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Indian Journal of Physics

, Volume 92, Issue 11, pp 1397–1402 | Cite as

Analysis of barrier inhomogeneities in AuGe/n-Ge Schottky diode

  • A Buyukbas Ulusan
  • A Tataroglu
Original Paper
  • 74 Downloads

Abstract

The barrier inhomogeneities in AuGe/n-Ge Schottky diode have been analyzed by using current–voltage (I–V) measurements over a wide temperature range of 200 to 400 K. The electrical parameters such as ideality factor (n), zero-bias barrier height (ΦBo), and series resistance (Rs) of the diode were found to be strongly temperature dependent. The abnormal increase of the barrier height with temperature was attributed to the existence of barrier height inhomogeneities at the metal/semiconductor interface. Therefore, the conventional and modified Richardson plots were drawn to explain Gaussian distribution (GD) of barrier heights. The modified Richardson plot shows a good linearity over the temperature range. The modified Richardson constant (A*) was found to be 141.49 A cm−2 K−2, which is close to the theoretical value of 140 A cm−2 K−2 for n-Ge. Moreover, the barrier height values obtained from I–V and Norde methods are found to be in good agreement with each other.

Keywords

Schottky diode Barrier inhomogeneities Series resistance Gaussian distribution Temperature effect 

PACS Nos.

85.30.Kk 73.40.Qv 73.30.+y 73.20.-r 73.40.-c 

1 Introduction

The metal–semiconductor (MS) contacts have an important role in the performance of various semiconductor devices and integrated circuits. The Schottky diode, also known as Schottky barrier diode, may be used to study bulk defects and interface properties of a metal–semiconductor structure [1, 2, 3, 4]. Also, the Schottky diode is a semiconductor diode which has a low forward voltage drop and a very fast switching ability. The Schottky diodes are commonly used in various applications such as high power rectifiers, power supplies, detect signals, logic circuits, solar cells, and detectors. Moreover, the Schottky diode is a very useful for radio frequency applications due to its high switching speed and high frequency capability.

The performance of Schottky diodes depends on different parameters such as the barrier homogeneity, the presence of localized interface traps, the series resistance and the formation of interfacial layer. Moreover, the temperature variation has significant effects on the diode parameters of Schottky diode, i.e., saturation current, ideality factor and barrier height [1, 2, 3, 4]. Therefore, temperature dependent diode performance should be investigated in detail.

The important Schottky diode parameters were determined by thermionic emission (TE) theory and analyzed by using the current–voltage (I–V) characteristics. The most common approach for analysing the Schottky behaviour is pure thermionic emission of carriers over the barrier. At low temperatures, the barrier height for current transport decreases and the ideality factor increases. In other words, an increase in temperature causes an increase in barrier height and a decrease in ideality factor. This case is attributed to the deviation from the pure thermionic emission theory of a Schottky barrier. Also, this abnormal behavior has been explained based on barrier height inhomogeneities at the metal–semiconductor interface. The Gaussian distribution is used to describe these barrier inhomogeneities [5, 6, 7, 8, 9, 10, 11, 12, 13, 14].

The main aim of the present study is to investigate the barrier inhomogeneities in the prepared AuGe/n-Ge Schottky diode. The temperature dependence of the diode parameters was analyzed by using I–V characteristics which was measured at a wide temperature range.

2 Experimental details

AuGe/n-Ge Schottky diodes were fabricated on Sb-doped (100) n-type Ge substrate with 400 µm thickness and < 0.4 Ω cm resistivity. The native oxide on the substrate was etched in a mixture of H2O2 (30%):H2O (1:5) for 1 min. Then, the substrate was rinsed in deionized water using an ultrasonic bath for 10–15 min. Finally, the substrate was dried with filtered N2. To prepare the diode, the ohmic and rectifier contacts were formed by using a thermal evaporation system. The ohmic back contact with a thickness of ~ 150 nm was formed by the deposition of AuGe (88:12 wt%) onto the whole back surface of the substrate under 10−6 mbar vacuum. Then, the substrate was annealed in the nitrogen ambient at 350 °C for 3 min to achieve low resistivity ohmic back contact. After then, circular dot shaped rectifier front contacts with 1 mm diameter and ~ 120 nm thickness were deposited onto the front of n-Ge substrate under 10−6 mbar vacuum. Thus, AuGe/n-Ge diodes were fabricated for the electrical measurements. The electrode connections were made by silver paste. The schematic diagram of the fabricated AuGe/n-Ge (MS) type Schottky barrier diodes (SBDs) was given in the Fig. 1.
Fig. 1

