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Defect-induced electric fields in ZnS
Solid State Communications, Vol. 18, PP. 135—138, 1976.
Pergamon Press.
Printed in Great Britain
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS B.G. Yacobi and Y. Brada* Racah Institute of Physics, the Hebrew University, Jerusalem, Israel (Received 5 August 1975 by W Low)
The optical absorption edge in cubic ZnS shows both phonon- and impurity-induced effects which determine its precise shape. Applying external electric fields and measuring the shift of the absorption edge makes it also possible to compute the impurity excitonic mass which was found to be O.02m0. Comparing the edge shifts due to the impurityinduced electric fields with those due to the external fields, one finds the approximate value for the average impurity-induced field as being about 3 x iO’ V/cm.
THE FUNDAMENTAL optical absorption edge in 2 ZnS crystals’ follows well known Urbach’sa Rule, according to which thethe absorption coefficient changes as: a
=
of ln aTwo in a distinctive cubic ZnS regions crystal for temperatures. are different clearly observable. The high density region (“intrinsic edge”) has been attributed to the phonon-generated electric field interacting with the direct [‘-point transitions through 3’5’6 In the lower a Franz—Keldysh mechanism. density region (“impurity tail”) the measured value of a(hv) depends on the particular impurity and 7itsand concentration, as has been first observed in InAs GaAs.8 The slope parameter a for the “intrinsic edge” has been studied recently for different ZnS structures6 and was found to depend on temperature and a phonon energy hw 0 as:
a
0 exp {a(hv hvo)/kT}. 0 and v,~are constants of the material, a is the slope parameter, hv is the photon energy, and k and T have usual meaning. This exponential behaviour of thethe absorption coefficient has been observed in various materials (ionic, covalent and amorphous).3 Recently an attempt was made by Dow and Redfield3 to explain this behaviour via an unified model which
Here a
—
considers the influence of defect-induced electric fields on the optical absorption edge through a Franz— Keldysh mechanism.
a
a~(2kT/h~) tanh (hwo/2kT)
(2)
with 0~= 2.5 and hw0 = FL.LO = 43.5 meV. The same functional dependence can also be observed for the slope parameter of the “impurity tail”. Figure 2 presents the measured values of a as points,while the solid curve represents a function of the form of equation (2) with ao = 1.2 and the same hw0 as before. Fig. 1 we also observe thattothehigher meeting point ofInthe two straight lines shifts values of a as the temperature increases. This is due to additional impurities being ionized at these temperatures.8
The purpose of the present work is to study the combined influence of different electric fields on the absorption edge shape in cubic ZnS. The crystals and their growth procedure as well as the experimental set-up for optical 4’5 absorption measurements were described previously. Figure 1 shows the measured spectral dependence ________________
*
=
Present address: Department of Physics, Syracuse University, Syracuse, N.Y. 13210, U.S.A.
Introducing equation (2) into equation (I), the 135
136
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
I
0K 293°K195°K
/~
650°K580°K 375
6 0
0
54
~ _________________ 3.30 3.40
_____________
3.60
PHOTON ENERGY
tO
r-.
tO
r-
8.0
7.0 0
6.0 5.0 4.0
3.70
~
“te
tt ~S
“p‘t.
(eV)
The spectral dependence oflna of cubic ZnS at different temperatures.
FIG. 1.
Vol. 18, No. 1
___________________________________
0.70
0.80 0.90 tanh(~Lo/2kT)
1.00
3. Logarithmic plot of absorption coefficient a vs tanh (hwLo/2kT) at constant values of photon energy hv. FIG.
We will now consider the “impurity tail” in detail, b
1.0
-
the high density region having been considered previously.5’6 The Franz—Keldysh effect has been studied in the impurity region as well.9 In the limit of the weak-field approximation10”1 we make use of the Franz equation for exponential edges, which is written as:
w FUi
0.5
-
-J
2h2/24p*)(u/kT)2F2 = ~‘~yF2 (4) _(e and connects the shift of the absorption edge /~Egat constant optical density with the square of the applied electric field F2. /2* is the reduced effective mass of the exciton. For the band-to-band transitions 9 p = ~ ~, From the same measurements9 we find for the “impurity tail” region the low value of L1E
O.O~
0
I
I
I
100
200
300
TEMPERATURE
9
I
400
500
600
700
,
FIG. 2.
