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Optical transitions in CdTe thin films produced by hot- wall vacuum evaporation
Thin Solid Films, 147 (1987) 9-16 ELECTRONICS AND OPTICS
O P T I C A L T R A N S I T I O N S IN CdTe T H I N F I L M S P R O D U C E D BY HOTWALL VACUUM EVAPORATION s. CHAUDHURI,S. K. DAS AND A. K. PAL Department of General Physics and X-rays, Indian Association for the Cultivation of Science, Calcutta 700032 (India)
(Received December 13, 1985;acceptedJuly 29, 1986)
Optical properties of p-type CdTe films produced by the hot-wall evaporation technique were critically studied to obtain information on different parameters, e.g. refractive index and absorption coefficient. Variations in the parameters with incident photon energy indicated an indirect transition at a gap width of approximately 1.3 eV while the direct transition was observed at a gap width of approximately 1.5 eV.
1. INTRODUCTION Cadmium telluride is considered at present one of the most promising materials for device applications. It has a high absorption coefficient in the visible range of the solar spectrum and its band gap (1.45 eV) is close to the optimum value for efficient solar energy conversion. The material can be prepared in n-type and p-type forms so that solar cells can be formed in both homojunction and heterojunction configurations. A survey of the literature shows that different techniques of deposition have been developed to obtain device-grade CdTe thin films, among which electrodeposition 1, r.f. sputtering 2, closed space vapour transport 3, spray pyrolysis 4, screen printing 5 and vacuum evaporation 6'7 are worth mentioning. All these techniques have their own merits and demerits in producing high quality CdTe films. The possibility of twin formation due to stacking faults 8 was the main hindrance in the manufacture of single-crystal CdTe films. In most cases the deep levels 9' 1o which are often present in CdTe limit the carrier lifetime 11. CdTe in thin film form is generally polycrystalline 12"1a in nature and as such the electron transport in these films is controlled by grain boundary diffusion phenomena 14. Recently, we have reported our studies 15 on the growth and microstructure of CdTe films deposited onto NaCI and glass substrates by the hot-wall evaporation technique. As a continuation of the above work, we present here the optical properties of CdTe films deposited onto glass with a view to obtaining a clearer understanding of the optical transitions in these films. 0040-6090/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
l0
2.
S. CHAUDHURI, S. K. DAS, A. K. PAL.
EXPERIMENTAL DETAILS
CdTe films were deposited by the hot-wall technique which is similar to that used in our laboratory for CdS films 16. CdTe bulk material was synthesized from spectroscopically pure (99.999~) cadmium and tellurium in the usual way and the compositions of the mother material and the films were determined by an energydispersive X-ray (EDX) method. The requisite amount of CdTe powder was put in a quartz tube placed inside a cylindrical graphite heater. The material was evaporated at a rate of 1 nm s - 1 with source temperature 870 K at a chamber pressure of approximately 10 -4 Pa. The optimum values of substrate and chimney temperatures were 620 K and 650 K respectively. Some of the films were doped by mixing the requisite amount of PbC12 with the CdTe powder. Optical properties of the films were studied with a Cary 17D spectrophotometer. Analysing the data for a number of films, optical parameters, e.g. refractive index n and absorption coefficient ct, were determined in the energy range 1.3-1.8 eV of incident photons. The effect of doping on CdTe films is discussed here with reference to two representative films doped with 2 wt.~o PbC12 and 5 wt.~o PbC12. 3.
RESULTS AND DISCUSSION
Figure 1 shows the optical transmittance data of p-type CdTe films measured as a function of the wavelength of incident photons for three representative films-undoped, doped with 2 wt.~o PbC12 and 5 w t . ~ PbC12 and 1.2 ~tm, 1.3 ~tm and 1.5 Ixm thick respectively. Sharp interference fringes may be observed for undoped films which gradually smeared out with an increasing amount of dopant.
10
0"8 A I
a
T06 Oq / 02
o
¢
I~i
i (
i~5
i
lJ9
10 2 nm )
Fig. 1. Plot of optical transmittance T vs. wavelength 2 of three respresentative CdTe films: curve a, undoped; curve b, doped with 2 wt.~oPbCI2;curve c, doped with 5 wt.~ PbC12.
