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Fine structure in reflectivity near the band gap of Cd1−xZnxS solid solutions
Solid State Communications, Vol. 5, pp. 573-576, 1967. Pergamon Press Ltd. Printed in Great Britain
FINE STRUCTURE IN REFLECTIVITY NEAR THE BAND GAP OF Cd~...1Zn~ S SOLID SOLUTIONS E.A. Davis,* R.E. Drews and E.L.Lind Research Laboratories, Xerox Corporation, Rochester, New York, U.S.A. (Received 26 May 1967 by E. Burstein)
The energy variation of E0 reflectivity peaks in Cd~ ~Z; S hexagonal single crystals has been measured as a function of x. At 80°K, fine structure associated with splitting of the uppermost valence band is resolved across the whole composition range. The quasi-cubic model of Hopfield is used to calculate the variation in spin orbit and crystal field splittings between CdS and ZnS. -
THE REFLECTIVITY of mixed single crystals of Cd1 Zn,~S has been measured as a function of x the molecular percentage of ZnS in order to study the electronic structure of the uppermost valence bands. Measurements have been made at room temperature and at 80°K, with incident light polarized both parallel and perpendicular to the c-axis of the hexagonal crystals.
tion with lock-in techniques. For low temperatare measurements the samples were mounted with GE7031 varnish on to the cold finger of a liquid nitrogen dewar.
-
-
-
At room temperature the reflectivity of all crystals showed a broad (~ 0.05eV) peak at a photon energy close to the band gap. For a given crystal the peak for light polarized paralisi to the c-axis was broader and occurred at a slightly higher energy than that for light polarized perpendicular to the c-axis. At high ZnS concentrations a small shoulder was seen on the high energy side of the peaks for ~ i c. The peak posttions were accurately located with the aid of a differential modulation technique. ~ Figure 1. shows the variation of the peak positions in energy with alloy composition. A smooth variation of the band gap with mole % ZnS is observed.
The crystals were grown by chemical transport of polycrystalline material which had previously been prepared by firing pure powders of CdS and ZnS mixed in the required proportions. X-ray studies confirmed that the crystals used were uniform solid solutions, were relatively strain-free and exhibited hexagonal structure. Composition was determined to ~ 1 mole % by a combined X-ray fluorescence and Debye-S~ierrer technique. ~ Where possible natural (1010) faces were used for the reflectance measurements but otherwise correctly oriented faces were prepared by grinding, polishing and etching. For room temperature measurements the crystals were mounted alongside a freshly evaporated Al mirror on a slide arrangement which permitted rapid measurement of the mcident light flux. The monochromator used was a Leiss single prism instrument and detection was with an EMI 9558 photomultiplier tube in conjunc-
Fine structure associated with the uppermost valence band splitting was observed at 80°K. A few typical spectra are shown in Fig. 2. The diagram at the right of this figure shows the splitting of the r15 valence band at k = 0 in crystale with wurtzite structure. Selection rules permit direct optical transitions between the r, conduction band and valence bands A, B and C for £ i C, but only to B and C for ~H c. For CdS these transitions (which have been attributed
~ndish
toe~cttona):verYclYlved~nb~e
Laboratory, 573
574
FINE STRUCTURE IN REFLECTIVITY
Vol. 5, No. 8
average of that due to the B and C valence bands. The high energy shoulder observed for ~i C for high ZnS concentrations arises because the B and C peaks become stronger relative to A for these samples.
4.C 39 38
3.7 3.6
The spin orbit and crystal field splittings = 0 can be calculated from the observed E0 splittings using the quasi-cubic model 6 In terms of the separations E~ of andHopfleld. EBC Hopileld’s formulae can be written in the form: (8 and a)at k
34
3.3 3.2
elIc
>31 3.0
2.9
eic
28
o~ 8
2.7
=
((2EAB+EBC)
± [(2EAN +
2.6
EBC)2
-
6E~(E~
(1) +
EBC)]4)/2.