The slope parameter a (“impurity tail”) vs temperature for cubic ZnS. Points experimental, solid line theoretical, according to equation (2) with ~0 = 1.2 and hw 0 = hWLO = 43.5 meV. —
—
value of a as function of temperature at a given constant photon energy hi.’ can be written as: a = a0 exp [Ctanh (hwLo/2kT)1, (3) where C contains all the constants. Therefore a semilogarithmic plot ofwavelength the measured absorption coefficient at constant vs tanh (hwLo!2kT) should yield straight lines. This plot is represented in Fig. 3, which shows the expected behaviour for high values of a, i.e. in the “intrinsic edge” region. At lower densities, as expected, a different slope is observed. This is connected with the transit from the “intrinsic edge” absorption to the “impurity tail” absorption as the temperature is decreased.
=
0.02m0. This is due to the fact that we deal with impurity states, in which we expect a decrease of the reduced effective mass~~ for larger core impurities, such as heavy metals (Ag, Cd, In, Pb) or a negative value for a smaller core impurity. It is interesting to note that similar low values for p~have been reported previously from Franz-—Keldysh effect measurements 3 but have been attributed to the band-toin ZnS,’ band transitions. All the pertinent results of our experiments are summed up in Table 1. The magnitude of the impurity-induced field can be evaluated from the shift of the “impurity tail” as compared to the extrapolated “intrinsic edge” at the same value of the absorption coefficient. As the LO~phonon-generated field at room temperature is about
Vol. 18, No. 1
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
Table 1. Cubic ZnS; the slope parameter constant a0 reduced effective mass p* (in units ofm0); the Franz— Keldysh coefficients 7for the “intrinsic edge”and the “impurity tail” at room temperature _____________________________________________
~ “Intrinsic edge” “Impurity tail”
2.5 1.2
p* (m0) 0.12 0.02
~ ~ i0’~2)/V2 (eV x cm 1.72 2.30
3.9 x iO~V/cm,5 we will consider this to be the larger field and assume that the impurity-induced field is a perturbation on this state. In these cases the Franz equation (4) is applicable.’4”5 This is certainly true when external fields are applied on the phonondisturbed crystal. The process is found to be simply additive; we can add up the shifts due to the different fields: L~Eg(total)
=
L~Egp(phonon) +~Ege(external),
with the same a5’9”4 and same mass If we reduced compareeffective the observed being involved. shift due to F~(impurity-induced field) and Fe (external field) in the “impurity tail” region, we obtam, using previous measurements,9 from: F?
137
The experiments show that the individual edge shifts due to electric fields of different character (i.e. HF (phonon), radial (impurity), and directed (exter. nal)}do add algebraically. This means that these fields cannot in a simple way; some cases this is also duebetoadded the different values ofin a and p~which have to be considered for each case. From spectrochemical analysis we know that in our crystals we had typically a heavy ion impurity content of about 20 ppm (N 5 x iO~cm3). If we assume that these impurities have one superfluous electric charge, we find in cubic ZnS a characteristic field16 F 0 2.8 x iO~V/cm. As there can be large variation in the impurity content, this value is only approximate. The computation of (Ft) is even more complicated because of its dependence on screening parameters. Computing the upper limit for an unscreened potential, we obtained for ((Ft ))1/2 (the root mean square field), as averaged over one excitonic radius, the magnitude of about l0~ which is an acceptable value. The averaging overV/cm, one excitonic radius was done in accordance with the basic ideas of the Dow—Rédfield theory of field-disturbed transitions.3
(5)
The above experimental results fit well the estab-
F~ 2.7 x i04 V/cm (L~Egjis the additional shift due to the impurity-induced field F 1). The shift L~E~J~ was taken to mean the average value between zero and the maximum observable impurity-induced shifts in our crystals. The maximum observed value for the impurity-induced field was about 4 x l0~V/cm, which fulfils the condition F1
lished theories of electron transitions disturbed by the
=
F~(L~Egj/L~Ege),
action of electric fields. The decrease of the reduced effective mass in impurity states was also observed. The fields due to charged impurities were estimated through their optical effects.
