length exactly equals the energy gain per unit length due to the electric field. All this is to say that \(\alpha\) quickly achieves a constant value for a given combination of pressure and field strength, and the cascade can be treated as a linear amplifier of the original electron emission current.

For a given anode bias and gap, the cascade gain is a function of gas pressure, starting at unity in a perfect vacuum, rising to a maximum at some intermediate pressure, and then slowly decaying as pressure is increased further. This can be understood following the considerations discussed above: at low pressures, the stopping power of the gas is minimal and thus the mean free path between ionizing collisions is large relative to \(d\). The average number of ionizing collisions an electron undergoes before an electron reaches the anode is small, and the resulting gas ionization efficiency \(\alpha\) and gain are low. At high pressures, the frequency of collisions with gas molecules is very high. Electrons in the cascade are seldom able to acquire sufficient kinetic energy to exceed the ionization threshold of the gas and so \(\alpha\) and gain are again small. The highest gain occurs when the density of gas molecules is such that the cascading electrons are able to have ionizing collisions shortly after exceeding the ionization threshold, maximizing the number of ionization collisions an electron undergoes before reaching the anode. It follows that for a given gap distance and anode bias, there is a pressure \(P_{\text{max}}\) at which the maximum gain occurs. As the field strength is increased, either by making the gap smaller or increasing the bias, \(P_{\mathrm{max}}\) increases.

Gas pressure, anode bias, and gap distance have a complicated interdependency in determining cascade gain, however some simple and useful relationships can be stated. First, is that as with the skirt, pressure and distance have a reciprocal relationship. Considering (6.6) and (6.7), either gas pressure or cascade distance can be varied independently, and so long as the other is adjusted to keep the product constant, the gain will be unchanged. For example, if an experiment calls for changing the pressure of water vapor to affect the state of specimen hydration, the working distance and anode bias can be changed accordingly to maintain approximately constant imaging conditions. Second, is that all three parameters can be collapsed into a single reduced variable \(Pd/V=P/E\). (In the field of plasma physics, the ratio of field strength to pressure is known as the reduced field , which is a frequently used metric.) In some circumstances, it can be helpful to think of controlling the amplification conditions by balancing the mfp (via pressure) with field strength. It is more common, however, just to consider the \(Pd\) product, as this is also the primary determinant of skirt scattering. A plot of gain as a function of \(Pd\) can allow the user to quickly identify optimal amplification and skirt conditions, depending upon which parameters are dictated by experimental considerations.

Plotting gain as a function of \(Pd\) also provides a practical means for comparing the amplification behavior of different gases. Because the Townsend coefficients \(A\) and \(B\) are gas-specific, the optimal pressure-to-field strength ratio also varies for different gases. So-called master amplification plots for a few common gases are shown in Fig. 6.8. These plots can assist users in gas selection depending on experimental constraints. For example, it can be seen that while water vapor gives the highest amplification under most conditions, at very low values of \(Pd\), other gases might perform better in this aspect.

Fig. 6.8

Master amplification curves for various gases plotted as a function of pressure–distance product. Absolute amplification increases exponentially as a function of anode bias

The ionization coefficient is constant for fixed pressure and electric field strength as in the case of the gas capacitor model. More complicated situations arise when nonuniform electric fields and gas pressure gradients are present. In VPSEM, the specific electrode/detector design, chamber design, specimen geometry, and experimental conditions all contribute to creating the electric field geometry and pressure gradients. Accordingly, ionization efficiency \(\alpha\) varies from point to point as a function of local pressure and field strength, and the secondary electron signal gain is therefore determined by a more complicated integral of (6.5) along the nominal path from the emission point to the anode. Regardless of the field geometry and pressure gradients, the maximum possible gain (the gain at \(P_{\text{max}}\)) scales with the anode bias as that is the sole input of energy into the amplifier.

The Townsend gas capacitor model described above describes a linear amplification process. That is, the cascade current arriving at the anode is directly proportional to the emission current from the cathode. Supra- and sublinear effects are also possible, depending on field strength, gas type, and cathode composition. Supralinear effects are the phenomena that lead to arcing breakdown . In addition to positive ions, electronically excited neutral gas species are also created in the cascade. When these molecules relax back to the ground state, it is possible for a photon to be ejected. If that photon has sufficient energy, and strikes the surface of a low work function material, it may be able to cause photoelectric emission of an electron. That electron can in turn undergo cascade amplification, creating a second generation of excited neutrals, which can then repeat the process ad infinitum. If efficiency of electron ejection is high, the process runs away in a feedback loop until the density of charge carriers becomes so high that arcing occurs. If the efficiency is low, the process will die down after a few cycles. A similar feedback effect can occur when a positive ion strikes a surface and ejects an electron. This mechanism of secondary electron emission from molecular impact is typically associated with noble gas ions and excited neutrals impinging on low work function dielectrics.

The number of additional electrons (and ions) created in the first cascade triggered by a secondary ionization event is given by \(\kappa=\gamma[\exp(\alpha d)-1]\), where Townsend's second ionization coefficient \(\gamma\) is the probability of an ion or excited neutral causing the emission of a secondary electron when it strikes a surface. Since each of the new ions or neutrals can repeat the process, the gain multiplication factor \(M\) of additional electrons (and ions) resulting from the initial impact is given by an infinite series
$$\begin{aligned}\displaystyle M&\displaystyle\cong 1+\gamma[\exp(\alpha d)]+\gamma^{2}[\exp\alpha d)]^{2}+\cdots\\ \displaystyle&\displaystyle=\sum_{n=0}^{\infty}\kappa^{n}\;,\end{aligned}$$
(6.8)
assuming that \(\exp(\alpha d)\gg 1\). The gain increase is incorporated into the gas capacitor model by multiplying (6.6) by \(M\). When \(\kappa<1\), a finite gain increase results given by \(M=(1-\gamma)^{-1}\). Arcing breakdown is the condition resulting from \(\kappa> 1\), and \(M\rightarrow\infty\). The form of (6.8) leads to a practical recommendation—when breakdown arcing is problematic, stable imaging conditions can often be obtained simply by reducing the gain, thus bringing \(\kappa\) under unity.

Experimental values for \(\gamma\) are scattered throughout the literature and are highly inconsistent as they depend heavily on the composition and quality of the surfaces involved. The topic is covered in detail by von Engel, including experimental values [6.7]. Although the phenomenon as it relates to VPSEM has not been studied in detail, evidence suggests that this phenomenon occurs primarily with noble gases, and diatomic and other linear molecules (e. g., \(\mathrm{CO_{2}}\) and \(\mathrm{N_{2}O}\)). Reported values for those molecules are in the range of \(\mathrm{10^{-1}}\). For noble gases, the value of \(\gamma\) correlates with the first ionization potential, as it is related to the energy of the relaxation photon. Nonlinear polyatomic molecules, such as water vapor, are more easily able to undergo nonradiative relaxation by transferring the energy into vibrational modes, and so reported values are much less than unity.

The production of positive gaseous ions exactly parallels the electron cascade. The electric field accelerates the ions in the opposite direction as the electrons. However, because the collision cross section with neutral gas molecules is very high, and momentum transfer during elastic collisions is substantial, the ions never gain sufficient kinetic energy to participate in further ionization collisions. The gas capacitor model shows that the vast majority of electrons and ions are created very near the anode. One important difference, however, is that while all of the cascade electrons flow to the anode, the gaseous positive ions flow to all grounded components in the chamber, including the specimen. If the concentration of positive ions at the sample surface becomes high enough, the cascade amplification process can be partially suppressed, resulting in sublinear amplification behavior . The implications for this condition on imaging are discussed later in the context of signal formation and charge neutralization.

