The effect of impurity concentration ratios on the depth profile of electric field within monolayer film is presented. SnO2 monolayer thin film material was prepared and doped with Co using spray chemical pyrolysis. The concentration ratios of impurity were 1 %, 3 %, 5 % and 7 %. The analysis utilizes matrix formulas based on Abele's formulas from the calculation of reflectance and transmittance. Present study gives an information to contamination sensitivity in optical coating issue.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2779

Habubi, N.F.

Mishjil, Kh.A.

Rashid, H.G.

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS  ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 4 No 2, 02024(4pp) (2012) Том 4 № 2, 02024(4cc) (2012)   2077-6772/2012/4(2)02024(4) 02024-1  2012 Sumy State University Effect of Impurity Concentration on the Depth Profile of the Electric Field  within Monolayer Thin Film  N.F. Habubi, Kh.A. Mishjil, H.G. Rashid  Al-Mustansiryah University, College of Education, Physics Department, Baghdad, Iraq   (Received 24 December 2012; revised manuscript received 12 March 2012; published online 04 June 2012)  The effect of impurity concentration ratios on the depth profile of electric field within monolayer film is presented. SnO2 monolayer thin film material was prepared and doped with Co using spray chemical py-rolysis. The concentration ratios of impurity were 1 %, 3 %, 5 % and 7 %. The analysis utilizes matrix for-mulas based on Abele's formulas from the calculation of reflectance and transmittance. Present study gives an information to contamination sensitivity in optical coating issue.  Keywords: Electric field intensity, Matrix formulas, Contamination sensitivity.    PACS numbers: 71.20.Nr.Хх, 81.40.Tv.Хх   1. INTRODUCTION  At optical frequencies, it is the electric field of the light that is responsible for many interactions with material. An understanding of the distribution of elec-tric field in an optical coating leads immediately to an understanding of many important effects including absorption, scattering and contamination sensitivity [1-5]. For a multilayer system, the profile of the electric field system has played an important role in the analy-sis of various kinds of spectroscopy, spatially reflection spectroscopy [6]. The basic idea depends on the fact that the electric field amplitude of an isolated plane progressive harmonic wave propagation through a completely uniform medium is constant if the medium is free from absorption and exponentially decreasing in the presence of absorption [5]. A standing wave is cre-ated as soon as there is any counter propagating wave and then the electric field amplitude shows an oscilla-tory variation with position. Therefore, coating is an interface and so there is invariably significant counter propagating energy. The electric field amplitude can exhibit not only significant variation but also consider-able magnification compared with the incident field. Fry [7] first depicted the variation of the electric field intensity at the surface of metals versus the inci-dent angle of the light. Later, Francis and Ellison [8] used same picture to explain the mechanism of the en-hancement of absorption of thin films on a metal at the grazing angle of incidence. Hansen [9] derived a meth-od for arbitrary depth for stratified films with N phase using a matrix method [4] in terms of the electric field E and magnetic field H, which includes the calculation of inversion of the matrices. Ohta and Ishdia [6] intro-duce a new algorithm to calculate the electric field in-tensities for stratified films including metal without need to the calculation of inverse matrices. There method was limited to IR spectrum.  