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Hall mobility and conductivity in ZnxCd1-xS mixed crystals
844
Journal of Crystal Growth 101 (1990) 844—849 North-Holland
HALL MOBILITY AND CONDUCTIVITY IN Zn~Cd1 ~S MIXED CRYSTALS
M.K.B. SAIDIN, G.J. RUSSELL, A.W. BRINKMAN and J. WOODS Applied Physics Group, School of Engineering and Applied Science, University of Durham, South Roa4 Durham DH] 3LE, UK
The electrical conductivity and Hall mobility of mixed crystals of Zn~Cd1_~Shave been measured from 95 to 300 K for a range of compositions with 0 x 0.45. Crystals were grown from the vapour phase over the full range of composition and were found to have the hexagonal wurtzite structure for 0 0.45 were semi-insulating and were unsuitable for electrical measurements. Crystals with 0
1. Introduction
The alloy system Zn5Cd~~S is completely miscible throughout the whole range of compositions so that ternary compounds with band gaps extending from 2.42 eV (CdS) to 3.66 eV (ZnS) are readily obtainable. This has traditionally been exploited in cathodoluminescent phosphors doped with copper where the material is usually prepared in powder form. More recently a number of attempts have been made to produce highly efficient thin film photovoltaic cells consisting of a layer of p-type Cu2S formed on a substrate of Zn5Cd15S. The reason for this is that the efficiency of the thin film solar cell based on CdS/Cu2S appears to be limited to about 10% because of differences in the electron affinities and lattice spacings of the two compounds [1]. Palz et al. [2] first suggested that these discrepancies could be reduced if the CdS was replaced by Zn5Cd1~S with x 0.2. Although various workers [3,4] soon showed that the open circuit voltage increased as x was increased towards 0.2, efficiencies failed to exceed 10%, largely because the short circuit currents obtainable were simultaneously reduced. =
0022-0248/90/$03.50 © 1990
—
The literature on the electrical properties of the Zn~Cd 1~~S alloy system is very sparse. Chenn et al. [5] and Davis and Lind [6] investigated bulk single crystals grown by the iodine transport technique, and Sakurai et a!. [7] grew epitaxial layers on ZnS substrates, but most other workers studied alloys prepared by spray pyrolysis [8-10] or by thermal evaporation [11]. Although there would appear to be a substantial consensus about the structural properties of the alloy system, there is a considerable variation in the reported electrical properties. Consequently a programme has been carried to growofand measure the crystals resistivity and Hallout coefficient a range of single of Zn~Cd~ ~S,
such as had been used in this labora-
tory previously [4] to investigate the photovoltaic properties of single crystal Zn~Cd~~S/Cu2S solar cells. 2. Experimental 2.1. Crystal growth
Alloy crystals were grown using the technique described by Clark and Woods [12]. A pre-sintered
Elsevier Science Publishers B.V. (North-Holland)
M.KB. Saidin et a!. / Hall mobility and conductivity in Zn~Cd
1— ~S mixed crystals
charge of Zn5Cd1~Swas sublimed from bottom to top of an evacuated silica capsule held vertically in a temperature gradient. The charge was maintained at 1150°Cand condensation to form a crystalline boule occurred at 1050°C. While the crystal was growing, over a period of several days, the growth capsule was slowly pulled through the furnace in an attempt to ensure that the growth interface was maintained under constant conditions. Al! the grown crystals were transparent, being colourless when x > 0.5 and becoming gradually more yellow as the zinc concentration was reduced. Many boules showed a gradation of colour along their length indicating a progressive change in composition during growth. In general more zinc was incorporated during the later stages of growth. The cadmium rich crystals were of better quality than the zinc rich ones. 2.2. Determination of composition The as-grown boules were cut into 1 mm slices which, after polishing, were used to provide samples in the form of Hall bars, clover leaves or millimetre dice. All other samples were degreased and etched in cold concentrated HC1 before being investigated further, The boules were assessed for compositional uniformity using EDAX (energy dispersive analysis by X-rays) in a scanning electron microscope; and the absolute composition of the mixed crystals was determined by atomic absorption spectroscopy. Because this technique is destructive it was deployed after all other measurements had been completed. The two important features of the EDAX spectrum were the Cd Li and the Zn Ka lines. The relative intensities of these Cd and Zn lines could be used to give a non-destructive estimate of the relative Cd and Zn compositions by utilizing the procedure described by Bertin [13]. According to Bertin, in a binary compound, a log-log plot of the ratio of the intensities of lines characteristic of the elements versus the composition ratio should be linear, independently of sample size and shape etc. This technique can be extended to a ternary compound such as
102
845
I
1 it
~
2 10
0
1
10
10
2 10
.