OPTICAL TRANSITIONS IN C d T e FILMS
11
The composition of the doped and undoped films was determined by X-ray diffraction analysis (Phillips PW 1050, 51, Cu K0c radiation) and is shown in Fig. 2. Sharp peaks of CdTe corresponding to (111), (220), (311) and (400) planes were observed for both doped and undoped films. This is in good agreement with results reported by Pessa et al. 8 It was observed that the composition of the bulk alloy is retained in the films produced by the hot-wall technique as indicated by EDX analysis. N o peak corresponding to C d l _ x P b x T e was observed. A small peak of lead (Fig. 2) observed in our doped films indicated that the total amount of PbC12 added was not effective as a dopant. At high concentrations (approximately 5 wt.~) of dopant some of the lead probably acted as an inclusion and thus caused a reduction in the transmittance of the doped films (Fig. 1) compared with that in the undoped films. This was supported by our electrical measurements 17. Another significant peak corresponding to the tellurium phase can be observed in the X-ray trace which will also affect the absorption significantly.
,~
~.'',220} dTe
~CdTe II(l,l)
:dTe
311~
cctTe
(400)
Te Pb (20'2) (311)
2'o
3b
'
.'o
'
5b
'
o'o
2O ( degree )
Fig. 2. X-ray diffraction spectrum of three representative CdTe films: curve a, undoped; curve b, doped with 2 wt.% PbCI2; curve c, doped with 5 wt.% PbCI z.
Hall effect studies indicated a hole concentration p of 8.6 x 1013 cm -3 for undoped films at 300 K whereas for films doped with 2 w t . ~ PbC12 and 5 wt.~o PbCI2 p was observed to be 2.4 x 10X4cm -3 and 3.4 x 10Z4cm -3 respectively at 300 K. The corresponding conductivities for undoped films, films doped with 2 wt.% PbCI 2 and with 5 w t . ~ PbC12 were 2.3 x 10- 4 f2 - 1 c m - t, 1.7 x 10- 3 f~ - 1 c m - 1 and 3.2 x 10 -3 ~ - 1 c m - 1 respectively at 300 K. It may be noticed that for concentrations of PbC12 greater than 2 wt.~o no significant change in carrier concentrations or conductivity was observed. The transmittance T vs. wavelength 2 plot was found to vary as la T =
16n~ngn 2 exp(-- ctt) R 12 + RE 2 exp( -- 2eft) + 2R zR2 exp( -
where R 1 = (n+na)(ng+n) R E = (n--na)(ng--n)
(1) ~xt)
cos(4nnt/2)
12
s. CHAUDHURI, S. K. DAS, A. K. PAL
is the absorption coefficient and n, na, ng are the refractive indices of the film, air and substrate respectively. The maxima and minima in the T vs. 2 plot occur when 4nnt
Rrc (2) 2 where R represents the order number and t is the thickness of the film. Beyond the absorption edge the absorption coefficient ~ in CdTe films was determined from a8 the envelopes of the maxima and minima of the T vs. 2 plot using -
e = t In
(3)
where 16nang(n 2 + K 2) A = {(na + n) z + Kz } {(n, + n) 2 + K 2}
(4)
K is the extinction coefficient and T' -
R1 l--(Tmax/Tmin) 1/2
(5)
R2 1 +(Tmax/Tml.) 1/2 Here, Tm~xand Tmi, represent the envelopes of the maxima and minima positions in the T vs. 2 plot (Fig. 1). Near the absorption edge an exponential variation in T with absorption coefficient was most probable so a may be determined from T = A e x p ( - at)
(6)
where A was found to be nearly equal to unity at the absorption edge. Figure 3 shows the absorption spectrum of CdTe films in the entire range of incident photon
]
6 E × 4 v
2
0 13
l'~
15
1"6 r7 he ( ev ) Fig. 3. Variation in the absorption coefficient ~ with incident photon energy hv for three representative CdTe films: El, undoped; O, doped with 2 wt.~ PbCI2; A, doped with 5 wt.~ PbC12.
