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Fine structure of the excitonic absorption spectra and interband magneto-optics of CdTe crystals
802
Journal of Crystal Growth 101 (1990) 802—807 North-Holland
FINE STRUCTURE OF TILE EXCITONIC ABSORPTION SPECTRA AND INTERBAND MAGNETO-OPTICS OF CdTe CRYSTALS M.A. ABDULLAEV, O.S. COSCHUG, S.I. KOKHANOVSKII and R.P. SEISYAN A.F. loffe Physical-Technical Institute, 194021 Leningrad USSR
Excitomc absorption spectra of super-thin (d = 0.4—0.8 ~m) CdTe samples as well as photoluminescence, differential photoabsorption and reflection were investigated. Fine structure including the ground is, excited 2s and bound exciton states, the broad peak at > and other peculiarities were observed. Measurements allowed us to find the peculiarities resulting from the LO-phonon and LA-phonon assisted transitions into the minimum of the excitonic band at k 0 3.4 X 106 cm’. Although the condition of strong magnetic field $ >> 1 is not fulfilled, the rich oscillatory structure is clearly seen beginning from 1.5 to 2.0 T. This is connected with the presence of the 2s-excited state at zero magnetic field. The investigation of the diamagnetic exciton series (v = 0, 1, 2) allows one to determine the band parameters of CdTe. The value obtained for m~(0)= 0.074m is sufficiently lower than the one determined from the cyclotron resonance, even by taking into consideration the electron—phonon interaction.
(1) Direct transitions into the ground exciton states in CdTe are associated with a high absorption coefficient (a) which provides some difficulties in the detailed study of the absorption spectra. Usually, the coefficient a is reaches ten times 3B5 and thelarger valuethan of that2 Xini0~ Ge or A cm That is why the experiment needs crystals with thickness d ~z 1 ~tm. This probably is the reason why not only the fine structure including excited (n 0 2) and bound exciton states, but ~.
also the exciton ground state (n0 1) in optical absorption spectra were not investigated up to now. =
(2) The experiments made unstressed, “free” single crystals inwere a range of on sample thicknesses d 0.4—0.8 ~tm. Suitable chemical etching applied after mechanical polishing reduced the sample thickness value to the value needed. Fi=
nally, the samples were put into a special thin
,&‘,,,/,esce’wce
t
~
K
—
__
k~J
Q~1
I
I
1.49
pCdTh
1’,CO 4v, e7T—iFig. 1. Fine structure of the excitonic absorption spectra of CdTe (solid curve) compared with PL spectra (dotted curve). Insert: Exciton polariton dispersion in CdTe with the degenerate valence band consideration. The dashed lines show the relative positions of the branches, according to ref. [10]. 0022-0248/90/$03.50 © 1990
—
152
1~5~
Elsevier Science Publishers B.V. (North-Holland)
MA. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
glass box and immersed in pumped liquid helium. The natural heating allowed one to measure the temperature dependence of the absorption spectra. All transmission data were obtained with a grating spectrophotometer; the spectral bandwidth was
803
fl-i;
0
—
\ E,=21.2..,r \
IC
(3) Fig. 1 shows the excitonic absorption spectra at 2 K. To our knowledge, we are the first to see such complicated spectra including the free exciton ground (e(ls) = 1.5965 eV), excited ((2s) = 1.6042 eV) and bound states. It is interesting that the continuum is superimposed by the K-peak with energy 1.6165 eV, at an energy larger than the ground exciton state energy by approximately the LO-phonon energy. The photoluminescence spectra show the dominating line at 1.5884 eV assigned to an exciton bound to a neutral acceptor (A°,X) and its phonon replicas. The spacing between the maxima equals the energy hQL0 = 21.2 meV, which practically coincides with values published previously (21.3 meV) [1] (4) The binding energy of a free exciton ground state can be estimated by using the band parameters deduced from cyclotron resonance (CR) [2]: R * = R0 + Z~ed = 9.05 meY. Here, R0 is the isotropic part determined as 2 R — ~m~’+ Yi e m) ~ 2h2ac~’
\
—
is the anisotropic part depending on Y2 and m and m~ are the free and effective electron masses, ac~is the dielectric constant, and Y~ and y~are the Luttmger parameters. The binding energy for the excited exciton state is R = ~R 0 + &~= 2.3 meV. The determination of from R is more accurate, because the exchange interaction and nonmonotonic behaviour of (K) ar less significant, so this yields the energy gap value of e~(0)= 1606.5 ±0.3 meV. The use of this value leads to some discrepancy between the experimental and calculated position of n0 = 1: e~~’ is by 1.05 meV lower than the calculated one. ~
~
-
\ \
~-
0
~,
f
.51’
1OO
\/E
34~eY
E =4.~ \2,,
meV
-/0
I
0
I
I
I
2
,, g 40~’i; K —‘ 1. The inclinations of the linear part Fig. 2. The temperature dependent part of the exciton linewidth are E in CdTe versus T 1 = 21.2 meV and E2 = 4.3 meV. Insert: Whole line-width
as a function of T.