2.5 ~
i~o ~o o
~o ~o io ~
Mo4e percent Zn S FIG. i Energy variation of reflectivity peaks in Cd rized parallel 1 and Zn~perpendicular S for light polato the crystal c-axis (300°K). -
the separations between A, B and C could be measured to ± 0. 005eV. The selection rules appropriate to CdS operate throughout4thehave whole composition difficulty range. Previous workers experienced in observing this fine structure and have suggested the instability of excitons in mixed crystals as responsible. It would appear that as long as the crystals are relatively free from strain this Is not the case. The variation of the separations between A, B and C as a function of molecular percent ZnS is shown in Fig. 3. (A least-squares analysts has been used on the data). The arrows at each side of this figure are values previously published6 for CdS and ZnS. Within experimental error a linear variation of E~ and EAC are obtained, The room temperature reflectivity data can be explained quite easily. For c, A transitions (r7c I~g’)contribute most strongly to the reflectivity and thus, for this direction of polarization, the room temperature peaks meaT) are sure the smallest energy gap at k = 0. For II C, B andwith C transitions (both r, andr7the reboth allowed similar strengths flectivity observed for this direction of polarization, peaks at an energy which is a weighted ~
.
-
-
Inview of the special nature of the equations given in Ref. 6 it is not possible to say unambiguously which of the two values calcu]atedfrom the right hand side of equation (1) corresponds to a and which to 6. In hexagonal CdS the spin 3 larger than the orbit splitting crystal field splitting 6 has been a. Values found given in Ref. 3 are a = 68 meV and a = 28 meV. In hexagonal ZnS, substitution of the splittings observedv into equation (1) leads to (a, 8) = (53,84meV). However the E 0 splitting observed In cubic ZnS’, which should be just 6, is 68 meV. This distion (1) from It can be that the crepancy can which be resolved by shown examination of equavalues of (a, 6) become extremely sensitive to values of E and E , when EBC1E~ approaches (1L9,/3). A~l~r8 has preferr o accept the experimental determination of 6=68 meV In cubic ZnS and recalculate E~ and EBC for hexagonal ZnS. These then become 29 and 80 meV which are close to the values of 27 and 84 meV observed. A similar procedure cannot be used for CdS because spin orbit splitting data on cubic CdS has not yet been reported. However, the values of a and 6 calculated from the observed E 0 splittings in hexagonal CdS are not quite as sensitive to the values chosen for E~ and EBC as is the case with ZnS. Combining our data on the A, B, C splittinge in Cd1 Zn~S with the value of the spin orbit splitting observed In cubic ZnS at 80°K, the plot of a and a shown in Fig. 4 is obtained. arising fromareas existing experimental data. A comThe hatched represent the uncertainties position-invariant spin orbit splitting is expected from the presumption that the uppermost valence band In CdZnS arises from the p states -
-
FKNESTRUCTURE IN REFLECTMTY
Vol. 5, No. 8
575
*...,I,*
2.50 . 22
m
2.54 I
2.66
I
,
Cdo,s4~"0.36:S
‘2.62
’
rV
Ic’
El+ AND EIIC---
2.64
2.66
2.92
2.96
-UC DNLy
rV
r1I’rr’a.f
22-
FIG. 2
A
Typical fine structure of reflectivity peaks in Cd,-, Zn,S at 80°K. R-relative reflectivity. Diagram at right shows the uppermost valence band splittings and the transitions involved.
16 3.66
3.70
3.74
rV
3.78
Oaloo-
.
B
20
FIG. 3
_
.
40
MOLEPERCENT
60 ZnS
60
100
Energy variation of A, B and C splittings with mole percent of ZnS Zn,S (80%). in Cd,_,
576
FINE STRUCTURE IN REFLECTIVITY
90
I
80
Spin Orbit 8
Vol. 5, No. 8
I
—
7O______________________________________ 60
5:5 40
Crystal Field a
FIG. 4 Spin orbit and crystal field splIttings
~30 20 ‘0
______________________________ 0 lo 20 30 40 so 60 70 80 90 100 Mole percent ZnS
of the sulfur ions. Thus its splitting from spinorbit interaction is essentially independent of the nature of the cation. The crystal field splitting arises from the uniaxial nature of hexagonal crystals which shifts the p, states. A departure from the ideal wurtzite structure will contribute1 to this splitting. 9 in Cd1_~Zn,~S An ideal structure at x— 0.7(c/a=(8/3)i) but the is obtained
calculated according to the quasicubic model. 8 The values In ZnS are based on the experimental determination of 6 in the cubic structure.
precision of our measurements is not sufficient to observe any effect on the valence band splittings which might arise in passing through this point. Acknowledgments The authors gratefully ackknowledge many helpful discussions with Dr. R. Zallen. -
References 1.