OPTICAL TRANSITIONS IN CdTe FILMS
13
energies. Equations (6) and (3) were used to calculate ct at the absorption edge and beyond the absorption edge respectively. The absorption coefficient ~ may, in general, be written as a function of the incident photon energy h v so that 19
Eg)"
= Ao(hv -
(7)
where A o is a constant given by e2 Ao -
nch2me ,
(2mr) 3/2
(8)
me* and m r being the effective and reduced mass of charge carriers respectively. Eg is the optical band gap at which an optical transition occurs, the nature of which is determined by the value of m. N o w m in eqn. (7) can have values ½, 2, a2 and 3 for allowed direct, allowed indirect, forbidden direct and forbidden indirect transitions respectively. Using eqn. (7) we can obtain a set of values ( m , E ~ ) from the plots of ctTM vs. hv for the above probable m values. The band gaps Eg corresponding to these m values were obtained by extrapolating the linear portion of the above plots to ~1/,, = 0. Then, depending on the actual nature of transition occurring in the system, a single set of values of (m, Eg) obtained above will indicate a linear fit to the plot of log ~ vs. log hv. Figure 4
75
SO CI
30
D
3
//
I~ ¢qfJ O
/t
/
oJ
I
1.2
/
I
1.8
o
ha~(eV) Fig. 4. Plots of ~l/m /)S. hv with m = ½ and m = 2: curves At, A2, undoped; curves Bt, B2, doped with 2 wt.~ PbCI2; curves Ct, C2, doped with 5 wt.~ PbCI 2.
14
s. CHAUDHURI, S. K. DAS, A. K. PAL
shows the plots of ~z and 0~1/2 l)S. hv for undoped and doped films which indicate a good linear fit as discussed above. This clearly shows (Fig. 4) that allowed direct and indirect transitions occur in our films at optical band widths of 1.5 eV and 1.3 eV respectively. The values of m and Eg obtained as above are shown in Table I. The direct band gap of 1.5 eV obtained here is in good agreement with that computed from electrical conductivity data which has been reported17 separately elsewhere.
TABLE I OPTICAL PARAMETERSFOR THREE REPRESENTATIVECdTe FILMS
Sample Undoped Doped with 2 wt.~o PbC12 Doped with 5 w t . ~ PbCI z
Egl
Egd
(eV)
(eV)
1.34 1.31 1.30
1.51 1.49 1.48
m Indirecttransition
Directtransition
2.0 2.1 2.1
0.55 0.53 0.52
The optical transitions observed by different w o r k e r s 1 3 ' 2 ° - 2 4 a r e more or less in agreement with one another as far as the gap width of approximately 1.5 eV is concerned. However, as to the character of the transition associated with the optical band gap of approximately 1.5 eV, Aranda et al. 2°, Thutupalli and Tomlin 23, Cardona et al. 24 and Myers et al. 13 found it to be direct while others have found direct and indirect gaps with very similar energy values 21'22. Our results, however, confirm the direct character of the transition occurring at a gap width of 1.5 eV. Regarding the indirect transitions occurring in CdTe films E1-Shazly et al. 21, Davis and Shilliday 22 and Thutupalli and Tomlin 23 reported the values of band gap widths of 1.47 eV, 1.44 eV and 1.82 eV respectively whereas the value of the band gap obtained by us for indirect transition is approximately 1.3 eV which is not at all in agreement with the above reported values. It may be noted (Fig. 4) that all the films (undoped and doped) showed distinct linear behaviour of the plots of 0~1/2 VS. hv indicating an indirect transition at approximately 1.3 eV. The refractive index n may be computed from 25
n2na2+ng2 --
2
+ 2nang T" +
{!na2+ng2+4nangT,,)2 4
}1/2
?/a2ng2
(9)
where T" = (Tma x -- Tmin)/TmaxTml nFigure 5 shows the variation in the refractive index with incident photon energy. It may be observed from this figure that the refractive index is more or less constant in our spectral range of measurement except for the film doped with approximately 5 wt.~o PbC12 where the refractive index could be seen to increase with increasing energy. This variation in refractive index of the samples containing less than or approximately 5 wt.~o PbC12 may be caused by the separation of lead as a second phase.
OPTICAL TRANSITIONS IN
CdTe FILMS
15
3
1
I
07
1.0
I
1.3 h'~' (eV)
J
1.6
Fig. 5. Variati•ninrefractiv••ndexnwithincidentph•t•nenergyhvf•rthreerepresentativeCdTe••ms: IS], undoped; O, doped with 2 wt.~o PbC12; A, doped with 5 wt.~o PbCI2.