Macleod [5, 10, 11] assume that the contamination is presented as an ex-tremely thin layer of absorbing material and the con-tamination sensitivity begins with his idea of electric field distribution. In this report the sensitivity of electric field intensi-ty profile to the change in impurity concentration was study based on Abele's matrix method [12] in terms of forward and backward propagating electric fields to calculate the reflectance and transmittance. Such idea may be useful in contamination sensitivity in optical coating studies.  2. BASIC THEORY  The basic matrix technique for the calculation of the properties of an optical coating actually contains already the electric and magnetic field so only a slight modifica-tion is required to extract it. The matrix expression, with the usual meaning for the symbols, is [4]:   sincos''sin cosiE EyH Hiy   where E and H are the components of the complex total electric and magnetic field amplitudes parallel to the surface which include the relative phase. For a single propagating plane harmonic wave the magnetic and electric fields are associated through the characteristic admittance, y, of the medium.   H = y E   in terms of B and C   sincos 1B.Csin cosextiyyiy (1)  The corresponding terms in the other column ma-trix, are normalized total tangential electric and mag-netic fields. The admittances y, too, are normalized so that they are in free space units (1 / 377siemens) rather than SI units. To have absolute values for the total tangential electric field amplitude through the multi-layer, it remains simply to give an absolute value to one of the E’s. The easiest is to put a value on the final tangential component at the emergent interface, which is the interface with the substrate. This is normalized to unity in (1) and is related to the incident irradiance through the transmittance T. If the incident irradiance is Iinc, then [5].   N.F. HABUBI, KH.A. MISHJIL, H.G. RASHID J. NANO- ELECTRON. PHYS. 4, 02024 (2012)   02024-2  *0.5Re exit exit incE H T I× = ×    but   ,exit exit exitH y Ez=    so that   2 .incexit exitexitT IEye z×= =    If T is  zero  then the field  must  be  designated at  a  different place, usually some convenient interface where there is a non-zero B value.  2.1 Irradiance and electric field  Irradiance defined as the mean power per unit area at any point carried by the waves, the orientation of the surface being chosen to maximize the power. The direc-tion of the irradiance is then considered to be parallel to the surface normal. Any other orientation receives a component of the irradiance. The component of irradi-ance across any unit surface is given by [4]:   I = 0.5 Re [EH*], (2)  The admittance y at optical frequencies,   y = (n – ik)x,  x being the admittance of free space (1/377 Siemens). Then we can write the irradiance of the wave as   2 20.5 .I Yz e e= ¥    2.2 Absorption of Light  From (1) and (2) ,the input and exit irradiances are given by,   1 Re ' '2inI E H= ×  and *1 Re .2exitI E H= ×    The irradiance lost by absorption in the layer is the difference between these two quantities. Since the layer is absorbing, the phase thickness at normal incidence is then given by,   ( )2 .n ik d ipd q a bl= - = -  (3)  Equation (3) defines the quantities α and b.  By ex-tremely thin, we mean that d/l should be sufficiently small to make both a and b vanishingly small, whatev-er the size of either n or k. Then substituting (3) in (1),   ( ) ( )1' ( ) ( ) .' ( )( ) 1 ( )( )( )i i i i HEE En ik n ikH Hi i n ik i i n ik E Ha b a bz za b z a b z- -é ù é ù+é ù é ùê ú ê ú- -= =ê ú ê úê ú ê úë û ë û- - - - +ê ú ê úë û ë û i.e.   sin( )cos( )' ,' sin( ) cos( )i iiE EyH Hiy i ia ba ba b a b-é ù-é ù é ùê ú=ê ú ê úê úë û ë û- -ê úë û  where we are including terms up to the first order only in a and b. The irradiance at the entrance to this layer will then be given by  { }a b z a b zé ù= + - - - - +ë û*1 Re ( ) / ( ) ( )( )( )2inI E i i n ik i i n ik E H   1   A R T= - -  (4)  The second of the two terms in (4) is zero. This fol-lows since (a – ib) / (n – ik) is real [from (4)] and HH* is also real. The content of the square brackets is there-fore imaginary and the real part, zero. We could also deduced this from