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On the interpretation of extrinsic photoconductivity spectrum
(~)Solid State Coninunications, Vol.36, pp. 509—511. ‘~.‘ Pergamon Press Ltd. 1980. Printed in Great Britain.
ON THE INTERPRETATION OF EXTRINSIC PHOTO~0NDUCTIVITy N.
SPECTRUM
V. Joshi
Universidad de Los Andes
Departamento de Fisica
-
Venez ue 1 a Received
on
June 10. 1979
The interpretation of extrinsic photoconductivity spectrum has been reanalysed on the basis of crystal field splitting. It has been found out that the application of electric field reduces the symmetry environment from Td to andp states do split in two components B 2 and E. The electric field dependence of the separation has been experimentally observed and theoretically estimated.
1—5 Recently much work related to the electronic structure of shallow donors of high purity materials is being carried out by far infrared Spectroscopic Techniques. This gives not Only the information about the different types of impurity contents but also the nature and magnitude of the central cell correction, which in turn helps to understand the various models and tho parameters involved to construct5.the wave If one SuCceedo forin the making adequate theoretical functions impurity atoms models, it is possible to predict the nature of the impurity atom by cpectroacopic study. A large amount of information of shallow donor states comes from extrinsic photocondutivity or transmission spectrosco py. Both techniques are treated equivalent since they give apparently the same information. The purpose of the present note is to reanalyse the data obtained by the photoconductivity technique and evaluate its consequences. In the
electric fields which reduce the syrmietry environment of the impurity atom. Therefore, crystal field splitting has to be considered according to the reduced symmetry. Extensive Study of the extrinsic photoconductivity has been carried out o-8 in several high purity materials such as Ge. Si, CdTe. InP. GaAs etc. Lvun thou7h these semiconductors have different atom impurity crystalline sees Id symetry structure, in the all cases. For this reason subsequent discussion is carried Out with reference to Td symmetry. In fact,wave functions of p symmotry are not split up in Td symmetry (we are rbfarring only to the zero magnetic fielà case), but the application of an electric field in <100> direction reduces the simmetry from Td to 02d9. Characters X,. for p wavefunctions in 02d symmetry been worked out and found to be E
2S 4
extrinsic photoconductivity and optical transmission measurements, one essentially observes the energy difference between the ground states and the excited states. or the difference between two excited states of the impurity atom. However a close look reveals that there is a small but Important differences which needs to be considered before interpretingdata. Not every line observed Inthe photo conductivity spectrum needs to be Interpreted as arising from Impurity atoms of different chemical nature. This is particularly true for the linee observed in the fine structure of ls—~2p transitions (even In single valley semiconductors). It is true that p state might not split in a particular syornatry however In the process of photoconductlvity measurements one needs to apply
x
3
-l
C2
2C~
-l
-l
This decomposes 0P 082 ~ 0E
20’ d 1 p wavefunctions
into
The wavefunctions of the perturbed impurity atom can be obtained by syrwnetry consideration. The magnitude 0f the splitting is estimated by the usual. methOd for a degenarate states. The• elgen values E1 and E2 are given by. _____________________
c E
509
~ 1’~2
+
£22
±\Ji~l1- £22 2
2
__________
2
2
]
~~12
510
INTERPRETATION OF EXTRINSIC PHOTOCONDUCTIVITY SPECTRUM
Vol. 36, No. 6
where £11
<
‘V B~
£22
<
‘V E
<
‘V B
£12 e is
=
IeEZI
‘V ~2
JeEZI ‘V E
}
>
>
2!eEZ~ ‘V E
a charge of an electron
E Is electric field
volts/cm,
R2~ Y 10
=
~-~.--
R21
;~,
~
Cr)
,~
[~1l
—
1]
R is a radial part of the atomic wavef~ction and ym is spherical harmonics. The above considerations have a dIrect consequences on the interpretation of the photoconductivity spectra.We have, therefore, carried out the investigation in high purity n type CdTe single crystal. This material was found to be more adequate since it is a single valley semiconductor with the minimum in the conduction band at K o and has an isotropic effective mass. Experimental work was carried out at Oxford University with 3~3 In the which same detailed Study of donors samples, (CNRS sample)States and Chemical shifts have been studiud earlier. If there is any effect of the crystal field splitting originated from the reduction of the symmetry caused by the applied electric field, then it should be revealed as a function of applied electric field. We. therefore, ic~vestigated the electric field dependeR ce of the ls - 2p transition observed in the extrinsic photoconductivity spectrum. A Fourier transform spectrometer was employed for recording the photoconductivity spectrum at 4.2 k. The low temperature technique and other expenimental procedures used in the present work are well known13. Fig. 1 shows ls-2p sharp transition recorded in the photonductivity spectrum at 4 different applied voltages. The other weak lines originated from different chemical species are not shown here. A close look will show that at higher voltages the shoulder on the low energy side of the main peak becomes more prominent and in fig. c the shoulder does show the splitting tendency In fig. d, where the applied voltage was 10.5 volts/cm the shoulder does unurllbiguoLJs splitting, It is well known that in high purity samples the lines obtained in the photonductivity spactrum are really sharp and details of the structure can be observed, As mentioned earlier we did record these lines (not shown in fi~ure). The prominent line located at 82 cm is in close agreement with tho prominent line C reported earlier in all the samples GE,
Fig.