4. CONCLUSION It may be concluded from the above studies that in the region of incident photon energy 1.3-1.8 eV both direct and indirect transitions take place in CdTe films. In the lower range (less than 1.5eV) of energy the indirect transition predominates (with gap width 1.3 eV) over the direct transition (with gap width 1.5 eV). The band gaps of doped and undoped films were observed to have a similar value indicating no formation of C d l _ x P b x T e even at the high doping concentration (approximately 5 wt.~) of PbC12. ACKNOWLEDGMENTS
The authors wish to thank Professor S. P. Sengupta and Professor M. Chaudhuri of the Indian Association for the Cultivation of Science for the X-ray diffraction trace and the spectrophotometer traces respectively. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
M. Takahashi, K. Uosaki and H. Kita, J. Appl. Phys., 55 (1984) 3879. F. Wang and D. K. Reinhard, J. Appl. Phys., 55 (1984) 3702. T.C. Anthony, A. L. Fahrenbruch and R. H. Bube, J. Vae. Sci. Technol. A, 2 (1984) 1296. B.J. Feldman, J. L. Boone and T. V. Van Doren, Appl. Phys. Lett., 38 (1981) 703. N. Matsumura, T. Ohshima, J. Saraie and Y. Yodogawa, J. Cryst. Growth, 71 (1985) 361. H. Matsumoto, K. Kuribayashi, H. Uda, Y. Komatsu, A. Nakano and S. Ikegami, Sol. Cells, 11 (1984) 367. S. Gongoi and K. Barua, Thin Solid Films, 92 (1982) 227. M. Pessa, O. Jylha, P. Huttunen and M. A. Herman, J. Vac. Sci. Technol. A, 2 (1984) 418. H. Sitter, H. Heinrich, K. Lischka and A. Lopez-Otero, J. Appl. Phys., 53 (1982) 4948. L.C. Isett and P. K. Roychaudhuri, J. Appl. Phys., 55 (1984) 3605. M. Rodot, Rev. Phys. Appl., 12 (1977) 411. W.H. Huber, A. L. Fahrenbruch, C. Fortmann and R. H. Bube, J. Appl. Phys., 54 (1983) 4038. T.H. Myers, S. W. Edwards and J. F. Schetzina, J. Appl. Phys., 52 (1981) 4231.
16
s. CHAUDHURI, S. K. DAS, A. K. PAL
14
A . L . Fahrenbruch and R. H. Bube, Fundamentals of Solar Cells, Academic Press, New York, 1983, p. 387. R . L . Basak, S. Chaudhuri, S. K. Das and A. K. Pal, J. Cryst. Growth, 73 (1985) 392. S. Chaudhuri, J. Bhattacharya, D. De and A. K. Pal, Sol. Energy Mater., 10 (1984) 223. S.K. Das, R. L. Basak, S. Chaudhuri and A. K. Pal, submitted to Phys. Status Solidi A. J. C, Manifacier, J. Gasiot and J. P. Fillard, J. Phys. E, 9 (1976) 1002. J.J. Pankove, Optical Processes in Semiconductors, Prentice Hall, N J, 1971. J. Aranda, J. L. Morenza, J. Esteve and J. M. Codina, Thin Solid Films, 120 (1984) 23. A . A . E1-Shazly, H. T. E1-Shair and M. K. El-Mourley, Thin Solid Films, 78 (1981) 295. P . W . Davis and T. S. Shilliday, Phys. Rev., 118 (1960 1020. G . K . M . Thutupalli and S. G. Tomlin, J. Phys. D, 9 (1976) 1639. M. Cardona, K. L. Shaklee and F. H. Pollak, Phys. Rev., 154 (1967) 696. J.C. Manifacier, M. De Murcia, J. P. Fillard and E. Vicario, Thin Solid Films, 41 (1977) 127.
15 16 17 18 19 20 21 22 23 24 25
O P T I C A L T R A N S I T I O N S IN CdTe T H I N F I L M S P R O D U C E D BY HOTWALL VACUUM EVAPORATION s. CHAUDHURI,S. K. DAS AND A. K. PAL Department of General Physics and X-rays, Indian Association for the Cultivation of Science, Calcutta 700032 (India)
(Received December 13, 1985;acceptedJuly 29, 1986)
Optical properties of p-type CdTe films produced by the hot-wall evaporation technique were critically studied to obtain information on different parameters, e.g. refractive index and absorption coefficient. Variations in the parameters with incident photon energy indicated an indirect transition at a gap width of approximately 1.3 eV while the direct transition was observed at a gap width of approximately 1.5 eV.