CHERIN P., DAVIS E. A. and BIELAN C., (to be published).
2.
BREWS R.E., Bull. Am. Phys. Soc. 12, 384 (1967).
3.
THOMAS D. G. and HOPFIELD J. J.,
4.
REYNOLDS B. C. and LITTON C. W., Bull. Am. Phys. Soc. 6, 111 (1961). BRODIN M. S., KURIK M. V. and VITRIKHOVSKII N, r., Proc~edingsof the International Conference on the Physics of Semiconductors, Kyoto. J. Phys. Soc. Japan 21, 127 (1966).
5.
REYNOLDS D.C., LITTON C.W. and COLLINS T. C., Phys. Stat. 801. 12, 13 (1965).
6.
HOPFIELD J. J.,
7.
BIRMAN J. L., SAMELSON H. and LEMPICKI A., G. T. E. Research and Development Journal 2 (1961).
8.
ADLER S. L., Phys. Rev. 126, 118 (1962).
9.
CHERIN P., LIND E. L. and DAVIS E.A, (to be published).
•
Phys. Rev. 116, 573 (1959).
J. Phys. Chem. Solids 15, 97 (1960).
!~
Die Energteanderung der Reflexionsspitzen 5,, in hexagonalen Cdl~,Zn.AS Einkristallen wurde ala Funktton von x gemessen. Bel 80°Kimdie Feinstruktur die mit der Aufspaltung des höchsten Valenzbandes zusa.mmenbAngt, uber den gesammten Zusammensetzungs bereich auflOsbar. Dan quasl-Kubische Modell von Hopfield wurde benutzt urn die Anderung der spin Balm mid Kristallfeldaufspaltungen zwichen CdS and ZnS zu berechnen.
FINE STRUCTURE IN REFLECTIVITY NEAR THE BAND GAP OF Cd~...1Zn~ S SOLID SOLUTIONS E.A. Davis,* R.E. Drews and E.L.Lind Research Laboratories, Xerox Corporation, Rochester, New York, U.S.A. (Received 26 May 1967 by E. Burstein)
The energy variation of E0 reflectivity peaks in Cd~ ~Z; S hexagonal single crystals has been measured as a function of x. At 80°K, fine structure associated with splitting of the uppermost valence band is resolved across the whole composition range. The quasi-cubic model of Hopfield is used to calculate the variation in spin orbit and crystal field splittings between CdS and ZnS. -
THE REFLECTIVITY of mixed single crystals of Cd1 Zn,~S has been measured as a function of x the molecular percentage of ZnS in order to study the electronic structure of the uppermost valence bands. Measurements have been made at room temperature and at 80°K, with incident light polarized both parallel and perpendicular to the c-axis of the hexagonal crystals.
tion with lock-in techniques. For low temperatare measurements the samples were mounted with GE7031 varnish on to the cold finger of a liquid nitrogen dewar.
-
-
-
At room temperature the reflectivity of all crystals showed a broad (~ 0.05eV) peak at a photon energy close to the band gap. For a given crystal the peak for light polarized paralisi to the c-axis was broader and occurred at a slightly higher energy than that for light polarized perpendicular to the c-axis. At high ZnS concentrations a small shoulder was seen on the high energy side of the peaks for ~ i c. The peak posttions were accurately located with the aid of a differential modulation technique. ~ Figure 1. shows the variation of the peak positions in energy with alloy composition. A smooth variation of the band gap with mole % ZnS is observed.
