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A simple method to determine the optical constants and thicknesses of ZnxCd1−xS thin films
ELSEVIER
ThinSolidFilms289 (1996) 238-241
A simple m e t h o d to determine the optical constants and thicknesses o f ZnxCdl _ xS thin films J. Torres a, J.I. Cisneros ¢, G. Gordillo b, F. Alvarez c a Pontificia UniversidadJaveriana, Bogotd. Colombia b Departamentode F[sica, UniversidadNacional de Colombia Bogotd, Colombia ¢instituto de F(sica 'Gleb Wataghin', UNICAMP.CP 6165, CEP 13083-970, Cidade Universitdria, Campinas. Brazil
Received30 November1995;accepted 10 May 1996
Abstract A new method to determine the optical parameters of ZnxCdl _~S polycrystailine thin films is proposed. Sub-gap absorption, caused by aceeptor states, is taken into account in the determination of the refractive index and film thickness. This procedure avoids errors in the results, frequently observed when the absorption is ignored. In the low and medium absorption region the refractive index is parametrized by the Wemple and DiDomenico (W-D) single oscillator model. The W-D parameters are further used in order to extrapolate the refractive index at the absorption edge to compute the absorption coefficient and the optical gap. The transmission spectra of typical CdS, (Zn,Cd)S and ZnS thin films and their corresponding values of n, a and Eg are presented. Keywords: Cadmiumsulphide;Evaporation;Inorganiccompounds;Opticalproperties;Opticalspectroscopy;Semiconductors;Solarcells;Sulfides;Vacancies
1. Introduction Cadmium sulfide is widely used as a photoconductor in the visible spectral region and as window material for CdTe and CulnSe2 based solar cells [ 1,2]. It is important for the development of these devices to obtain information about some optoelectrical properties of the constituent materials; in particular, the determination of the CdS optical constants is necessary to achieve a good design for the devices. Several authors have developed different theoreticai models to calculate the optical constants of semiconductor thin films from transmission and reflection measurements [ 3-7 ]. However, these models are not suitable for the determination of all optical constants of our CdS thin films deposited by evaporation of CdS-powder from a graphite crucible heated indirectly by radiation. In this article we describe a simple method which allows us to determine from transmittance measurements, the optical constants of (Zn,Cd)S thin films deposited by evaporation on 7059 glass substrates.
2. T h e o r y
The transmission of the system shown in Fig. 1, can be calculated using the following equations [8]: 0040-6090/96/$15.00 © 1996ElsevierScienceS.A. All rightsreserved Pi!50040-6090(96)08931-6
T=
A exp(ad) B exp(2ad) + C exp(ad) + D
(1)
where A = 16no(1 - p ) ( n 2 , + ~ ) U B= st- psvU
C = [ ( 4 n 3 ~ - zy ) 2 cos ~ + (n3Y + Z) 4k2 sin ~b] - p U 2 [ ( z - n a y ) 4 k 2 sin t h - ( z y + 4 n 3 ~ ) 2 cos ~b] D = uv - ptuU 2 u=(nl-n2)2
+~
/) = (n2-- n3)2-t- k~2 $ = (n I "l"n2)2"~"k~2 t=(n2+n3)2+~
y=n~-n~+~ z=n~,-n~+~ dp= 4~'n2d/ A
\n t + n3]
(2)
J. Torteset al. I ThinSolidFilms289(1996)238--241
239
1.0 AIR (nI - I)
[~TO
I ==+1'
oum (c~,~o, n3~t.sO
0.8
I
~0.6
i0.4
Fig. 1. System of an absorbing CdS thin film on a finite-ticknesstransparent substrate.
