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.

The Analysis of Inhomogeneous Barrier Height in In/SnTe/Si/Ag Diode

“…The same behavior of the ideality factor is observed in the literature and has been interpreted in terms of interface state density distribution ( ) [21]. The obtained non-ideal I-V characteristics in TE theory can be analyzed by considering the fluctuations due to the barrier inhomogeneity and suggesting Gaussian distribution (GD) in barrier height, [13][14][15]. This model estimated to analyze the transport properties of In/SnTe/Si/Ag diode, helps to explain the barrier differences and also n with their temperature dependence.…”

“…As listed in Table 1, these values show an abnormal behavior in which they are directly proportional to change in temperature. This temperature dependence indicates the inhomogeneous barrier formation in the diode, and the current flow can be explained by the existence of low barrier height patches [13,14]. In this case, charge carriers gain enough energy to overcome the higher barrier with increase in ambient temperature whereas they can pass over the lower barriers that triggers the current flow through patches having lower barrier height [15].…”

“…According to the Werner's model, these observed potential fluctuations is assumed to be a continuous barrier distribution at the interface [22]. In this approach, the diode with was approximated to be made of parallel diodes with different barrier heights which effect the current transport in the junction independently [14]. Therefore, the total current flow through the barrier at forward bias can be re-written as,…”

“…In addition, 0 is used to measure the deviation from the homogeneity of barrier height in the junction [14], and and are the apparent barrier height and apparent ideality factor, respectively. By using the Gaussian function to explain the inhomogeneous barrier height formation in the diode, the temperature variation of 0 distribution can be represented as,…”

Analysis of temperature dependent current-voltage and capacitance-voltage characteristics of an Au/V2O5/n-Si Schottky diode

“…8,27 In order to evaluate the activation energy, Richardson constant and homogeneous barrier height, the Eq. (2) can be rewritten as: 28 [29][30][31] have treated as a discrete regions or "patches" of lower barrier height to explain the observed barrier inhomogeneity between MS junction. In this case the current transport across the Schottky diode may be affected by the presence of barrier inhomogeneity.…”