by the fact that H has no interaction with the material. The first term gives   * ** * *1 Re . . ( )( )21 1 1Re . . ( ) .2 2 2inI E H E i i n ik HE H E H k n E Ea b za b zé ù= + - - =ë ûé ù é ù é ù= + +ë û ë û ë û (5)  where   (4 / )k n nkda b p l+ =  and  *.E E e=  (6)  Equation (5) show that the irradiance that has been absorbed is given by the difference between the irradi-ance incidents on the thickness element Iin, and that emerging on the exit side Iexit, that is:   l z e= 2(2 ) / . . ,absorbedI nkd    where the magnitude of the absorbed energy is directly proportional to the multiplication of n and k. Both must be nonzero for absorption to occur. The absorption will be small both for a metal with vanishingly small n and a dielectric with vanishingly small k absorption.   2.3 Potential transmittance and absorption  Potential transmittance [5], y,  of  any  element  of  a  coating system is defined as the ratio of the output to the input irradiance, the input being the net irradiance rather than that incident. Potential transmittance has several advantages over transmittance when dealing with absorbing systems because it can completely avoid any problems associated with the mixed Poynting vec-tor in absorbing media. The potential transmittance of a complete system is simply the product of the individ-ual potential transmittances.   exitinIIy =    1 2 3 4 5... qy y y y y y y=  (8)  with the eventual overall transmittance given by  1 . .systemT Ry= -  (9)  The potential transmittance of the thin elemental film is given by   1 1 ,exit absorbedin inI I AI Iy = - = -  (10)   EFFECT OF IMPURITY CONCENTRATION ON THE DEPTH PROFILE… J. NANO- ELECTRON. PHYS. 4, 02024 (2012)   02024-3 where A is the potential absorptance. But   21 Re ,2inI Yz e= × × ×  (11)  where Y is given in free space units. Then   2 21 1 ,RenkdAYpy l= - = -  (12)  and so   2 12 .RenkdAYpl= × ×  (13)  To move from potential absorption to absorption is straightforward when the absorption is confined to a very thin layer, the rest of the multilayer being essen-tially transparent. Then the absorption, A, is given by:   1 .A R T= - -  (14)  3. RESULTS AND DISCUSSION  3.1 Experimental Work  SnO2 thin films were deposited by chemical spray pyrolysis (CSP) technique onto glass substrates from aqueous solution of 0.1 M of SnCl4.5H2O. For the care-ful cleaning of glass substrate, the substrates were ini-tially boiled in chromic acid for 15 min, washed with distilled water. These substrates were further treated in ultrasonic bath for 15 min prior to deposition. The optimized preparation conditions being arrived at the followings: substrate temperature was kept at 500 °C and ,controlled within ± 5 °C through a chromel- alu-mel thermocouple as, a sensor for the temperature con-troller .the distance between nozzle and substrate was about 30 cm , the spraying rate was maintained at 5 ml/min , compressed air was used to atomize the solu-tion containing the precursor compounds through a spray nozzle over the heated substrate. Weighting method was used to measure the thickness of the de-posited films and was in the range of 0.35 ± 0.05 mm. The obtained films exhibit good adherence to substrate surface. Transmittance and absorbance were recorded with a Shimadzu 1650 double beam UV/Vis spectropho-tometer in the wavelength range (350-900) nm.  3.2 Electric Field Intensity Profile  The profile of normalized electric field intensity vs. film depth was computed with the aid of TF calc. soft-ware package [13]. SnO2 was prepared as thin film us-ing the chemical spray pyrolysis. The thickness of pre-pared thin film was 400 nm evaluated using the weighting method. The profile was computed over three zones:  M represent the incident medium; 1 monolayer; S the substrate (may be air). as shown in Fig. 1. The reference wavelength was 632 nm.    