REFERENCES 1.
PIPER W.W.,Phys. Rev. 92,23(1953).
2.
URBACH F.,Phys. Rev. 92,1324(1953); MOSER F. & URBACH F.,Phys. Rev. 102,15 19 (1956).
3.
DOW J.D. & REDFIELD D., Phys. Rev. B5, 594 (1972).
4.
6.
STEINBERGER I.T., ALEXANDER E., BRADA Y., KALMAN Z.H., KIFLAWI I. & MARDIX S., J. C,yst. Growth 13/14, 285 (1972). YACOBI B.G., BRADA Y., LACHISH U. & HIRSCH C.,Phys. Rev. 1311, 2990 (1975). BRADA Y., YACOBI B.G. & PELED A., Solid State Commun. 17, 193 (1975).
7.
DIXONJ.R.&ELLISJ.M.,Phys. Rev. 123,1560(1961).
8.
REDFIELD D. & AFROMOWITZ M.A.,App/. Phys. Lett. 11, 138 (1967).
5.
138
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
Vol. 18, No. 1
9. 10.
YACOBI B.G. & BRADA Y.,Phys. Rev. BlO, 665 (1974). FRANZ W.,Z.Natur. A13,484 (1958).
11.
CARDONA M., Modulation Spectroscopy, Suppi. 11 ofSolid State Phys. (Edited by SEITZ F., TURNBULL D. & EHRENREICH H.) Academic Press NY (1969).
12. 13.
PANTELIDES S.T., in Proc. 12th mt. Conf Phys. Semicond. (Edited by PILKUHN M.H.), p. 396. Teubner, Stuttgart (1974). SCHANDA J., GERGELY G. & GAL M.,Z. Natur. 24a, 1353 (1969).
14.
KRIEGJ.G.,Z.Phys. 205,425 (1967).
15.
ESSER B.,Phys. Status Solidi(b) 51, 735 (1972).
16.
REDFIELD D.,Phys. Rev. 130,914,916 (1963).
Pergamon Press.
Printed in Great Britain
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS B.G. Yacobi and Y. Brada* Racah Institute of Physics, the Hebrew University, Jerusalem, Israel (Received 5 August 1975 by W Low)
The optical absorption edge in cubic ZnS shows both phonon- and impurity-induced effects which determine its precise shape. Applying external electric fields and measuring the shift of the absorption edge makes it also possible to compute the impurity excitonic mass which was found to be O.02m0. Comparing the edge shifts due to the impurityinduced electric fields with those due to the external fields, one finds the approximate value for the average impurity-induced field as being about 3 x iO’ V/cm.
THE FUNDAMENTAL optical absorption edge in 2 ZnS crystals’ follows well known Urbach’sa Rule, according to which thethe absorption coefficient changes as: a
=
of ln aTwo in a distinctive cubic ZnS regions crystal for temperatures. are different clearly observable. The high density region (“intrinsic edge”) has been attributed to the phonon-generated electric field interacting with the direct [‘-point transitions through 3’5’6 In the lower a Franz—Keldysh mechanism. density region (“impurity tail”) the measured value of a(hv) depends on the particular impurity and 7itsand concentration, as has been first observed in InAs GaAs.8 The slope parameter a for the “intrinsic edge” has been studied recently for different ZnS structures6 and was found to depend on temperature and a phonon energy hw 0 as:
a
0 exp {a(hv hvo)/kT}. 0 and v,~are constants of the material, a is the slope parameter, hv is the photon energy, and k and T have usual meaning. This exponential behaviour of thethe absorption coefficient has been observed in various materials (ionic, covalent and amorphous).3 Recently an attempt was made by Dow and Redfield3 to explain this behaviour via an unified model which
Here a
—
considers the influence of defect-induced electric fields on the optical absorption edge through a Franz— Keldysh mechanism.