1
-
:
±~,
Electric field dependence of 1 s = 2~ transition recorded In photoconductlvity spectrum at 4.2 K in n type high punty CdTe single Crystal.
a b
2 volts/gm. 2.75 volts/cm
c d
4.00 volts/cm 10.5 volts/cm
CNRS 1 and CNRS 2. It is worth mentioning den that onthetheCNRS low 1 energy sample side, does however show a shou! the origin was not stui1i~d. The substitutional impurity has a site symmetry Td in CdTe crystal and p level decomposc~ into B & E symmetry. It Is clear that sopara~ion between the energy states depends on the strength of the porturbing field and our expenimental data do show the expected field dependence. Line shape and broadening of the ls-2 p transition has been studied earlier both theoretically10 and experimentally3. The work of Korn and Larsen1’ does explain the broodening on the basis of the stark effect produccii by the local electric field oniginated from the ionization, of the impurity atom, There is a remarkable agreement between the experimentally obtained and the theoretically predicted line shapes. However, in the theoretical calculation six independent parameters are used which cannot be determined by other independent experimental methods. Moreover, the line shape reported by Bajaj3 and his coworkers have a some what triangular shape whose origin is not clear, certainly it does mean that ~he stark effect is not playing a predomini~nt. role in the broadening process but it is not the only process. The unequal transition probability and the close separation between the E and 82 states can explain the observed triangular shape, and therefore one should take the above effect also into account before making a least square fit.
Vol. 36, No. 6
INTERPRETATION OF EXTRINSIC PHOTOCONDUCTIVITY SPECTRUM
12have studied Wagner and McinCombe is ls-2p transition transmission and photoconductivity spectrum of n type CdTe. Transmission spectrum clearly shows only one absorption line while the photoconductivity spectrum does show two lines (See fig 1 0f reference 12). The origin for this discrepancy was not clear. However, the present analysis removes the discrepancy since the applied electric field was enough to separate and E components. Close examination shows that the photoconductivlty peak does not exactly coincide with the absorption line but lies on either side of it. This suggests that in the photoconductivity spectrum the P line really undergoes splitting. Therefore the appearance of the additional lines in the photoconductivity spectrum should not be considered as a sign of a better sensitivity of detection. In
such circumstances one has to be careful for Identifying the origin of the new lines. This will avoid the obvious misinterpretation that the lines are originated from impurity atoms of different chemical nature. Such an error has beefl Incurred in the case of multivalley semi conductors where is energy state was found to be split up and the effect was attnibutated to the central ceilcorrection.
Acknowledgements We acknowledge with thanks to Or. R. A. Stradling for his hospitality at Clarendon Labo ratory, Oxford and also for making the s~nples available. We also thank to Or, A. Redondo for valuable discussion.
REFERENCES 1. 2. 3. 4. 5. 6. 7, 8. 9. 10. 11. 12.
511
Simmonds P.E. . Stradling R.A. , Birch J. R. and Bradley c.c. Phys. Stat. Sol. (6) 64, 195 (1974) SkolnIck 1TS., Eaves L., Stradling R.A., Portal J.C.,, and Askeuazy S.Solid State Communication, 15, 1403 (1974) Bajaj K.K. , Birch J.R., Eaves L. , Hoult R.A. , Klrkman R.F, , Simmonds P.E. and Stradling R.A. , 3. Phys. C 18, 530 (1975) Pantelidas S.T. • Rev, Mod. Phys. 50, 797 (1978) Ozkei M. • Kltahara K., Nakal K., ~ibatomi A., Dazal K., Okawa S. and Ryuzan 0., Jap. Journal of Phy. 16, 1617 (1977) Chamberlain J.M., Ergun M.B., Gehning K. A. and Stradling R.A., Solid State Communication, 9 1563 (1971) Skolnick M.S.. CartenA.C. • Clouder y, and Stradllng R.A., J. OptI. Joc. America 67, 947 (1977) Larsen D.M. , Phys. Rev. 8 8. 535, (1973) Watts R.K. , Point defects In crystals John Wiley and Sons, (1976) Fetterman, H., Wahdman 3. and Wolfe C.M., Solid State Communication, 11. 375 (1972) ~rn 0. (1. Larsen D.M. . Solid State Communication. 13, 807 (1973) Wagner R.J.& Mc Combo B.0.,Phys. Stat. Soldi. (6), 64, 205 (1974).