(5) One of the main peculiarities of the absorption spectra is the peak K. This peak could be identified as energy exciton—phonon bound state (EPBS). The binding of the EPBS is estimated to be h~2Lo (k~Cno=O) = 1.2 ±0.1 meV and corresponds to the predicted one in refs. [3,4]. How—
ever, an LO-phonon assisted exciton transition with the final step placed at the band minimum near K = 0 is also possible. The calculated [5,6] minimum depth of the exciton band Zlk = 1.08 meV agrees with the “binding” energy data, as
~‘
~‘
well. Temperature dependent experiments of the absorption spectra (fig. 2) show that the high temperature broadening of the line is associated with LO-phonon interaction, and, for n0 = 1, is proportional to the number of filling: I’ = r’ + a * hQ N 0
LO
q’
where Nq = [exp(hQLO/kT) — 1]~. It should be mentioned that a * seems to be essentially higher
804
M.A. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
than the Fröhlich constant for electron—phonon (aF = 0.36) or hole—phonon interaction, and reaches the values of 4.5. The theoretical estimation based on ref. [7] and correlated with experimental data shows that besides the dissociation of an exciton caused by LO-phonon scattering, the exciton scattering and scattering with the excited state transitions gave a contribution of approximately the same order. The “K”-line in CdTe disappears almost simultaneously with the ground state when the excited state n0 2 having the
Cc/Te
—
=
binding energy of 2.3 meV is already vanished. This supports the argument of LO-phonon assisted exciton transitions. The plotted curve F( T) exhibits an additional exponential part inclined as E 4.3 meV with lower ag’. The curve for n0 = 2 has a similar inclination, but with higher a~.This energy practically coincides with the TA-phonon energy, which is almost the same in the major part of the Brillouin zone [8].
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(6) The is line shape investigation allows one to consider the existence of some pecularities (er, ~2) on both slopes of the absorption maximum. They are clearly seen in photoabsorption [9] studies made in a wide range of temperatures. Differential photoabsorption spectra were obtained by using a modulated He—Ne laser beam, with a modulation frequency of COrn = 40—1000 Hz. Synchronous transmission signal detection was made at the modulation Thephotons/cm2. light flow density was not higherfrequency. than iO’7 s; 2 s. the this effect was the observed 10N mainly photons/cm In case, effect atcan~ be associated with exciton electric field effects caused by the charged surface states. Both slopes of the is line are superimposed by structures confirming the peculiarities ~ and e 2. An increase of temperature up to 30 K yields a disappearance of e~and a broadening of ~2 (fig. 3). If the low-energy peculiarity ~ can be identified as an exciton bound to a neutral donor (D°,X), the high energy peculiarity 2 has no obvious analogy in the absorption spectra. The extremum of 2 is located by 1.7 meV higher than the is maximum. This value coincides with Ltc = hsk0, where s 5iscm/s the velocity of the LA-phonon, SLA = 3.39 x i0
/
d=04~.im
\
\ //
!‘
\
\ / Fig. 3. Differential photoabsorption spectra at T = 2, 7.3 and 30 K; dashed curve: the original absorption spectra.
1(2m~’/m)1”4[6], and gives for [iO], k0 = a~ k CdTe a value 0 = 3.4 that x 106~2cm’. Due to this coincidence we suggest is responsible for the indirect transitions with LA-phonon emission. Thus the discussed feature of the fine structure of the absorption spectra seems to be an expenmental argument that the absolute minimum of the exciton band is really placed at k0 cm’.