Fig. 1. The ratio of the intensities of the Zn Ka and Cd LI lines in the EDAX spectrum plotted as a function of the ratio of the molar concentrations of ZnS and CdS determined by Atomic Absorption Spectroscopy.
Zn~Cd 1~Sprovided the third element, i.e. sulphur, does not preferentially absorb any of the X-ray fluorescence from either of the other two elements. A calibration curve of log( ‘Zn/lCd) against ~ proved to be linear (fig. 1), and was then used to allow compositions to be determined from EDAX measurements. ‘Zn is the intensity of the Zn Ka line and I~ that of the Cd Li line. ~ and CCds are the fractional molar concentrations of ZnS and CdS. 2.3. Structure and lattice parameter A Philips diffractometer was used to record the diffraction patterns obtained from finely ground powders of Zn5Cd1 ~S. Each sample was prepared by spreading a powder layer of the material on to a glass slide with acetone. A scan was then made across the sample using Co Ka radiation (X 1.7902 A) with a goniometer scanning rate of 1° per minute. The structure of all the mixed crystals with 0
=
846
M.K.B. Saidin et at
/ Hall mobility and conductivity in Zn~Cdj
—
on the high energy side of this peak was plotted against energy,of good lines were obtainedphoton for crystals each straight composition. Esti-
I 67
\
41
~N.
~
66-
mates of the band gaps were obtained by extrapolating these lines to the energy axis. The resultant
N.~
\
\
‘N
\
~S mixed crystals
~N
variation of band gap nearly with composition in fig. 3 and was very linear with is shown
y-~
~
Eg=(2.43+1.28x)eV. N
45-
N
2.5. Electrical properties N
o
“
64-
3.8
Measurements of electrical conductivity and Hall coefficient could only be made satisfactorily over the composition range 0 0.45 the material became semi-insulating and reliable transport measurements could not be made. Ohmic contacts were provided of Inand withannealed iO%Cd which was pressed onbytoanthealloy samples at 300°C =
=
-
63
6.2 0
02
0.4 06 Compos,t,on lx)
-
0,8
~
1
-
~6
-
Fig. 2. Lattice parameters a and c as a function of composition(x).
in an atmosphere of argon for 10 mi
I
I
I
s-.’
// /
c=6.705—0.46x.
2.4. Band gap measurements
.
Estimates of the band gaps of the vanous alloys with 0
Measure-
ments were made from 95 to 300 K on conventional Hall bars with dimensions of 8 x 2 x 1 mm3,
hexagonal lattice parameters a and c were calculated from the X-ray data. Their variation with composition is shown in fig. 2 and clearly Vegard’s Law was obeyed rather well with: a=4.i36—0.34x,
=
1
/
/
-
/
/ / /
~
/ /
3~
-
2.9
/ / 27
9.
/
2.5
23
‘
‘
04
‘
Compositi~IxI
Fig. 3. Forbidden bandgap of the alloy crystals as a function of composition.
M.KB. Saidin et al.