6.3.4 Detectors

Several strategies for detecting secondary electron signals have evolved as VPSEM technology has transitioned into widespread use. Different manufacturers use unique approaches, and some manufacturers offer a range of detectors for different use cases. All designs use an anode to power the secondary electron amplification cascade, but the signal detection strategies vary. This section will discuss several categories of detectors and provide guidelines to their selection and optimal use. The descriptions below are generic models for illustrating the main underlying principles and operating considerations of broad classes of detectors, and are not intended to represent specific commercial designs.

Coaxial Detectors

The first class of so-called gaseous secondary electron detectors were based on the design by Danilatos [6.3]. In this straightforward design, the final pressure-limiting aperture doubles as the detector: it protrudes a few millimeters into the specimen chamber and is held at an adjustable positive bias, as illustrated in Fig. 6.9. The cascade current arriving at the anode is monitored to form the SE signal. Because the electrode is located directly above the specimen, relatively flat, and coaxial with the beam, the electric field created closely approximates the Townsend gas capacitor described. The effect of operating parameters including bias voltage, gas pressure, gap distance (controlled by the working distance) and landing energy on the cascade gain characteristics, signal composition, and skirt formation can readily be predicted and understood from that model. Accordingly, this detector will be discussed at length, and other detectors will be described in terms of modifications to this design.

Fig. 6.9

Schematic cross section of a coaxial anode/detector structure positioned at the bottom of the final lens. Since the distance from the detector to the specimen surface is typically less than the detector diameter, the electric field created is approximately constant. Equipotential lines are drawn with \({\mathrm{100}}\%\) being the anode bias. The annular opening in the anode also serves as the final PLA (features are not to scale)

Some manufacturers use an arrangement similar to the Danilatos design but use the stage current to form the SE signal. Signal currents collected at the anode and at the stage contain nearly identical information. Herein lies an important functional distinction between SE signal collection in a VPSEM versus a high-vacuum SEM: an Everhart–Thornley detector is a particle counter. That is, no signal is recorded until a secondary electron emitted from the sample reaches the detector and makes a pulse. Conversely, the VPSEM detectors that measure the cascade current are actually particle detectors. As soon as a charged particle appears and begins moving in the detector field, current flows in the external circuit providing the bias to the anode. The information used to form the image is the work done by the external circuit in moving the charged particles—both electrons and ions—to the anode and cathode, respectively. In fact, because most of the electrons and ions are created very close to the anode, most of the signal is generated by the movement of ions in the field: the majority of electrons only move a short distance whereas the majority of ions need to travel nearly the entire gap length back to the specimen or stage.

A consequence of using a particle detector strategy is that a charged particle will continue to induce a signal for as long as it is moving. Specifically, the drift of positive ions to ground through the gas determines the time response characteristics of the secondary electron cascade signal. Because of their comparatively low mass and low collision cross sections, the electrons in the ionization cascade reach the anode within nanoseconds. Conversely, the ions require a few microseconds to travel from their point of creation to the grounded stage. If the ions take substantially longer than the pixel dwell time to reach ground, the signal associated with a feature in a particular pixel may bleed into subsequent pixels as excess intensity. Fast scans (i. e., short pixel dwell times) can occasionally result in bright streaks trailing from high secondary electron yield features. The effect becomes particularly pronounced when the distance from the anode to the closest grounded object is large. (Dark streaks result from a different phenomenon, as will be discussed later.) For coaxial style detectors, this condition translates to long working distances. If bright streaking is a problem in images, it often can be reduced by:
  1. 1.

    Using slower scan speeds

     
  2. 2.

    Decreasing the working distance

     
  3. 3.

    Lowering the pressure.

     
Signal Content

The total cascade current contains background components in addition to the amplified secondary electron signal. The main background components are derived from the ionization of gas molecules by backscattered and primary electrons, and from cascade amplification of secondary electrons emitted from the skirt region. An important attribute of this detector is that because the final PLA doubles as the anode, the gas pathlength \(l\) of the primary beam and the cascade distance \(d\) are identical. Changing the gas amplification conditions with either pressure or working distance has a commensurate effect on the skirt formation.

Secondary electrons generated by impact of the primary beam are amplified according to the Townsend gas capacitor model (6.6). However, the primary beam is partitioned into the unscattered probe and the skirt. Since the skirt extends to an area significantly larger than the typical image frame (particularly at high magnification), secondary electrons originating from the skirt contain no modulated specimen information. The amplified current forms a featureless background signal. Equation (6.3) gives the fraction \(f\) of electrons scattered from the beam, so that the cascade amplified secondary electron signal \(I_{\text{SE}}\) originating from the unscattered portion of the probe is given by
$$I_{\text{SE}}=\delta I_{0}(1-f)g=\delta I_{0}\left(\mathrm{e}^{\frac{-\sigma Pl}{k_{\mathrm{B}}T}}\right)(\mathrm{e}^{\alpha d})\;,$$
(6.9)
where \(I_{0}\) is the total probe current and \(\delta\) is the local secondary electron emission coefficient of the point on the specimen surface being imaged. The amplitude of the cascade current from the skirt region \(I_{\text{sk}}\) scales with a spatially averaged secondary electron emission coefficient \(\delta_{\text{av}}\)
$$I_{\text{sk}}=\delta_{\text{av}}I_{0}\left(1-\mathrm{e}^{\frac{-\sigma Pl}{k_{\mathrm{B}}T}}\right)(\mathrm{e}^{\alpha d})\;.$$
(6.10)
Electrons in the incident beam have a probability of ionizing gas molecules before impacting the specimen surface. The ionizations per unit length per Pascal \(S_{\text{PE}}\) follow directly from the pressure-dependent mean free path equation (6.2), using the ionization cross section. Each ionization event triggers a cascade propagating to the electrode, with the magnitude of the cascade current determined by the distance from the anode at which it was initialized. Integrating over the full pathlength \(d\) gives an expression for the cascade current \(I_{\text{PE}}\) due to this mechanism
$$I_{\text{PE}}\approx I_{0}\frac{S_{\text{PE}}Pl}{\alpha d}(\mathrm{e}^{\alpha d})\;.$$
(6.11)
Since this current is independent of any specimen attribute, it just creates a constant background to the amplified secondary electron signal.
Backscattered electrons can also ionize gas molecules as they travel from the specimen surface to the pole-piece. The mechanism is essentially the same as that for the primary electrons, except that the average ionizations per unit length per Pascal term \(S_{\text{BSE}}\) is larger than \(S_{\text{PE}}\) due to the fact that the backscattered electrons have a lower average energy. This current does contain some specimen-dependent information since its amplitude is modulated by the local backscattered electron emission coefficient \(\eta\), as the primary beam moves across the specimen. The current contribution is therefore
$$I_{\text{BSE}}\approx I_{0}\eta\frac{S_{\text{BSE}}Pl}{\alpha d}(\mathrm{e}^{\alpha d})\;.$$
(6.12)
Note that in (6.9)–(6.12) the distance parameters \(d\) and \(l\) are identical for the coaxial anode design, further emphasizing the pressure–distance reciprocity. The terms are left distinct in these equations as the phenomena occur with all anode structures and (6.9)–(6.12) can be modified accordingly. An additional component can arise from the cascade amplification of so-called SE3 electrons, that is, secondary electrons created by backscattered electrons striking surfaces inside the chamber. These contributions are likely small, however. In this geometry where \(d\) is typically only a few millimeters, the vast majority of backscattered electrons strike the anode directly, where the high positive bias would suppress SE emission. BSE with larger angles will strike the pole-piece, but the average distance to the anode is relatively small so these will not be amplified substantially. Regardless of the magnitude of the contribution from this mechanism, it is modulated by the backscattered emission coefficient, and therefore would just contribute to the current approximated by (6.12).
The total cascade current nominally is given by the sum of all components, so
$$I_{\mathrm{c}} =I_{\text{SE}}+I_{\text{sk}}+I_{\text{BSE}}+I_{\text{PE}}\;,$$
(6.13)
$$ \begin{aligned}\displaystyle I_{\mathrm{c}}&\displaystyle=I_{0}(\mathrm{e}^{\alpha d})\left[\vphantom{\frac{S_{\text{BSE}}Pd}{\alpha d}}\delta\mathrm{e}^{\frac{-\sigma Pd}{k_{\mathrm{B}}T}}+\delta_{\text{av}}\left(1-\mathrm{e}^{\frac{-\sigma Pd}{k_{\mathrm{B}}T}}\right)\right.\\ \displaystyle&\displaystyle\left.\quad\,+\eta\frac{S_{\text{BSE}}Pd}{\alpha d}+\frac{S_{\text{PE}}Pd}{\alpha d}\right].\end{aligned}$$
(6.14)
Clearly, the signal composition has a complex dependency on both sample parameters and operating conditions, but (6.14) shows that the desired secondary electron component of the imaged area decreases as the pressure–distance product increases. This observation gives rise to a guiding principle that the gas pressure and working distance should be kept to the lowest values that the experimental constraints will allow. Practically speaking, this type of detector is most suited for environmental applications where the pressure exceeds \({\mathrm{400}}\,{\mathrm{Pa}}\) and the gap distance between the sample surface and the detector is no more than \(2{-}5\,{\mathrm{mm}}\).
The Signal Chain

