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Determination of refractive index of thin films beyond the absorption edge
1 O/pages 979 to 981 I1 993
Vacuum/volume 44lnumber Printed in Great Britain
0042-207X/93$6.00+.00 @ 1993 Pergamon Press Ltd
Determination of refractive index of thin films beyond the absorption edge DBhattacharyya, S K Bhattacharyya”, S Chaudhuri and A K Pal, Department of Materials Science, Indian Association for the Cultivation *Central Glass and Ceramic Research received
22 August
of Science, Calcutta-700 032, India Institute, Calcutta- 700 032, India
1992
A novel methodology substrate is indicated.
for accurate
determination
of refractive
I. Introduction Accurate determination of the refractive index of a film (deposited onto nonabsorbing substrate) beyond the absorption edge has previously been reported ’ ‘. This involved utilization of the interference fringes appearing in the transmittance (T) or reflectance (R) vs wavelength (i) traces to determine the thickness (r) for computing the n and x (the absorption coefficient of the film) values from the respective expressions derived by different workers’ 7. The derivation of n and a becomes questionable due to the presence of multiple solutions of equations at the maxima and minima of the interference fringes’,‘. Moreover, the jnterference fringes may not appear in the T or R vs J traces for films with low thicknesses and as such utilization of the expression involving quantities r,,,,, r,,,, R,,, and R,,, for deriving the values of n and t becomes redundant. In an earlier paper’, we presented a new technique and relevant formulation for determining a and n at the band edge which did not involve the utilization of thickness of the film. Recently, Hishikawa et a/’ described a method to determine the optical absorption coefficient (c() from the transmittance (T) and rcflectancc (R) measurements. They have indicated that the T/( 1- R) vs i plot completely eliminates the disturbances from the interference effect. However, the expression for T/(1 -R) involved three unknown quantities, like n, LXand I, and as such an iterative technique to generate values of the above quantities will not be as straightforward as has been anticipated. We present here a more tangible and accurate method of determining the optical constants (n and a) by measuring transmittance (T), reflectance (R) measured from the film side and reflectance (R,) measured from the substrate side’. The expression for n becomes completely free from intcrferencc rendering the determination of n and s( unambiguous. 2. Theory When multiple the expressions
reflections occur at the film substrate for Tand R become’ ‘:
interface,
index (n) of thin film deposited
onto nonabsorbing
where s = exp (-n/), IZ”and n, are the refractive and the substrate respectively. Expression (1) can be rewritten as :
(2)
Similarly.
(3)
T/(1-R)
__- 4n,nx =f(+#_(n,-n)y]’
Similarly.
it can be shown that
T/(1-R,)
~
4n0nx = ~ [(no +n)‘~-n,,)52]
It is to be noted that 7, R and R, are to be measured exactly at the same position of the sample when the film does not have a uniform thickness over a reasonable area. This will eliminate the errors arising out of the variation of thickness in the film. Now, equations (4) and (5) may be rewritten as :
(n, -n)‘x2.4+4n,nx-(n,
+n)‘A
= 0
(6)
= 0,
(7)
16n,In,n’x and
T = (I?+n,)?(n+n,)2+(n--,,)2(~~)?SZ1 +2(n2
--n,2)(nf
-n?)
indices of air
cos (4nnt/R)
(n--no)2_r2B+4n,nx-(n+-no)2B
979
D Bhatzacharyya
et a/: Refractive
index
determination
+
31, n
3nfn’
i
in)’
(II,
-n)'il' + (n,-n)'._ (II, --,7):/l dL (II, /=
1
(/?+/l,,)‘m
417;i +' (T7-rr,,)JB’ (II-- r7,,)‘B il k,,ll
Thus.
the rcfractivc
(IO)
+ (,7--n,,)'_. I
index (n) can he computed
from equation
(IO) without any prior assumption of film parameters required for the iterative
tcchniqucs adopted
I) is kno\+n. .\ ( --c‘ ccluations (8) or (9).
by previous workers.
Once
“) can bc c‘0mputcd from clthcr of the NOM puttIn, 11 these values of II and
3. Experimental
results
The above formulation 1 alucs of refractive wcrc prepared
and method were utilized to gcncrate the
index and absorption
hand edge of CulnSe:.
coel’fcicnt
by three sout-cc evaporation
of the rcspcctivc
beyond the
C‘dTc and CdS films. The CulnSe,
C‘dTc and CdS lilms wcrc prcparcd materials.
The
films
tcchniquc” while thu
by hot wall evaporation” tilms
The
wcrc deposited
Corning
705Y glass substrates.
obtained
by using a Gary 3000 spectrophotometcr.