/ Hall mobility and conductivity in Zn~Cd1 ~S mixed crystals
847
—
or on Van der Pauw clover leaf samples some 1 cm in diameter. The electrical properties of the CdS crystals were very similar to those reported by Subhan et a!. [14] for crystals grown in this laboratory some 15 years ago. Thus the free electron 3 with concentration a mobility of at 300 was about 1017 cm 300 cm2K V1 s~. The mobility increased to a maximum of approximately 800 cm2 V1 s1 at about 100 K, while the free carrier concentration dropped by a factor of 3 at 90 K. Activation energies in the range 0.01 to 0.016 eV were derived from the curves of ln( n) versus reciprocal temperature. The variation of the electron mobility with temperature could be fitted satisfactorily to a combination of optical mode, piezoelectric and ionised impurity scattering as had been demonstrated by Subhan et a!. previously. The room temperature conductivity and the corresponding free carrier concentration increased with increasing concentration of zinc to a maximum at about x 0.05, when values of 16 ~ii cm’ and n 3.6 x 1017 cm were reached. The corresponding electron mobility was 285 cm2 V 1 1 With increasing zinc content beyond o.os, the conductivity fell slightly until a concentration of x 0.15 was reached. At this composition the conductivity was only slightly less than that of CdS. The free carrier concentration was still of the order of 1017 cm while the electron mobility had fallen to 235 cm2 V~ s~. The electrical conductivity began to decrease even more rapidly when the zinc concentration exceeded x 0.15. This was almost entirely associated with a collapse in the value of the electron mobility (for example a value of 5 cm2 V1 s~ was measured for a crystal with x 0.22), while the free carrier concentration remained in the vicinity of iO’~cm The variation in the room temperature Hall mobility with composition is shown by the experimental points in fig. 4. With crystals with zinc concentrations in the range 0 x <0.15, plots of ln(n) versus i/T indicated little change in the values of donor activation energies which remained in the vicinity of 0.013 eV. The electron mobilities, although smaller in value as x approached 0.15, still increased with
106
io~
~io2
101
1000
=
—
—
—
.~ =
=
~,
=
=
~
~
02
‘
‘
05
04
=
Fig. 4. Hall mobility at 300 K as a function of composition. Experimental point (•). The solid lines a, b and c are mobilities calculated to be expected if (a) polar optical mode scattering, (b) piezoelectnc scattering or (c) a combination of (a) and (b) were operative. The full lone through the expenmental points was calculated assuming space charge scattering was operative.
decreasing temperature to a maximum between 100 and 150 K. The first dramatic change in behaviour occurred when values of x exceeded 0.15. Then very low values of mobility were found at room temperature, but in addition the mobility decreased as the temperature was reduced, and became 3 or 4 times smaller at 100 K, more or less following a T~3/2 variation. It is interesting to note that in this mobility regime, plots of ln a T3 versus 1/T led to good straight lines, the slopes of which indicated activation energies of 0.032 eV.
-<
3. Discussion In general the large mixed crystals of Zn~ Cd 3~Swere non-uniform. It was for this reason
M.K.B. Saidin et a!. / Hall mobility and conductivity in Zn~Cdj— ~ mixed crystals
848
that the EDAX technique was adapted to provide a quick and non-destructive method of determining the composition of each piece of crystal investigated. This proved invaluable, Although the two binary compounds at either end of the compositional range crystallised with different structures, i.e. CdS as hexagonal wurtzite and ZnS as predominantly cubic sphalerite, the structure of all the alloys from 0
of each sample subjected to X-ray analysis led to more reliable results. In rather similar vein the present investigation suggested that there is a linear relationship between the bandgap energy and composition, at least up to x 0.5. This agrees with the observations of Agnihotri and Gupta [8], Kane et a!. [ii], Romeo et al. [17] and Kwok et al. [9], but not with those of Vitrikhovskii and Mietskaya [18] and Davis and Lind [6] who found a bowed type of relationship Eg andproperties composition. Reports ofbetween the electrical of the alloy crystals as a function of composition are for the most part limited to measurements of resistivity only, and indicate a fair spread of results, although there is general agreement that the resistivity increases as x increases. According to Davis and Lind [6], the conductivity of their crystals containing iodine decreased abruptly by 7—8 orders of magnitude when x reached a value of 0.15. This is quite different from our experience =
where a room temperature conductivity of 4 X i0~ Q~ cm~could still be achieved at x 0.45. However, our results do indicate that some new factor comes into play as the zinc content exceeds x 0.15. Then the mobility collapses and begins to exhibit a temperature variation characteristic of ionised impurity scattering. With 0
=
150 K or so. With x > 0.15 the free carrier con3, while centration at 300 K remains near 1017 cm the donor activation energy increases to 0.03 eV and the mobility decreases by factors of 10—50 and exhibits a temperature variation suggestive of ionised impurity scattering. It seems likely, however, that at higher values of x the mobility is being limited by other processes. Possible processes include alloy scattering and space charge scattering [20]. Approximate calculations of mobilities limited by alloy scattering gave values which were much too large. Space charge scattering limited mobility is given by [20]: 2 3.2 X iO~T’°” (m~’/m 2(N 0)~ 5A) =
where T is the temperature, m~’ the electron effective mass, m0 the rest mass and (NSA) is the density-cross section product for the scattering centres. Although N5A was not known, a curve could be fitted to the mobility data by assuming that (N5A) varied linearly with composition as assumed by Stringfellow [19] and Kaneko et al. [21] in a study of GaA1As. Adopting such a procedure led to the full line curve in fig. 4,1.where The values of (N5A) were of the order iO~cmof samtemperature dependence of the mobility pies with x > 0.15 suggests that ionised impurity scattering is important, but possibly a combination of this with space charge scattering may be able to explain the observations. In summary the electrical conductivity of the alloy crystals is strongly affected by a decrease in mobility for compositions with x > 0.5. The free carrier concentration remains fairly constant after peaking at x 0.05, up to compositions with x =
=
M.K.B. Saidin et a!.