3.4 x 106
(7) Assuming the peak at 1.6165 eV to be the LO-phonon assisted transition at the k0 minimum, it is required to take into account the phonon dispersion law and thus to introduce the small correction of hQLO determined for the center of the1.2Brillouin zone. is meV and doesThe notnecessary contradictcorrection the experi—
MA. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
Table 1 Comparison of the characteristic values for the “Rydberg” states of hydrogen atom with n
0
=
805
30 and a typical semiconductor crystal
with exciton excited states Parameter ~
~ dependence
Units
8cm n~ 10 R n~2 103eV 103eV H,~., n 2 T 0 R is the binding energy, ~ a) is the mean size,
H atom, n0 = 30 480 15 1 270 is the spacing
sc0, ~i dependence
Crystal,
c0
10,
=
~t =
0.05m
n0=1 n0=2 ~ 106 424 ~s/~c~ 6.8 1.7 js/ic~ 5 1.25 j//K2 6.25 1.56 between neighbouring energy levels and H
n0=3 960 0.7 0.5 0.69 1~...,is the critical
magnetic field to achieve
$
=
1.
mental data obtained for CdTe [8]. The reflectance and photoluminescence spectra show the peculiarities typical for the lower and the upper polariton branches of the free exciton, with hCOLT 1.2 meV. This result gave us the possibility to assume that the exciton dispersion law for the is state is similar to the calculated ones in ref. [10],
tory structure being typical for Landau subband spectroscopy; for example, these are Sn02 and Cu20 with /3 4Z i, CdS and CdSe [i2] with /3 < i, 30
H~
slightly but the larger minimum (see insert depthof e(k0) fig. 1). and hcoLT are (8) The band parameters needed for the calculation of e ( k) may be obtained from interband magneto-optical (MO) studies. It is known [ii] that interband MO phenomena are characterized by the behaviour of a special exciton arising in the presence of magnetic field and named the “diarow-gap semiconductors, where the Elliott— magnetic exciton” (DE). This is proved for narLoudon (EL) criterion of strong magnetic field 2>a i) is easily reached. (/3 h~2/2R* (a*/L) frequencies of the * is the Here, Q co~electron is the and sumetheof hole, the a cyclotron magnetic length. In this case, the system of the radius of the exciton ground state and L is the interacting electron and hole becomes one-dimensional when the cyclotron rotation with radius L occurs in the plane perpendicular to the magnetic field H, while the slow Coulomb motion with length a ~ is possible only along H. So we have the problem of a one-dimensional exciton with main quantum number v 0, i, =
—
EI
2.0
~ H
K
i.o L~
0
~
I
.~
I
30
~.
~~ 2)
—
=
=
=
=
...
(9) Strictly speaking, there are some cases for which the criterion of a strong magnetic field /3>> i is not fulfilled, but there exists the oscilla-
~ 1’ 2 0
j
/
~
‘1 ~ I 6Z I. ~4 ~~6 I é~ E,ev Fig. 4. Experimental MO spectra at T = 2 K, H 7.5 T and c 2 H in the Faraday configuration HI q. The theoretical spectra of DE are also given; notation of the transitions is for G(LCP) polarization: a*(l)a~(l + 1), b~(l)b(l + 1), a_(l)ac(l+1), b(l)bc(l+1),and for a~(RCP)polarization: a~(l)a’~(l~1),b~(l)b’~(l~1), a(l)a’~(l—1), b(l)b’~(l— 1); 1 is the Landau number.
806
MA. Abdullaev et aL
/ Fine structure of excitonic absorption spectra of CdTe crystal
and GaAs, InP and CdTe with /3 i. The case is similar to the situation occurring in Rydberg spectroscopy of atoms and molecules. It was found that under special conditions, it was possible to detect the large-number “Rydberg” state spectra of hydrogen and other materials with the first quantum number n0 20—500 [i3]. It is not dif=
ficult to compare the excitonic phenomena in semiconductors with the classic hydrogen atom with n0 30, for example (table i). =
(iO) Fig. 4 shows the CdTe magnetoabsorption spectra at H 7.5 T and 2 K, detected in Faraday configuration for two circular polarizations. Such a rich spectrum was only seen in the case of GaAs [i4,ii]. Magnetoabsorption appears on the continuum background and contains a large number of sharp oscillatory peaks. The similarity to “Rydberg” spectroscopy is evident and is correlated synonymously with the conditions of observation of the excited states. Yet, to detect such MO spectra for CdTe, it is sufficient to detect the first excited exciton state n0 2 at H 0. The “oscillatory” structure is observed at i.5—2.0 T as it was predicted in table i. It should be stressed that the exciton state n0 1 does not show up in