1. INTRODUCTION Cadmium telluride is considered at present one of the most promising materials for device applications. It has a high absorption coefficient in the visible range of the solar spectrum and its band gap (1.45 eV) is close to the optimum value for efficient solar energy conversion. The material can be prepared in n-type and p-type forms so that solar cells can be formed in both homojunction and heterojunction configurations. A survey of the literature shows that different techniques of deposition have been developed to obtain device-grade CdTe thin films, among which electrodeposition 1, r.f. sputtering 2, closed space vapour transport 3, spray pyrolysis 4, screen printing 5 and vacuum evaporation 6'7 are worth mentioning. All these techniques have their own merits and demerits in producing high quality CdTe films. The possibility of twin formation due to stacking faults 8 was the main hindrance in the manufacture of single-crystal CdTe films. In most cases the deep levels 9' 1o which are often present in CdTe limit the carrier lifetime 11. CdTe in thin film form is generally polycrystalline 12"1a in nature and as such the electron transport in these films is controlled by grain boundary diffusion phenomena 14. Recently, we have reported our studies 15 on the growth and microstructure of CdTe films deposited onto NaCI and glass substrates by the hot-wall evaporation technique. As a continuation of the above work, we present here the optical properties of CdTe films deposited onto glass with a view to obtaining a clearer understanding of the optical transitions in these films. 0040-6090/87/$3.50
© Elsevier Sequoia/Printed in The Netherlands
l0
2.
S. CHAUDHURI, S. K. DAS, A. K. PAL.
EXPERIMENTAL DETAILS
CdTe films were deposited by the hot-wall technique which is similar to that used in our laboratory for CdS films 16. CdTe bulk material was synthesized from spectroscopically pure (99.999~) cadmium and tellurium in the usual way and the compositions of the mother material and the films were determined by an energydispersive X-ray (EDX) method. The requisite amount of CdTe powder was put in a quartz tube placed inside a cylindrical graphite heater. The material was evaporated at a rate of 1 nm s - 1 with source temperature 870 K at a chamber pressure of approximately 10 -4 Pa. The optimum values of substrate and chimney temperatures were 620 K and 650 K respectively. Some of the films were doped by mixing the requisite amount of PbC12 with the CdTe powder. Optical properties of the films were studied with a Cary 17D spectrophotometer. Analysing the data for a number of films, optical parameters, e.g. refractive index n and absorption coefficient ct, were determined in the energy range 1.3-1.8 eV of incident photons. The effect of doping on CdTe films is discussed here with reference to two representative films doped with 2 wt.~o PbC12 and 5 wt.~o PbC12. 3.
RESULTS AND DISCUSSION
Figure 1 shows the optical transmittance data of p-type CdTe films measured as a function of the wavelength of incident photons for three representative films-undoped, doped with 2 wt.~o PbC12 and 5 w t . ~ PbC12 and 1.2 ~tm, 1.3 ~tm and 1.5 Ixm thick respectively. Sharp interference fringes may be observed for undoped films which gradually smeared out with an increasing amount of dopant.
10
0"8 A I
a
T06 Oq / 02
o
¢
I~i
i (
i~5
i
lJ9
10 2 nm )
Fig. 1. Plot of optical transmittance T vs. wavelength 2 of three respresentative CdTe films: curve a, undoped; curve b, doped with 2 wt.~oPbCI2;curve c, doped with 5 wt.~ PbC12.
OPTICAL TRANSITIONS IN C d T e FILMS
11
The composition of the doped and undoped films was determined by X-ray diffraction analysis (Phillips PW 1050, 51, Cu K0c radiation) and is shown in Fig. 2. Sharp peaks of CdTe corresponding to (111), (220), (311) and (400) planes were observed for both doped and undoped films. This is in good agreement with results reported by Pessa et al. 8 It was observed that the composition of the bulk alloy is retained in the films produced by the hot-wall technique as indicated by EDX analysis. N o peak corresponding to C d l _ x P b x T e was observed. A small peak of lead (Fig. 2) observed in our doped films indicated that the total amount of PbC12 added was not effective as a dopant. At high concentrations (approximately 5 wt.~) of dopant some of the lead probably acted as an inclusion and thus caused a reduction in the transmittance of the doped films (Fig. 1) compared with that in the undoped films. This was supported by our electrical measurements 17. Another significant peak corresponding to the tellurium phase can be observed in the X-ray trace which will also affect the absorption significantly.