/ Hall mobility and conductivity in
0.5. Thereafter the crystals rapidly become semiinsulating with the result that no meaningful measurements have been made. It seems clear however that prospects of making an efficient Zn~Cdi 5S/ Cu2S solar cell with x 0.2 will be affected by the reduction in carrier mobility which occurs at this composition. —
=
References [1] A.M. Barnett and A. Rothwarf, IEEE Trans. Electron Devices ED-27 (1980) 615. [2] W. Pa!z, J. Besson, TN. Duy and J. Vedel, in: Proc. 10th IEEE Photovoltaic Specialists Conf., Palo Alto, CA, 1973, p. 69. [3] RB. Hall, R.W. Birkmire, J.E. Phillips and J.D. Meakin, App!. Phys. Letters 38 (1981) 925. [4] S. Oktik, G.J. Russell and J. Woods, J. Crystal Growth 59 (1982) 414. [5] P. Cherin, EL. Lind and E.A. Davis, J. Electrochem. Soc. 117 (1970) 233. [6] E.A. Davis and EL. Lind, J. Phys. Chem. Solids 29 (1968) 79. [7] Y. Sakurai, Y. Kokubun, H. Watanabe, M. Watanabe and M. Kaka, Japan. J. AppI. Phys. 16 (1977) 2115.
Zn~,Cd
1 ~S mixed crystals
849
[8] OP. Agnihotri and BK. Gupta, Japan. J. Appi. Phys. 18 (1979) 317. [9] H.H.L. Kwok MY. Leung and Y.W. Lam J. Crystal Growth 59 (1982) 421. [10] V.P. Singh and J.F. Jordan, IEEE Electron Device Letters EDL-2 (1983) 137. [11] W.M. Kane, J.P. Spratt, LW. Hershinger and I.H. Khan, J. Electrochem. Soc. 113 (1966) 136. [12] L. Clark and J. Woods, J. Crystal Growth 3/4 (1968) 126. [13] E.P. Bertin, Anal. Chem., 34 (1964) 326. [14] MA. Subhan, N.M. Islam and J. Woods, J. Phys. Chem. Solids 33 (1972) 229. [15] D.G.W. Ballentyne and B. Ray, Physica 27 (1961) 337. [16] W. Uchida, Phys. Status Solidi (a) 80 (1983) K199. [17] N. Romeo, G. Sberveglieri and L. Tarricone, App!. Phys. Letters 32 (1978) 807. [18] NI. Vitrikhovskii and lB. Mietskaya, Soviet Phys.-Solid State 2 (1961) 2301. [19] GB. Stringfellow, J. Appi. Phys. 50 (1979) 4147. [20] L.R. Weisberg, J. App!. Phys. 33 (1962) 1817. [21] K. Kaneko, M. Ayabe, and N. Watanabe in: Proc. European Session of 6th Intern. Symp. on GaAs and Related Compounds, Edinburgh, 1976, Inst. Phys. Conf. Ser. 33a, Ed. L.F. Eastman (Inst. Phys., London—Bristol, 1977) p. 216.