a
a~(2kT/h~) tanh (hwo/2kT)
(2)
with 0~= 2.5 and hw0 = FL.LO = 43.5 meV. The same functional dependence can also be observed for the slope parameter of the “impurity tail”. Figure 2 presents the measured values of a as points,while the solid curve represents a function of the form of equation (2) with ao = 1.2 and the same hw0 as before. Fig. 1 we also observe thattothehigher meeting point ofInthe two straight lines shifts values of a as the temperature increases. This is due to additional impurities being ionized at these temperatures.8
The purpose of the present work is to study the combined influence of different electric fields on the absorption edge shape in cubic ZnS. The crystals and their growth procedure as well as the experimental set-up for optical 4’5 absorption measurements were described previously. Figure 1 shows the measured spectral dependence ________________
*
=
Present address: Department of Physics, Syracuse University, Syracuse, N.Y. 13210, U.S.A.
Introducing equation (2) into equation (I), the 135
136
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
I
0K 293°K195°K
/~
650°K580°K 375
6 0
0
54
~ _________________ 3.30 3.40
_____________
3.60
PHOTON ENERGY
tO
r-.
tO
r-
8.0
7.0 0
6.0 5.0 4.0
3.70
~
“te
tt ~S
“p‘t.
(eV)
The spectral dependence oflna of cubic ZnS at different temperatures.
FIG. 1.
Vol. 18, No. 1
___________________________________
0.70
0.80 0.90 tanh(~Lo/2kT)
1.00
3. Logarithmic plot of absorption coefficient a vs tanh (hwLo/2kT) at constant values of photon energy hv. FIG.
We will now consider the “impurity tail” in detail, b
1.0
-
the high density region having been considered previously.5’6 The Franz—Keldysh effect has been studied in the impurity region as well.9 In the limit of the weak-field approximation10”1 we make use of the Franz equation for exponential edges, which is written as:
w FUi
0.5
-
-J
2h2/24p*)(u/kT)2F2 = ~‘~yF2 (4) _(e and connects the shift of the absorption edge /~Egat constant optical density with the square of the applied electric field F2. /2* is the reduced effective mass of the exciton. For the band-to-band transitions 9 p = ~ ~, From the same measurements9 we find for the “impurity tail” region the low value of L1E
O.O~
0
I
I
I
100
200
300
TEMPERATURE
9
I
400
500
600
700
,
FIG. 2.
The slope parameter a (“impurity tail”) vs temperature for cubic ZnS. Points experimental, solid line theoretical, according to equation (2) with ~0 = 1.2 and hw 0 = hWLO = 43.5 meV. —
—
value of a as function of temperature at a given constant photon energy hi.’ can be written as: a = a0 exp [Ctanh (hwLo/2kT)1, (3) where C contains all the constants. Therefore a semilogarithmic plot ofwavelength the measured absorption coefficient at constant vs tanh (hwLo!2kT) should yield straight lines. This plot is represented in Fig. 3, which shows the expected behaviour for high values of a, i.e. in the “intrinsic edge” region. At lower densities, as expected, a different slope is observed. This is connected with the transit from the “intrinsic edge” absorption to the “impurity tail” absorption as the temperature is decreased.
=
0.02m0. This is due to the fact that we deal with impurity states, in which we expect a decrease of the reduced effective mass~~ for larger core impurities, such as heavy metals (Ag, Cd, In, Pb) or a negative value for a smaller core impurity. It is interesting to note that similar low values for p~have been reported previously from Franz-—Keldysh effect measurements 3 but have been attributed to the band-toin ZnS,’ band transitions. All the pertinent results of our experiments are summed up in Table 1. The magnitude of the impurity-induced field can be evaluated from the shift of the “impurity tail” as compared to the extrapolated “intrinsic edge” at the same value of the absorption coefficient. As the LO~phonon-generated field at room temperature is about
Vol. 18, No. 1
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
Table 1. Cubic ZnS; the slope parameter constant a0 reduced effective mass p* (in units ofm0); the Franz— Keldysh coefficients 7for the “intrinsic edge”and the “impurity tail” at room temperature _____________________________________________
~ “Intrinsic edge” “Impurity tail”
2.5 1.2
p* (m0) 0.12 0.02
~ ~ i0’~2)/V2 (eV x cm 1.72 2.30
3.9 x iO~V/cm,5 we will consider this to be the larger field and assume that the impurity-induced field is a perturbation on this state. In these cases the Franz equation (4) is applicable.’4”5 This is certainly true when external fields are applied on the phonondisturbed crystal. The process is found to be simply additive; we can add up the shifts due to the different fields: L~Eg(total)
=
L~Egp(phonon) +~Ege(external),
with the same a5’9”4 and same mass If we reduced compareeffective the observed being involved. shift due to F~(impurity-induced field) and Fe (external field) in the “impurity tail” region, we obtam, using previous measurements,9 from: F?