,~
~.'',220} dTe
~CdTe II(l,l)
:dTe
311~
cctTe
(400)
Te Pb (20'2) (311)
2'o
3b
'
.'o
'
5b
'
o'o
2O ( degree )
Fig. 2. X-ray diffraction spectrum of three representative CdTe films: curve a, undoped; curve b, doped with 2 wt.% PbCI2; curve c, doped with 5 wt.% PbCI z.
Hall effect studies indicated a hole concentration p of 8.6 x 1013 cm -3 for undoped films at 300 K whereas for films doped with 2 w t . ~ PbC12 and 5 wt.~o PbCI2 p was observed to be 2.4 x 10X4cm -3 and 3.4 x 10Z4cm -3 respectively at 300 K. The corresponding conductivities for undoped films, films doped with 2 wt.% PbCI 2 and with 5 w t . ~ PbC12 were 2.3 x 10- 4 f2 - 1 c m - t, 1.7 x 10- 3 f~ - 1 c m - 1 and 3.2 x 10 -3 ~ - 1 c m - 1 respectively at 300 K. It may be noticed that for concentrations of PbC12 greater than 2 wt.~o no significant change in carrier concentrations or conductivity was observed. The transmittance T vs. wavelength 2 plot was found to vary as la T =
16n~ngn 2 exp(-- ctt) R 12 + RE 2 exp( -- 2eft) + 2R zR2 exp( -
where R 1 = (n+na)(ng+n) R E = (n--na)(ng--n)
(1) ~xt)
cos(4nnt/2)
12
s. CHAUDHURI, S. K. DAS, A. K. PAL
is the absorption coefficient and n, na, ng are the refractive indices of the film, air and substrate respectively. The maxima and minima in the T vs. 2 plot occur when 4nnt
Rrc (2) 2 where R represents the order number and t is the thickness of the film. Beyond the absorption edge the absorption coefficient ~ in CdTe films was determined from a8 the envelopes of the maxima and minima of the T vs. 2 plot using -
e = t In
(3)
where 16nang(n 2 + K 2) A = {(na + n) z + Kz } {(n, + n) 2 + K 2}
(4)
K is the extinction coefficient and T' -
R1 l--(Tmax/Tmin) 1/2
(5)
R2 1 +(Tmax/Tml.) 1/2 Here, Tm~xand Tmi, represent the envelopes of the maxima and minima positions in the T vs. 2 plot (Fig. 1). Near the absorption edge an exponential variation in T with absorption coefficient was most probable so a may be determined from T = A e x p ( - at)
(6)
where A was found to be nearly equal to unity at the absorption edge. Figure 3 shows the absorption spectrum of CdTe films in the entire range of incident photon
]
6 E × 4 v
2
0 13
l'~
15
1"6 r7 he ( ev ) Fig. 3. Variation in the absorption coefficient ~ with incident photon energy hv for three representative CdTe films: El, undoped; O, doped with 2 wt.~ PbCI2; A, doped with 5 wt.~ PbC12.
OPTICAL TRANSITIONS IN CdTe FILMS
13
energies. Equations (6) and (3) were used to calculate ct at the absorption edge and beyond the absorption edge respectively. The absorption coefficient ~ may, in general, be written as a function of the incident photon energy h v so that 19
Eg)"
= Ao(hv -
(7)
where A o is a constant given by e2 Ao -
nch2me ,
(2mr) 3/2
(8)
me* and m r being the effective and reduced mass of charge carriers respectively. Eg is the optical band gap at which an optical transition occurs, the nature of which is determined by the value of m. N o w m in eqn. (7) can have values ½, 2, a2 and 3 for allowed direct, allowed indirect, forbidden direct and forbidden indirect transitions respectively. Using eqn. (7) we can obtain a set of values ( m , E ~ ) from the plots of ctTM vs. hv for the above probable m values. The band gaps Eg corresponding to these m values were obtained by extrapolating the linear portion of the above plots to ~1/,, = 0. Then, depending on the actual nature of transition occurring in the system, a single set of values of (m, Eg) obtained above will indicate a linear fit to the plot of log ~ vs. log hv. Figure 4
75
SO CI
30
D
3
//
I~ ¢qfJ O
/t
/
oJ
I
1.2
/
I
1.8
o
ha~(eV) Fig. 4. Plots of ~l/m /)S. hv with m = ½ and m = 2: curves At, A2, undoped; curves Bt, B2, doped with 2 wt.~ PbCI2; curves Ct, C2, doped with 5 wt.~ PbCI 2.
