Page 99 - Photonics Essentials an introduction with experiments

Photoconductivity

Photoconductivity 93

–3
–1
rate of electrons = f, where f has units of cm -sec . In the steady
state, the generation rate and the recombination rate must be the
same.
The treatment that follows is based on the description of sensitiza-
tion given by Rose in Concepts in Photoconductivity (see Bibliogra-
phy). In Fig. 5.14, we show an energy level diagram for a typical pho-
toconductor material such as CdS.
A recombination level is formed by addition of a single type of impu-
rity that forms a level near the center of the band gap. The Fermi lev-
el will fall in the center of these levels, as shown in the figure. Sup-
pose that the density of the recombination sites is N. We can now
define some parameters that we will need for the discussion of sensiti-
zation:

1. n r = the density of centers occupied by electrons
2. p r = the density of centers unoccupied by electrons

When an electron recombines on an unoccupied site, p r , the site
changes to an occupied site and counts as part of n r . At all times, n r +
p r = N r .
The chance that an electron recombines on an unoccupied site is
2
measured by the cross-section of the site, s n , which has units of cm .
The capture cross section for holes by a site occupied by an electron is
s p . In the steady state:

n = f n
n r
(5.15)
p = f p
p r
A charge carrier moving with a velocity v will travel a distance = v
on the average before it recombines. The product of the capture cross
section with this distance gives the effective volume of the recombina-
tion center, as shown in Fig. 5.15
The density of unoccupied centers for electrons, p r , is just the in-
verse of this volume. Thus,
1
= volume of a center = n vs n (5.16)
p r
and
f
n = f n = (5.17)
p r vs n
To appreciate what these equations mean, we give some typical val-
ues for these parameters in Table 5.1 for electrons in silicon.
Since recombination centers promote recombination, their presence
in general shortens the carrier lifetime. It is always true that increas-

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.