Laplace-transform Transient Photocurrent Spectroscopy as a Probe of Metastable Defect Distributions in Hydrogenated Amor
- PDF / 110,848 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 55 Downloads / 240 Views
Laplace-transform Transient Photocurrent Spectroscopy as a Probe of Metastable Defect Distributions in Hydrogenated Amorphous Silicon Mariana J. Gueorguieva, Charlie Main and Steve Reynolds School of Science and Engineering, University of Abertay Dundee, Bell Street, Dundee, DD1 1HG, U.K. ABSTRACT Three Laplace transform methods for recovering the density of electronic states from transient photocurrent data are evaluated through a study of light-induced defect creation in PECVD a-Si:H films. A mathematically approximate method is shown to be sufficient to resolve the deep defects, whose density is estimated to increase by a factor of five from the annealed state after 3 hours’ exposure to simulated AM1 illumination. An exact method, and a method employing Tikhonov regularisation, are found to give very similar results, provided the current-time data are smoothed beforehand in the former case. The increased resolution available is, however, unnecessary here, and these methods are shown to be more suited to the study of discrete levels or narrow distributions.
INTRODUCTION Recently, several methods employing Laplace transformation of transient photocurrent (TPC) data for determination of the density of electronic states in disordered semiconductors have been developed [1-6]. The starting point in all such analyses is the linearised system of rate equations arising from the well-known multiple-trapping model. Upon Laplace transformation, a Fredholm integral equation of the first kind is obtained: EF ν exp( − E / kT ) d I( 0 ) − 1 = ∫ συg( E ) dE , ˆ ds I ( s ) [s + ν exp( − E / kT )]2 0
(1)
where I(0) is the current at t=0, Î(s) is the Laplace transform of the current, σ is the capture cross section, υ is the thermal velocity, ν is the attempt-to-escape frequency, k is the Boltzmann constant and T is the absolute temperature. The inversion of equation (1) to obtain the DOS requires care if its ‘ill-posed’ nature is to be overcome. We have previously reported on the development and verification of a solution method that avoids this problem, by ensuring that the resulting system of linear algebraic equations remains weakly diagonally dominant [4]. Work carried out by the Osaka group has shown that specialised minimisation techniques such as Tikhonov regularisation [5] can be successfully applied to the study of DOS distributions in disordered organic and inorganic semiconductors using TPC [6]. The above two methods are capable of arbitrarily high resolution since no inherent mathematical approximations are made. However, approximate methods, in which the kernel of the integral in equation (1) (or a related variant) is replaced by a delta function peaked at E0 to yield g(E0) [1,2,3] have also been developed. These methods, which allow the DOS to be obtained explicitly, are computationally straightforward and robust but are subject to resolution A19.3.1
limitations of order kT, and have been shown to broaden narrow features in the DOS and to distort the slope of an exponential tail of states [3,6]. In
Data Loading...