ON THE INTERPRETATION OF EXTRINSIC PHOTO~0NDUCTIVITy N.
SPECTRUM
V. Joshi
Universidad de Los Andes
Departamento de Fisica
-
Venez ue 1 a Received
on
June 10. 1979
The interpretation of extrinsic photoconductivity spectrum has been reanalysed on the basis of crystal field splitting. It has been found out that the application of electric field reduces the symmetry environment from Td to andp states do split in two components B 2 and E. The electric field dependence of the separation has been experimentally observed and theoretically estimated.
1—5 Recently much work related to the electronic structure of shallow donors of high purity materials is being carried out by far infrared Spectroscopic Techniques. This gives not Only the information about the different types of impurity contents but also the nature and magnitude of the central cell correction, which in turn helps to understand the various models and tho parameters involved to construct5.the wave If one SuCceedo forin the making adequate theoretical functions impurity atoms models, it is possible to predict the nature of the impurity atom by cpectroacopic study. A large amount of information of shallow donor states comes from extrinsic photocondutivity or transmission spectrosco py. Both techniques are treated equivalent since they give apparently the same information. The purpose of the present note is to reanalyse the data obtained by the photoconductivity technique and evaluate its consequences. In the
electric fields which reduce the syrmietry environment of the impurity atom. Therefore, crystal field splitting has to be considered according to the reduced symmetry. Extensive Study of the extrinsic photoconductivity has been carried out o-8 in several high purity materials such as Ge. Si, CdTe. InP. GaAs etc. Lvun thou7h these semiconductors have different atom impurity crystalline sees Id symetry structure, in the all cases. For this reason subsequent discussion is carried Out with reference to Td symmetry. In fact,wave functions of p symmotry are not split up in Td symmetry (we are rbfarring only to the zero magnetic fielà case), but the application of an electric field in <100> direction reduces the simmetry from Td to 02d9. Characters X,. for p wavefunctions in 02d symmetry been worked out and found to be E
2S 4
extrinsic photoconductivity and optical transmission measurements, one essentially observes the energy difference between the ground states and the excited states. or the difference between two excited states of the impurity atom. However a close look reveals that there is a small but Important differences which needs to be considered before interpretingdata. Not every line observed Inthe photo conductivity spectrum needs to be Interpreted as arising from Impurity atoms of different chemical nature. This is particularly true for the linee observed in the fine structure of ls—~2p transitions (even In single valley semiconductors). It is true that p state might not split in a particular syornatry however In the process of photoconductlvity measurements one needs to apply
x
3
-l
C2
2C~
-l
-l
This decomposes 0P 082 ~ 0E
20’ d 1 p wavefunctions
into
The wavefunctions of the perturbed impurity atom can be obtained by syrwnetry consideration. The magnitude 0f the splitting is estimated by the usual. methOd for a degenarate states. The• elgen values E1 and E2 are given by. _____________________
c E
509
~ 1’~2
+
£22
±\Ji~l1- £22 2
2
__________
2
2
]
~~12
510
INTERPRETATION OF EXTRINSIC PHOTOCONDUCTIVITY SPECTRUM
Vol. 36, No. 6
where £11
<
‘V B~
£22
<
‘V E
<
‘V B
£12 e is
=
IeEZI
‘V ~2
JeEZI ‘V E
}
>
>
2!eEZ~ ‘V E
a charge of an electron
E Is electric field
volts/cm,
R2~ Y 10
=
~-~.--
R21
;~,
~
Cr)
,~
[~1l
—
1]
R is a radial part of the atomic wavef~ction and ym is spherical harmonics. The above considerations have a dIrect consequences on the interpretation of the photoconductivity spectra.We have, therefore, carried out the investigation in high purity n type CdTe single crystal. This material was found to be more adequate since it is a single valley semiconductor with the minimum in the conduction band at K o and has an isotropic effective mass. Experimental work was carried out at Oxford University with 3~3 In the which same detailed Study of donors samples, (CNRS sample)States and Chemical shifts have been studiud earlier. If there is any effect of the crystal field splitting originated from the reduction of the symmetry caused by the applied electric field, then it should be revealed as a function of applied electric field. We. therefore, ic~vestigated the electric field dependeR ce of the ls - 2p transition observed in the extrinsic photoconductivity spectrum. A Fourier transform spectrometer was employed for recording the photoconductivity spectrum at 4.2 k. The low temperature technique and other expenimental procedures used in the present work are well known13. Fig. 1 shows ls-2p sharp transition recorded in the photonductivity spectrum at 4 different applied voltages. The other weak lines originated from different chemical species are not shown here. A close look will show that at higher voltages the shoulder on the low energy side of the main peak becomes more prominent and in fig. c the shoulder does show the splitting tendency In fig. d, where the applied voltage was 10.5 volts/cm the shoulder does unurllbiguoLJs splitting, It is well known that in high purity samples the lines obtained in the photonductivity spactrum are really sharp and details of the structure can be observed, As mentioned earlier we did record these lines (not shown in fi~ure). The prominent line located at 82 cm is in close agreement with tho prominent line C reported earlier in all the samples GE,
Fig.