A fundamental operational difference between VPSEMs and their high-vacuum counterparts is in the signal chain. In a conventional SEM, for example one using an Everhart–Thornley secondary electron detector, the secondary electron signal is emitted, detected, amplified, and then processed to optimize image contrast and brightness. Shot-noise in the beam current is the primary source of noise in the system, as photomultipliers are generally considered low noise devices. In variable-pressure systems, the secondary electron signal is emitted, amplified by the gas cascade, then detected and processed electronically. From the user's perspective, the bias on the anode can be used to control the image contrast, as it directly affects the absolute difference in the current that the detector senses from regions on the sample having different secondary emission coefficients.

Gas cascade amplification is a stochastic process, and so introduces an additional noise component prior to detection. Under typical high gain conditions, on the order of \(E2{-}E3\), the ionization events in the cascade are normally distributed, and so the gain realized by any one emitted secondary electron falls on a normal distribution, with an average of \(\langle g\rangle\), given by (6.6), and a standard deviation given by \(\langle g\rangle^{1/2}\). Increasing the gain by changing the pressure, cascade path, or anode bias will also increase the cascade noise. Increasing the \(Pd\) product may increase or decrease the average gain, and associated noise, depending on the regime where one is operating on the amplification curves in Fig. 6.8. However, increasing \(Pd\) will always increase the fraction of the primary beam current that is redirected into the skirt, thus degrading the signal-to-noise ratio.

Additional Considerations

A final aspect of this detector worth noting is that its coaxial location with respect to the incident beam tends to reduce the shadowing effects that contribute to the topographical appearance of secondary electron images. In an SEM image, the apparent source of illumination is determined by the detector position whereas the electron beam direction provides the nominal point of view. Hence, images made with this style of detector appear flat as compared to images taken with an off-axis detector.

A few commercial variations on this style of detector exist. Additional electrodes are sometimes used to shape the field to enhance cascade efficiency or to minimize the SE3-derived signal by directing those cascade chains to secondary electrodes.

Off-Axis Detectors

When the primary objective of the analysis is imaging of poorly conducting specimens, off-axis secondary electron detectors can be used. With these designs, the anode is located above and to the side of the specimen, typically at a distance of a few centimeters away. Figure 6.10 illustrates the generic features and construction for this class of detector. By not placing the cascade bias on the PLA, the gas pathlength for the primary beam can be decoupled from the gas amplification cascade pathlength. Because the latter is a much larger value than for the coaxial detectors, a very low gas pressure can be used and still result in a \(Pd\) combination that gives excellent gain. These instruments typically operate with \(20{-}200\,{\mathrm{Pa}}\) of gas. Conversely, the pressure–distance product \(Pl\) for determining the fraction of the primary beam that scatters to form the skirt can remain comparatively low. Thus, the working distance can be dictated by experimental design or optimizing electron optics.

Fig. 6.10

Schematic perspective of an off-axis anode/detector structure. Here, the cascade distance to the anode is decoupled from the gas path of the primary beam. Equipotential lines illustrate that the field is nonlinear. Very short working distances can suppress contrast, as the field may not have sufficient penetration into the gap between the sample and pole-piece (features are not to scale)

The electric field created by an off-axis anode is determined by the shape of the anode itself and the locations of surrounding components in the chamber, in particular the pole-piece. Because the field is not constant, it is not possible to develop a generic expression for cascade gain, noise, or the signal composition as it was for the coaxial detector. Gain still increases exponentially with anode bias, but the behavior as a function of the pressure–distance product \(Pd\), is situation dependent. However, since the cascade gain is less closely coupled to the skirt formation, imaging is more forgiving.

Unlike the coaxial design, the off-axis anode pushes most of the positive ions to the grounded pole-piece. This design allows easier self-regulation of the charge state at the sample surface. When the surface potential drifts negative, additional positive ions are attracted. When excess positive charge develops, the ions tend to drift elsewhere to ground.

Off-axis detectors are best suited for imaging poorly conducting specimens and imaging in conjunction with microanalysis where long working distances are required. Generally, they are not suitable for the higher pressures necessary for examining hydrated specimens, as the large \(Pd\) and \(Pl\) products would result in strong skirt formation, a large background signal, and poor amplification.

Magnetic Field-Assisted Coaxial Detectors

The highest resolution performance for any SEM requires very short working distances, with the sample nearly touching the pole-piece. Frequently these systems will also employ magnetic immersion lenses to aid in probe formation. In high-vacuum systems, the magnetic field causes secondary electrons to spiral back up into the lens where they can be detected using in-lens technology. These design constraints are not conducive to either standard coaxial or off-axis detector strategies, partly due to the short cascade path and partly due to the arced trajectory of electrons in a magnetic field. However, it is possible to place electrodes to create an electromagnetic field structure that facilitates the formation of a magnetron-like plasma that can amplify the secondary electron signal. An example of this detector design, illustrated in Fig. 6.11, places a coaxial anode in the pole-piece and a large diameter, annular cathode just below the anode [6.8]. The specimen surface is brought just under the cathode, which results in a very small electron-optical working distance that is conducive to high-resolution imaging. The cathode is typically grounded, which terminates the electrical field created by the anode, and creates a near-zero equipotential at the sample surface. The entire structure is immersed in the magnetic field from the final lens. Electrons emitted from the sample are injected into the electromagnetic field of the detector, where they follow a cycloidal trajectory interrupted by cascade collisions with gas molecules. Because of the magnetic field, electrons in the cascade cannot reach the anode until they have lost all of their kinetic energy to inelastic collisions. Accordingly, the amplification behavior of these detectors shows only a weak dependence on gas pressure. Very low pressures can therefore be used without sacrificing signal gain or control over specimen charging . As the cathode limits the cascade field, the distance between the sample surface and the cathode plane only determines the secondary electron collection efficiency of the detector, but not the amplification factor. These attributes taken together allow this style of detector to produce image resolution equivalent to that obtained by the same final lens in high vacuum on a conducting specimen.

