Gaussian distribution of inhomogeneous barrier height in Al/SiO2/p-Si Schottky diodes

Abstract

The forward and reverse bias current-voltage (I-V) characteristics of Al/SiO2/p-Si (metal-insulator-semiconductor) type Schottky diodes (SDs) were measured in the temperature range of 200–400 K. Evaluation of the experimental I-V data reveals a decrease in ΦB0 and Rs but an increase in n, with a decrease in temperature. To explain this behavior of ΦB0 with temperature, we have reported a modification which included n and the tunneling parameter αχ1/2δ in the expression of reverse saturation current I0. Thus, a corrected effective barrier height ΦB eff(I-V) vs T has a negative temperature coefficient (α≈−5×10−4 eV/K), and it is in good agreement with α=−4.73×10−4 eV/K of Si band gap. Such behavior of Rs estimated from Cheung’s method could be expected for semiconductors in the temperature region, where there is no carrier freezing out, which is non-negligible at low temperatures. Also, there is a linear correlation between ΦB0(I-V) and n due to the inhomogeneities of the barrier heights (BHs). The conventional activation energy (Ea) plot exhibits nonlinearity below 320 K with the linear portion corresponding to Ea of 0.275 eV. An A∗ value of 1.45×10−5 A cm−2 K−2,which is much lower than the known value of 32 A cm−2 K−2 for p-type Si, is determined from the intercept at the ordinate of this experimental plot. Such behavior is attributed to Schottky barrier inhomogeneities by assuming a Gaussian distribution (GD) of BHs due to BH inhomogeneities that prevail at the interface. We attempted to draw a ΦB0 vs q/2kT plot to obtain evidence of a GD of the BHs, and the values of Φ¯B0=1.136 eV and σ0=0.159 V for the mean BH and standard deviation at zero bias have been obtained from this plot. Therefore, the modified ln (I0/T2)−q2σ02/2k2T2 vs q/kT plot gives Φ¯B0 and A∗ values of 1.138 eV and 37.23 A cm−2 K−2, respectively, without using the temperature coefficient of the BH. This A∗ value of 37.23 A cm−2 K−2 is very close to the theoretical value of 32 A K−2 cm−2 for p-type Si. Therefore, it has been concluded that the temperature dependence of the forward bias I-V characteristics of the Al/SiO2/p-Si SDs can be successfully explained based on the thermionic emission mechanism with a GD of the BHs.