Effect of Experimental Noise on Recovery of the Electronic Density of States from Transient Photocurrent Data
- PDF / 88,001 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 96 Downloads / 208 Views
Effect of Experimental Noise on Recovery of the Electronic Density of States from Transient Photocurrent Data Steve Reynolds, Charlie Main and Mariana J. Gueorguieva School of Science and Engineering, University of Abertay Dundee, Bell Street, Dundee DD1 1HG, U.K. ABSTRACT The effects of random noise on density of states determination from transient photocurrent data are examined by superimposing noise levels similar to those found experimentally (1% to 20%) on computer-simulated current-time data. Mathematically approximate methods based on Fourier and Laplace transformations are found to operate effectively at noise levels of up to 20%. Mathematically exact methods offer higher resolution, but this is compromised by greater susceptibility to noise. A Tikhonov regularisation method yields both high resolution and good noise tolerance.
INTRODUCTION Transient and modulated photocurrent measurements (TPC and MPC respectively) have been used for many years to probe the density of localised states (DOS) in disordered semiconductors. In the context of a multiple-trapping model, the current at any instant following pulsed excitation I(t) is subject to a combination of trapping, emission and recombination events, and does not map directly to the DOS at a particular energy unless a priori assumptions as to the form of the DOS, or the kinetics, are introduced. However, the current response I(ω) to sinusoidal excitation at an angular frequency ω is related directly to the magnitude of the DOS within approximately kT of an energy Eω = kT ln(ν/ω), where ν is the attempt-to-escape frequency and T the experimental temperature. Thus by taking the discrete Fourier transform [1] of I(t) to yield I(ω) the wider effective energy range obtainable with TPC [2] may be preserved, whilst benefiting from the ‘spectroscopic’ MPC analysis [3] which makes no prior assumptions as to the form of the DOS, or recombination parameters. A variety of methods for extracting the DOS from I(t), based on both Fourier and Laplace transformations, have been developed [4-8]. An exact implicit solution for the DOS is possible in the s-domain from a Fredholm integral equation, although care is needed to avoid the problem becoming ill-posed [4]. Tikhonov regularisation has also been employed successfully as a means of solving this equation [5], by trading the agreement between data and solution and the smoothness or stability of the solution. However, the methods most frequently used to date involve approximating the energy-selective kernels by a delta function [6-8], yielding the DOS explicitly in terms of I(ω), I(s) or their derivatives. While these approximate solutions are stable and straightforward to compute, energy resolution is inherently limited to order kT, which results in broadening of sharp features and distortion of steep tails in the DOS. Previous work has highlighted the benefits of computer simulations [6,9] of photocurrent decay in studying the accuracy and resolution of DOS recovery methods. Here, we extend these studies to include the effe
Data Loading...