1
-
:
±~,
Electric field dependence of 1 s = 2~ transition recorded In photoconductlvity spectrum at 4.2 K in n type high punty CdTe single Crystal.
a b
2 volts/gm. 2.75 volts/cm
c d
4.00 volts/cm 10.5 volts/cm
CNRS 1 and CNRS 2. It is worth mentioning den that onthetheCNRS low 1 energy sample side, does however show a shou! the origin was not stui1i~d. The substitutional impurity has a site symmetry Td in CdTe crystal and p level decomposc~ into B & E symmetry. It Is clear that sopara~ion between the energy states depends on the strength of the porturbing field and our expenimental data do show the expected field dependence. Line shape and broadening of the ls-2 p transition has been studied earlier both theoretically10 and experimentally3. The work of Korn and Larsen1’ does explain the broodening on the basis of the stark effect produccii by the local electric field oniginated from the ionization, of the impurity atom, There is a remarkable agreement between the experimentally obtained and the theoretically predicted line shapes. However, in the theoretical calculation six independent parameters are used which cannot be determined by other independent experimental methods. Moreover, the line shape reported by Bajaj3 and his coworkers have a some what triangular shape whose origin is not clear, certainly it does mean that ~he stark effect is not playing a predomini~nt. role in the broadening process but it is not the only process. The unequal transition probability and the close separation between the E and 82 states can explain the observed triangular shape, and therefore one should take the above effect also into account before making a least square fit.
Vol. 36, No. 6
INTERPRETATION OF EXTRINSIC PHOTOCONDUCTIVITY SPECTRUM
12have studied Wagner and McinCombe is ls-2p transition transmission and photoconductivity spectrum of n type CdTe. Transmission spectrum clearly shows only one absorption line while the photoconductivity spectrum does show two lines (See fig 1 0f reference 12). The origin for this discrepancy was not clear. However, the present analysis removes the discrepancy since the applied electric field was enough to separate and E components. Close examination shows that the photoconductivlty peak does not exactly coincide with the absorption line but lies on either side of it. This suggests that in the photoconductivity spectrum the P line really undergoes splitting. Therefore the appearance of the additional lines in the photoconductivity spectrum should not be considered as a sign of a better sensitivity of detection. In
such circumstances one has to be careful for Identifying the origin of the new lines. This will avoid the obvious misinterpretation that the lines are originated from impurity atoms of different chemical nature. Such an error has beefl Incurred in the case of multivalley semi conductors where is energy state was found to be split up and the effect was attnibutated to the central ceilcorrection.
Acknowledgements We acknowledge with thanks to Or. R. A. Stradling for his hospitality at Clarendon Labo ratory, Oxford and also for making the s~nples available. We also thank to Or, A. Redondo for valuable discussion.
REFERENCES 1. 2. 3. 4. 5. 6. 7, 8. 9. 10. 11. 12.
511
Simmonds P.E. . Stradling R.A. , Birch J. R. and Bradley c.c. Phys. Stat. Sol. (6) 64, 195 (1974) SkolnIck 1TS., Eaves L., Stradling R.A., Portal J.C.,, and Askeuazy S.Solid State Communication, 15, 1403 (1974) Bajaj K.K. , Birch J.R., Eaves L. , Hoult R.A. , Klrkman R.F, , Simmonds P.E. and Stradling R.A. , 3. Phys. C 18, 530 (1975) Pantelidas S.T. • Rev, Mod. Phys. 50, 797 (1978) Ozkei M. • Kltahara K., Nakal K., ~ibatomi A., Dazal K., Okawa S. and Ryuzan 0., Jap. Journal of Phy. 16, 1617 (1977) Chamberlain J.M., Ergun M.B., Gehning K. A. and Stradling R.A., Solid State Communication, 9 1563 (1971) Skolnick M.S.. CartenA.C. • Clouder y, and Stradllng R.A., J. OptI. Joc. America 67, 947 (1977) Larsen D.M. , Phys. Rev. 8 8. 535, (1973) Watts R.K. , Point defects In crystals John Wiley and Sons, (1976) Fetterman, H., Wahdman 3. and Wolfe C.M., Solid State Communication, 11. 375 (1972) ~rn 0. (1. Larsen D.M. . Solid State Communication. 13, 807 (1973) Wagner R.J.& Mc Combo B.0.,Phys. Stat. Soldi. (6), 64, 205 (1974).