Fig. 6.11

Schematic cross section of a magnetic field-assisted, coaxial structure positioned at the bottom of the final lens. The upper and lower electrodes, together with the middle anode, define the electric field geometry and decouple the amplification field from the specimen. The magnetic field lines run vertically through the structure, resulting in a complex electron cascade process where the gain is largely independent of pressure. The distance from the sample to the bottom electrode should be as small as possible to permit maximum collection of secondary electrons (features are not to scale)

Luminescence Detectors

For some gas molecules, relaxation from an excited state can result in the emission of a visible photon. This radiative relaxation is the source of the glow associated with plasmas. Some VPSEM detector designs exploit this phenomenon and use the light intensity emitted by the ionization cascade as a signal. Just as the number of ionization events in the cascade is proportional to the secondary electron current, so is the number of excitation collisions. Hence, the cascade glow intensity is directly modulated by the secondary electron emission current, and can be used as a proxy for the secondary electron signal [6.9]. Although any electrode geometry can be used to generate the luminous plasma, it is beneficial to have the electrode in close proximity to the photodetector to maximize light collection efficiency. Light detectors tend to be optimized for specific wavelength bands, so the detector and gas composition need to be matched for optimal performance.

Aside from the restrictions on the gas composition, the chief drawback of this style of detector is that the chain of events from emission to detection has an additional step as compared to the current detectors: the excited species needs to undergo radiative decay, and the emitted photon needs to be detected. Excited states have an associated relaxation lifetime that varies by molecular species and specific excited state, and can range from nanoseconds to hours. If the decay times are longer than the pixel dwell time in the SEM, the signal can spread into adjacent pixels. As with the case of the induced current from the flow of positive ions, the resultant streaking effect in the images can be minimized by using long pixel dwell times.

Backscattered Detectors

Most semiconductor-based backscattered electron detectors work equally well in high- and low-vacuum conditions. There are no special considerations for using these in variable-pressure applications. Depending on the physical arrangement of the detector segments, however, optimal signal collection efficiency may indicate using a relatively long working distance, which can result in significant skirt formation. Using the lowest possible pressure is advisable, or using an extended analytical bullet can minimize the skirt formation. Backscattered electron detectors that use a scintillator and a light-pipe may experience interference due to gas luminescence, so their utility depends on the properties of the chamber gas. There have been some commercial attempts to develop conversion style backscatter detectors, where SE3 electrons (secondary electrons created from backscattered electron impact) are amplified through a gas ionization cascade, but there are limited use cases for these as conventional detectors appear to function adequately.

Transmission Mode Detectors

A variety of transmission mode detectors have been demonstrated, some of which are based on direct detection of transmitted electrons using a modified solid-state backscattered detector, while others are based on conversion of the transmitted electrons into a secondary electron cascade. Direct detection configurations are subject to the same considerations that are outlined for the primary beam skirt formation in Sect. 6.3.1. Depending on gas pressure and type, electron energy and distance from the specimen to the detector, some fraction of the transmitted electrons will be scattered by gas molecules. This skirting process can lead to loss of signal and increased background when using a multisegment detector to collect bright and dark field images. Considerations for using conversion style detectors are extremely dependent on the design and operation of the specific detector, so general statements are not possible. However, the principles underlying skirt scattering and the secondary electron–gas interactions discussed in this chapter are applicable.

6.3.5 Charge Neutralization

One of the great strengths of VPSEM is the ability to image uncoated poorly conducting specimens without resorting to low-voltage imaging. Applying Kirchhoff's junction rule to a specimen in an SEM being irradiated by an electron beam yields the following equation
$$\frac{\mathrm{d}Q}{\mathrm{d}t}=I_{0}(1-\delta-\eta)-I_{\text{sc}}\;.$$
(6.15)
In other words, if the incident probe current is not balanced by the emission and specimen currents, charge \(Q\) will accumulate in the sample. In high vacuum, if a sample is either insulating or does not have a path to ground, the specimen current is null, and then the sum of the secondary and backscattered emission coefficients must equal unity, or else charging will occur. This condition occurs at the so-called E2 cross-over energy described elsewhere in this volume. In low-vacuum conditions, gaseous positive ions flowing to the surface provide another current leg \(I_{\text{ions}}\) for negative charge to flow out of the specimen. Under these conditions, (6.15) becomes
$$0=I_{0}(1-\delta-\eta)-I_{\text{ions}}\;,$$
(6.16)
for steady-state imaging. As long as the ion flux is significantly greater than the probe current (as is the case with a typical cascade), the flow of positive ions to the sample is self-regulating—if the sample charges slightly positive, excess ions tend to flow elsewhere to nearby grounded surfaces.

It should be noted that it is incorrect to say that charging does not occur in VPSEM. Rather, the ions ameliorate and mitigate the effects of charging. Because of the processes described above, the sample surface usually maintains a potential near zero, implying that the landing energy of the primary electrons is approximately that set by the operator. Below the surface, however, the dielectric properties of the sample material still determine the transport behavior of energetic electrons. Depending on the landing energy, the primary electrons become thermalized at a depth given by the electron range in the material. Excess negative charge is therefore accumulated at a depth that is on the order of \(\upmu{}\)m. The secondary electrons are emitted (depleted) from the escape depth, thus a net positive charge develops in the few nanometers below the surface. Additionally, if the implanted negative charge exceeds the magnitude of the positive surface charge, gaseous positive ions are attracted to the surface above that region. As a result, a dipole field develops between the implanted negative charge and the total positive charge at the surface. The dipole field likely helps sweep the excess electrons towards the surface, either to fill the holes created by SE emission, or to recombine with ions at the surface. As the sample surface strictly lies inside the dipole field, it is possible that the work function of the sample could be reduced locally, influencing the escape probability of secondary electrons.

6.3.6 Contrast Mechanisms

Imaging dielectric samples in a high vacuum requires either coating the sample with a thin conductive layer, or using a suitably low landing energy for the primary electrons. In this case, one is essentially imaging the film itself and not the specimen. While very thin layers provide topographic contrast, all other forms of secondary electron contrast are suppressed. The aim of using low-voltage conditions for imaging is to find a balanced condition (the so-called E2 cross-over energy) where the combined secondary and backscattered emission currents exactly balance the incident probe current. In other words, where
$$\delta+\eta=1\;.$$
(6.17)
Rearranging (6.17) to give the secondary electron yield suggests that under charge balance conditions, the secondary electron contrast will predominantly be the complementary signal to the backscattered emission profile. In some ways, this is a lost opportunity: consider that the magnitude of the secondary electron emission coefficient reflects the escape depth of low-energy electrons from the sample. For dielectric materials (i. e., insulators), the escape depth increases with the band gap (or forbidden energy gap in molecular materials). In a defect-free insulator, the escape depth is substantially larger than for a metal, which accounts for the very high SE yields observed in wide band-gap insulators [6.10]. Any aspect of the sample which causes a point-to-point variation in the escape depth should give rise to secondary electron contrast. It is not surprising, then, that there have been a number of reports of interesting contrast phenomena observed from dielectrics in VPSEM [6.11].

A particularly striking example of a dynamic contrast mechanism in VPSEM was shown by Griffin's work on synthetic gibbsite minerals, \(\mathrm{Al(OH)_{3}}\) [6.12]. Under imaging conditions that normally would be used for producing high-quality, low-noise images (i. e., slow scan, high dose, high cascade gain), polished cross sections of the mineral grains showed no contrast related to the grain microstructure. Lowering the dose rate by increasing scan speed, for example, revealed a rich contrast and extensive information on the grain's internal structure.