0.2 0.0~'~i:
Where a is the absorption coefficient of the CdS film, nt, n2 and n 3 the refractive indexes of air, film and glass respectively, k2 the extinction coefficient of the film and U is a correction factor which is intreduced if absorption is present in the substrate. In the transparent region, the extreme values of the transmittance occur at wavelengths Am,defined by the relation: ~=~-~:mlr
(3)
Where m is the interference order and d and n2 the thickness and refractive index of the CdS film. When n2>n3, as in our films, the maxima and minima of the transmission correspond to even and odd values of m respectively. Assuming weak variation of n 2, In can be calculated using the following equations:
t~
" Im
~
2see
~.(am) Fig. 2. Typicaltransmissionspectrumof a CdS thin film deposi~ by evaporation. 3. Results and discussion Fig. 2. shows a typical transmission spectrum of a CdS, thin film deposited by evaporation of CdS powder using an evaporation system described elsewhere [9]. The transmission .spectrum of the CdS thin films obtained by using a specu'ophotometer PERKIN-ELMER, Lambda 9 shows that the CdS samples do not present a transparent region between 500 and 2500 nm; this typical hehaviour of evaporated (Zn,Cd) S thin films give problems with the class of envelope methods like Swanepoel's [6,7]. The wide absorption region in the samples can he attributed to deep acceptor states generated by Cd-Vacancies and complexes formed by metal vacancy-donor nearest neighbor pairs, as was verified from photoluminiscencemeasurements [9,10].
Ara- I
(a)In -- Am- I - Am '"
-
o)m
=
3.1. Determination of the optical constants of CdS thin films deposited by evaporation
A,.+
A,,----A-~m, +t
(4)
Assuming that, in the low absorption region k2 = 0, the extreme of the interference fringes can be written as: T.
'~
T,~
2ntn3 = 2 2 nl
-I- n 3
4nln2n3 (n2+n2)(n[+n2)
(5a)
(5b)
In the transparent region of the spectrum the values of the maximum are determined by Eq. (5a); therefore, these values are independent of the film's refractive index n2. This indicates that in these spectral points the system of Fig. 1. behaves as a glass substrate without film. (Therefore the transmission maxima of the fiim/substrate system, in the transparent region, must be equal to the transmission of the nude substrate). Eq. (5a) and Eq. (5b) are used to determine n3 and obtain an approximate value of n2, as described below, respectively.
Our CdS films are not transparent, even in the interference region. For the calculation of the film refractive index and thickness in the low absorption or in the interference region, Eq. (1) and Eq. (3) should be used at the wavelengths corresponding to the maxima and minima. The la'ocedure includes basically the following steps: a) The determination of the interference orders using Eq. (4) and calculation of an approximate value of n2 by using of Eq. (5). b) calculation of k2 at the maxima (m even) imposing ~b--mm This is done solving numericallyfor k2 tho following equation: T(nt,n2,n3,m,k2) - Texp = 0
(6)
In this calculation the general expression for the transmission, Eq. ( I ), is used with the only restriction of Eq. (3). This result is rather accurate, even if approximate values ofn 2 are used, because k2depend weakly on n2. At the minima (m odd), k2 is found by interpolating its values at the neighboring maxima.
240
J. Tortes et al, /Thin Solid Films 289 (1996) 238-241
c) n2 is determined at the minima (m odd) by solving Eq. (6) for n 2, using values of k2 calculated in the previous step. Using a set of n2 values and the Eq. (3), the film thickness d can be calculated with a rather small dispersion. Knowing the value ofdallows the determination of n2 at the maxima, again using Eq. (3). Steps a) through c) are usually applied to the extreme far from the absorption edge, where the interference fringes are quite distinct. However, the determination of n2, using Eq. (3) can be extended to the whole interference region after properly determining d. It should be emphasize that the merit of this method for the determination of n2 and d, is the inclusion of the absorption in the calculation, which improves dramatically the quality of the values of the refractive index in the low and medium absorption region. d) Once/22 is known, Eq. (6) can be used again to determine k2 in all extreme. This is extremely useful information related to the sub-gap absorption, usually not determined from optical data. e) Finally, we use a model (W-D) proposed by Wemple and DiDomenieo [ 11 ], which consists of fitting the n2 data, obtained in the medium and weak regions to the expression
