Analysis of temperature dependent $I–V$ measurements on Pd/ZnO Schottky barrier diodes and the determination of the Richardson constant

Abstract

Temperature dependent current–voltage $(I–V)$ and Hall measurements were performed on Pd/ZnO Schottky barrier diodes in the range 20–300 K. The apparent Richardson constant was found to be $8.60\times {10}^{-9}\mathrm{A}{\mathrm{K}}^{-2}{\mathrm{cm}}^{-2}$ in the 60–160 K temperature range, and mean barrier height of 0.50 eV in the 180–300 K temperature range. After barrier height inhomogeneities correction, the Richardson constant and the mean barrier height were obtained as $167\mathrm{A}{\mathrm{K}}^{-2}{\mathrm{cm}}^{-2}$ and 0.61 eV in the temperature range 80–180 K, respectively. A defect level with energy at 0.12 eV below the conduction band was observed using the saturation current plot and $(0.11\pm 0.01)\mathrm{eV}$ using deep level transient spectroscopy measurements.

Introduction

In determining the Schottky barrier height, ${\Phi }_b$ of metal/semiconductor contacts, general $I–V$ and capacitance–voltage $(C–V)$ measurements are usually employed at room temperature, which use the assumption that only thermionic emission is responsible for the flow of electrons across the potential barrier. In this paper, we have assumed that other current transport processes also contribute towards the movement of electrons within the depletion region and across the barrier in Schottky contacts, to determine the barrier height. The equations usually used for the determination of the barrier height according to Schroder [1], indicate the dependence of the barrier height on the saturation current, $I_s$:

$${\Phi }_b=\frac{\mathit{kT}}{q}\ln \frac{{\mathit{AA}}^{*}{T}^2}{I_s}$$

where $A^{*}$ is the effective Richardson constant, A is the Schottky contact area, $I_s$ is the saturation current, k the Boltzmann constant and T is the Kelvin temperature, assuming pure thermionic emission over the barrier, such that,

$$I=I_s\left\{\exp \left(\frac{\mathit{qV}}{\mathit{kT}}\right)-1\right\}$$

This approximation factors out the effect of the series resistance, $R_s$ and the ideality factor, n. The barrier height determined using this method is for zero bias [1]. There usually exists uncertainity because of using an incorrect value of $A^{*}$ [1]. The Richardson constant has a tendency of varying with temperature, and so there is need to know the actual value of the constant in a range of temperatures, which the barrier height is being evaluated. Different values of the Richardson constant have been obtained by different researchers [2], [3], [4], [5], [6] using different temperature ranges. Since $A^{*}$ appears in the ‘ln’ term in Eq. (1), an error of two would mean the value of ${\Phi }_b$ will be affected by a factor of 0.7 kT/q [1]. Incorporating other current transport mechanisms, to make the diode non-ideal, i.e. $n>1$, the series resistance and the ideality factor, n need to be factored into Eq. (2) [7]:

$$I=I_s\exp \left[\frac{q\left(V-{\mathit{IR}}_s\right)}{\mathit{nkT}}\right]\left\{1-\exp \left(-\frac{[q(V-{\mathit{IR}}_s)]}{\mathit{kT}}\right)\right\}$$

where

$$I_s={\mathit{AA}}^{*}{T}^2\exp \left(\frac{-q{\Phi }_b}{\mathit{kT}}\right)$$

Eq. (3) is commonly used in computing the values of $I_s$ and ${\Phi }_b$ providing $n⩽1.1$ [1]. When thermionic emission is no longer the only dominant mechanism or the series resistance is too large, the ideality factor n increases. By extrapolating the semi-logarithmic plot of the general $I–V$ relationship, $I_s$ is obtained as the intercept on the vertical axis, acceptable when the pure thermionic emission vanishes and therefore no physical interpretation in calculating ${\Phi }_b$ from Eq. (4) is justified [7]. Another type of error arises when choosing the linear range from the semi-logarithmic $I–V$ relationship plot. Since the series resistance influences the upper limit while the lower part is affected by other current transport mechanisms, especially for structures with high barrier heights ${\Phi }_b$, they push the interval limit up, thus reducing the linear region [7], making it slightly impossible to fit the experimental $I–V$ curves within a wide temperature range. Gu et al. [2], and Sheng et al. [4] performed temperature dependent $I–V$ measurements on the Ag/ZnO Schottky diodes in the higher temperature ranges (200–500 K) and (265–340 K), and obtained the effective Richardson constant to be 0.248 and $0.15\mathrm{A}{\mathrm{K}}^{-2}{\mathrm{cm}}^{-2}$, respectively. Grossner et al. [8] performed some measurements on the Pd/ZnO Schottky diodes and revealed the stability of the Schottky barrier diode (SBD) in the temperature range 130–340 K. In this study, analysis of the temperature dependence of the hydrogen peroxide treated Pd/ZnO SBD and calculation of the effective mean barrier height ${\Phi }_b$, the Richardson constant $A^{*}$, the modified Richardson constant $A^{**}$ and the thermal activation energy of a defect in the ZnO sample in the temperature range (20–300 K) has been performed.