Fig. 1 – The depth profile of electric field distribution for SnO2 thin film of thickness 400 nm  The refractive index n and extinction coefficient k was computed from the measurement of film transmittance within the spectral region (350-900 nm) taken into ac-count the effect of dispersion. Fig. 2 and 3 illustrate the dispersion phenomena and the transmittance of SnO2 with impurity concentration (1 %,3 %,5 % and 7 %).  WAVELENGTH   (nm)300 400 500 600 700 800 900 1000REFRACTIVE INDEX   ,  n0.00.51.01.52.02.53.0SnO3 (PURE)SnO3-CO (1%)SnO3-CO (3%)SnO3-CO (5%)SnO3-CO (7%)  WAVELENGTH   (nm)300 400 500 600 700 800 900 1000EXTINICTION COEFFICENT ,  K0.000.020.040.060.080.100.120.14SnO3 (PURE)SnO3-CO (1%)SnO3-CO (3%)SnO3-CO (5%)SnO3-CO (7%)  Fig. 2 – Dispersion phenomena of n and k for SnO2 with impu-rity concentration (1 %,3 %,5 % and 7 %)   N.F. HABUBI, KH.A. MISHJIL, H.G. RASHID J. NANO- ELECTRON. PHYS. 4, 02024 (2012)   02024-4 WAVELENGTH (nm)300 400 500 600 700 800 900 1000TRANSMITTANCE (%)020406080100SnO3 :PURESnO3 :Co (1%)SnO3 :Co (3%)SnO3 :Co (5%)SnO3 :Co (7%)  WAVELENGTH  (nm)300 400 500 600 700 800 900 1000ABSORPTION0.00.20.40.60.81.0PURE SnO2SnO2:CO ( 1%)SnO2:CO ( 3%)SnO2:CO ( 5%)SnO2:CO ( 7%)  Fig. 3 – Measured transmittance and absorption vs avelength of SnO2 of various impurity concentration  3.3 Shifting in Electric Field Intensity Profile  The effect of impurity concentration ratio on the electric field intensity profile versus film depth were also investigated in Fig. 4 as extended of the second zone.  Depth (nm)0 100 200 300 400 (Normalized Electric Field Intensity )20.00.10.20.30.40.50.60.70.8SnO3:PureSnO3:Co(1%)SnO3:Co(3%)SnO3:Co(5%)SnO3:Co(7%) Fig. 4 – The extended 2nd zone of depth profile of electric field distribution for different impurity concentration ratios  It is clear from figure that maxima of electric field were reduced in its value in addition to shifting in their depth position as concentration ratio increased. This behaviour may be due the fact that the interface in a layer coating usually exhibit greater concentrations of defects than elsewhere and then susceptible to absorp-tion and scattering to great extent.  4. CONCLUSIONS  From the results one can conclude the following: 1. The electric field description of the light absorbed at a certain thickness to the total absorption can be eval-uated using the profile of the field along the direction of the depth. 2. It is possible to reduce the electric field everywhere using monolayer of weakly absorbing layer. 3. The best selection of layer thickness reduces the field at the interface to a great extent. 4. Present study offers useful tool in understanding the mechanism of light absorption in many applications spatially contamination sensitivity. REFERENCES  1. A.H. Macleod, C. Clark, 40th Annual Technical Conference Proceedings, 1997, 221  (New  Orleans:  Society  of  Vacuum  Coaters: 1997).  2. A.H. Macleod, C. Clark, Proceedings in Eleventh Interna-tional Conference on Vacuum Web Coatings, 176 (Miami, Florida: Bakish Materials Corporation, New Jersey: 1997).  3. A.H. Macleod, C. Clark, Assessing contamination sensitivi-ty in optical coatings. in 42nd Annual Technical Conference Proceedings, 232 (Chicago: Society of Vacuum Coaters: 1999).  4. A.H. Macleod, Thin-Film Optical Filters, 4th ed. (Bristol and Philadelphia: Institute of Physics Publishing: 2010). 5. A.H. Macleod, Optical Science OPTI575. Notes produced (USA, Tusson: Thin Film Center Inc.: 1999 – 2007). 6. K. Ohta, H. Ishida, Appl. Opt. 29, 1952 (1990). 7. T.C. Fry, J. Opt. Soc. Am. 22, 307 (1930).  8. S.A. France, A.H. Ellison, J. Opt. Soc. Am. 49, 131 (1959). 9. W.N. Hansen, Advances in Electrochemistry and Electro-chemical Engineering, V. 9 (New York: Wily: 1973). 10. A.H. Macleod, C. Clark, Processing in Eleventh Interna-tional Conference on Vacuum Web Coatings, 176 (Miami, Florida: Bakish Materials Corporation, New Jersey: 1997).  11. A.H. Macleod, C. Clark. 42nd Annual Technical Confer-ence Proceedings, 232 (Chicago: Society of Vacuum Coat-ers: 1999). 12. F. Abeles, Ann. de Physiqe. 5, 596 (1950). 13. http://www.sspectra.com  