ferent Zn concentration. The samples were prepared by evaporation,using a source constituted by two coaxial chambers, one for CdS-powder and one for ZnS.powder [9]. The Zn-concentration was determined by EDS. Fig. 4 shows a typical transmission spectra of Zn,~Cdt-xS thin films with three different Zn-eoncentrations ( x = 0 (CdS), x =0.38 and x = 1 (ZnS)). With these experimental data the corresponding absorption coefficient and the refractive index were calcu2ated. Fig. 5 shows the curves of a 2 vs hv corresponding to the three samples of (ZnCd) S studied. The optical gaps Eg of the three samples were determined from the intercepts of the hv axis with the straight lines which fitting the o~2 vs h v curves in the region of strong absorption, considering here that these CdS- a13 d;2.621 gm ~' 2.4 2.3
(EdEo)
,~ 2.2
n~ - 1 =~_--2--~ deduced using the model of a single-effective-oscillator; where ~w is the photon energy, Eo is the single oscillator energy and Ed is the dispersion energy. The parameter Ed, which is a measure of the intensity of the inter band optical transitions, does not depend significantly on the bandgap. The values of Ed and Eo are obtained from the intercepts resulting from the extrapolation of the curve 1
n]--- 1vs(~ca)z
/ /
.2;/ i
0.5
,
i
1.0
,
i
,
f
,
t
1.5 2.0 2.5 hv(ev) Fig. 3. Variationof a refractiveindexof a CdS sample,calculatedusinga procedure which includes a single oscillatorfitting to the form n2-1 E~o/ ~ - ~ z. Table I Values of parameters Ea and Eo obtained from the W-D fiuing, using the simplearmonicoscillatormodel
(7)
The n 2 values in the absorption edge are obtained by extrapolating the n 2 vs ~w curve of the W-D model. A detailed discussion of the single-effective oscillator model, used by Wemple and DiDomenico to obtain Eq. (7) is given in [ 12]. Fig. 3 shows the experimental results for the refractive index of a typical CdS sample. The full line corresponds to the fitting according to the W - D model. In Table 1 are listed the values of Ed and Eo obtained for the tree samples CdS, ZnxCdt_~S ( x = 3 8 % ) and ZnS studied in this work, and values of Ea and Eo reported for crystalline CdS and ZnS samples [ 11 ]. The difference between the values of Ed and Eo obtained for our samples and those reported for crystalline samples could be attributed to the presence of accepter states, which introduce changes in n and then in the Ed and E0 values. Using the values of n 2 obtained with the procedure described above, the values ofk and a in the strong absorption region, can be calculated by using Eq. ( 1). The method developed in this work was applied to calculate the optical constants of ZnxCd, _~S thin films with dif-
Sample
Ed (eV)
Eo (eV)
CdS ZnxCdl_~S,(x=0.38) ZnS CdS* ZnS*
20.3 22.1 21.8 20.4 25.2
6.1 6.7 7.3 4.9 6
* Reportedvaluefor crystallinesamples [ I I l
o.s
1"t ~0.6
.................. /"/"~ /",
•
~/'\
f o.21ill o.ot~J
"
....
o.
.............~
500 1000 1500 2000 2500 ~.(nm) Fig. 4. Typicaltransmission spectra of Zn~¢d,_~S thin films with three differentgn-concentrations.
J. Torres et at. / Thin Solid Films 289 (1996) 238-241
6"
~
xl09
4. C o n c l u s i o n s
-CdS . . . . ZnxCdl.xS,x=0.38 3.0 ~ ....... ZnS
A simple procedure for the determination o f the optical constant o f Z n ~ C d t - x S pollycrysmllinc thin films was proposed and tested. The refractive index and the film thickness are determinated using the transmission data in the interference region o f the transmission spectrum. Since these films present appreciable sub-band gap absorption, this determination includes the calculation o f the absorption coefficient in order to avoid deviations observed when transparency is erroneously postulated. The calculation o f n, ot and Es using this procedure can be carried out using a programmable pocket calculator. The procedure has been used on a large number o f ( Z n , C d ) S films with different compositions measured with a Perkin Elmer L a m b d a 9 spectrophotometer. T h e reliability o f the method was tested by reproducing the transmission curve using the calculated parameters. T h e comparison with the experimental and calculated spectra is satisfactory with respect to the interference fringe and absorption edge positions and shapes. T h e method could also be applicable to other thin films, based on materials presenting interference fringes.
2.0 ¸
% 1.0
2
3
hu (eV) Fig. 5. Curves of o~2 vs hv correspondingto ZnxCd~_.S thin filmswith three different Zn-concentrations. 2.8
2.6
~ cus
2 . 4
-
A ¢
i
241
---- za=cdl.,s
.°
r=0.38
:"'
"'"" /"
-
~
2 . 2
•
Acknowledgements .......