The crystals were grown by chemical transport of polycrystalline material which had previously been prepared by firing pure powders of CdS and ZnS mixed in the required proportions. X-ray studies confirmed that the crystals used were uniform solid solutions, were relatively strain-free and exhibited hexagonal structure. Composition was determined to ~ 1 mole % by a combined X-ray fluorescence and Debye-S~ierrer technique. ~ Where possible natural (1010) faces were used for the reflectance measurements but otherwise correctly oriented faces were prepared by grinding, polishing and etching. For room temperature measurements the crystals were mounted alongside a freshly evaporated Al mirror on a slide arrangement which permitted rapid measurement of the mcident light flux. The monochromator used was a Leiss single prism instrument and detection was with an EMI 9558 photomultiplier tube in conjunc-
Fine structure associated with the uppermost valence band splitting was observed at 80°K. A few typical spectra are shown in Fig. 2. The diagram at the right of this figure shows the splitting of the r15 valence band at k = 0 in crystale with wurtzite structure. Selection rules permit direct optical transitions between the r, conduction band and valence bands A, B and C for £ i C, but only to B and C for ~H c. For CdS these transitions (which have been attributed
~ndish
toe~cttona):verYclYlved~nb~e
Laboratory, 573
574
FINE STRUCTURE IN REFLECTIVITY
Vol. 5, No. 8
average of that due to the B and C valence bands. The high energy shoulder observed for ~i C for high ZnS concentrations arises because the B and C peaks become stronger relative to A for these samples.
4.C 39 38
3.7 3.6
The spin orbit and crystal field splittings = 0 can be calculated from the observed E0 splittings using the quasi-cubic model 6 In terms of the separations E~ of andHopfleld. EBC Hopileld’s formulae can be written in the form: (8 and a)at k
34
3.3 3.2
elIc
>31 3.0
2.9
eic
28
o~ 8
2.7
=
((2EAB+EBC)
± [(2EAN +
2.6
EBC)2
-
6E~(E~
(1) +
EBC)]4)/2.
2.5 ~
i~o ~o o
~o ~o io ~
Mo4e percent Zn S FIG. i Energy variation of reflectivity peaks in Cd rized parallel 1 and Zn~perpendicular S for light polato the crystal c-axis (300°K). -
the separations between A, B and C could be measured to ± 0. 005eV. The selection rules appropriate to CdS operate throughout4thehave whole composition difficulty range. Previous workers experienced in observing this fine structure and have suggested the instability of excitons in mixed crystals as responsible. It would appear that as long as the crystals are relatively free from strain this Is not the case. The variation of the separations between A, B and C as a function of molecular percent ZnS is shown in Fig. 3. (A least-squares analysts has been used on the data). The arrows at each side of this figure are values previously published6 for CdS and ZnS. Within experimental error a linear variation of E~ and EAC are obtained, The room temperature reflectivity data can be explained quite easily. For c, A transitions (r7c I~g’)contribute most strongly to the reflectivity and thus, for this direction of polarization, the room temperature peaks meaT) are sure the smallest energy gap at k = 0. For II C, B andwith C transitions (both r, andr7the reboth allowed similar strengths flectivity observed for this direction of polarization, peaks at an energy which is a weighted ~
.
-
-
Inview of the special nature of the equations given in Ref. 6 it is not possible to say unambiguously which of the two values calcu]atedfrom the right hand side of equation (1) corresponds to a and which to 6. In hexagonal CdS the spin 3 larger than the orbit splitting crystal field splitting 6 has been a. Values found given in Ref. 3 are a = 68 meV and a = 28 meV. In hexagonal ZnS, substitution of the splittings observedv into equation (1) leads to (a, 8) = (53,84meV). However the E 0 splitting observed In cubic ZnS’, which should be just 6, is 68 meV. This distion (1) from It can be that the crepancy can which be resolved by shown examination of equavalues of (a, 6) become extremely sensitive to values of E and E , when EBC1E~ approaches (1L9,/3). A~l~r8 has preferr o accept the experimental determination of 6=68 meV In cubic ZnS and recalculate E~ and EBC for hexagonal ZnS. These then become 29 and 80 meV which are close to the values of 27 and 84 meV observed. A similar procedure cannot be used for CdS because spin orbit splitting data on cubic CdS has not yet been reported. However, the values of a and 6 calculated from the observed E 0 splittings in hexagonal CdS are not quite as sensitive to the values chosen for E~ and EBC as is the case with ZnS. Combining our data on the A, B, C splittinge in Cd1 Zn~S with the value of the spin orbit splitting observed In cubic ZnS at 80°K, the plot of a and a shown in Fig. 4 is obtained. arising fromareas existing experimental data. A comThe hatched represent the uncertainties position-invariant spin orbit splitting is expected from the presumption that the uppermost valence band In CdZnS arises from the p states -
-
FKNESTRUCTURE IN REFLECTMTY
Vol. 5, No. 8
575
*...,I,*
2.50 . 22
m
2.54 I
2.66
I
,
Cdo,s4~"0.36:S
‘2.62
’
rV
Ic’
El+ AND EIIC---
2.64
2.66
2.92
2.96
-UC DNLy
rV
r1I’rr’a.f
22-
FIG. 2
A
Typical fine structure of reflectivity peaks in Cd,-, Zn,S at 80°K. R-relative reflectivity. Diagram at right shows the uppermost valence band splittings and the transitions involved.