Schematic diagram of AuGe/n-Ge Schottky diode

The I–V measurements were performed by the use of a Keithley 2400 source-meter in the temperature range of 200–400 K using a temperature-controlled Janes vpf-475 cryostat. The diode temperature was always monitored by using a copper-constant thermocouple close to the sample, and measured with a dmm/scanner Keithley model 199 and a Lake Shore model 321 auto-tuning temperature controller with sensitivity better than ±0.1 K.

3 Results and discussion

3.1 Current–voltage (I–V) characteristics

The current–voltage (I–V) characteristics were analyzed on the basis of thermionic emission (TE) theory. For a Schottky diode, the current is due to thermionic emission. The relation between the current (I) and applied bias voltage (V) for Schottky diode with series resistance (Rs) can be written as [1, 2],
$$ I = I_{o} \left[ {\exp \left( {\frac{{q(V - IR_{s} )}}{nkT}} \right) - 1} \right]\quad {\text{for}}\;{\text{V}} \ge 3{\text{kT}}/{\text{q}} $$
(1)
where Io is the reverse saturation current, V is the applied voltage, k is the Boltzmann constant, T is the absolute temperature, n is the ideality factor and IRs is the voltage drop across the series resistance of the junction. The ln(I) versus V curve should be a straight line at forward bias region. The Io value can be determined from the straight line intercept of the ln(I)–V curve at zero bias and is given by,
$$ I_{o} = A\,\;A^{ * } \;T^{2} \;\exp \;\left( { - \frac{{q\Phi_{Bo} }}{kT}} \right) $$
(2)
where A is the Schottky contact area, A* is the effective Richardson constant (140 A cm−2 K−2 for n-type Ge) and ΦBo is the zero-bias barrier height, which can be calculated from Eq. (2). The n value can be determined from the slope of the linear region of the ln(I)–V plot and is given by,
$$ n = \frac{q}{kT}\left( {\frac{dV}{d(\ln I)}} \right) $$
(3)
Figure 2 shows the I–V characteristics of the AuGe/n-Ge Schottky diode in the temperature range of 200–400 K. As seen in Fig. 2, the I–V plots exhibit strong temperature dependence. The current increases with increasing temperature which can be attributed to the drift velocity of heat-generated electrons and holes. This result suggests that the temperature gives a significant effect on the carrier transport through Schottky diodes. Furthermore, at forward bias region, the I–V plots deviate from linearity due to the effect of series resistance [1, 2, 15, 16, 17, 18, 19, 20, 21].
Fig. 2

I–V characteristics of the Schottky diode in the temperature range of 200–400 K

The obtained saturation current (Io), ideality factor (n) and zero-bias barrier height (ΦBo) values are given in Table 1. As seen in Table 1, while the ΦBo value increases, n value decreases with increasing temperature. The increase of ΦBo indicates that current transport across metal–semiconductor interface is temperature activated process, that is, electrons at low temperatures are able to surmount the lower barriers or patches. The n values are found to be higher than unity. High value of n can be attributed to the special density distribution of surface states at M/S interface, the wide distribution of low Schottky barrier height patches caused by lateral barrier inhomogeneities, series resistance effect, image force lowering of Schottky barrier in electric field and generation-recombination [17, 18, 19, 20, 21, 22, 23, 24, 25]. Also, such higher values of n especially at low temperatures is indicated the deviation from pure or ideal thermionic emission (TE) theory and it cannot be explained solely by tunneling mechanism, the existence of surface states and native or deposited interfacial layer. In addition, this behavior of ΦBo and n with temperature is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution of the barrier heights at the MS interface.
Table 1