2 . 0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
hv (eV) Fig. 6. Variation of the refractive index n as a functionof the photonenergy, for gnxCdm_ aS thin films with three different Zn-concentrations. semiconductors are direct band gap kind. The optical gaps obteined for the three Zn~Cdt _~S samples were: 2.43 eV for CdS, 2.88 eV for gno.3sCdo.62S and 3.48 eV for ZnS. Fig, 6 s h o w s the variation of the refractive index as a function o f the photon energy, corresponding to the three ( Z n C d ) S samples mentioned previously. The thicknesses o f a large number o f ( Z n C d ) S samples, determined through the calculation described previously,
were compared with the ones obtained using a profiler (Alpha-Step 200) and the difference spread was found to be less than 6%. However, comparison between the values of Eg calculated and measured by photoconductivity and photoluminescence, yields differences of less than 8%. Since the results presented in this work are in agreement with those reported in the literature for CdS [ 13-15], it can be concluded that the simple method proposed in this article, permits the determination, with good reliability, the optical constants (a, n), the thickness and the optical gap of Zn~Cd=_ ~S thin films prepared by evaporation.
This work was supported by C O L C I E N C I A S (Contract 075-93), Universidad Nacional de Colombia and IPPS o f Sweden.
References [ ! ] D. Hariskos, M. Ruck,T. Walter and H.W. Schock. Proc. 1st WCPEC. Hawaii, 1994, pp. 91-94. [2] R. W. Bir~nire and P.V. Meyers, Proc. 1st WCPEC, Hawaii, 1994, pp. 76-82. [3] D.A. Hinkov, J. Phys. D: Appl. Phys.. 22 (1989) 199-205. [4] P. Meredith, G.S. Bullet and A. C. Walker, Appl. Optics. 32 (28) (1993) 5619-5627. [5 ] J. C. Manifacier,J. Gasiot and J. P. Fillard, J. Phys. E.. 9 (1976) 10021004. [6] R. Swanepoel,J. Phys. E.. 17 (1984) 896-903. [7] R. Swanepoel,J. Phys. E. 16 (1983) 1214-1222. [8] 7-..Knitti, Optics of Thin Films, Wiley, New York, 1976. 19] J. Tones and (3. GordiUo.Thin Solid Films, 207 (1992) 231-235. [ 10] G. GordillooSolar Energy Mat. Solar Cells, 25 (1992) 41-49. [Ill S. W. Wemple and M. Didomenico, J. Phys. Roy. R. 3 (4) (1971) 1338. 112] S. H. Wemple and DiDomenico,Jr., Physical Review Letter~. 23 (20) (1969) 1156, [ 13l G, Gordillo, Solar Cells. 14 (1985) 219-228. 114] E. Elizalde and F. Rueda, Thin solidfilms. 122 (1984) 45-57. [ 15] Dubois, Laser Handbook, Vol. I, North-Holland.Amsterdam, 1972,.
ThinSolidFilms289 (1996) 238-241
A simple m e t h o d to determine the optical constants and thicknesses o f ZnxCdl _ xS thin films J. Torres a, J.I. Cisneros ¢, G. Gordillo b, F. Alvarez c a Pontificia UniversidadJaveriana, Bogotd. Colombia b Departamentode F[sica, UniversidadNacional de Colombia Bogotd, Colombia ¢instituto de F(sica 'Gleb Wataghin', UNICAMP.CP 6165, CEP 13083-970, Cidade Universitdria, Campinas. Brazil
Received30 November1995;accepted 10 May 1996
Abstract A new method to determine the optical parameters of ZnxCdl _~S polycrystailine thin films is proposed. Sub-gap absorption, caused by aceeptor states, is taken into account in the determination of the refractive index and film thickness. This procedure avoids errors in the results, frequently observed when the absorption is ignored. In the low and medium absorption region the refractive index is parametrized by the Wemple and DiDomenico (W-D) single oscillator model. The W-D parameters are further used in order to extrapolate the refractive index at the absorption edge to compute the absorption coefficient and the optical gap. The transmission spectra of typical CdS, (Zn,Cd)S and ZnS thin films and their corresponding values of n, a and Eg are presented. Keywords: Cadmiumsulphide;Evaporation;Inorganiccompounds;Opticalproperties;Opticalspectroscopy;Semiconductors;Solarcells;Sulfides;Vacancies
1. Introduction Cadmium sulfide is widely used as a photoconductor in the visible spectral region and as window material for CdTe and CulnSe2 based solar cells [ 1,2]. It is important for the development of these devices to obtain information about some optoelectrical properties of the constituent materials; in particular, the determination of the CdS optical constants is necessary to achieve a good design for the devices. Several authors have developed different theoreticai models to calculate the optical constants of semiconductor thin films from transmission and reflection measurements [ 3-7 ]. However, these models are not suitable for the determination of all optical constants of our CdS thin films deposited by evaporation of CdS-powder from a graphite crucible heated indirectly by radiation. In this article we describe a simple method which allows us to determine from transmittance measurements, the optical constants of (Zn,Cd)S thin films deposited by evaporation on 7059 glass substrates.