the MO spectra. The MO spectra investigation allows one to distinguish DE state series in the CdTe. Although /3 i, itthe is allowed to calculate binding energies of quasi-one-dimensional DE excited states with v 1, 2 using the method of Hasegawa and Howard, demanding the criterion /3>> 1 to be satisfied [15,il]. This gives the possibility for a reliable determination of the DE series dissociation edges or the transitions between L subbands. As a consequence, the band parameters can be calculated and compared with values obtained by other methods; for example, by CR. However, the number of DE series is not large enough to carry out this procedure with precision. Thus, a new theory “working” at significantly low fields is needed. =
=
=
=
=
of this method suited for an exciton in diamondlike semiconductors and completed by a variational calculation of the one-dimensional equation was used here to make it more accurate. The obtained binding energies are suitable for the states lying higher than g by one or several R *~ The theoretical energy values are in good agreement with the experimental data (fig. 4). Only the first excitonic maximum is the exception to this rule. Its location can be determined from the Zeeman effect and diamagnetic shift theory. (i2) After identifying the experimental spectra and adding the calculated value of the binding DE energy to each maximum, one can reconstruct the energy system for L subbands which are the dissociation edges of the DE series and are not seen experimentally. Then it is possible to determine the band parameters of CdTe, such as effective masses, nonparabolicity coefficients, g * factors, etc. Surprisingly, the value obtained for m~(0) turned out to be much lower than that obtained from CR. It should be noted that the CR method determines the polaron mass which is higher than the optical one. So the value of 0.096m [i7] is the polaron mass. But even taking into account the second term of +decomposition, (1 + 6 + 0.025a~ does not m~~01 save them~ situaaF/ tion. Our experiments resulted in a value m~(0) 0.074m, which is significantly lower than the polaron-corrected CR mass (m~’ 0.088m [2]). The effective heavy and light hole masses have the reasonable values m~h 0.6m and m~ 0.iim. Studying the fan charts, we observed many nonregularities of m (H) dependences with a number of pinnings and crossings, which cannot be explained in the frame of the up-to-date theories. It is obvious now that in our case a magnetoabsorption theory, which consistently accounts for the exciton—phonon interaction, is needed. =
...),
=
=
=
=
References (ii) Such a calculation procedure for a hydrogen-like donor, based on adiabatic approximation was proposed in ref. [16] for a much weaker condition than the EL one, namely /3!> 1; here, I is the Landau quantum number. The development
[1] B. Segal and D.T.F. Marple, in: Physics and Chemistry of Il—VI Compounds, Eds. M. Aven and J.S. Prener (NorthHolland, Amsterdam, 1967). [21 Le Si Dang, G. Neu and R. Romestain, Solid State Commun. 44(1982) 1187.
MA. Abdullaev et aL
/ Fine structure of excitonic absorption spectra of CdTe crystal
[3]I. Dillinger, C. Konak, V. Prosser, J. Sak and M. Svara, Phys. Status Solidi 29 (1968) 707. [4] I. Hermanson, Phys. Rev. B2 (1970) 5043. [5] E.O. Kane, Phys. Rev. Bli (1975) 3850. [6] Al.L. Efros and B.L. Gelmont, Solid State Commun. 49 (1984) 883. [7] K. Trallero Giner, 1G. Land and S.T. Pavlov, Fiz. Tverd. Tela 21(1979) 2028. [8] P. Plumelle and M. Vandevyver, Phys. Status Solidi (b) 73 (1976) 271. [9] A.V. Varfolomeev, R.P. Seisyan and U.L. Shelekhin, Fir. Tekh. Poluprovodn. 10 (1976) 1063. [10] R. Sooryakumar, M. Cardona and IC. Merle, Solid State Commun. 48 (1983) 581. [11] R.P. Seisyan, Diamagnetic Exciton Spectroscopy (Nauka, Moscow, 1984) (in Russian).
807
[12] B.L. Gelmont, G.V. Mikhailov, A.G. Panfilov, B.S. Razbirin, R.P. Seisyan and Al.L. Efros, Fiz. Tverd. Tela 29 (1987) 1730. [13] A. Dalgarno, Rydberg State Spectroscopy (Moscow, 1985) (in Russian). [14] R.P. Seisyan, M.A. Abdullaev and B.P. Zakharchenya, Fiz. Tekh. Poluprovodn. 7 (1972) 957. [15] H. Hasegawa and R.E. Howard, J. Phys. Chem. Solids 8 (1959) 382. [16] V.G. Golubev, V.1. Ivanov-Omskii, A.G. Osutin, R.P. Seisyan, AlL. Efros and T.V. Yazeva, Fir. Tekh. Poluprovodn. 22 (1988) 1416. [17] R. Romestain and C. Weisbuch, Phys. Rev. Letters 45 (1980) 2067.