P i and
(4) and (5).
and H = r:( I~ R,) as given in cquatians
respectively.
(D
Now solving for .s we get from equations 6nfn’+4(vr,
-4r?,n+v’[1
-
(6) and (7)
:
R i ~raccswcrc
2(n,
n)‘(n, +n)‘A’]
-4,2,,/7+y'[16n,?,r7'+4(r7-/7,,)~(n+rr,,)~B~] (4) Z(n-n,,)'B
i compares
refractive
well with
2.7
For
one another”
IX.
1000
Acnm)
1500
for CdTe
’
and
and arc
the sake of com-
w general npreement
It may bc noted thai the evaluation the previous techniques *crc
prejudiced
by the uncertainties
c I 1000 A
tnm) (b)
with
of n and Y by utilizing
the value of thickness which amounted
500
of II
valuc~’
the data of some of the frcquentl)
results which indicate
2oc1
980
coekcicnt
by using this technique
cited previous
'; E 0 3oc) d
c
500
reported
4oc1r
3.01
tilmh
( - 1.14)
than that for the film
rcccntly
2 and 3 respectively.
MC have included
ratio
( - I IS). The variation
index and absorption
shown in Figures
determining
.Y from (8) and (9). WC get
coefficient ralio
CdS films were also evaluated parison
and
Eliminating
;I lower absorption
and 3 with
(8)
--rz)‘il
15) with higher Cu/In
100) having lower Gil/In
The
.Y =
.\=
indicated
The film (R
‘I’
on 1~)
Figure I shows the plots of/z and :! for two representative of CuInSc,. whcrc A = T/(1 -K)
Y in
(I ). MCcan c~aluatc the thickness (t) and hcncc %.
equation
\ 1:
in
to the num-
D Bhattacharyya
et a/: Refractive index determination
c
t
htnml
h(nml
(b)
(a) Figure 3. Variations of n and r with E.for CdS films : (a)-@ value).
: o--present
ber of multiple experimental uncertainties. Also films with low thicknesses do not show very many interference fringes to allow one to evaluate thickness with reasonable accuracy in order to compute rational values of n and CI.Thus this method will permit one to evaluate optical constants beyond the absorption edge for films deposited on to nonabsorbing substrates in a very straightforward way involving iteration of a single variable. References ‘0 S Heavens, Opticul Properties of Thin Solid Films. Butterworth, London (1955). ‘J I Pankove, Optical Processes in Semiconducrors. p 92. Prentice-Hall, Englewood Cliffs, NJ (1971). ‘J C Manifacier, J Gasiot and J P Fillard, J Php,s E. 9, 1002 (1976). ‘J C Manifacier, M de Murcia, J P Fillard and E Vicario, Thin So/id Films, 41, 127 (1977). ‘D Bhattacharyya, S Chaudhuri and A K Pal, Vacuum, 43,313 (1992).
value ;
ref
18; l-ref
15 ; q-ref
16; r-rcf
17)
: (b)- (z : o-present
‘R E Denton, R D Campbell and S G Tomhn, J PII~x D, 5, 852 (1972). ‘Y Hishikawa, N Nakamura, S Tsuda. S Nakano. Y Kishi and Y Kuwano, Japan J Appl Phys, 30, 1008 (1991). ’ I Sanyal, K K Chattopadhyay, S Chaudhuri and A K Pal. J Appl Phys. 70,841 (1992). ‘S Chaudhuri. J Bhattacharyya, D De and A K Pal. Solrrr Energy Mum, 10,223 (1984). I” R L Basak, S Chaudhuri. S K Das and A K Pal, J Cgwni Growth, 73, 392 (1985). ” K K Chattopadhyya, I Sanyal, S Chaudhuri and A K Pal. Vucuum, 42, 915 (1991). “J Aranda, J L Moreza, J Esteve and J M Codina, Thin So/id Films, 120,23 (1984). “A A El-Shazhy and H T El-Sahir, Thin Solid Films. 78, 287 (1981). “S Chaudhuri, S K Das and A K Pal, Thin Solid Films, 147, 9 (1987). “G Kuwabara. J Pjt_vs Sot Japan. 9,97 (1954). “J Gottesan and W F C Ferguson, J Opt Sot Am. 44, 368 (1954). “3 Hall Jr, J Opi Sot Am, 46, 1013 (1956). ‘“I Martil De La Plaza. G Gonzalez-Diaz, F Sanchez-Quesada and M Rodriguez-Vidal, Thin Solid Films, 120, 3 I (1984).