2. T h e o r y
The transmission of the system shown in Fig. 1, can be calculated using the following equations [8]: 0040-6090/96/$15.00 © 1996ElsevierScienceS.A. All rightsreserved Pi!50040-6090(96)08931-6
T=
A exp(ad) B exp(2ad) + C exp(ad) + D
(1)
where A = 16no(1 - p ) ( n 2 , + ~ ) U B= st- psvU
C = [ ( 4 n 3 ~ - zy ) 2 cos ~ + (n3Y + Z) 4k2 sin ~b] - p U 2 [ ( z - n a y ) 4 k 2 sin t h - ( z y + 4 n 3 ~ ) 2 cos ~b] D = uv - ptuU 2 u=(nl-n2)2
+~
/) = (n2-- n3)2-t- k~2 $ = (n I "l"n2)2"~"k~2 t=(n2+n3)2+~
y=n~-n~+~ z=n~,-n~+~ dp= 4~'n2d/ A
\n t + n3]
(2)
J. Torteset al. I ThinSolidFilms289(1996)238--241
239
1.0 AIR (nI - I)
[~TO
I ==+1'
oum (c~,~o, n3~t.sO
0.8
I
~0.6
i0.4
Fig. 1. System of an absorbing CdS thin film on a finite-ticknesstransparent substrate.
0.2 0.0~'~i:
Where a is the absorption coefficient of the CdS film, nt, n2 and n 3 the refractive indexes of air, film and glass respectively, k2 the extinction coefficient of the film and U is a correction factor which is intreduced if absorption is present in the substrate. In the transparent region, the extreme values of the transmittance occur at wavelengths Am,defined by the relation: ~=~-~:mlr
(3)
Where m is the interference order and d and n2 the thickness and refractive index of the CdS film. When n2>n3, as in our films, the maxima and minima of the transmission correspond to even and odd values of m respectively. Assuming weak variation of n 2, In can be calculated using the following equations:
t~
" Im
~
2see
~.(am) Fig. 2. Typicaltransmissionspectrumof a CdS thin film deposi~ by evaporation. 3. Results and discussion Fig. 2. shows a typical transmission spectrum of a CdS, thin film deposited by evaporation of CdS powder using an evaporation system described elsewhere [9]. The transmission .spectrum of the CdS thin films obtained by using a specu'ophotometer PERKIN-ELMER, Lambda 9 shows that the CdS samples do not present a transparent region between 500 and 2500 nm; this typical hehaviour of evaporated (Zn,Cd) S thin films give problems with the class of envelope methods like Swanepoel's [6,7]. The wide absorption region in the samples can he attributed to deep acceptor states generated by Cd-Vacancies and complexes formed by metal vacancy-donor nearest neighbor pairs, as was verified from photoluminiscencemeasurements [9,10].
Ara- I
(a)In -- Am- I - Am '"
-
o)m
=
3.1. Determination of the optical constants of CdS thin films deposited by evaporation
A,.+
A,,----A-~m, +t
(4)
Assuming that, in the low absorption region k2 = 0, the extreme of the interference fringes can be written as: T.