Journal of Crystal Growth 101 (1990) 844—849 North-Holland
HALL MOBILITY AND CONDUCTIVITY IN Zn~Cd1 ~S MIXED CRYSTALS
M.K.B. SAIDIN, G.J. RUSSELL, A.W. BRINKMAN and J. WOODS Applied Physics Group, School of Engineering and Applied Science, University of Durham, South Roa4 Durham DH] 3LE, UK
The electrical conductivity and Hall mobility of mixed crystals of Zn~Cd1_~Shave been measured from 95 to 300 K for a range of compositions with 0 x 0.45. Crystals were grown from the vapour phase over the full range of composition and were found to have the hexagonal wurtzite structure for 0
1. Introduction
The alloy system Zn5Cd~~S is completely miscible throughout the whole range of compositions so that ternary compounds with band gaps extending from 2.42 eV (CdS) to 3.66 eV (ZnS) are readily obtainable. This has traditionally been exploited in cathodoluminescent phosphors doped with copper where the material is usually prepared in powder form. More recently a number of attempts have been made to produce highly efficient thin film photovoltaic cells consisting of a layer of p-type Cu2S formed on a substrate of Zn5Cd15S. The reason for this is that the efficiency of the thin film solar cell based on CdS/Cu2S appears to be limited to about 10% because of differences in the electron affinities and lattice spacings of the two compounds [1]. Palz et al. [2] first suggested that these discrepancies could be reduced if the CdS was replaced by Zn5Cd1~S with x 0.2. Although various workers [3,4] soon showed that the open circuit voltage increased as x was increased towards 0.2, efficiencies failed to exceed 10%, largely because the short circuit currents obtainable were simultaneously reduced. =
0022-0248/90/$03.50 © 1990
—
The literature on the electrical properties of the Zn~Cd 1~~S alloy system is very sparse. Chenn et al. [5] and Davis and Lind [6] investigated bulk single crystals grown by the iodine transport technique, and Sakurai et a!. [7] grew epitaxial layers on ZnS substrates, but most other workers studied alloys prepared by spray pyrolysis [8-10] or by thermal evaporation [11]. Although there would appear to be a substantial consensus about the structural properties of the alloy system, there is a considerable variation in the reported electrical properties. Consequently a programme has been carried to growofand measure the crystals resistivity and Hallout coefficient a range of single of Zn~Cd~ ~S,
such as had been used in this labora-
tory previously [4] to investigate the photovoltaic properties of single crystal Zn~Cd~~S/Cu2S solar cells. 2. Experimental 2.1. Crystal growth
Alloy crystals were grown using the technique described by Clark and Woods [12]. A pre-sintered
Elsevier Science Publishers B.V. (North-Holland)
M.KB. Saidin et a!. / Hall mobility and conductivity in Zn~Cd
1— ~S mixed crystals
charge of Zn5Cd1~Swas sublimed from bottom to top of an evacuated silica capsule held vertically in a temperature gradient. The charge was maintained at 1150°Cand condensation to form a crystalline boule occurred at 1050°C. While the crystal was growing, over a period of several days, the growth capsule was slowly pulled through the furnace in an attempt to ensure that the growth interface was maintained under constant conditions. Al! the grown crystals were transparent, being colourless when x > 0.5 and becoming gradually more yellow as the zinc concentration was reduced. Many boules showed a gradation of colour along their length indicating a progressive change in composition during growth. In general more zinc was incorporated during the later stages of growth. The cadmium rich crystals were of better quality than the zinc rich ones. 2.2. Determination of composition The as-grown boules were cut into 1 mm slices which, after polishing, were used to provide samples in the form of Hall bars, clover leaves or millimetre dice. All other samples were degreased and etched in cold concentrated HC1 before being investigated further, The boules were assessed for compositional uniformity using EDAX (energy dispersive analysis by X-rays) in a scanning electron microscope; and the absolute composition of the mixed crystals was determined by atomic absorption spectroscopy. Because this technique is destructive it was deployed after all other measurements had been completed. The two important features of the EDAX spectrum were the Cd Li and the Zn Ka lines. The relative intensities of these Cd and Zn lines could be used to give a non-destructive estimate of the relative Cd and Zn compositions by utilizing the procedure described by Bertin [13]. According to Bertin, in a binary compound, a log-log plot of the ratio of the intensities of lines characteristic of the elements versus the composition ratio should be linear, independently of sample size and shape etc. This technique can be extended to a ternary compound such as
102
845
I
1 it
~
2 10
0
1
10
10
2 10
.
Fig. 1. The ratio of the intensities of the Zn Ka and Cd LI lines in the EDAX spectrum plotted as a function of the ratio of the molar concentrations of ZnS and CdS determined by Atomic Absorption Spectroscopy.
