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

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## 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 (Φ_{Bo}), and series resistance (R_{s}) 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

_{2}O

_{2}(30%):H

_{2}O (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 N

_{2}. 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.

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

_{s}) can be written as [1, 2],

_{o}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 IR

_{s}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 I

_{o}value can be determined from the straight line intercept of the ln(I)–V curve at zero bias and is given by,

^{*}is the effective Richardson constant (140 A cm

^{−2}K

^{−2}for n-type Ge) and Φ

_{Bo}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,

_{o}), ideality factor (n) and zero-bias barrier height (Φ

_{Bo}) values are given in Table 1. As seen in Table 1, while the Φ

_{Bo}value increases, n value decreases with increasing temperature. The increase of Φ

_{Bo}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 Φ

_{Bo}and n with temperature is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution of the barrier heights at the MS interface.

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

T (K) | I | n (I–V) | Φ | Φ | R |
---|---|---|---|---|---|

200 | 7.35 × 10 | 4.50 | 0.43 | 0.38 | 627.49 |

250 | 4.89 × 10 | 3.76 | 0.51 | 0.47 | 210.22 |

300 | 2.07 × 10 | 3.47 | 0.58 | 0.55 | 90.60 |

350 | 8.39 × 10 | 3.00 | 0.64 | 0.63 | 51.61 |

400 | 2.69 × 10 | 2.62 | 0.70 | 0.72 | 29.02 |

_{b}values are in good agreement with the values obtained from the conventional I–V method.

_{s}) can be calculated from the Norde function as:

_{min}is the current in the diode corresponding to voltage V

_{min}. The calculated R

_{s}values for each temperature are given in Table 1. It is seen that the R

_{s}value decreases with increasing temperature. The increase of R

_{s}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.

_{Bo}versus n plot for the diode at various temperatures. It is seen that there is a linear relationship between Φ

_{Bo}and n. This is explained by lateral inhomogeneities of the barrier heights [29, 30]. The extrapolation of the Φ

_{Bo}versus n plot to n = 1 has given a homogeneous Φ

_{Bo}of approximately 0.94 eV.

### 3.2 Barrier inhomogeneities

_{o}/T

^{2}) vs q/kT] is drawn. Equation (2) can be rewritten as

_{o}/T

^{2}) 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 (E

_{a}) 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].

_{s}) can be expressed as,

_{Bo}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 σ

_{s}and \( \bar{\Phi }_{Bo} \) value were found to be about 0.14 and 0.95 eV, respectively. The σ

_{s}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].

_{o}/T

^{2}) − q

^{2}σ

_{0}

^{2}/2k

^{2}T

^{2}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.

## 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 I_{o}, n and Φ_{Bo} were found as a strong function of temperature. The value of the activation energy (E_{a}) 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 Φ_{Bo} increases, n value decreases with increasing temperature. The increase of Φ_{Bo} 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 Φ_{Bo} versus n and Φ_{Bo} 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 Φ_{Bo} 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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