'~
T,~
2ntn3 = 2 2 nl
-I- n 3
4nln2n3 (n2+n2)(n[+n2)
(5a)
(5b)
In the transparent region of the spectrum the values of the maximum are determined by Eq. (5a); therefore, these values are independent of the film's refractive index n2. This indicates that in these spectral points the system of Fig. 1. behaves as a glass substrate without film. (Therefore the transmission maxima of the fiim/substrate system, in the transparent region, must be equal to the transmission of the nude substrate). Eq. (5a) and Eq. (5b) are used to determine n3 and obtain an approximate value of n2, as described below, respectively.
Our CdS films are not transparent, even in the interference region. For the calculation of the film refractive index and thickness in the low absorption or in the interference region, Eq. (1) and Eq. (3) should be used at the wavelengths corresponding to the maxima and minima. The la'ocedure includes basically the following steps: a) The determination of the interference orders using Eq. (4) and calculation of an approximate value of n2 by using of Eq. (5). b) calculation of k2 at the maxima (m even) imposing ~b--mm This is done solving numericallyfor k2 tho following equation: T(nt,n2,n3,m,k2) - Texp = 0
(6)
In this calculation the general expression for the transmission, Eq. ( I ), is used with the only restriction of Eq. (3). This result is rather accurate, even if approximate values ofn 2 are used, because k2depend weakly on n2. At the minima (m odd), k2 is found by interpolating its values at the neighboring maxima.
240
J. Tortes et al, /Thin Solid Films 289 (1996) 238-241
c) n2 is determined at the minima (m odd) by solving Eq. (6) for n 2, using values of k2 calculated in the previous step. Using a set of n2 values and the Eq. (3), the film thickness d can be calculated with a rather small dispersion. Knowing the value ofdallows the determination of n2 at the maxima, again using Eq. (3). Steps a) through c) are usually applied to the extreme far from the absorption edge, where the interference fringes are quite distinct. However, the determination of n2, using Eq. (3) can be extended to the whole interference region after properly determining d. It should be emphasize that the merit of this method for the determination of n2 and d, is the inclusion of the absorption in the calculation, which improves dramatically the quality of the values of the refractive index in the low and medium absorption region. d) Once/22 is known, Eq. (6) can be used again to determine k2 in all extreme. This is extremely useful information related to the sub-gap absorption, usually not determined from optical data. e) Finally, we use a model (W-D) proposed by Wemple and DiDomenieo [ 11 ], which consists of fitting the n2 data, obtained in the medium and weak regions to the expression
ferent Zn concentration. The samples were prepared by evaporation,using a source constituted by two coaxial chambers, one for CdS-powder and one for ZnS.powder [9]. The Zn-concentration was determined by EDS. Fig. 4 shows a typical transmission spectra of Zn,~Cdt-xS thin films with three different Zn-eoncentrations ( x = 0 (CdS), x =0.38 and x = 1 (ZnS)). With these experimental data the corresponding absorption coefficient and the refractive index were calcu2ated. Fig. 5 shows the curves of a 2 vs hv corresponding to the three samples of (ZnCd) S studied. The optical gaps Eg of the three samples were determined from the intercepts of the hv axis with the straight lines which fitting the o~2 vs h v curves in the region of strong absorption, considering here that these CdS- a13 d;2.621 gm ~' 2.4 2.3
(EdEo)
,~ 2.2
n~ - 1 =~_--2--~ deduced using the model of a single-effective-oscillator; where ~w is the photon energy, Eo is the single oscillator energy and Ed is the dispersion energy. The parameter Ed, which is a measure of the intensity of the inter band optical transitions, does not depend significantly on the bandgap. The values of Ed and Eo are obtained from the intercepts resulting from the extrapolation of the curve 1
n]--- 1vs(~ca)z
/ /
.2;/ i
0.5
,
i
1.0
,
i
,
f
,
t
1.5 2.0 2.5 hv(ev) Fig. 3. Variationof a refractiveindexof a CdS sample,calculatedusinga procedure which includes a single oscillatorfitting to the form n2-1 E~o/ ~ - ~ z. Table I Values of parameters Ea and Eo obtained from the W-D fiuing, using the simplearmonicoscillatormodel
(7)
The n 2 values in the absorption edge are obtained by extrapolating the n 2 vs ~w curve of the W-D model. A detailed discussion of the single-effective oscillator model, used by Wemple and DiDomenico to obtain Eq. (7) is given in [ 12]. Fig. 3 shows the experimental results for the refractive index of a typical CdS sample. The full line corresponds to the fitting according to the W - D model. In Table 1 are listed the values of Ed and Eo obtained for the tree samples CdS, ZnxCdt_~S ( x = 3 8 % ) and ZnS studied in this work, and values of Ea and Eo reported for crystalline CdS and ZnS samples [ 11 ]. The difference between the values of Ed and Eo obtained for our samples and those reported for crystalline samples could be attributed to the presence of accepter states, which introduce changes in n and then in the Ed and E0 values. Using the values of n 2 obtained with the procedure described above, the values ofk and a in the strong absorption region, can be calculated by using Eq. ( 1). The method developed in this work was applied to calculate the optical constants of ZnxCd, _~S thin films with dif-
Sample
Ed (eV)
Eo (eV)
CdS ZnxCdl_~S,(x=0.38) ZnS CdS* ZnS*
20.3 22.1 21.8 20.4 25.2
6.1 6.7 7.3 4.9 6
* Reportedvaluefor crystallinesamples [ I I l
o.s
1"t ~0.6
.................. /"/"~ /",
•
~/'\
f o.21ill o.ot~J
"
....