Journal of Crystal Growth 101 (1990) 802—807 North-Holland
FINE STRUCTURE OF TILE EXCITONIC ABSORPTION SPECTRA AND INTERBAND MAGNETO-OPTICS OF CdTe CRYSTALS M.A. ABDULLAEV, O.S. COSCHUG, S.I. KOKHANOVSKII and R.P. SEISYAN A.F. loffe Physical-Technical Institute, 194021 Leningrad USSR
Excitomc absorption spectra of super-thin (d = 0.4—0.8 ~m) CdTe samples as well as photoluminescence, differential photoabsorption and reflection were investigated. Fine structure including the ground is, excited 2s and bound exciton states, the broad peak at > and other peculiarities were observed. Measurements allowed us to find the peculiarities resulting from the LO-phonon and LA-phonon assisted transitions into the minimum of the excitonic band at k 0 3.4 X 106 cm’. Although the condition of strong magnetic field $ >> 1 is not fulfilled, the rich oscillatory structure is clearly seen beginning from 1.5 to 2.0 T. This is connected with the presence of the 2s-excited state at zero magnetic field. The investigation of the diamagnetic exciton series (v = 0, 1, 2) allows one to determine the band parameters of CdTe. The value obtained for m~(0)= 0.074m is sufficiently lower than the one determined from the cyclotron resonance, even by taking into consideration the electron—phonon interaction.
(1) Direct transitions into the ground exciton states in CdTe are associated with a high absorption coefficient (a) which provides some difficulties in the detailed study of the absorption spectra. Usually, the coefficient a is reaches ten times 3B5 and thelarger valuethan of that2 Xini0~ Ge or A cm That is why the experiment needs crystals with thickness d ~z 1 ~tm. This probably is the reason why not only the fine structure including excited (n 0 2) and bound exciton states, but ~.
also the exciton ground state (n0 1) in optical absorption spectra were not investigated up to now. =
(2) The experiments made unstressed, “free” single crystals inwere a range of on sample thicknesses d 0.4—0.8 ~tm. Suitable chemical etching applied after mechanical polishing reduced the sample thickness value to the value needed. Fi=
nally, the samples were put into a special thin
,&‘,,,/,esce’wce
t
~
K
—
__
k~J
Q~1
I
I
1.49
pCdTh
1’,CO 4v, e7T—iFig. 1. Fine structure of the excitonic absorption spectra of CdTe (solid curve) compared with PL spectra (dotted curve). Insert: Exciton polariton dispersion in CdTe with the degenerate valence band consideration. The dashed lines show the relative positions of the branches, according to ref. [10]. 0022-0248/90/$03.50 © 1990
—
152
1~5~
Elsevier Science Publishers B.V. (North-Holland)
MA. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
glass box and immersed in pumped liquid helium. The natural heating allowed one to measure the temperature dependence of the absorption spectra. All transmission data were obtained with a grating spectrophotometer; the spectral bandwidth was
803
fl-i;
0
—
\ E,=21.2..,r \
IC
(3) Fig. 1 shows the excitonic absorption spectra at 2 K. To our knowledge, we are the first to see such complicated spectra including the free exciton ground (e(ls) = 1.5965 eV), excited ((2s) = 1.6042 eV) and bound states. It is interesting that the continuum is superimposed by the K-peak with energy 1.6165 eV, at an energy larger than the ground exciton state energy by approximately the LO-phonon energy. The photoluminescence spectra show the dominating line at 1.5884 eV assigned to an exciton bound to a neutral acceptor (A°,X) and its phonon replicas. The spacing between the maxima equals the energy hQL0 = 21.2 meV, which practically coincides with values published previously (21.3 meV) [1] (4) The binding energy of a free exciton ground state can be estimated by using the band parameters deduced from cyclotron resonance (CR) [2]: R * = R0 + Z~ed = 9.05 meY. Here, R0 is the isotropic part determined as 2 R — ~m~’+ Yi e m) ~ 2h2ac~’
\
—
is the anisotropic part depending on Y2 and m and m~ are the free and effective electron masses, ac~is the dielectric constant, and Y~ and y~are the Luttmger parameters. The binding energy for the excited exciton state is R = ~R 0 + &~= 2.3 meV. The determination of from R is more accurate, because the exchange interaction and nonmonotonic behaviour of (K) ar less significant, so this yields the energy gap value of e~(0)= 1606.5 ±0.3 meV. The use of this value leads to some discrepancy between the experimental and calculated position of n0 = 1: e~~’ is by 1.05 meV lower than the calculated one. ~
~
-
\ \
~-
0
~,
f
.51’
1OO
\/E
34~eY
E =4.~ \2,,
meV
-/0
I
0
I
I
I
2
,, g 40~’i; K —‘ 1. The inclinations of the linear part Fig. 2. The temperature dependent part of the exciton linewidth are E in CdTe versus T 1 = 21.2 meV and E2 = 4.3 meV. Insert: Whole line-width
as a function of T.