14
s. CHAUDHURI, S. K. DAS, A. K. PAL
shows the plots of ~z and 0~1/2 l)S. hv for undoped and doped films which indicate a good linear fit as discussed above. This clearly shows (Fig. 4) that allowed direct and indirect transitions occur in our films at optical band widths of 1.5 eV and 1.3 eV respectively. The values of m and Eg obtained as above are shown in Table I. The direct band gap of 1.5 eV obtained here is in good agreement with that computed from electrical conductivity data which has been reported17 separately elsewhere.
TABLE I OPTICAL PARAMETERSFOR THREE REPRESENTATIVECdTe FILMS
Sample Undoped Doped with 2 wt.~o PbC12 Doped with 5 w t . ~ PbCI z
Egl
Egd
(eV)
(eV)
1.34 1.31 1.30
1.51 1.49 1.48
m Indirecttransition
Directtransition
2.0 2.1 2.1
0.55 0.53 0.52
The optical transitions observed by different w o r k e r s 1 3 ' 2 ° - 2 4 a r e more or less in agreement with one another as far as the gap width of approximately 1.5 eV is concerned. However, as to the character of the transition associated with the optical band gap of approximately 1.5 eV, Aranda et al. 2°, Thutupalli and Tomlin 23, Cardona et al. 24 and Myers et al. 13 found it to be direct while others have found direct and indirect gaps with very similar energy values 21'22. Our results, however, confirm the direct character of the transition occurring at a gap width of 1.5 eV. Regarding the indirect transitions occurring in CdTe films E1-Shazly et al. 21, Davis and Shilliday 22 and Thutupalli and Tomlin 23 reported the values of band gap widths of 1.47 eV, 1.44 eV and 1.82 eV respectively whereas the value of the band gap obtained by us for indirect transition is approximately 1.3 eV which is not at all in agreement with the above reported values. It may be noted (Fig. 4) that all the films (undoped and doped) showed distinct linear behaviour of the plots of 0~1/2 VS. hv indicating an indirect transition at approximately 1.3 eV. The refractive index n may be computed from 25
n2na2+ng2 --
2
+ 2nang T" +
{!na2+ng2+4nangT,,)2 4
}1/2
?/a2ng2
(9)
where T" = (Tma x -- Tmin)/TmaxTml nFigure 5 shows the variation in the refractive index with incident photon energy. It may be observed from this figure that the refractive index is more or less constant in our spectral range of measurement except for the film doped with approximately 5 wt.~o PbC12 where the refractive index could be seen to increase with increasing energy. This variation in refractive index of the samples containing less than or approximately 5 wt.~o PbC12 may be caused by the separation of lead as a second phase.
OPTICAL TRANSITIONS IN
CdTe FILMS
15
3
1
I
07
1.0
I
1.3 h'~' (eV)
J
1.6
Fig. 5. Variati•ninrefractiv••ndexnwithincidentph•t•nenergyhvf•rthreerepresentativeCdTe••ms: IS], undoped; O, doped with 2 wt.~o PbC12; A, doped with 5 wt.~o PbCI2.
4. CONCLUSION It may be concluded from the above studies that in the region of incident photon energy 1.3-1.8 eV both direct and indirect transitions take place in CdTe films. In the lower range (less than 1.5eV) of energy the indirect transition predominates (with gap width 1.3 eV) over the direct transition (with gap width 1.5 eV). The band gaps of doped and undoped films were observed to have a similar value indicating no formation of C d l _ x P b x T e even at the high doping concentration (approximately 5 wt.~) of PbC12. ACKNOWLEDGMENTS
The authors wish to thank Professor S. P. Sengupta and Professor M. Chaudhuri of the Indian Association for the Cultivation of Science for the X-ray diffraction trace and the spectrophotometer traces respectively. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13
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