o.
.............~
500 1000 1500 2000 2500 ~.(nm) Fig. 4. Typicaltransmission spectra of Zn~¢d,_~S thin films with three differentgn-concentrations.
J. Torres et at. / Thin Solid Films 289 (1996) 238-241
6"
~
xl09
4. C o n c l u s i o n s
-CdS . . . . ZnxCdl.xS,x=0.38 3.0 ~ ....... ZnS
A simple procedure for the determination o f the optical constant o f Z n ~ C d t - x S pollycrysmllinc thin films was proposed and tested. The refractive index and the film thickness are determinated using the transmission data in the interference region o f the transmission spectrum. Since these films present appreciable sub-band gap absorption, this determination includes the calculation o f the absorption coefficient in order to avoid deviations observed when transparency is erroneously postulated. The calculation o f n, ot and Es using this procedure can be carried out using a programmable pocket calculator. The procedure has been used on a large number o f ( Z n , C d ) S films with different compositions measured with a Perkin Elmer L a m b d a 9 spectrophotometer. T h e reliability o f the method was tested by reproducing the transmission curve using the calculated parameters. T h e comparison with the experimental and calculated spectra is satisfactory with respect to the interference fringe and absorption edge positions and shapes. T h e method could also be applicable to other thin films, based on materials presenting interference fringes.
2.0 ¸
% 1.0
2
3
hu (eV) Fig. 5. Curves of o~2 vs hv correspondingto ZnxCd~_.S thin filmswith three different Zn-concentrations. 2.8
2.6
~ cus
2 . 4
-
A ¢
i
241
---- za=cdl.,s
.°
r=0.38
:"'
"'"" /"
-
~
2 . 2
•
Acknowledgements .......
2 . 0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
hv (eV) Fig. 6. Variation of the refractive index n as a functionof the photonenergy, for gnxCdm_ aS thin films with three different Zn-concentrations. semiconductors are direct band gap kind. The optical gaps obteined for the three Zn~Cdt _~S samples were: 2.43 eV for CdS, 2.88 eV for gno.3sCdo.62S and 3.48 eV for ZnS. Fig, 6 s h o w s the variation of the refractive index as a function o f the photon energy, corresponding to the three ( Z n C d ) S samples mentioned previously. The thicknesses o f a large number o f ( Z n C d ) S samples, determined through the calculation described previously,
were compared with the ones obtained using a profiler (Alpha-Step 200) and the difference spread was found to be less than 6%. However, comparison between the values of Eg calculated and measured by photoconductivity and photoluminescence, yields differences of less than 8%. Since the results presented in this work are in agreement with those reported in the literature for CdS [ 13-15], it can be concluded that the simple method proposed in this article, permits the determination, with good reliability, the optical constants (a, n), the thickness and the optical gap of Zn~Cd=_ ~S thin films prepared by evaporation.
This work was supported by C O L C I E N C I A S (Contract 075-93), Universidad Nacional de Colombia and IPPS o f Sweden.
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