16 3.66
3.70
3.74
rV
3.78
Oaloo-
.
B
20
FIG. 3
_
.
40
MOLEPERCENT
60 ZnS
60
100
Energy variation of A, B and C splittings with mole percent of ZnS Zn,S (80%). in Cd,_,
576
FINE STRUCTURE IN REFLECTIVITY
90
I
80
Spin Orbit 8
Vol. 5, No. 8
I
—
7O______________________________________ 60
5:5 40
Crystal Field a
FIG. 4 Spin orbit and crystal field splIttings
~30 20 ‘0
______________________________ 0 lo 20 30 40 so 60 70 80 90 100 Mole percent ZnS
of the sulfur ions. Thus its splitting from spinorbit interaction is essentially independent of the nature of the cation. The crystal field splitting arises from the uniaxial nature of hexagonal crystals which shifts the p, states. A departure from the ideal wurtzite structure will contribute1 to this splitting. 9 in Cd1_~Zn,~S An ideal structure at x— 0.7(c/a=(8/3)i) but the is obtained
calculated according to the quasicubic model. 8 The values In ZnS are based on the experimental determination of 6 in the cubic structure.
precision of our measurements is not sufficient to observe any effect on the valence band splittings which might arise in passing through this point. Acknowledgments The authors gratefully ackknowledge many helpful discussions with Dr. R. Zallen. -
References 1.
CHERIN P., DAVIS E. A. and BIELAN C., (to be published).
2.
BREWS R.E., Bull. Am. Phys. Soc. 12, 384 (1967).
3.
THOMAS D. G. and HOPFIELD J. J.,
4.
REYNOLDS B. C. and LITTON C. W., Bull. Am. Phys. Soc. 6, 111 (1961). BRODIN M. S., KURIK M. V. and VITRIKHOVSKII N, r., Proc~edingsof the International Conference on the Physics of Semiconductors, Kyoto. J. Phys. Soc. Japan 21, 127 (1966).
5.
REYNOLDS D.C., LITTON C.W. and COLLINS T. C., Phys. Stat. 801. 12, 13 (1965).
6.
HOPFIELD J. J.,
7.
BIRMAN J. L., SAMELSON H. and LEMPICKI A., G. T. E. Research and Development Journal 2 (1961).
8.
ADLER S. L., Phys. Rev. 126, 118 (1962).
9.
CHERIN P., LIND E. L. and DAVIS E.A, (to be published).
•
Phys. Rev. 116, 573 (1959).
J. Phys. Chem. Solids 15, 97 (1960).
!~
Die Energteanderung der Reflexionsspitzen 5,, in hexagonalen Cdl~,Zn.AS Einkristallen wurde ala Funktton von x gemessen. Bel 80°Kimdie Feinstruktur die mit der Aufspaltung des höchsten Valenzbandes zusa.mmenbAngt, uber den gesammten Zusammensetzungs bereich auflOsbar. Dan quasl-Kubische Modell von Hopfield wurde benutzt urn die Anderung der spin Balm mid Kristallfeldaufspaltungen zwichen CdS and ZnS zu berechnen.