Figure 6.12a,b depicts a pair of images showing these effects. Furthermore, altering nearly any variable-pressure imaging parameter, such as landing energy, probe current, field of view, working distance, or gas pressure, produced significant changes in the image contrast. Other systems have been shown to exhibit this behavior as well, but gibbsite is useful for illustrating the general principles.

Fig. 6.12a,b

A polished gibbsite crystal imaged at two different scan rates. (a) Fast scan rates (\({\mathrm{0.1}}\,{\mathrm{s/frame}}\)) show significant contrast attributed to structural defects while at slow scan rates (b) (\({\mathrm{30}}\,{\mathrm{s/frame}}\)) the internal contrast is suppressed. Specimen courtesy of Dr. Brendan Griffin

To understand these contrast effects, it is necessary to move beyond the simple current balance model for a specimen being irradiated by an electron beam, and consider the time-dependent model proposed by Shaffner and colleagues, which treats a dielectric sample under an electron beam as a resistor–capacitor (RC ) circuit responding to a periodic current pulse, as shown schematically in Fig. 6.13 [6.13]. When the beam passes over a region of the sample corresponding to one image pixel, a pulse of charge \(Q\) is deposited. The amount of charge is determined by the probe current (less the secondary and backscattered emission currents) multiplied by the pixel dwell time. The pulse repeats at a frequency that is the inverse of the frame time \(F\). Initially, the charge is stored by the capacitive nature of the material, and then slowly decays via bulk and surface resistive pathways, and via defects such as grain boundaries and dislocations. Following the RC circuit analogy, the charge decays exponentially, with a time constant \(\tau\) determined by the permittivity and conductivity of the material.
$$\frac{\mathrm{d}Q}{\mathrm{d}t}=Q_{0}\,\mathrm{e}^{-\frac{t}{\tau}}\;.$$
(6.18)
For a good conductor, \(\tau\ll F\), meaning that the charge decays away completely before the probe returns during the next frame. For a good insulator, \(\tau\gg F\), so charge accumulates between frames, leading to the usual charging behaviors, including enhanced secondary electron emission. Nearly all materials fall into these two categories, so the original model had limited utility. The ion flux to the sample in variable-pressure SEM provides an additional path to ground for the excess charge. Since resistors in parallel add in reciprocal, the overall time constant for charge decay can be expressed in terms of the contributions from bulk, surface, defect and ion pathways
$$\tau^{-1}=\tau_{\text{bulk}}^{-1}+\tau_{\text{surface}}^{-1}+\tau_{\text{defects}}^{-1}+\tau_{\text{ions}}^{-1}\;.$$
(6.19)
Further, the user can affect the efficiency of the ion conduction pathway by changing the cascade conditions. Essentially, this variable conduction path allows the overall time constant for charge decay to become comparable to the frame time. Under the conditions of \(\tau\approx F\), a steady-state charging condition is established where the charge input by each visit of the probe decays to a consistent, nonzero value. Any point-to-point variations of permittivity or resistivity within the field of view, such as those induced by structural defects or impurities, are manifest by changes to the terms in (6.19). These variations cause a local deviation in the charge state, which in turn gives rise to secondary electron contrast. It follows that any operating parameter that affects the density of charge implanted, ion flux, or secondary electron emission will shift the overall steady-state charge balance conditions and alter contrast.
Fig. 6.13

Resistor–capacitor circuit analogy for the time-dependent surface potential \(V_{\mathrm{s}}(t)\) corresponding to an individual pixel on the specimen surface. The probe delivers a charge pulse during the dwell time, which then decays to ground via bulk \(R_{\text{bulk}}\), surface \(R_{\text{surface}}\), defect \(R_{\text{defects}}\), and ion \(R_{\text{ions}}\) pathways. Charge is stored by the bulk capacitance \(C_{\text{bulk}}\) and trap states from defects \(C_{\text{defects}}\)

6.3.7 Imaging Artifacts

For most situations, the self-regulating aspect of the charge control provides very good imaging conditions. Occasionally, however, some samples in conjunction with suboptimal imaging conditions, perhaps imposed by experimental design constraints, yield poor image quality. The two main culprits are excess signal coming from the skirt, and excess positive ions.

Space Charge, Recombination, and Signal Scavenging

Under conditions when the cascade current is particularly large, either because the gain is high or because a large probe current is being used, a significant concentration of gaseous ions can develop above the specimen surface. If the charge density is sufficiently high, the electric field between the sample and anode can be diminished, thus reducing the cascade gain and suppressing contrast [6.14, 6.15]. Large dielectric specimens are particularly vulnerable to this process, especially when a coaxial style detector is used, and the ions do not have a convenient path to ground. Continuing the gas capacitor analogy, this state is equivalent to a capacitor in a charged state. A common example of this situation is when the sample of interest (e. g., a powder) is placed on a piece of undoped silicon wafer that is a few centimeters in size. Typically, the user then increases the anode bias intending to improve contrast. The result, however, is increased ion flux to the surface, which only exacerbates the problem and further deteriorates the imaging conditions. Eventually, when the bias is increased beyond a critical value, arcing breakdown results.

If the ion density is sufficiently high around the secondary electron emission point on the sample surface, an emitted electron can be captured by and recombine with an ion. Since (6.6) assumes that all emitted electrons trigger an amplification cascade resulting in an average gain factor, each recombination event results in a substantial loss to the absolute cascade current, which manifests as sublinear gain behavior. When the recombination process results in a loss of image contrast, the condition is signal scavenging.

The most prominent effects of recombination and space charge are the formation of dark streaks trailing after particularly bright features in an image. Bright features, which are associated with regions of high emission, result in a proportionally higher flux of positive ions moving towards the sample. As the probe continues its raster, the space charge reduces gain, effectively suppressing contrast. Obviously this phenomenon has exactly the opposite effect on the image contrast as the bright streaks due to the extended signal development time caused by ions that have a lengthy transit time to ground. No simple model is possible for these two competing phenomena, as their magnitude is determined by a complex relationship between the ion mobility in the gas, specimen topography and conductivity, and the electric field strength and shape as determined by the specimen and chamber geometry. Our purpose here is to help the user understand the origins of these artifacts, which may aide in the identification of alternate conditions to minimize their presence.

Ion Traps

When good contrast is difficult to obtain, or when scavenging and space charge effects suppress normal emission and gain, contrast can often be improved by providing an efficient path to ground for excess positive ions. Keeping in mind that ions generally flow along electric field lines, a grounded conductor near the imaged area can act as an ion sink. This could take the form of a grounding finger, copper tape, or a thin wire or wire mesh, as in Fig. 6.14. Even on samples that are grounded conductors, a grounded mesh suspended just above the sample surface has been shown to substantially improve contrast and reduce signal scavenging [6.15]. Additionally, the grounded wires force a zero volt equipotential near the sample surface. This ensures that no positive potential develops on the sample surface and maximizes the potential drop for the ionization cascade.

