Extension of the impedance field method to the noise analysis of a semiconductor junction: Analytical approach

Abstract

We present an analytical procedure to perform the local noise analysis of a semiconductor junction when both the drift and diffusive parts of the current are important. The method takes into account space-inhomogeneous and hot-carriers conditions in the framework of the drift-diffusion model, and it can be effectively applied to the local noise analysis of different devices: n ϩ nn ϩ diodes, Schottky barrier diodes, field-effect transistors, etc., operating under strongly inhomogeneous distributions of the electric field and charge concentration.

Impedance field and noise of submicrometer n+nn+ diodes: Analytical approach

“…This results in the possibility of finding analytical formulas for the Green functions of the linearized operator, and once the steady-state field distribution is found, the local impedance and noise can be immediately obtained by simple integration over the steady-state quantities, without computing numerically the evolution of perturbations throughout the device. The effectiveness of this technique has been demonstrated on various nonhomogeneous structures such as n ϩ n homojunctions, 5,6 Schottky barrier contacts, 7 and Schottky diodes. 8 The aim of this article is to apply the DD framework to the local noise analysis of submicron n ϩ nn ϩ diodes and to obtain in a closed analytical form the impedance field and the local noise characteristics.…”

“…5,6 Although the DD model is based on the local field approximation, i.e., the kinetic coefficients ͑mobility, diffusion coefficient͒ are functions of the local electric field, the system of equations to be solved is simpler, which gives the possibility of avoiding the second step in the calculations. Indeed, in the DD framework the transport equation is reduced to a second-order differential equation with respect to the electric field.…”

“…In the DD approximation, combining the current and Poisson equations, the electric transport in the diode is governed by the second-order differential equation for the steady electric-field profile E(x). 5,6 We write this equation for the n and n ϩ regions as…”

Impedance field and transition from thermal to shot noise inCd1−xZnxTesemi-insulating Ohmic detectors

“…The impedance field is a physical valuable quantity in itself, and a rigorous calculation of this quantity involves the solution of a second-order stochastic differential equation. 13 Here we detail the derivation of the impedance field for the case of a homogeneous resistor within the drift-diffusion model. In particular, we discuss the effect of the presence or the absence of long-range Coulomb interactions and their implications in the calculation of the macroscopic impedance and noise.…”

“…12 For this purpose we make use of a standard impedance field method generalized to include the presence of the diffusion term in the stochastic equation. 13 The impedance field method 14 is a powerful technique to calculate voltage and/or current fluctuations in two terminal devices. Within this scheme, the voltage ͑current͒ spectral density is obtained by convolving in a spatial integral the two basic ingredients, namely, the local impedance field and the local noise source.…”