Electrical parameters determined from I–V and Norde methods of the Schottky diode

T (K)

Io (A) (I–V)

n (I–V)

ΦBo (eV) (I–V)

Φb (eV) (Norde)

Rs (Ω) (Norde)

200

7.35 × 10−7

4.50

0.43

0.38

627.49

250

4.89 × 10−6

3.76

0.51

0.47

210.22

300

2.07 × 10−5

3.47

0.58

0.55

90.60

350

8.39 × 10−5

3.00

0.64

0.63

51.61

400

2.69 × 10−4

2.62

0.70

0.72

29.02

To calculate the series resistance and barrier height of the diode, an alternative method developed by Norde [26] was used. In this method, Norde function, F(V), is plotted against the V and is expressed as
$$ F(V) = \frac{V}{\gamma } - \frac{kT}{q}\ln \left( {\frac{I}{{AA^{*} T^{2} }}} \right) $$
(4)
where γ is an integer greater than the ideality factor. The barrier height can be determined from the expression
$$ \Phi_{b} = F(V_{\hbox{min} } ) + \frac{{V_{\hbox{min} } }}{\gamma } - \frac{kT}{q} $$
(5)
Figure 3 shows F(V) versus V plots of the diode at various temperatures. It is seen that these plots give a minimum point at each temperature. As seen in Table 1, the barrier height values obtained from Norde function increase with increase in temperature. This corresponds to reduction of free charge carriers. Meanwhile, the Φb values are in good agreement with the values obtained from the conventional I–V method.
Fig. 3

F(V) versus V plots of the Schottky diode

The series resistance (Rs) can be calculated from the Norde function as:
$$ R_{s} = \frac{(\gamma - n)kT}{{qI_{\hbox{min} } }} $$
(6)
where Imin is the current in the diode corresponding to voltage Vmin. The calculated Rs values for each temperature are given in Table 1. It is seen that the Rs value decreases with increasing temperature. The increase of Rs is explained by lack of free carrier concentration at low temperatures [27, 28]. In addition, the value of conductivity σ becomes increase or the value of resistivity (ρ = 1/σ) decreases with increasing temperature.
Figure 4 shows ΦBo versus n plot for the diode at various temperatures. It is seen that there is a linear relationship between ΦBo and n. This is explained by lateral inhomogeneities of the barrier heights [29, 30]. The extrapolation of the ΦBo versus n plot to n = 1 has given a homogeneous ΦBo of approximately 0.94 eV.
Fig. 4

ΦBo versus n plot for the Schottky diode

3.2 Barrier inhomogeneities

Alternatively, for the evaluation of the barrier height, the conventional Richardson plot [ln(Io/T2) vs q/kT] is drawn. Equation (2) can be rewritten as
$$ \ln \left( {\frac{{I_{0} }}{{T^{2} }}} \right) = \ln (A\,\;A^{ * } \;) - \frac{{q\Phi_{Bo} }}{kT} $$
(7)
The ln(Io/T2) versus q/kT plot should be a straight line with intercept and slope. Figure 5 shows the conventional Richardson plot of the diode. It is clear that this plot shows a straight line. From slope of the straight line, the activation energy (Ea) was found to be 154 meV. From the intercept of the straight line portion of the plot, the Richardson constant (A*) was found to be about 1.46×10−5 A cm−2 K−2. The obtained A* value is much lower than the known theoretical value of 140 A cm−2 K−2 for n-Ge. This difference is attributed to the spatially inhomogeneous barrier heights and potential fluctuations at the contact interface [31, 32, 33, 34, 35, 36, 37].
Fig. 5

