The Richardson constant and barrier inhomogeneity at Au/Si₃N₄/n-Si (MIS) Schottky diodes

Abstract

Si3N4 films were deposited on n-type silicon substrate by the radio frequency magnetron sputtering technique. The current–voltage (I–V) characteristics of Au/Si3N4/n-Si (metal–insulator–semiconductor) Schottky diodes were investigated in the temperature range of 160–400 K. Experimental results show an abnormal increase in the zero-bias barrier height (BH) (ΦBo) and a decrease in the ideality factor (n) with increasing temperature. This behavior is attributed to barrier inhomogeneities by assuming a Gaussian distribution (GD) of BHs. The conventional Richardson plot (ln(Io/T2) versus 1000/T) exhibits a linearity above about 300 K. The values of activation energy (Ea) and Richardson constant (A*) were found to be 0.350 eV and 1.242 × 10–3 A cm−2 K−2 from the slope and the intercept at the ordinate of the linear region of this plot, respectively. Also, we attempted to draw a ΦBo versus q/2kT plot to determine evidence of the GD of BHs, and the values of and σs = 0.137 eV for the mean BH and zero-bias standard deviation, respectively, were obtained from this plot; then, a modified ln(Io/T2) − q2σs2/2k2T2 versus q/kT plot gives and A* as 0.992 eV and 108.228 A cm−2 K−2, respectively. This value of A* is very close to the theoretical value of 112 A cm−2 K−2 for n-type Si.

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

“…The temperature dependence of n was investigated by linear fitting of the relation observed in Fig.4. Thus, the linear relation found in ( −1 − 1) vs 2 ⁄ plot confirms voltage deformation of the GD of the barrier height in terms of calculated n values [15]. The voltage coefficients were calculated from the slope and intercept as, 2 = 0.0346 V and 3 = 0.0315, respectively.…”

“…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.…”

“…It shows that the investigated the fabricated In/SnTe/Si/Ag diode has an interfacial layer with inhomogeneities having a GD of barrier heights [22]. The single straight line observed in Fig.3 also verifies a presence of a single GD of barrier height [15]. …”

“…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]. Therefore, this barrier differences over the whole temperature can be explained with TE modified under the consideration of barrier inhomogeneity.…”

“…where is the voltage independent [13][14][15]. Use of ( −1 − 1) predicts a general understanding on the dependence of of the diode structure with inhomogeneous barrier formation in which it is expected to be inversely proportional to temperature.…”