Effect of Impurity Concentration on the Depth Profile of the Electric Field within Monolayer Thin Film

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS  ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 4 No 2, 02024(4pp) (2012) Том 4 № 2, 02024(4cc) (2012) 
 
 
2077-6772/2012/4(2)02024(4) 02024-1  2012 Sumy State University 
Effect of Impurity Concentration on the Depth Profile of the Electric Field  
within Monolayer Thin Film 
 
N.F. Habubi, Kh.A. Mishjil, H.G. Rashid 
 
Al-Mustansiryah University, College of Education, Physics Department, Baghdad, Iraq 
 
 (Received 24 December 2012; revised manuscript received 12 March 2012; published online 04 June 2012) 
 
The effect of impurity concentration ratios on the depth profile of electric field within monolayer film is 
presented. SnO2 monolayer thin film material was prepared and doped with Co using spray chemical py-
rolysis. The concentration ratios of impurity were 1 %, 3 %, 5 % and 7 %. The analysis utilizes matrix for-
mulas based on Abele's formulas from the calculation of reflectance and transmittance. Present study gives 
an information to contamination sensitivity in optical coating issue. 
 
Keywords: Electric field intensity, Matrix formulas, Contamination sensitivity. 
 
  PACS numbers: 71.20.Nr.Хх, 81.40.Tv.Хх 
 
 
1. INTRODUCTION 
 
At optical frequencies, it is the electric field of the 
light that is responsible for many interactions with 
material. An understanding of the distribution of elec-
tric field in an optical coating leads immediately to an 
understanding of many important effects including 
absorption, scattering and contamination sensitivity [1-
5]. For a multilayer system, the profile of the electric 
field system has played an important role in the analy-
sis of various kinds of spectroscopy, spatially reflection 
spectroscopy [6]. The basic idea depends on the fact 
that the electric field amplitude of an isolated plane 
progressive harmonic wave propagation through a 
completely uniform medium is constant if the medium 
is free from absorption and exponentially decreasing in 
the presence of absorption [5]. A standing wave is cre-
ated as soon as there is any counter propagating wave 
and then the electric field amplitude shows an oscilla-
tory variation with position. Therefore, coating is an 
interface and so there is invariably significant counter 
propagating energy. The electric field amplitude can 
exhibit not only significant variation but also consider-
able magnification compared with the incident field. 
Fry [7] first depicted the variation of the electric 
field intensity at the surface of metals versus the inci-
dent angle of the light. Later, Francis and Ellison [8] 
used same picture to explain the mechanism of the en-
hancement of absorption of thin films on a metal at the 
grazing angle of incidence. Hansen [9] derived a meth-
od for arbitrary depth for stratified films with N phase 
using a matrix method [4] in terms of the electric field 
E and magnetic field H, which includes the calculation 
of inversion of the matrices. Ohta and Ishdia [6] intro-
duce a new algorithm to calculate the electric field in-
tensities for stratified films including metal without 
need to the calculation of inverse matrices. There 
method was limited to IR spectrum.  Macleod [5, 10, 11] 
assume that the contamination is presented as an ex-
tremely thin layer of absorbing material and the con-
tamination sensitivity begins with his idea of electric 
field distribution. 
In this report the sensitivity of electric field intensi-
ty profile to the change in impurity concentration was 
study based on Abele's matrix method [12] in terms of 
forward and backward propagating electric fields to 
calculate the reflectance and transmittance. Such idea 
may be useful in contamination sensitivity in optical 
coating studies. 
 
2. BASIC THEORY 
 
The basic matrix technique for the calculation of the 
properties of an optical coating actually contains already 
the electric and magnetic field so only a slight modifica-
tion is required to extract it. The matrix expression, with 
the usual meaning for the symbols, is [4]: 
 
 
sin
cos'
'
sin cos
i
E E
y
H H
iy
  
 
where E and H are the components of the complex total 
electric and magnetic field amplitudes parallel to the 
surface which include the relative phase. For a single 
propagating plane harmonic wave the magnetic and 
electric fields are associated through the characteristic 
admittance, y, of the medium. 
 
 H = y E  
 
in terms of B and C 
 
 
sin
cos 1B
.
C
sin cos
ext
i
y
y
iy
 (1) 
 
The corresponding terms in the other column ma-
trix, are normalized total tangential electric and mag-
netic fields. The admittances y, too, are normalized so 
that they are in free space units (1 / 377siemens) rather 
than SI units. To have absolute values for the total 
tangential electric field amplitude through the multi-
layer, it remains simply to give an absolute value to 
one of the E’s. The easiest is to put a value on the final 
tangential component at the emergent interface, which 
is the interface with the substrate. This is normalized 
to unity in (1) and is related to the incident irradiance 
through the transmittance T. If the incident irradiance 
is Iinc, then [5]. 
 
 
N.F. HABUBI, KH.A. MISHJIL, H.G. RASHID J. NANO- ELECTRON. PHYS. 4, 02024 (2012) 
 
 
02024-2 
 *0.5Re exit exit incE H T I× = ×   
 
but 
 
 ,exit exit exitH y Ez=   
 
so that 
 
 2 .incexit exit
exit
T IE
y
e z
×= =   
 
If T is  zero  then the field  must  be  designated at  a  
different place, usually some convenient interface 
where there is a non-zero B value. 
 