981
Vacuum/volume 44lnumber Printed in Great Britain
0042-207X/93$6.00+.00 @ 1993 Pergamon Press Ltd
Determination of refractive index of thin films beyond the absorption edge DBhattacharyya, S K Bhattacharyya”, S Chaudhuri and A K Pal, Department of Materials Science, Indian Association for the Cultivation *Central Glass and Ceramic Research received
22 August
of Science, Calcutta-700 032, India Institute, Calcutta- 700 032, India
1992
A novel methodology substrate is indicated.
for accurate
determination
of refractive
I. Introduction Accurate determination of the refractive index of a film (deposited onto nonabsorbing substrate) beyond the absorption edge has previously been reported ’ ‘. This involved utilization of the interference fringes appearing in the transmittance (T) or reflectance (R) vs wavelength (i) traces to determine the thickness (r) for computing the n and x (the absorption coefficient of the film) values from the respective expressions derived by different workers’ 7. The derivation of n and a becomes questionable due to the presence of multiple solutions of equations at the maxima and minima of the interference fringes’,‘. Moreover, the jnterference fringes may not appear in the T or R vs J traces for films with low thicknesses and as such utilization of the expression involving quantities r,,,,, r,,,, R,,, and R,,, for deriving the values of n and t becomes redundant. In an earlier paper’, we presented a new technique and relevant formulation for determining a and n at the band edge which did not involve the utilization of thickness of the film. Recently, Hishikawa et a/’ described a method to determine the optical absorption coefficient (c() from the transmittance (T) and rcflectancc (R) measurements. They have indicated that the T/( 1- R) vs i plot completely eliminates the disturbances from the interference effect. However, the expression for T/(1 -R) involved three unknown quantities, like n, LXand I, and as such an iterative technique to generate values of the above quantities will not be as straightforward as has been anticipated. We present here a more tangible and accurate method of determining the optical constants (n and a) by measuring transmittance (T), reflectance (R) measured from the film side and reflectance (R,) measured from the substrate side’. The expression for n becomes completely free from intcrferencc rendering the determination of n and s( unambiguous. 2. Theory When multiple the expressions
reflections occur at the film substrate for Tand R become’ ‘:
interface,
index (n) of thin film deposited
onto nonabsorbing
where s = exp (-n/), IZ”and n, are the refractive and the substrate respectively. Expression (1) can be rewritten as :
(2)
Similarly.
(3)
T/(1-R)
__- 4n,nx =f(+#_(n,-n)y]’
Similarly.
it can be shown that
T/(1-R,)
~
4n0nx = ~ [(no +n)‘~-n,,)52]
It is to be noted that 7, R and R, are to be measured exactly at the same position of the sample when the film does not have a uniform thickness over a reasonable area. This will eliminate the errors arising out of the variation of thickness in the film. Now, equations (4) and (5) may be rewritten as :
(n, -n)‘x2.4+4n,nx-(n,
+n)‘A
= 0
(6)
= 0,
(7)
16n,In,n’x and
T = (I?+n,)?(n+n,)2+(n--,,)2(~~)?SZ1 +2(n2
--n,2)(nf
-n?)
indices of air
cos (4nnt/R)
(n--no)2_r2B+4n,nx-(n+-no)2B
979
D Bhatzacharyya
et a/: Refractive
index
determination
+
31, n
3nfn’
i
in)’
(II,
-n)'il' + (n,-n)'._ (II, --,7):/l dL (II, /=
1
(/?+/l,,)‘m
417;i +' (T7-rr,,)JB’ (II-- r7,,)‘B il k,,ll
Thus.
the rcfractivc
(IO)
+ (,7--n,,)'_. I
index (n) can he computed
from equation
(IO) without any prior assumption of film parameters required for the iterative
tcchniqucs adopted
I) is kno\+n. .\ ( --c‘ ccluations (8) or (9).
by previous workers.
Once
“) can bc c‘0mputcd from clthcr of the NOM puttIn, 11 these values of II and
3. Experimental
results
The above formulation 1 alucs of refractive wcrc prepared
and method were utilized to gcncrate the
index and absorption
hand edge of CulnSe:.
coel’fcicnt
by three sout-cc evaporation
of the rcspcctivc
beyond the
C‘dTc and CdS films. The CulnSe,
C‘dTc and CdS lilms wcrc prcparcd materials.
The
films
tcchniquc” while thu
by hot wall evaporation” tilms
The
wcrc deposited
Corning
705Y glass substrates.
obtained
by using a Gary 3000 spectrophotometcr.
