World Journal of Nano Science and Engineering, 2012, 2, 1-5

http://dx.doi.org/10.4236/wjnse.2012.21001 Published Online March 2012 (http://www.SciRP.org/journal/wjnse)

1

New Numerical Method to Calculate the True Optical

Absorption of Hydrogen ated Nanocrystalline

Silicon Thin Films

Fatiha Besahraoui, Larbi Chahed, Yahia Bouizem, Jamal Dine Sib

Laboratory of Physics of Thin Films and Materials for Electronics, University of Oran Es-Senia, Oran, Algeria

Email: fatiha.besahraoui@yahoo.fr, {larbi.chahed, yahia.bouizem, jamaldine.sib}@univ-oran.dz

Received November 14, 2011; revised December 18, 2011; accepted January 12, 2012

ABSTRACT

The enhanced optical absorption measured by Constant Photocurrent Method (CPM) of hydrogenated nanocrystalline

silicon thin films is due mainly to bulk and/or surface light scattering effects. A new numerical method is presented to

calculate both true optical absorption and scattering coefficient from CPM absorption spectra of nanotextured nano-

crystalline silicon films. Bulk and surface light scattering contributions can be unified through the correlation obtained

between the scattering coefficient and surface roughness obtained using our method.

Keywords: Solution Hydrogenated Nanocrystalline Silicon; Constant Photocurrent Method; Optical Absorption; Bulk

Light Scattering; Surface Roughness; Film Thickness

1. Introduction

Materials with nanometer crystallites constitute an im-

portant class with some of their properties distinctly dif-

ferent from either amorphous or large grain materials or

single crystals. Especially, hydrogenated nanocrystalline

and polymorphous silicon thin films. Hydrogenated nano-

crystalline silicon (nano-Si:H) is an heterogeneous mate-

rial. It consists of an ordered nanocrystallites of spherical

form with size varies from 2 to 100 nm embedded in

amorphous matrix [1]. These semiconducting nanomate-

rials are very promising to the photovoltaic applications

[2]. The important key for the success of nano-Si:H films

as a PV absorbent materials is their enhanced absorption

compared to the monocrystalline silicon (c Si), mainly in

infrared region [3]. The main reason of this optical be-

havior is due to their particular structure which gives

place to the bulk and/or surface light scattering phenom-

ena [3-5]. The Constant Photocurrent Method measure-

ments of these heterogeneous mediums give us an “ap-

parent” optical absorption coefficient at en-

ergy E. is affected by light scattering effects

different from true

app E

app E

measured for homogeneous medi-

ums, i.e., amorphous or monocrystalline silicon [3]. In

this paper, we suggest a new numerical method to calcu-

late the true optical absorption. A numerical resolution of

Equation (1) is given at energy E = 1.1 eV. The contribu-

tion of bulk light scattering, from the spectral depend-

ence of apparent optical absorption coefficient

app E

in thin films of nano-Si:H is measured by Constant

Photocurrent Method (CPM). The details of CPM method

and its experimental configuration are described else-

where [6]. This method is developed in order to under-

stand the subgap part of the true optical absorption spec-

tra related to the defect states within the energy gap. It’s

introduced with the help of a recent theory [3] which

describes the different contributions of light scattering in

terms of photocurrent

h

deduced from CPM meas-

urements. This procedure has a crucial importance to

determine true

in the case of weak bulk light scattering,

without need to compare a several CPM measurements

(for different interelectrodes spacing) [3]. We will pre-

sent the details of our procedure and discuss its validity

by comparing a calculated spectrum with the

experimental one obtained by CPM for the same sample

of nano-Si:H. Finally, we will apply this method on a

series of nano-Si:H which have a different surface rough-

ness in order to determine the correlation between this

material parameter and the scattering coefficient

true E

c

.

2. Numerical Method

In the following, let us consider a nano-Si:H thin film

with a typical thickness df configured according to the

CPM setup. If the standard CPM evaluation method will

be applied to the measured spectrum, we will obtain an

“apparent” optical absorption coefficient app

fhich

the following equation is valid [3]:

or w

C

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