Fig. 6.14

Ion trap mesh . Schematic of an ion-trapping grid placed just above the sample surface. Fine wires spaced around a millimeter apart provide an adequate sink for ions with minimal interference for imaging. Absolute dimensions of the structure are not important as long as the area of interest is covered

Imaging Fibers in Space

Fibrous materials are excellent candidates for examination by variable-pressure SEM, as coating can be difficult, and their high surface-to-volume ratio can make charge control by low voltage challenging. Since the gaseous ions readily penetrate filamentous and porous media, and the ions are drawn to regions of excess negative charge, imaging such samples is straightforward in VPSEM. However, unlike high-vacuum SEM, the space surrounding the fibers is not empty and so can generate background signal. An extreme, but commonplace example of this situation is when fibers are imaged during a tensile testing experiment, illustrated in Fig. 6.15. High quality images are difficult to obtain for two reasons. First, the fiber is typically not grounded. The amplification field is determined by the anode at the one end, but the ground potential is created by the tensile testing jaws and the substage, all of which can be several millimeters to centimeters away. The fiber itself floats to some higher potential in that field, reducing the potential drop to the anode. Since amplification depends exponentially on the potential drop even a small increase in specimen potential over ground can have a significant impact on amplification and therefore measured contrast. Furthermore, the positioning of grounded objects may result in a nonlinear amplification field, with a substantial fraction of the distance to the anode having low field strength. In that region, cascade efficiency is very low and most of the energy gain from the field goes into nonionizing, inelastic losses, further reducing the measured signal. The second issue is background signal coming from gas ionization by the primary beam when it is not on the fiber. When the beam is away from the fiber, it continues along its trajectory until it finally encounters a solid object, such as the substage. This can make the gas pathlength centimeters long, so considering (6.11), a substantial ionization current can develop. Additionally, if the fiber is sufficiently thin, some primary electrons can be transmitted and then trigger gas ionizations until they strike the substage. Finally, with these geometries, the transit time for ions to reach ground can be extremely long relative to the pixel dwell time, so that background intensity can easily bleed into pixels corresponding to the fiber position, further blurring the image. Taken together, these factors result in a poorly amplified signal from the fiber riding on a very bright background. The edges in particular become poorly defined, as the beam may only partially strike the sample, and have increased probability of forward scattering as well. One approach is to bring a low atomic number block of material, to just under the fiber. A grounded block of metal covered with a carbon tab, works very well for the purpose. This simple remedy addresses all of the issues identified above.

Fig. 6.15

Illustration of a fiber suspended by a mechanical testing jig. The relative positions of grounded metal components and the distance to the cascade anode determine the electrical field structure in the vicinity of the fiber

6.4 Working with Hydrated Specimens

If a specimen is hydrated, as in biological materials, or contains liquid water, as in slurries, colloidal suspensions, or emulsions, the system can be stabilized to prevent water loss by using a sufficiently high pressure of water vapor in conjunction with a cooled stage. The phase diagram for water (Fig. 6.16) indicates the stable form of water under a given combination of temperature and pressure [6.16]. The lines separating the phase fields represent conditions where the two adjacent phases are in equilibrium. Under equilibrium conditions, liquid water will not evaporate from, nor condense onto the specimen. Equilibrium can be maintained when changing either temperature or pressure, so long as the other parameter is adjusted to fall on the phase boundary.

Fig. 6.16

Phase diagram of water over the temperature and pressure ranges accessible by VPSEM

If any temperature gradients exist across the specimen, then local conditions may vary. Specimens with poor thermal conductance may be in equilibrium near the stub, but far from it at the specimen extremities. In extreme cases, some regions of the specimen can undergo dehydration while others are being saturated with water. Good thermal contact with the stage and slow, incremental steps when changing temperature are essential to minimizing this effect. If colloidal silver paint cannot be used, some success has been seen with gels or viscous, nonvolatile liquids.

Not all systems are capable of using water vapor as the chamber gas or operating at sufficiently high pressure. From the phase diagram in Fig. 6.16, it can be seen that the minimum pressure needed to stabilize liquid water is \({\mathrm{610}}\,{\mathrm{Pa}}\), with the specimen temperature just above \({\mathrm{0}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). Some hydrated specimens can be examined at lower pressures of water vapor, particularly those where there is a cell wall or other impediment to water egress, but these specimens should be regarded as slowly dehydrating. It is important to keep in mind that it is the partial pressure of water vapor that is relevant. The presence of other gases, regardless of pressure, does not affect the equilibrium conditions or the rates of evaporation/condensation.

6.4.1 Pumpdown

The time when the chamber is being pumped down to operating conditions is critical to the integrity of the specimen. Regardless of the relative humidity of the air initially in the chamber, the partial pressure of water vapor remaining after pumpdown is negligible, thus the specimen experiences dehydrating conditions throughout much of that time. Unless precautions are taken, a hydrated specimen can be severely compromised before imaging can begin. If dehydration is not a concern, the chamber initially should be pumped to the lowest pressure possible, and then flooded with water vapor up to the desired operating pressure. If this is not done, then the gas in the chamber is primarily nitrogen and oxygen. As the chamber continues to be pumped through the PLA, water vapor will be added, meaning that the gas composition and therefore gas amplification properties and image quality will change continuously.

A potentially messy issue that can occur during pumpdown is boiling of liquid water. Boiling occurs when the equilibrium vapor pressure at a given temperature exceeds the total ambient pressure. As the ambient pressure is being reduced during pumpdown, that differential can become significant, making the boiling vigorous. Violent boiling can damage fragile specimens or displace them from their mount. For this reason, among many others, it is advisable to keep the specimen lowered away from the detectors and pole-piece during pumpdown.

While pumpdown artifacts are not an issue for all specimens, some can be quite fragile. Several measures can be taken to combat this problem. First, the specimen can be cooled prior to pumpdown. Not only does this lower the equilibrium partial pressure of water vapor, it also reduces the rate at which water molecules leave the specimen. It is advisable to cool the specimen with the chamber door closed to prevent excess water from condensing on the specimen and stage, particularly in humid conditions.

Another preventative measure is to place a few droplets of water at warmer locations around the chamber before pumpdown. During the pumpdown process, these droplets will evaporate, adding water vapor as the total chamber pressure drops. The volume fraction of water vapor in the residual chamber gas can be increased considerably with this method, although it will still not be \({\mathrm{100}}\%\). Some drawbacks to this method include splatter from boiling of the droplets, and increased pumpdown time. Experience is needed to determine the optimal amount of water droplets and best locations.

If the objective during pumpdown is to minimize evaporation losses but not to soak the sample, a pump-flood cycling procedure is recommended. Cameron and Donald presented an iterative process of pumping to just below the equilibrium pressure, then flooding in water vapor to just above the equilibrium pressure, repeating this several times [6.17]. This procedure gradually increases the water vapor partial pressure until it approaches \({\mathrm{100}}\%\) of the gas while minimizing sample disruption. The further the minimum and maximum pressures are from the equilibrium pressure (\(\Updelta P\)), the fewer cycles are needed, at the cost of increased evaporative losses during the pumping phases. Some manufacturers provide an automated pumping cycle feature that allows the user to select the \(\Updelta P\) and number of cycles. For most situations, a \(\Updelta P\) of \({\mathrm{100}}\,{\mathrm{Pa}}\) with \(4{-}6\) cycles is adequate. Samples vary considerably in their nature and sensitivity, so experience is essential to developing an optimal procedure.

6.4.2 Dynamic Experiments

Moving beyond stabilization of hydrated specimens, the ability to control specimen temperature and water vapor pressure enables dynamic experiments to be designed wherein the effects of hydration, dehydration, and even sublimation rates on sample morphology can be studied. Examples of hydration experiments include swelling of absorbent fibers, deliquescence and dissolution of salts, coalescence of water droplets, wetting behavior, and water-initiated chemical reactions. Dehydration rates may be altered to examine the effect on morphology of salt or sugar crystals grown from solution. Freezing a liquid sample such as coffee can be used to explore the freeze-drying process.

