Electrical and Optical Properties of Amorphous Silicon and Its Alloys
This chapter will concern itself with a detailed description of the basic concepts of electrical and optical properties of amorphous semiconductors with respect to the specific example of amorphous silicon. Using a simplified physical model, we will discu
- PDF / 2,378,317 Bytes
- 26 Pages / 439.37 x 666.142 pts Page_size
- 4 Downloads / 220 Views
Electrical and Optical Properties of Amorphous Silicon and Its Alloys Hiroaki
o kamoto
This chapter will concern it self with a detailed description of the basic concepts of electrical and optic al properties of amorphous semiconductors with respect to the specific example of amorphous silicon. Using a simplified physical model, we will discuss how the electronic states in the vicinity of the band edge, and the optical and electronic processes associated with these, are affected by the structural disorder. An attempt will be made to interpret and explain the various physical properties of hydrogenated amorphous silicon (a-Si:H) including the photoinduced changes.
3.1 Simplistic Model for Band-Edge Electronic Properties 3.1.1 Fundamental Aspects Near the Mobility Edge 3.1.1.1 Density-of-States in the Band-Edge Region In this section, the band-edge structure in a system involving weak disorder is examined within the context of a site-diagonal disordered simple tightbinding model. The electronic system is supposed to be described by a linear combinat ion of Wannier states li) localized at regularly arranged atomic or molecular orbit al sites [1, 2]. If the site energy is assumed to take a random value Vi, and the transfer energy between the nearest-neighbor sites is constant at V, then the Hamiltonian is given by
H
=
VI: li)(jl + I: li)(il
.
(3.1)
i#j
As is well known, the off-diagonal term gives the energy dispersion relationship of the regular lattice system E = Ea (k), and the width of the created band B is represented by 2zlVl, where z is the coordination number. Let us assume that
Y. Hamakawa (ed.), Thin-Film Solar Cells © Springer-Verlag Berlin Heidelberg 2004
44
Hiroaki Okamoto
the diagonal component Vi of the second term follows a Gaussian distribution with zero mean and variance W 2 , and consider this as the perturbation term of disorder for the regular system presented by the first term in (3.1). A rough sketch ofthe density-of-states (DOS) spectrum, D(E), in the vicinity of the band edge is given according to the renormalized second-order perturbation method. It is now assumed that the DOS of a nonperturbed system is proportional to E1 / 2 ne ar the band edge [3].
D(E)
= 2~7f2(Va2)~3/2(J(E-ar)2+a;+E-arf/2 ,
(3.2)
where a denotes the interatomic distance, ar a negative value close to -4 W 2 / B which corresponds to the shift in the DOS spectrum, and ai is the imaginary part of the self-energy representing "blur" of the spectrum, being proportional to W2V~3/2 E1/2. From (3.2), it is evident that for the energy region E > ar + 4W 3 / B 2 , the DOS resembles that of a nonperturbed system shifted by ar. While it is difficult to show explicitly by using such a simple analysis, it is expected that a band tail of the exponential form [2] (3.3) follows the energy behavior mentioned above toward the lower-energy side, with the characteristic energy E bu being proportional to W 2 / B. The basic concept of the above discussion is that the electron state of a disordered system is composed of superimp
Data Loading...