P i and
(4) and (5).
and H = r:( I~ R,) as given in cquatians
respectively.
(D
Now solving for .s we get from equations 6nfn’+4(vr,
-4r?,n+v’[1
-
(6) and (7)
:
R i ~raccswcrc
2(n,
n)‘(n, +n)‘A’]
-4,2,,/7+y'[16n,?,r7'+4(r7-/7,,)~(n+rr,,)~B~] (4) Z(n-n,,)'B
i compares
refractive
well with
2.7
For
one another”
IX.
1000
Acnm)
1500
for CdTe
’
and
and arc
the sake of com-
w general npreement
It may bc noted thai the evaluation the previous techniques *crc
prejudiced
by the uncertainties
c I 1000 A
tnm) (b)
with
of n and Y by utilizing
the value of thickness which amounted
500
of II
valuc~’
the data of some of the frcquentl)
results which indicate
2oc1
980
coekcicnt
by using this technique
cited previous
'; E 0 3oc) d
c
500
reported
4oc1r
3.01
tilmh
( - 1.14)
than that for the film
rcccntly
2 and 3 respectively.
MC have included
ratio
( - I IS). The variation
index and absorption
shown in Figures
determining
.Y from (8) and (9). WC get
coefficient ralio
CdS films were also evaluated parison
and
Eliminating
;I lower absorption
and 3 with
(8)
--rz)‘il
15) with higher Cu/In
100) having lower Gil/In
The
.Y =
.\=
indicated
The film (R
‘I’
on 1~)
Figure I shows the plots of/z and :! for two representative of CuInSc,. whcrc A = T/(1 -K)
Y in
(I ). MCcan c~aluatc the thickness (t) and hcncc %.
equation
\ 1:
in
to the num-
D Bhattacharyya
et a/: Refractive index determination
c
t
htnml
h(nml
(b)
(a) Figure 3. Variations of n and r with E.for CdS films : (a)-@ value).
: o--present
ber of multiple experimental uncertainties. Also films with low thicknesses do not show very many interference fringes to allow one to evaluate thickness with reasonable accuracy in order to compute rational values of n and CI.Thus this method will permit one to evaluate optical constants beyond the absorption edge for films deposited on to nonabsorbing substrates in a very straightforward way involving iteration of a single variable. References ‘0 S Heavens, Opticul Properties of Thin Solid Films. Butterworth, London (1955). ‘J I Pankove, Optical Processes in Semiconducrors. p 92. Prentice-Hall, Englewood Cliffs, NJ (1971). ‘J C Manifacier, J Gasiot and J P Fillard, J Php,s E. 9, 1002 (1976). ‘J C Manifacier, M de Murcia, J P Fillard and E Vicario, Thin So/id Films, 41, 127 (1977). ‘D Bhattacharyya, S Chaudhuri and A K Pal, Vacuum, 43,313 (1992).
value ;
ref
18; l-ref
15 ; q-ref
16; r-rcf
17)
: (b)- (z : o-present
‘R E Denton, R D Campbell and S G Tomhn, J PII~x D, 5, 852 (1972). ‘Y Hishikawa, N Nakamura, S Tsuda. S Nakano. Y Kishi and Y Kuwano, Japan J Appl Phys, 30, 1008 (1991). ’ I Sanyal, K K Chattopadhyay, S Chaudhuri and A K Pal. J Appl Phys. 70,841 (1992). ‘S Chaudhuri. J Bhattacharyya, D De and A K Pal. Solrrr Energy Mum, 10,223 (1984). I” R L Basak, S Chaudhuri. S K Das and A K Pal, J Cgwni Growth, 73, 392 (1985). ” K K Chattopadhyya, I Sanyal, S Chaudhuri and A K Pal. Vucuum, 42, 915 (1991). “J Aranda, J L Moreza, J Esteve and J M Codina, Thin So/id Films, 120,23 (1984). “A A El-Shazhy and H T El-Sahir, Thin Solid Films. 78, 287 (1981). “S Chaudhuri, S K Das and A K Pal, Thin Solid Films, 147, 9 (1987). “G Kuwabara. J Pjt_vs Sot Japan. 9,97 (1954). “J Gottesan and W F C Ferguson, J Opt Sot Am. 44, 368 (1954). “3 Hall Jr, J Opi Sot Am, 46, 1013 (1956). ‘“I Martil De La Plaza. G Gonzalez-Diaz, F Sanchez-Quesada and M Rodriguez-Vidal, Thin Solid Films, 120, 3 I (1984).
981