(5) One of the main peculiarities of the absorption spectra is the peak K. This peak could be identified as energy exciton—phonon bound state (EPBS). The binding of the EPBS is estimated to be h~2Lo (k~Cno=O) = 1.2 ±0.1 meV and corresponds to the predicted one in refs. [3,4]. How—
ever, an LO-phonon assisted exciton transition with the final step placed at the band minimum near K = 0 is also possible. The calculated [5,6] minimum depth of the exciton band Zlk = 1.08 meV agrees with the “binding” energy data, as
~‘
~‘
well. Temperature dependent experiments of the absorption spectra (fig. 2) show that the high temperature broadening of the line is associated with LO-phonon interaction, and, for n0 = 1, is proportional to the number of filling: I’ = r’ + a * hQ N 0
LO
q’
where Nq = [exp(hQLO/kT) — 1]~. It should be mentioned that a * seems to be essentially higher
804
M.A. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
than the Fröhlich constant for electron—phonon (aF = 0.36) or hole—phonon interaction, and reaches the values of 4.5. The theoretical estimation based on ref. [7] and correlated with experimental data shows that besides the dissociation of an exciton caused by LO-phonon scattering, the exciton scattering and scattering with the excited state transitions gave a contribution of approximately the same order. The “K”-line in CdTe disappears almost simultaneously with the ground state when the excited state n0 2 having the
Cc/Te
—
=
binding energy of 2.3 meV is already vanished. This supports the argument of LO-phonon assisted exciton transitions. The plotted curve F( T) exhibits an additional exponential part inclined as E 4.3 meV with lower ag’. The curve for n0 = 2 has a similar inclination, but with higher a~.This energy practically coincides with the TA-phonon energy, which is almost the same in the major part of the Brillouin zone [8].
-
—
I
I—~I I
I
.~
\
/
“~
I
1
~—
/
~
/
/
~
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/
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io
.
/
~../
l.7~’
\ \~
(6) The is line shape investigation allows one to consider the existence of some pecularities (er, ~2) on both slopes of the absorption maximum. They are clearly seen in photoabsorption [9] studies made in a wide range of temperatures. Differential photoabsorption spectra were obtained by using a modulated He—Ne laser beam, with a modulation frequency of COrn = 40—1000 Hz. Synchronous transmission signal detection was made at the modulation Thephotons/cm2. light flow density was not higherfrequency. than iO’7 s; 2 s. the this effect was the observed 10N mainly photons/cm In case, effect atcan~ be associated with exciton electric field effects caused by the charged surface states. Both slopes of the is line are superimposed by structures confirming the peculiarities ~ and e 2. An increase of temperature up to 30 K yields a disappearance of e~and a broadening of ~2 (fig. 3). If the low-energy peculiarity ~ can be identified as an exciton bound to a neutral donor (D°,X), the high energy peculiarity 2 has no obvious analogy in the absorption spectra. The extremum of 2 is located by 1.7 meV higher than the is maximum. This value coincides with Ltc = hsk0, where s 5iscm/s the velocity of the LA-phonon, SLA = 3.39 x i0
/
d=04~.im
\
\ //
!‘
\
\ / Fig. 3. Differential photoabsorption spectra at T = 2, 7.3 and 30 K; dashed curve: the original absorption spectra.
1(2m~’/m)1”4[6], and gives for [iO], k0 = a~ k CdTe a value 0 = 3.4 that x 106~2cm’. Due to this coincidence we suggest is responsible for the indirect transitions with LA-phonon emission. Thus the discussed feature of the fine structure of the absorption spectra seems to be an expenmental argument that the absolute minimum of the exciton band is really placed at k0 cm’.
3.4 x 106
(7) Assuming the peak at 1.6165 eV to be the LO-phonon assisted transition at the k0 minimum, it is required to take into account the phonon dispersion law and thus to introduce the small correction of hQLO determined for the center of the1.2Brillouin zone. is meV and doesThe notnecessary contradictcorrection the experi—
MA. Abdullaev et al.
