Abstract
Interfaces to other semiconductors, producing a heterojunction, or to conductors, acting as contacts, are important parts of almost every semiconductor device. Their basic interface properties are a decisive element of the device operation and its performance. Layers of different semiconductors with a common interface may be coherently strained up to a to a critical layer thickness, which is roughly inverse to the mismatch of their in-plane lattice parameters. In thicker layers strain is at least partially relaxed by misfit dislocations.
The electronic properties of semiconductor heterojunctions and metal-semiconductor contacts are governed by the alignment of their electronic bands. Early models describe band offsets and barrier heights as the difference of two bulk properties. While related chemical trends are found for certain conditions, the band lineup cannot be predicted with sufficient accuracy by a single universal model. Interdiffusion on an atomic scale, defects located at the interface, and leaking out of eigenfunctions from one into the other material create interface dipoles, which modify alignments guessed from simple properties of the bulk materials. Additional shifts originate from strain. Various models exist, each describing certain groups of materials forming interfaces. Linear models define reference levels within each material such as charge neutrality levels or branch-point energies within the bandgap, average interstitial potentials, or use localized states of impurities lying deep in the bandgap. Nonlinear models account for the formation of interface dipoles; such charge accumulation can be induced by band states near the interface in one semiconductor lying in the bandgap of the other or by disorder at the interface inducing gap states. More recent first-principle approaches model heterointerfaces explicitly or align bands with respect to the vacuum level by including surfaces.
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- 1.
The electron affinity of a semiconductor is defined as the energy difference from the lower edge of the conduction band to the vacuum level, i.e., the energy gained when an electron is brought from infinity into the bulk of a crystal, resting at E c. It should be distinguished from the electron affinity of an atom, which is equal to the energy gained when an electron is brought from infinity to attach to an atom and forms an anion.
- 2.
The substrate remains almost unstrained due to its large thickness.
- 3.
It must be noted that also other definitions for f are used in literature, particularly f = (a L–a S)/a S or f = (a L–a S)/a L.
- 4.
In a stack of layers, strain compensation may be applied by using different layer materials with counteracting positive and negative strain to keep the accumulated overall strain low.
- 5.
Linear elasticity theory is not applicable at the highly strained dislocation core. Only the elastic strain energy outside a somewhat arbitrary cutoff radius r cutoff about the dislocation line is hence calculated and a term comprising r cutoff is added to account for nonlinear elastic energy and dangling bonds in the core. Usually r cutoff = b/ρ is chosen yielding in Eq. 8 the term ln(t c/r cutoff) = ln(ρ t c/b), also written ln(t c/b)+const with const = ln(ρ).
- 6.
The Debye length L D is a function of the carrier density. It is typically on the order of \( 30\sqrt{10^{16}{\mathrm{cm}}^3/n} \left(\mathrm{nm}\right) \) with n (cm−3) as the density of free carriers.
- 7.
The workfunction ϕ and the electron affinity χ are in literature also defined in terms of potentials, yielding an additional factor e to obtain an energy.
- 8.
The contact potential can be measured by the Kelvin method, i.e., by shaping the two materials into the plates of a capacitor and vibrating these plates against each other. With an induced areal charge
$$ {Q}_A={\varepsilon}_0{V}_{\mathrm{c}}/d $$and d oscillating in time, the charge must also oscillate since V c does not depend on the distance d between both plates; hence an ac current will flow between the plates when externally connected with a wire. The current vanishes when a counterpotential is applied which is equal and opposite to the contact potential. This null method is a convenient one to directly determine the contact potential.
- 9.
The Thomas-Fermi length in a metal, in which the carriers are constrained by the Fermi-Dirac distribution, is the equivalent of the Debye length in a semiconductor.
- 10.
E(z) energies within a low-dimensional nanostructure are usually drawn without slope or bending in absence of electric fields, because the nanostructure dimensions are commonly much smaller than Debye lengths.
- 11.
The valence-band lineup for InSb/GaSb/AlSb/InAs is 0, −0.45, −0.15 eV (Milnes, 1991, private communication).
- 12.
That is, such interfaces in which no other effects, e.g., strain, atomic defects, or dislocations, modify the bands or an interface dipole exists (see also Heinrich and Langer 1986).
- 13.
This applies not for point contacts; here, high-field tunneling effects (see chapter “Carrier Generation”) and phonon coupling determine the electrical behavior.
- 14.
Even though the electron density inside a metal is much higher than in the semiconductor, at its boundary to the semiconductor, this density is substantially reduced according to its effective workfunction. It is this electron density which causes a reduction of n in the semiconductor at the interface.
- 15.
A similar Schottky barrier appears in p-type semiconductors near a metal electrode with low workfunction (Fig. 16d), again when the hole density near the electrode is much smaller than in the bulk. Here the space-charge region is negatively charged and the resulting field is positive.
- 16.
This is slightly different from N c within the semiconductor bulk because of a different effective mass at the interface.
- 17.
The error encountered at the boundary of this range (here 80 nm) seems to be rather large (factor 2) when judging from the linear plot of Fig. 17. The accumulative error, when integrating from the metal/semiconductor interface, however, is tolerable, as shown in Fig. 18. The substantial simplification in the mathematical analysis justifies this seemingly crude approach.
- 18.
That is, the maximum field which lies in this approximation at the metal-semiconductor boundary (neglecting image forces)
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Böer, K.W., Pohl, U.W. (2018). Crystal Interfaces. In: Semiconductor Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-69150-3_16
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