2.1 Irradiance and electric field 
 
Irradiance defined as the mean power per unit area 
at any point carried by the waves, the orientation of the 
surface being chosen to maximize the power. The direc-
tion of the irradiance is then considered to be parallel 
to the surface normal. Any other orientation receives a 
component of the irradiance. The component of irradi-
ance across any unit surface is given by [4]: 
 
 I = 0.5 Re [EH*], (2) 
 
The admittance y at optical frequencies, 
 
 y = (n – ik)x, 
 
x being the admittance of free space (1/377 Siemens). 
Then we can write the irradiance of the wave as 
 
 2 20.5 .I Yz e e= ¥   
 
2.2 Absorption of Light 
 
From (1) and (2) ,the input and exit irradiances are 
given by, 
 
 1 Re ' '
2in
I E H= ×  and *1 Re .
2exit
I E H= ×   
 
The irradiance lost by absorption in the layer is the 
difference between these two quantities. Since the layer 
is absorbing, the phase thickness at normal incidence is 
then given by, 
 
 ( )2 .n ik d ipd q a bl= - = -  (3) 
 
Equation (3) defines the quantities α and b.  By ex-
tremely thin, we mean that d/l should be sufficiently 
small to make both a and b vanishingly small, whatev-
er the size of either n or k. Then substituting (3) in (1),  
 
( ) ( )1' ( ) ( ) .
' ( )( ) 1 ( )( )( )
i i i i HEE E
n ik n ik
H Hi i n ik i i n ik E H
a b a b
z z
a b z a b z
- -é ù é ù+é ù é ùê ú ê ú- -= =ê ú ê úê ú ê úë û ë û- - - - +ê ú ê úë û ë û
 
i.e. 
 
 
sin( )cos( )' ,
' sin( ) cos( )
i iiE Ey
H Hiy i i
a ba b
a b a b
-é ù-é ù é ùê ú=ê ú ê úê úë û ë û- -ê úë û
  
where we are including terms up to the first order only 
in a and b. 
The irradiance at the entrance to this layer will 
then be given by 
 
{ }a b z a b zé ù= + - - - - +ë û*
1 Re ( ) / ( ) ( )( )( )
2in
I E i i n ik i i n ik E H  
 1   A R T= - -  (4) 
 
The second of the two terms in (4) is zero. This fol-
lows since (a – ib) / (n – ik) is real [from (4)] and HH* is 
also real. The content of the square brackets is there-
fore imaginary and the real part, zero. We could also 
deduced this from by the fact that H has no interaction 
with the material. The first term gives 
 
 
* *
* * *
1 Re . . ( )( )
2
1 1 1Re . . ( ) .
2 2 2
inI E H E i i n ik H
E H E H k n E E
a b z
a b z
é ù= + - - =ë û
é ù é ù é ù= + +ë û ë û ë û
 (5) 
 
where 
 
 (4 / )k n nkda b p l+ =  and  *.E E e=  (6) 
 
Equation (5) show that the irradiance that has been 
absorbed is given by the difference between the irradi-
ance incidents on the thickness element Iin, and that 
emerging on the exit side Iexit, that is: 
 
 l z e= 2(2 ) / . . ,absorbedI nkd   
 
where the magnitude of the absorbed energy is directly 
proportional to the multiplication of n and k. Both must 
be nonzero for absorption to occur. The absorption will 
be small both for a metal with vanishingly small n and 
a dielectric with vanishingly small k absorption.  
 
2.3 Potential transmittance and absorption 
 
Potential transmittance [5], y,  of  any  element  of  a  
coating system is defined as the ratio of the output to 
the input irradiance, the input being the net irradiance 
rather than that incident. Potential transmittance has 
several advantages over transmittance when dealing 
with absorbing systems because it can completely avoid 
any problems associated with the mixed Poynting vec-
tor in absorbing media. The potential transmittance of 
a complete system is simply the product of the individ-
ual potential transmittances. 
 
 exit
in
I
I
y =   
 1 2 3 4 5... qy y y y y y y=  (8) 
 
with the eventual overall transmittance given by 
 1 . .systemT Ry= -  (9) 
 
