Materials Sciences and Applications, 2012, 3, 562-565
http://dx.doi.org/10.4236/msa.2012.38080 Published Online August 2012 (http://www.SciRP.org/journal/msa)
The High Energy Region of the Absorption Edge of
a-Si:H, a Theoretical Study—III
Salwan Kamal Jamil Al-Ani
*#
, Abdullah Ibrahim, Subhi Saeed Al-Rawi
Physics Department, College of Science for Women, Baghdad University, Baghdad, Iraq.
Email:
*
salwan_kamal@yahoo.com
Received May 4
th
, 2012; revised June 8
th
, 2012; accepted July 12
th
, 2012
ABSTRACT
In this paper we try to give a reasonable account for the origin of the experimental optical energy gap E
o
of a-Si:H de-
duced from the plot due to Cody (
12
2
vs. E). Using a realistic model density of states diagram for a-Si:H and the con-
stant dipole matrix element assumption, and a reasonable definition of the real optical energy gap E
G
, a new theoretical
equation for ε
2
(E) was derived. The plot of the square root of this function
12
2
as a function of the photon energy E
for appropriate fitting parameters gives a straight line fit in the energy region of significance extrapolating to the energy
axis at a value similar to the experimental optical gap but about 0.1 eV lower than the theoretical optical gap E
G
pro-
posed in our paper. We conclude that the experimental optical gap E
o
does not necessarily coincide with any optical
transition threshold in the density of states diagram of a-Si:H.
Keywords: High Energy; Absorption Edge
1. Introduction
In two previous papers [1,2], we concluded from the
re-analysis of the experimental results of Jackson et al. [3]
for the density of states convolution integral J(E) as a
function of photon energy E for GD a-Si:H in the energy
range (1.6 - 3.7 eV), that the theoretical model due to
Cody [4] is the suitable theoretical model for the inter-
pretation of the optical data at the high absorption region
of the optical absorption edge of this important material.
This model assumes a parabolic density of states (DOS)
distribution near each of the valence and conduction
band edges (similar to the Tauc [5] model), and a con-
stant dipole matrix element (Tauc assumed a constant
momentum matrix element).
The problem of the interpretation of the optical energy
gap E
opt
is still a matter of controversy in literature [4,6].
For example in the case of our analysis, the optical gap
obtained from the plot attributed to Cody (
12
2
vs. E)
which is ~1.68 eV does not match with the value of the
mobility gap of Jackson et al. [3] samples i.e. ~1.93 eV.
While the gap obtained from the famous Tauc plot
(
12
2
E vs. E) ~1.89 eV is significantly closer to the
value of the mobility gap for Jackson et al. samples.
In this paper we try to give a reasonable explanation
for this problem, which we hope that it gives a possible
clue towards the understanding of the problem of the
interpretation of the optical energy gap problem in amor-
phous semiconductors.
2. Theory
The imaginary part of the dielectric constant ε
2
(E) for
amorphous semiconductors is given by [3]:
2
2
const E R EJ E (1)
where R
2
(E) is the normalized average dipole matrix
element and J(E) is defined as:
d
V C
J E N EN E E
E
(2)
where N
v
(E') and N
c
(E') are the valence and conduction
band density of states functions respectively and E' is the
state energy.
It usually assumed that the density of states distribu-
tion near each of the valence and conduction band edges
is some simple power law i.e. N(E')αE'
m
. If R
2
(E) also
obeys a simple power law of the form R
2
(E)αE
−q
. The
general solution of Equation (1) using the above assump-
tions is [4]:
2
r
q
o
E KE E E
(3)
where K is a constant, r = 2m + 1 ( for symmetrical DOS),
and E
o
is a parameter usually identified with the optical
energy gap E
opt
(E
o
= E
opt
) though of course this is not
*
Corresponding author.
#
Present address: NCPW, P.O. Box (25777), Doha, Qatar.
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