Conventional Richardson plot of the Schottky diode

The barrier height inhomogeneities can be explained by assuming a Gaussian distribution (GD) of barrier heights (BHs). The apparent barrier height with a mean barrier height \( (\bar{\Phi }_{Bo} ) \) and standard deviation (σs) can be expressed as,
$$ \Phi_{Bo} = \bar{\Phi }_{Bo} - \frac{{q\sigma_{s}^{2} }}{2kT} $$
(8)
Figure 6 shows ΦBo versus q/2kT plot of the diode. It is seen that this plot gives a straight line. The mean barrier height and the standard deviation were obtained from the intercept and the slope of the linear region of the plot. The σs and \( \bar{\Phi }_{Bo} \) value were found to be about 0.14 and 0.95 eV, respectively. The σs value is lower than the \( \bar{\Phi }_{Bo} \) value. This result confirms the presence of barrier height inhomogeneties at the interface [35, 36, 37, 38, 39, 40, 41, 42, 43, 44].
Fig. 6

Barrier height (ΦBo) versus q/2kT plot of the Schottky diode

The conventional Richardson plot deviates from linearity due to the barrier inhomogeneity at low temperatures. Therefore, the Richardson plot can be modified by combining Eqs. (2) and (8), and it can be expressed as following,
$$ \ln \left( {\frac{{I_{0} }}{{T^{2} }}} \right) - \left( {\frac{{q^{2} \sigma_{0}^{2} }}{{2k^{2} T^{2} }}} \right) = \ln (A\,\;A^{ * } \;) - \frac{{q\bar{\Phi }_{Bo} }}{kT} $$
(9)
The modified Richardson plot [ln(Io/T2) − q2σ 0 2 /2k2T2 vs q/kT] should be a good straight line with slope and intercept. Figure 7 shows the modified Richardson plot of the diode. As seen in Fig. 7, this plot demonstrates a straight line. From the slope of the straight line, the mean barrier height \( (\bar{\Phi }_{Bo} ) \) was found to be 0.95 eV. From the intercept of the straight line, the modified Richardson constant (A*) was found to be 141.49 A cm−2 K−2. This value is very close to the theoretical value of 140 A cm−2 K−2 for n-Ge.
Fig. 7

Modified Richardson plot of the Schottky diode

4 Conclusions

In order to get more information on the current transport/conduction mechanisms and the formation of barrier height between AuGe and n-Ge, the forward bias I–V characteristics have been investigated in the temperature range of 200–400 K in detail. The obtained values of Io, n and ΦBo were found as a strong function of temperature. The value of the activation energy (Ea) and Richardson constant (A*) were found from the intercept and slope of the conventional Richardson plot as 154 meV and 1.46×10−5 A cm−2 K−2, respectively. It is clear that the obtained experimental value of A* is much lower than the known theoretical value of 140 A cm−2 K−2 for n-Ge. In addition, while the value of ΦBo increases, n value decreases with increasing temperature. The increase of ΦBo with increasing temperature is in agreement with the negative temperature coefficient of the band-gap of the Ge and it can be attributed barrier inhomogeneity. In this case, electrons at low temperatures are able to surmount the lower barriers or patches located at a round mean barrier height \( (\bar{\Phi }_{Bo} ) \). Therefore, both the ΦBo versus n and ΦBo versus q/2kT were drawn to get an evidence to the Gaussian distribution barrier height and these two figures show a straight line in the whole temperature range. The mean barrier height and the standard deviation were obtained from the intercept and the slope of the ΦBo versus q/2kT plot. The modified Richardson plot was drawn and it shows a good linear behavior. Thus, the values of effective Richardson constant (A*) and \( \bar{\Phi }_{Bo} \) were calculated from the intercept and slope of this plot as 141.49 A cm−2 K−2 and 0.95 eV, respectively. This value is very close to the theoretical value of 140 A cm−2 K−2 for n-Ge. In conclusion, the temperature dependence of current transport in the fabricated AuGe/n-Ge Schottky diode can be successfully explained by using TE theory with single Gaussian distribution (SGD) of the barrier height.

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Copyright information

© Indian Association for the Cultivation of Science 2018

Authors and Affiliations

  1. 1.Department of Physics, Faculty of ScienceGazi UniversityAnkaraTurkey

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