The potential transmittance of the thin elemental 
film is given by 
 
 1 1 ,exit absorbed
in in
I I A
I I
y = - = -  (10) 
 
 
EFFECT OF IMPURITY CONCENTRATION ON THE DEPTH PROFILE… J. NANO- ELECTRON. PHYS. 4, 02024 (2012) 
 
 
02024-3 
where A is the potential absorptance. But 
 
 21 Re ,
2in
I Yz e= × × ×  (11) 
 
where Y is given in free space units. Then 
 
 2 21 1 ,
Re
nkdA
Y
py l= - = -  (12) 
 
and so 
 
 2 12 .
Re
nkdA
Y
p
l= × ×  (13) 
 
To move from potential absorption to absorption is 
straightforward when the absorption is confined to a 
very thin layer, the rest of the multilayer being essen-
tially transparent. Then the absorption, A, is given by: 
 
 1 .A R T= - -  (14) 
 
3. RESULTS AND DISCUSSION 
 
3.1 Experimental Work 
 
SnO2 thin films were deposited by chemical spray 
pyrolysis (CSP) technique onto glass substrates from 
aqueous solution of 0.1 M of SnCl4.5H2O. For the care-
ful cleaning of glass substrate, the substrates were ini-
tially boiled in chromic acid for 15 min, washed with 
distilled water. These substrates were further treated 
in ultrasonic bath for 15 min prior to deposition. The 
optimized preparation conditions being arrived at the 
followings: substrate temperature was kept at 500 °C 
and ,controlled within ± 5 °C through a chromel- alu-
mel thermocouple as, a sensor for the temperature con-
troller .the distance between nozzle and substrate was 
about 30 cm , the spraying rate was maintained at 
5 ml/min , compressed air was used to atomize the solu-
tion containing the precursor compounds through a 
spray nozzle over the heated substrate. Weighting 
method was used to measure the thickness of the de-
posited films and was in the range of 0.35 ± 0.05 mm. 
The obtained films exhibit good adherence to substrate 
surface. Transmittance and absorbance were recorded 
with a Shimadzu 1650 double beam UV/Vis spectropho-
tometer in the wavelength range (350-900) nm. 
 
3.2 Electric Field Intensity Profile 
 
The profile of normalized electric field intensity vs. 
film depth was computed with the aid of TF calc. soft-
ware package [13]. SnO2 was prepared as thin film us-
ing the chemical spray pyrolysis. The thickness of pre-
pared thin film was 400 nm evaluated using the 
weighting method. The profile was computed over three 
zones:  
M represent the incident medium; 
1 monolayer; 
S the substrate (may be air). 
as shown in Fig. 1. The reference wavelength was 
632 nm. 
 
 
 
Fig. 1 – The depth profile of electric field distribution for SnO2 
thin film of thickness 400 nm 
 
The refractive index n and extinction coefficient k was 
computed from the measurement of film transmittance 
within the spectral region (350-900 nm) taken into ac-
count the effect of dispersion. Fig. 2 and 3 illustrate the 
dispersion phenomena and the transmittance of SnO2 
with impurity concentration (1 %,3 %,5 % and 7 %). 
 
WAVELENGTH   (nm)
300 400 500 600 700 800 900 1000
R
E
FR
A
C
TI
VE
 IN
D
E
X
   
,  
n
0.0
0.5
1.0
1.5
2.0
2.5
3.0
SnO3 (PURE)
SnO3-CO (1%)
SnO3-CO (3%)
SnO3-CO (5%)
SnO3-CO (7%)
 
 
WAVELENGTH   (nm)
300 400 500 600 700 800 900 1000
E
XT
IN
IC
TI
O
N
 C
O
EF
FI
C
E
N
T 
,  
K
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
SnO3 (PURE)
SnO3-CO (1%)
SnO3-CO (3%)
SnO3-CO (5%)
SnO3-CO (7%)
 
 
Fig. 2 – Dispersion phenomena of n and k for SnO2 with impu-
rity concentration (1 %,3 %,5 % and 7 %) 
 
 
N.F. HABUBI, KH.A. MISHJIL, H.G. RASHID J. NANO- ELECTRON. PHYS. 4, 02024 (2012) 
 
