New Numerical Method to Calculate the True Optical Absorption of Hydrogenated Nanocrystalline Silicon Thin Films

doi:10.4236/wjnse.2012.21001

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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)

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: [email protected], {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





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



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

F. BESAHRAOUI ET AL.

 

1exp 1exp

cos1 exp

cos exp1

bulk

app fff

true

true sc

true



 











 











 



















 





 





































(1)

where



is the total optical absorption in the film

given by:

sc true





 (2)

bulk is the number of the scattering events between

the electrodes (to calculate this parameter see reference

[3]) and θ is the critical angle for total reflections. θ de-

fines the escape cone and can be calculated from the total

internal reflection condition

sin



, where n is the

refractive index of the outer medium. The function

“cosθ” presents the propability that the incident photon is

scattered outside the escape cone. The parameters,



and θ are known experimentally. We have considered the

experimental values measured by the authors of the ref-

erence [3], in order to compare our method with their

experimental one. We have taken cosθ = 0.5 calculated

for 2 µm thick nano-Si:H with an spectrum measured by

CPM method for 8 × 2 mm interelectrode spacing (Fig-

ure 3). The Equation (1) (with the variable



) cannot

be solved analytically and an adequate numerical method

will be used.

First, we give some estimated values for the true opti-

cal absorption coefficient true



, and we inject them in

Equation (1) in order to get a solution. We must take into

account that









apptrue .We note that for each

value, it corresponds a value at the

considered energy. After that, we choose the limited

true







true E





app E







values (minimum and maximum values) in order to

get an ,min,maxsc sc



interval. For each interval of





true



values, it corresponds an interval of



values

,min ,max



. Second, in order to calculate values

with a good precision at the considered energy, we select

the true

sc sc







values in which the interval ,min ,maxscsc

will be much reduced. It means that







true



values which

favour the following condition:

,max,min

true true







 (3)

Finally, we calculate the mean value ,true mean



of the

selected interval and we replace it in Equation (1) in or-

der to determine the corresponding solution



. Figure

1 shows the numerical resolution of Equation (1) ac-

cording to this process. After that, we suppose that the

spectral dependence of the calculated scattering coeffi-

cient has the following form in the energy range which

favours the previous inequality:





sc EE





 (4)

where β and γ are a constants.

Using the values of





sc E



at energy E estimated in

the first step and by a simple convolution, we can deter-

mine the constants β and γ (Figure 2).

In Figure 2, one can observe that the convoluted spec-

trum of scattering coefficient corresponds to the Rayleigh

type of scattering, i.e., a dependence of E4. Consequently,





sc E



can be calculated in all the considered energy

Figure 1. Numerical resolution of Equation (1) given at en-

ergy E = 1.1 eV.

Figure 2. Convoluted







spectrum in all considereted

energy rang e.

F. BESAHRAOUI ET AL. 3

range. Then, we inject values in Equation (1)

but this time with variable



sc E



true



in order to calculate the

spectral dependence of . However, in reference

[3], the authors have their specific experimental proce-

dure to extract true and spectra of nano-

Si:H samples. Indeed, they estimate the scattering coeffi-

cient from a comparison of several CPM measurements

(for different interelectrodes spacing) [3,7] and they sup-

posed a Rayleigh light scattering. Using the first equation

and by an iterative procedure, they obtained the true op-

tical absorption spectrum . Figure 3 shows a

perfect agreement of the calculated and measured true

optical absorption coefficient spectra.



true E









true E











3. Experiment

Nanocrystalline silicon layers were deposited by RF

magnetron sputtering of a silicon target, under different

pressure (2, 3 and 4 Pa) with different substrate tempera-

ture (100˚C, 150˚C, 200˚C). This process enables to de-

posit the silicon thin films on all types of substrates. With

respect to the deposition conditions, the layers result in a

rough (textured). The measured typical root mean square

surface roughness of the nanotextured silicon

samples varies between 4 and 12 nm. The CPM results of

nano-Si:H series deposited at 2 Pa are shown in Figure



rms



We note that rms



of this series is about 6 nm for

about 2.5 µm thick films. In order to exclude the influ-

ence of surface light scattering on the calculations, we

have polished numerically the surfaces of the samples.