/ Fine structure of excitonic absorption spectra of CdTe crystal
Table 1 Comparison of the characteristic values for the “Rydberg” states of hydrogen atom with n
0
=
805
30 and a typical semiconductor crystal
with exciton excited states Parameter ~
~ dependence
Units
8cm n~ 10 R n~2 103eV 103eV H,~., n 2 T 0 R is the binding energy, ~ a)
H atom, n0 = 30 480 15 1 270 is the spacing
sc0, ~i dependence
Crystal,
c0
10,
=
~t =
0.05m
n0=1 n0=2 ~ 106 424 ~s/~c~ 6.8 1.7 js/ic~ 5 1.25 j//K2 6.25 1.56 between neighbouring energy levels and H
n0=3 960 0.7 0.5 0.69 1~...,is the critical
magnetic field to achieve
$
=
1.
mental data obtained for CdTe [8]. The reflectance and photoluminescence spectra show the peculiarities typical for the lower and the upper polariton branches of the free exciton, with hCOLT 1.2 meV. This result gave us the possibility to assume that the exciton dispersion law for the is state is similar to the calculated ones in ref. [10],
tory structure being typical for Landau subband spectroscopy; for example, these are Sn02 and Cu20 with /3 4Z i, CdS and CdSe [i2] with /3 < i, 30
H~
slightly but the larger minimum (see insert depthof e(k0) fig. 1). and hcoLT are (8) The band parameters needed for the calculation of e ( k) may be obtained from interband magneto-optical (MO) studies. It is known [ii] that interband MO phenomena are characterized by the behaviour of a special exciton arising in the presence of magnetic field and named the “diarow-gap semiconductors, where the Elliott— magnetic exciton” (DE). This is proved for narLoudon (EL) criterion of strong magnetic field 2>a i) is easily reached. (/3 h~2/2R* (a*/L) frequencies of the * is the Here, Q co~electron is the and sumetheof hole, the a cyclotron magnetic length. In this case, the system of the radius of the exciton ground state and L is the interacting electron and hole becomes one-dimensional when the cyclotron rotation with radius L occurs in the plane perpendicular to the magnetic field H, while the slow Coulomb motion with length a ~ is possible only along H. So we have the problem of a one-dimensional exciton with main quantum number v 0, i, =
—
EI
2.0
~ H
K
i.o L~
0
~
I
.~
I
30
~.
~~ 2)
—
=
=
=
=
...
(9) Strictly speaking, there are some cases for which the criterion of a strong magnetic field /3>> i is not fulfilled, but there exists the oscilla-
~ 1’ 2 0
j
/
~
‘1 ~ I 6Z I. ~4 ~~6 I é~ E,ev Fig. 4. Experimental MO spectra at T = 2 K, H 7.5 T and c 2 H in the Faraday configuration HI q. The theoretical spectra of DE are also given; notation of the transitions is for G(LCP) polarization: a*(l)a~(l + 1), b~(l)b(l + 1), a_(l)ac(l+1), b(l)bc(l+1),and for a~(RCP)polarization: a~(l)a’~(l~1),b~(l)b’~(l~1), a(l)a’~(l—1), b(l)b’~(l— 1); 1 is the Landau number.
806
MA. Abdullaev et aL
/ Fine structure of excitonic absorption spectra of CdTe crystal
and GaAs, InP and CdTe with /3 i. The case is similar to the situation occurring in Rydberg spectroscopy of atoms and molecules. It was found that under special conditions, it was possible to detect the large-number “Rydberg” state spectra of hydrogen and other materials with the first quantum number n0 20—500 [i3]. It is not dif=
ficult to compare the excitonic phenomena in semiconductors with the classic hydrogen atom with n0 30, for example (table i). =
(iO) Fig. 4 shows the CdTe magnetoabsorption spectra at H 7.5 T and 2 K, detected in Faraday configuration for two circular polarizations. Such a rich spectrum was only seen in the case of GaAs [i4,ii]. Magnetoabsorption appears on the continuum background and contains a large number of sharp oscillatory peaks. The similarity to “Rydberg” spectroscopy is evident and is correlated synonymously with the conditions of observation of the excited states. Yet, to detect such MO spectra for CdTe, it is sufficient to detect the first excited exciton state n0 2 at H 0. The “oscillatory” structure is observed at i.5—2.0 T as it was predicted in table i. It should be stressed that the exciton state n0 1 does not show up in the MO spectra. The MO spectra investigation allows one to distinguish DE state series in the CdTe. Although /3 i, itthe is allowed to calculate binding energies of quasi-one-dimensional DE excited states with v 1, 2 using the method of Hasegawa and Howard, demanding the criterion /3>> 1 to be satisfied [15,il]. This gives the possibility for a reliable determination of the DE series dissociation edges or the transitions between L subbands. As a consequence, the band parameters can be calculated and compared with values obtained by other methods; for example, by CR. However, the number of DE series is not large enough to carry out this procedure with precision. Thus, a new theory “working” at significantly low fields is needed. =