Zn~Cd 1~Sprovided the third element, i.e. sulphur, does not preferentially absorb any of the X-ray fluorescence from either of the other two elements. A calibration curve of log( ‘Zn/lCd) against ~ proved to be linear (fig. 1), and was then used to allow compositions to be determined from EDAX measurements. ‘Zn is the intensity of the Zn Ka line and I~ that of the Cd Li line. ~ and CCds are the fractional molar concentrations of ZnS and CdS. 2.3. Structure and lattice parameter A Philips diffractometer was used to record the diffraction patterns obtained from finely ground powders of Zn5Cd1 ~S. Each sample was prepared by spreading a powder layer of the material on to a glass slide with acetone. A scan was then made across the sample using Co Ka radiation (X 1.7902 A) with a goniometer scanning rate of 1° per minute. The structure of all the mixed crystals with 0
=
846
M.K.B. Saidin et at
/ Hall mobility and conductivity in Zn~Cdj
—
on the high energy side of this peak was plotted against energy,of good lines were obtainedphoton for crystals each straight composition. Esti-
I 67
\
41
~N.
~
66-
mates of the band gaps were obtained by extrapolating these lines to the energy axis. The resultant
N.~
\
\
‘N
\
~S mixed crystals
~N
variation of band gap nearly with composition in fig. 3 and was very linear with is shown
y-~
~
Eg=(2.43+1.28x)eV. N
45-
N
2.5. Electrical properties N
o
“
64-
3.8
Measurements of electrical conductivity and Hall coefficient could only be made satisfactorily over the composition range 0
=
-
63
6.2 0
02
0.4 06 Compos,t,on lx)
-
0,8
~
1
-
~6
-
Fig. 2. Lattice parameters a and c as a function of composition(x).
in an atmosphere of argon for 10 mi
I
I
I
s-.’
// /
c=6.705—0.46x.
2.4. Band gap measurements
.
Estimates of the band gaps of the vanous alloys with 0
Measure-
ments were made from 95 to 300 K on conventional Hall bars with dimensions of 8 x 2 x 1 mm3,
hexagonal lattice parameters a and c were calculated from the X-ray data. Their variation with composition is shown in fig. 2 and clearly Vegard’s Law was obeyed rather well with: a=4.i36—0.34x,
=
1
/
/
-
/
/ / /
~
/ /
3~
-
2.9
/ / 27
9.
/
2.5
23
‘
‘
04
‘
Compositi~IxI
Fig. 3. Forbidden bandgap of the alloy crystals as a function of composition.
M.KB. Saidin et al.
/ Hall mobility and conductivity in Zn~Cd1 ~S mixed crystals
847
—
or on Van der Pauw clover leaf samples some 1 cm in diameter. The electrical properties of the CdS crystals were very similar to those reported by Subhan et a!. [14] for crystals grown in this laboratory some 15 years ago. Thus the free electron 3 with concentration a mobility of at 300 was about 1017 cm 300 cm2K V1 s~. The mobility increased to a maximum of approximately 800 cm2 V1 s1 at about 100 K, while the free carrier concentration dropped by a factor of 3 at 90 K. Activation energies in the range 0.01 to 0.016 eV were derived from the curves of ln( n) versus reciprocal temperature. The variation of the electron mobility with temperature could be fitted satisfactorily to a combination of optical mode, piezoelectric and ionised impurity scattering as had been demonstrated by Subhan et a!. previously. The room temperature conductivity and the corresponding free carrier concentration increased with increasing concentration of zinc to a maximum at about x 0.05, when values of 16 ~ii cm’ and n 3.6 x 1017 cm were reached. The corresponding electron mobility was 285 cm2 V 1 1 With increasing zinc content beyond o.os, the conductivity fell slightly until a concentration of x 0.15 was reached. At this composition the conductivity was only slightly less than that of CdS. The free carrier concentration was still of the order of 1017 cm while the electron mobility had fallen to 235 cm2 V~ s~. The electrical conductivity began to decrease even more rapidly when the zinc concentration exceeded x 0.15. This was almost entirely associated with a collapse in the value of the electron mobility (for example a value of 5 cm2 V1 s~ was measured for a crystal with x 0.22), while the free carrier concentration remained in the vicinity of iO’~cm The variation in the room temperature Hall mobility with composition is shown by the experimental points in fig. 4. With crystals with zinc concentrations in the range 0 x <0.15, plots of ln(n) versus i/T indicated little change in the values of donor activation energies which remained in the vicinity of 0.013 eV. The electron mobilities, although smaller in value as x approached 0.15, still increased with
106
io~
~io2
101
1000
=
—
—
—
.~ =
=
~,
=
=
~
~
02
‘
‘
05
04
=
Fig. 4. Hall mobility at 300 K as a function of composition. Experimental point (•). The solid lines a, b and c are mobilities calculated to be expected if (a) polar optical mode scattering, (b) piezoelectnc scattering or (c) a combination of (a) and (b) were operative. The full lone through the expenmental points was calculated assuming space charge scattering was operative.