137
The experiments show that the individual edge shifts due to electric fields of different character (i.e. HF (phonon), radial (impurity), and directed (exter. nal)}do add algebraically. This means that these fields cannot in a simple way; some cases this is also duebetoadded the different values ofin a and p~which have to be considered for each case. From spectrochemical analysis we know that in our crystals we had typically a heavy ion impurity content of about 20 ppm (N 5 x iO~cm3). If we assume that these impurities have one superfluous electric charge, we find in cubic ZnS a characteristic field16 F 0 2.8 x iO~V/cm. As there can be large variation in the impurity content, this value is only approximate. The computation of (Ft) is even more complicated because of its dependence on screening parameters. Computing the upper limit for an unscreened potential, we obtained for ((Ft ))1/2 (the root mean square field), as averaged over one excitonic radius, the magnitude of about l0~ which is an acceptable value. The averaging overV/cm, one excitonic radius was done in accordance with the basic ideas of the Dow—Rédfield theory of field-disturbed transitions.3
(5)
The above experimental results fit well the estab-
F~ 2.7 x i04 V/cm (L~Egjis the additional shift due to the impurity-induced field F 1). The shift L~E~J~ was taken to mean the average value between zero and the maximum observable impurity-induced shifts in our crystals. The maximum observed value for the impurity-induced field was about 4 x l0~V/cm, which fulfils the condition F1
lished theories of electron transitions disturbed by the
=
F~(L~Egj/L~Ege),
action of electric fields. The decrease of the reduced effective mass in impurity states was also observed. The fields due to charged impurities were estimated through their optical effects.
REFERENCES 1.
PIPER W.W.,Phys. Rev. 92,23(1953).
2.
URBACH F.,Phys. Rev. 92,1324(1953); MOSER F. & URBACH F.,Phys. Rev. 102,15 19 (1956).
3.
DOW J.D. & REDFIELD D., Phys. Rev. B5, 594 (1972).
4.
6.
STEINBERGER I.T., ALEXANDER E., BRADA Y., KALMAN Z.H., KIFLAWI I. & MARDIX S., J. C,yst. Growth 13/14, 285 (1972). YACOBI B.G., BRADA Y., LACHISH U. & HIRSCH C.,Phys. Rev. 1311, 2990 (1975). BRADA Y., YACOBI B.G. & PELED A., Solid State Commun. 17, 193 (1975).
7.
DIXONJ.R.&ELLISJ.M.,Phys. Rev. 123,1560(1961).
8.
REDFIELD D. & AFROMOWITZ M.A.,App/. Phys. Lett. 11, 138 (1967).
5.
138
DEFECT-INDUCED ELECTRIC FIELDS IN ZnS
Vol. 18, No. 1
9. 10.
YACOBI B.G. & BRADA Y.,Phys. Rev. BlO, 665 (1974). FRANZ W.,Z.Natur. A13,484 (1958).
11.
CARDONA M., Modulation Spectroscopy, Suppi. 11 ofSolid State Phys. (Edited by SEITZ F., TURNBULL D. & EHRENREICH H.) Academic Press NY (1969).
12. 13.
PANTELIDES S.T., in Proc. 12th mt. Conf Phys. Semicond. (Edited by PILKUHN M.H.), p. 396. Teubner, Stuttgart (1974). SCHANDA J., GERGELY G. & GAL M.,Z. Natur. 24a, 1353 (1969).
14.
KRIEGJ.G.,Z.Phys. 205,425 (1967).
15.
ESSER B.,Phys. Status Solidi(b) 51, 735 (1972).
16.
REDFIELD D.,Phys. Rev. 130,914,916 (1963).