=
=
=
=
of this method suited for an exciton in diamondlike semiconductors and completed by a variational calculation of the one-dimensional equation was used here to make it more accurate. The obtained binding energies are suitable for the states lying higher than g by one or several R *~ The theoretical energy values are in good agreement with the experimental data (fig. 4). Only the first excitonic maximum is the exception to this rule. Its location can be determined from the Zeeman effect and diamagnetic shift theory. (i2) After identifying the experimental spectra and adding the calculated value of the binding DE energy to each maximum, one can reconstruct the energy system for L subbands which are the dissociation edges of the DE series and are not seen experimentally. Then it is possible to determine the band parameters of CdTe, such as effective masses, nonparabolicity coefficients, g * factors, etc. Surprisingly, the value obtained for m~(0) turned out to be much lower than that obtained from CR. It should be noted that the CR method determines the polaron mass which is higher than the optical one. So the value of 0.096m [i7] is the polaron mass. But even taking into account the second term of +decomposition, (1 + 6 + 0.025a~ does not m~~01 save them~ situaaF/ tion. Our experiments resulted in a value m~(0) 0.074m, which is significantly lower than the polaron-corrected CR mass (m~’ 0.088m [2]). The effective heavy and light hole masses have the reasonable values m~h 0.6m and m~ 0.iim. Studying the fan charts, we observed many nonregularities of m (H) dependences with a number of pinnings and crossings, which cannot be explained in the frame of the up-to-date theories. It is obvious now that in our case a magnetoabsorption theory, which consistently accounts for the exciton—phonon interaction, is needed. =
...),
=
=
=
=
References (ii) Such a calculation procedure for a hydrogen-like donor, based on adiabatic approximation was proposed in ref. [16] for a much weaker condition than the EL one, namely /3!> 1; here, I is the Landau quantum number. The development
[1] B. Segal and D.T.F. Marple, in: Physics and Chemistry of Il—VI Compounds, Eds. M. Aven and J.S. Prener (NorthHolland, Amsterdam, 1967). [21 Le Si Dang, G. Neu and R. Romestain, Solid State Commun. 44(1982) 1187.
MA. Abdullaev et aL
/ Fine structure of excitonic absorption spectra of CdTe crystal
[3]I. Dillinger, C. Konak, V. Prosser, J. Sak and M. Svara, Phys. Status Solidi 29 (1968) 707. [4] I. Hermanson, Phys. Rev. B2 (1970) 5043. [5] E.O. Kane, Phys. Rev. Bli (1975) 3850. [6] Al.L. Efros and B.L. Gelmont, Solid State Commun. 49 (1984) 883. [7] K. Trallero Giner, 1G. Land and S.T. Pavlov, Fiz. Tverd. Tela 21(1979) 2028. [8] P. Plumelle and M. Vandevyver, Phys. Status Solidi (b) 73 (1976) 271. [9] A.V. Varfolomeev, R.P. Seisyan and U.L. Shelekhin, Fir. Tekh. Poluprovodn. 10 (1976) 1063. [10] R. Sooryakumar, M. Cardona and IC. Merle, Solid State Commun. 48 (1983) 581. [11] R.P. Seisyan, Diamagnetic Exciton Spectroscopy (Nauka, Moscow, 1984) (in Russian).
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[12] B.L. Gelmont, G.V. Mikhailov, A.G. Panfilov, B.S. Razbirin, R.P. Seisyan and Al.L. Efros, Fiz. Tverd. Tela 29 (1987) 1730. [13] A. Dalgarno, Rydberg State Spectroscopy (Moscow, 1985) (in Russian). [14] R.P. Seisyan, M.A. Abdullaev and B.P. Zakharchenya, Fiz. Tekh. Poluprovodn. 7 (1972) 957. [15] H. Hasegawa and R.E. Howard, J. Phys. Chem. Solids 8 (1959) 382. [16] V.G. Golubev, V.1. Ivanov-Omskii, A.G. Osutin, R.P. Seisyan, AlL. Efros and T.V. Yazeva, Fir. Tekh. Poluprovodn. 22 (1988) 1416. [17] R. Romestain and C. Weisbuch, Phys. Rev. Letters 45 (1980) 2067.