Figure 3. Comparison of true optical absorption spectra of

thin nano-Si:H film deposited by Very High Frequency

Glow Discharge (VHFGD) method. The results plotted by

black bolls correspond to the values calculated by our nu-

merical method and that plotted by empties bolls for αtrue

evaluated by the authors using their experimental proce-

dure [3].

Figure 4. Fitted apparent optical absorption spectra of

nano-Si: H series deposited by RF magnetron sputtering

method under different substrate temperature.







app

values are calculated after a numerical polishing of the film

surface (



rms = 0 nm).

The polishing procedure has been done using the surface

light scattering theory presented in reference [3]. Indeed,

in the calculations, we have supposed that the textured Si

has a smooth surface (rms



= 0 nm) and we have calcu-

lated





true E



values which are in reality the apparent

optical absorption coefficient





app E



values influ-

enced only by bulk light scattering effects (Figure 4).

The evaluated





app E



values will be after that, in-

jected in our program in order to calculate





true E



and





sc E



spectra.

4. Results

We have applied our numerical method on the silicon

series with their CPM data given in Figure 4. Figure 5

shows the calculated spectral dependence of the true op-

tical absorption





true E



and the scattering coefficient





sc E



of the sample deposited at 200˚C.

The calculated spectra of the samples of this series are

presented together in Figure 6.

5. Discussions

Results presented in Figure 5 and Figure 6 demonstrate

that the samples deposited at 2 Pa exhibit an important

bulk light scattering contribution especially in low ab-

sorption range (0.9 - 1.6 eV spectral region) compared

with the samples deposited at 3 and 4 Pa. These samples

have a considerable surface roughness, which leads to a

remarkably surface light scattering. Consequentially, the

contribution of the scattered light at the rough surface

will be dominant. Furthermore, the scattering coefficient

F. BESAHRAOUI ET AL.

Figure 5. Scattering and true optical absorption spectra

calculated from CPM data of nano-Silicon thin film depos-

ited under pressure of 2 Pa and substrate temperature of

200˚C.

Figure 6. True optical absorption spectra calculated by the

numerical method for a nano-Si:H samples deposite d by RF

magnetron sputtering method under different substrate

temperature.



evaluated for each sample deposited at 2 Pa has the

Rayleigh scattering form . This result is very

convenient with the nature of our sample. Indeed, we

study here nanotextured thin films, i.e., samples which

have a random rough surface with rms roughness smaller

than the wave length of the incident light. Furthermore,

they possess the property to have small heterogeneities

included in their volume similarly to the case of amor-

phous silicon. We must note that there are some nano-

Si:H rough samples which demonstrate an important

surface scattering and by a standard mechanical polishing,

the surface scattering disappears and the true optical ab-

sorption is directly measured by CPM. But there are



sc E





some other ones which exhibit a bulk scattering contribu-

tion, which cannot remove by polishing. We calculate

their true and scattering coefficients spectra using the

proposed numerical method. We can unify the bulk and

surface scattering in terms of the scattering coefficient



given by the following equation:



2π

1fa

















where

n n and a are respectively, the refraction in-

dexes of nano-Si:H film and the ambient. λ is the incident

wave length.

6. Conclusion

In this paper, we have developed a new numerical me-

thod in order to calculate the true optical absorption

spectra and the contribution of light scattering in CPM

measurements of hydrogenated nanocrystalline silicon

thin films. With the help of surface and bulk light scat-

tering theories presented by Poruba and al, we have con-

cluded that the contribution of bulk light scattering in

CPM spectra of nanocrystalline silicon samples depos-

ited at low pressure which have a low surface roughness

is due mainly to the included heterogeneities (nanocrys-

tallites, voids,...) similarly to the case of amorphous sili-

con.

7. Acknowledgements

We gratefully acknowledge Prof. Kacem Zellama from

Picardie Jules Vernes University in France for providing

the nano-Si:H samples. Thanks to all who contributed to

this work.

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