decreasing temperature to a maximum between 100 and 150 K. The first dramatic change in behaviour occurred when values of x exceeded 0.15. Then very low values of mobility were found at room temperature, but in addition the mobility decreased as the temperature was reduced, and became 3 or 4 times smaller at 100 K, more or less following a T~3/2 variation. It is interesting to note that in this mobility regime, plots of ln a T3 versus 1/T led to good straight lines, the slopes of which indicated activation energies of 0.032 eV.
-<
3. Discussion In general the large mixed crystals of Zn~ Cd 3~Swere non-uniform. It was for this reason
M.K.B. Saidin et a!. / Hall mobility and conductivity in Zn~Cdj— ~ mixed crystals
848
that the EDAX technique was adapted to provide a quick and non-destructive method of determining the composition of each piece of crystal investigated. This proved invaluable, Although the two binary compounds at either end of the compositional range crystallised with different structures, i.e. CdS as hexagonal wurtzite and ZnS as predominantly cubic sphalerite, the structure of all the alloys from 0
of each sample subjected to X-ray analysis led to more reliable results. In rather similar vein the present investigation suggested that there is a linear relationship between the bandgap energy and composition, at least up to x 0.5. This agrees with the observations of Agnihotri and Gupta [8], Kane et a!. [ii], Romeo et al. [17] and Kwok et al. [9], but not with those of Vitrikhovskii and Mietskaya [18] and Davis and Lind [6] who found a bowed type of relationship Eg andproperties composition. Reports ofbetween the electrical of the alloy crystals as a function of composition are for the most part limited to measurements of resistivity only, and indicate a fair spread of results, although there is general agreement that the resistivity increases as x increases. According to Davis and Lind [6], the conductivity of their crystals containing iodine decreased abruptly by 7—8 orders of magnitude when x reached a value of 0.15. This is quite different from our experience =
where a room temperature conductivity of 4 X i0~ Q~ cm~could still be achieved at x 0.45. However, our results do indicate that some new factor comes into play as the zinc content exceeds x 0.15. Then the mobility collapses and begins to exhibit a temperature variation characteristic of ionised impurity scattering. With 0
=
150 K or so. With x > 0.15 the free carrier con3, while centration at 300 K remains near 1017 cm the donor activation energy increases to 0.03 eV and the mobility decreases by factors of 10—50 and exhibits a temperature variation suggestive of ionised impurity scattering. It seems likely, however, that at higher values of x the mobility is being limited by other processes. Possible processes include alloy scattering and space charge scattering [20]. Approximate calculations of mobilities limited by alloy scattering gave values which were much too large. Space charge scattering limited mobility is given by [20]: 2 3.2 X iO~T’°” (m~’/m 2(N 0)~ 5A) =
where T is the temperature, m~’ the electron effective mass, m0 the rest mass and (NSA) is the density-cross section product for the scattering centres. Although N5A was not known, a curve could be fitted to the mobility data by assuming that (N5A) varied linearly with composition as assumed by Stringfellow [19] and Kaneko et al. [21] in a study of GaA1As. Adopting such a procedure led to the full line curve in fig. 4,1.where The values of (N5A) were of the order iO~cmof samtemperature dependence of the mobility pies with x > 0.15 suggests that ionised impurity scattering is important, but possibly a combination of this with space charge scattering may be able to explain the observations. In summary the electrical conductivity of the alloy crystals is strongly affected by a decrease in mobility for compositions with x > 0.5. The free carrier concentration remains fairly constant after peaking at x 0.05, up to compositions with x =
=
M.K.B. Saidin et a!.
/ Hall mobility and conductivity in
0.5. Thereafter the crystals rapidly become semiinsulating with the result that no meaningful measurements have been made. It seems clear however that prospects of making an efficient Zn~Cdi 5S/ Cu2S solar cell with x 0.2 will be affected by the reduction in carrier mobility which occurs at this composition. —
=
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Zn~,Cd
1 ~S mixed crystals
849
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