 
02024-4 
WAVELENGTH (nm)
300 400 500 600 700 800 900 1000
TR
A
N
S
M
IT
TA
N
C
E
 (%
)
0
20
40
60
80
100
SnO3 :PURE
SnO3 :Co (1%)
SnO3 :Co (3%)
SnO3 :Co (5%)
SnO3 :Co (7%)
 
 
WAVELENGTH  (nm)
300 400 500 600 700 800 900 1000
A
B
S
O
R
PT
IO
N
0.0
0.2
0.4
0.6
0.8
1.0
PURE SnO2
SnO2:CO ( 1%)
SnO2:CO ( 3%)
SnO2:CO ( 5%)
SnO2:CO ( 7%)
 
 
Fig. 3 – Measured transmittance and absorption vs avelength 
of SnO2 of various impurity concentration 
 
3.3 Shifting in Electric Field Intensity Profile 
 
The effect of impurity concentration ratio on the 
electric field intensity profile versus film depth were 
also investigated in Fig. 4 as extended of the second 
zone. 
 
Depth (nm)
0 100 200 300 400
 (N
or
m
al
iz
ed
 E
le
ct
ric
 F
ie
ld
 In
te
ns
ity
 )2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
SnO3:Pure
SnO3:Co(1%)
SnO3:Co(3%)
SnO3:Co(5%)
SnO3:Co(7%)
 
Fig. 4 – The extended 2nd zone of depth profile of electric field 
distribution for different impurity concentration ratios 
 
It is clear from figure that maxima of electric field 
were reduced in its value in addition to shifting in their 
depth position as concentration ratio increased. This 
behaviour may be due the fact that the interface in a 
layer coating usually exhibit greater concentrations of 
defects than elsewhere and then susceptible to absorp-
tion and scattering to great extent. 
 
4. CONCLUSIONS 
 
From the results one can conclude the following: 
1. The electric field description of the light absorbed at 
a certain thickness to the total absorption can be eval-
uated using the profile of the field along the direction of 
the depth. 
2. It is possible to reduce the electric field everywhere 
using monolayer of weakly absorbing layer. 
3. The best selection of layer thickness reduces the 
field at the interface to a great extent. 
4. Present study offers useful tool in understanding 
the mechanism of light absorption in many applications 
spatially contamination sensitivity. 
REFERENCES 
 
1. A.H. Macleod, C. Clark, 40th Annual Technical Conference 
Proceedings, 1997, 221  (New  Orleans:  Society  of  Vacuum  
Coaters: 1997).  
2. A.H. Macleod, C. Clark, Proceedings in Eleventh Interna-
tional Conference on Vacuum Web Coatings, 176 (Miami, 
Florida: Bakish Materials Corporation, New Jersey: 1997).  
3. A.H. Macleod, C. Clark, Assessing contamination sensitivi-
ty in optical coatings. in 42nd Annual Technical Conference 
Proceedings, 232 (Chicago: Society of Vacuum Coaters: 
1999).  
4. A.H. Macleod, Thin-Film Optical Filters, 4th ed. (Bristol 
and Philadelphia: Institute of Physics Publishing: 2010). 
5. A.H. Macleod, Optical Science OPTI575. Notes produced 
(USA, Tusson: Thin Film Center Inc.: 1999 – 2007). 
6. K. Ohta, H. Ishida, Appl. Opt. 29, 1952 (1990). 
7. T.C. Fry, J. Opt. Soc. Am. 22, 307 (1930).  
8. S.A. France, A.H. Ellison, J. Opt. Soc. Am. 49, 131 (1959). 
9. W.N. Hansen, Advances in Electrochemistry and Electro-
chemical Engineering, V. 9 (New York: Wily: 1973). 
10. A.H. Macleod, C. Clark, Processing in Eleventh Interna-
tional Conference on Vacuum Web Coatings, 176 (Miami, 
Florida: Bakish Materials Corporation, New Jersey: 1997).  
11. A.H. Macleod, C. Clark. 42nd Annual Technical Confer-
ence Proceedings, 232 (Chicago: Society of Vacuum Coat-
ers: 1999). 
12. F. Abeles, Ann. de Physiqe. 5, 596 (1950). 
13. http://www.sspectra.com 
 


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Effect of Impurity Concentration on the Depth Profile of the Electric Field within Monolayer Thin Film

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