Designing controlled hydration and dehydration experiments requires an understanding of the dependencies of these phenomena. When a liquid is in equilibrium with its vapor, the rate at which molecules in the liquid escape the surface \(R_{\mathrm{e}}\) is equal to the rate at which molecules from the vapor strike the surface \(R_{\mathrm{s}}\). Equations for the two processes are given by (6.20) and (6.21) [6.18]
$$R_{\mathrm{e}} \propto n_{\mathrm{l}}\left(\frac{k_{\mathrm{B}}T_{\mathrm{l}}}{2\uppi m}\right)^{\frac{1}{2}}\mathrm{e}^{\frac{-L}{RT_{\mathrm{l}}}}\;,$$
(6.20)
$$R_{\mathrm{s}} \propto\frac{P}{k_{\mathrm{B}}T_{\mathrm{v}}}\left(\frac{k_{\mathrm{B}}T_{\mathrm{v}}}{2\uppi m}\right)^{\frac{1}{2}}.$$
(6.21)
In these two equations, \(n_{\mathrm{l}}\) is the number density of molecules in the liquid, while the mass of the molecules is \(m\), and the latent heat of vaporization is \(L\) (in \({\mathrm{J{\,}mol^{-1}}}\)). Note that the gas and liquid are not generally at the same temperature. Some important observations arise from consideration of these two equations: First, as the gas temperature is essentially constant in the chamber, the strike rate depends on the gas pressure only . Second, the escape rate depends on the liquid temperature only . Each process is determined directly and independently by a user-controlled operating parameter. At equilibrium the sample temperature and gas pressure are set so that the two independent rates are exactly equal. When designing experiments, though, it is important to remember that the magnitude of the individual rates can be varied by the exact choice of pressure–temperature combination. It follows that the net rate of evaporation or condensation can be controlled by choosing the sample temperature and gas pressure.
Equations (6.20) and (6.21) are derived for ideal systems with flat liquid–vapor interfaces. If the interface has a curvature, as in the case of a droplet or liquid held in a capillary, the equilibrium vapor pressure will shift. The change in equilibrium vapor pressure depends inversely on the radius of curvature according to
$$\Updelta P=\frac{2\psi}{r}\;,$$
(6.22)
where \(\psi\) is the liquid–vapor interfacial energy. Accordingly, for droplets, where the radius of curvature is positive, the vapor pressure necessary to prevent evaporation increases. The net result is that smaller droplets will begin evaporating at a lower partial pressure of water vapor than bulk water. Conversely, water trapped in pores, valleys, or other nooks and crannies of the specimen, will remain stable to a lower partial pressure than bulk equilibrium, because of the negative radius of curvature of the capillary effect. It follows that for porous or granular materials, there can be a hysteresis effect when moving through wetting–drying cycles by changing water vapor pressure. In the absence of significant deliquescence effects, water will begin condensing when the pressure goes above the equilibrium value, but may not be completely removed from the specimen until the pressure is dropped considerably below the equilibrium value, depending on pore sizes and capillary effects .

An additional complication can arise when the pressure is changed rapidly. As evaporation is an endothermic process, if the pressure is dropped abruptly, the rate of evaporation is high, and unless the sample has sufficient thermal conductivity, the sample temperature can drop as heat is extracted. In extreme cases where the sample is nominally held just above \({\mathrm{0}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\), the sample can actually be made to freeze.

Equations (6.20) and (6.21) can also be used to estimate the rate of mass loss for liquids other than water, with the molecular mass and heat of vaporization being the critical parameters. This can be helpful when calculating the loss of solvents from a system, such as glycerol, ethanol, ethylene glycol, etc. Since the gas generally would not contain a significant partial pressure of those molecules, the sample temperature is the controlling factor in evaporation rate. Multiple liquid phases can then be stabilized effectively for observation by choosing a temperature that minimizes evaporative losses for one liquid, and then setting the water vapor pressure accordingly to stabilize the aqueous phase.

6.4.3 Working with Solutions

In many hydrated systems, the aqueous phase is not pure water, but a solution with dissolved species. For biological specimens in particular, the liquid phase can contain significant amounts of dissolved ionic species, sugars, amphiphiles, and various macromolecules. All these solutes, and ions in particular, decrease the thermodynamic activity of water, which has the effect of lowering the equilibrium vapor pressure. Thermodynamic activity \(a\) is frequently given as the ratio of the partial pressure of the solvent over a solution \(p^{*}\) to the equilibrium partial pressure of pure solvent \(p^{0}\), that is
$$a=\frac{p^{*}}{p^{0}}\;.$$
(6.23)
Strongly chaotropic solute species, such as lithium chloride disrupt the hydrogen bonding in water and reduce the escape probability. Activity values for saturated solutions of some common salts are given in Table 6.2. With such a system, the implication is that the vapor pressure needed to keep the sample in equilibrium may be sufficiently low that liquid water will not be present on the surface. The effect of various solutes on water activity is discussed at length in a paper by Blandamer et al [6.19].
Table 6.2

Thermodynamic activity of water in saturated solutions of various salts. Values from [6.19]

Salt

Thermodynamic activity of aqueous solution at \({\mathrm{4}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)

Thermodynamic activity of aqueous solution at \({\mathrm{20}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)

LiCl

\(\mathrm{0.113}\)

\(\mathrm{0.1131}\)

\(\mathrm{MgCl_{2}}\)

\(\mathrm{0.336}\)

\(\mathrm{0.3307}\)

\(\mathrm{K_{2}CO_{3}}\)

\(\mathrm{0.431}\)

\(\mathrm{0.4316}\)

KI

\(\mathrm{0.733}\)

\(\mathrm{0.699}\)

NaCl

\(\mathrm{0.757}\)

\(\mathrm{0.7547}\)

KCl

\(\mathrm{0.877}\)

\(\mathrm{0.8511}\)

Salts and other dissolved species can complicate experiments that aim to remove water from a system, even if the concentration is dilute. As water evaporates, the solute concentration increases, further driving down the thermodynamic activity. Once the saturation limit for the solute is reached, further removal of water depends on precipitation of solute, often leading to the formation of crystals on the sample.

The reverse process, or deliquescence, can also complicate experiments. Salts will absorb water vapor from the chamber and form droplets of concentrated solution. As long as the partial pressure of water vapor in the chamber is greater than \(p^{*}\), the solution will continue to absorb more vapor and dilute the salt concentration. The rate at which deliquescence occurs depends on the relative difference between chamber pressure and \(p^{*}\).

The situation during freezing can be even more complicated. The solubility of most salts is much higher in liquid water than in ice. As a briny solution freezes, it can only incorporate solute up to its solubility limit. Excess solute is ejected into the solution ahead of the freezing front, further increasing the concentration in the liquid phase. Once the solute reaches its solubility limit, it will begin to precipitate. Furthermore, increasing the salt content of liquid water will drive down the freezing temperature, a fact well known to anyone living in northern climates. The net result is that as freezing proceeds, the temperature necessary to freeze the remaining liquid gets lower and lower. The same is also true for sugars, acids, and many other solutes. If the solute is strongly reactive, such as an acid, the increased solute concentration can lead to damage of the specimen.

Freezing point depression \(\Updelta T\) caused by a solute with molality \(b\) can be estimated from Blagden's Law
$$\Updelta T=K_{\mathrm{f}}bv\;,$$
(6.24)
where \(K_{\mathrm{f}}\) is the cryoscopic constant of the solvent (\({\mathrm{1.86}}\,{\mathrm{K{\,}mol^{-1}{\,}kg}}\) for water) and \(v\) is the van t'Hoff factor , which is the number of species created if the solute dissociates in the solvent (e. g., \(v=2\) for NaCl in water).

6.5 Microanalysis in the VPSEM

All common forms of SEM-based microanalysis, including energy-dispersive x-ray spectroscopy ( ), wavelength-dispersive spectroscopy (WDS ), and cathodoluminescence ( ) can be conducted under variable-pressure conditions, although additional considerations apply. As with imaging, charge neutralization conditions apply for microanalysis of poorly conducting specimens, allowing the primary electron landing energy to be optimized for spectroscopic considerations rather than to minimize charging.

The primary complication for microanalysis introduced by the variable-pressure environment is signal generated by the skirt electrons. In imaging, the signal arising from the skirt creates a constant background: because the skirt area is significantly larger than the raster field of view, the point-to-point variations from the skirt background level are negligible. Analytic methods, however, measure a spectrum generated when the probe is focused at a single point on the specimen. Any spurious signal originating elsewhere will be included indiscriminately, compromising both qualitative and quantitative accuracy. More simply put, it is not possible, from a single spectrum, to know whether there is a trace amount of a given element within the interaction volume under the nominal probe position, or a large concentration of that element at some distance being weakly irradiated by the skirt. Although the approaches described below have been developed specifically for energy-dispersive x-ray spectroscopy, they apply equally well to wavelength-dispersive spectroscopy and cathodoluminescence.

A number of strategies have been developed to minimize the skirt effect, while a few others attempt to correct for it. In all cases, minimizing the skirt intensity is key: gas pressure should be kept to the minimum level required by experimental constraints, and the landing energy kept as high as possible without resulting in excess overvoltage. Since the analytic working distance is fixed by chamber design, the only way to minimize the gas path is by using an extended bullet . Mansfield and Newbury have provided critical reviews of the challenges and various approaches to improving the accuracy of energy-dispersive x-ray spectra [6.20, 6.21].

6.5.1 Capillary Optics

Capillary x-ray focusing optics can be used to minimize the acceptance angle of the x-ray detector [6.21]. These can be used to collect only the x-rays originating from within a few tens of micrometers of the beam impact point. Since this is only somewhat larger than the radius of a typical x-ray generation volume, the spatial filtering is mostly effective. The chief drawback to using optics is that they do not have perfect or constant transmission fidelity across the full energy range of the x-ray spectrum, adding an additional complication to quantification.

6.5.2 Background Subtraction

Various approaches have been used to measure the background spectrum arising from the skirt electrons. With the beam stop method, a fine needle of a substance not likely to be found in the specimen is inserted between the sample and the pole-piece, and a spectrum is collected at the desired pressure. This spectrum should be comprised of the spectrum generated by the skirt plus the characteristic peaks from the needle material. If the latter are stripped manually, the resulting spectrum should be from the skirt only, and can be subtracted from the raw experimental spectrum taken at the same pressure. Large differences in average atomic number between the sample and the needle material reduce the effectiveness of this approach as the Bremsstrahlung contributions to the background will be different.

Another approach is to collect a spectrum several hundred micrometers away from the location of interest, and subtract this from the initial spectrum. The accuracy of this method depends on the homogeneity of the specimen and how closely the second region resembles the area surrounding the feature of interest. A related method is to collect a background spectrum while rastering the probe over a large area, say a \({\mathrm{100}}\,{\mathrm{\upmu{}m}}\) frame width, centered on the feature of interest. While this background includes the region irradiated by the skirt, it irradiates the entire area uniformly, which is not the case for the actual skirt. Additionally, because the skirt now irradiates an area beyond the field of view, this background is also an approximation.

6.5.3 Pressure Correction

The most powerful methods for improving quantitative accuracy are pressure-correction algorithms. The general approach is to collect spectra at two or more pressures and attempt to extrapolate back to a zero-pressure spectrum, by making assumptions regarding the pressure dependence of the spectra. Doehne proposed that if spectra \(S\) are collected at two pressures where \(P_{1}<P_{2}\), then the spectrum at zero pressure \(S\)(0) can be estimated by [6.22]
$$S(0)=S(P_{1})-[S(P_{2})-S(P_{1})]\left(\frac{P_{1}}{\Updelta P}\right).$$
(6.25)
Equation (6.25) assumes that spectra consist of the zero-pressure spectrum plus a background component that is linearly dependent on pressure. Equation (6.3) indicates that the fraction of the beam that is scattered into the skirt has an exponential dependence on pressure rather than linear, but for small values of \(\Updelta P=P_{2}-P_{1}\), the relationship is approximately linear.
Bilde-Sørensen and Appel take this approach a step further and assume that spectra taken at any given pressure \(S_{\mathrm{p}}\) are a linear combination of the spectrum from the focused probe \(S_{0}\) and the spectrum arising from the skirt (\(S_{\mathrm{s}}\)) [6.23]. Using (6.3), \(S_{\mathrm{p}}\) is given by
$$S_{\mathrm{p}}=S_{0}\mathrm{e}^{\frac{-\sigma Pl}{k_{\mathrm{B}}T}}+S_{\mathrm{s}}\left(1-\mathrm{e}^{\frac{-\sigma Pl}{k_{\mathrm{B}}T}}\right).$$
(6.26)
Rearranging
$$S_{\mathrm{p}}=(S_{0}-S_{\mathrm{s}})\mathrm{e}^{\frac{-\sigma Pl}{k_{\mathrm{B}}T}}+S_{\mathrm{s}}\;.$$
(6.27)
Plotting the intensity of a given peak as a function of the exponential term should give a linear relationship where the intercept yields the intensity arising from the skirt and the zero-pressure intensity could be extracted from the slope. Correct interpretation, however, relies on exact knowledge of the appropriate scattering cross section.

Both correction algorithms implicitly assume that the intensity of the entire skirt spectrum simply scales with pressure, and the form of the spectrum is unchanged. This assumption is only true to the extent that the single-scattering approximation is valid for the skirt electrons. If a non-negligible fraction of the probe electrons undergo multiple scattering events before striking the specimen (Fig. 6.6a-c), then the form of the skirt spectrum itself will vary and compromise the accuracy of the extrapolated zero-pressure spectrum.

6.5.4 Mapping

X-ray mapping is less vulnerable to the skirt effects for the same reason as imaging; namely that the pixel-by-pixel construction of the map causes the skirt contribution to create a fairly uniform background, which can be suppressed through normal brightness and contrast adjustments. Semiquantitative information, at least to the level of approximate elemental ratios, can be obtained by appropriate processing and scaling of elemental maps.

6.5.5 Electron Backscattered Diffraction

Electron backscattered diffraction ( ) patterns can be recorded using the large-area detectors developed for that purpose, as they are compatible with the variable-pressure environment. However, EBSD detectors require a substantial working distance to accommodate the diffraction geometry, meaning that even at very low gas pressure, scattering will be significant. The problem is further compounded by the fact that the diffracted electrons must also traverse a substantial distance to reach the detector, and so will be subject to the same scattering considerations as the primary beam. Using extremely long bullets can help with this, at the expense of limited field of view.

6.6 Summary

The variable-pressure scanning electron microscope presents a remarkable opportunity for conducting in situ experiments that can be observed and analyzed with high spatial resolution. The low-vacuum environment tolerates a wide range of specimens and experimental equipment, while the instrument itself provides complete control over the gas chemistry and pressure. The key takeaway lessons for achieving quality results are:
  • Keep the gas pathlength of the primary beam as short as possible

  • Never use more gas pressure than is absolutely necessary for the experiment

  • Generate positive ions efficiently and ensure they flow where they are needed.

Elaborate and elegant experiments can be designed if proper attention is paid to identifying the optimal imaging conditions and if the results are interpreted with care.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.College of Nanoscale Engineering and Technology InnovationSUNY Polytechnic InstituteAlbany, NYUSA

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