OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT IN GaSb

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OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT IN GaSb

D. Bimberg, W. Rühle

To cite this version:

D. Bimberg, W. Rühle. OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT IN GaSb. Journal de Physique Colloques, 1974, 35 (C3), pp.C3-215-C3-221.

�10.1051/jphyscol:1974331�. �jpa-00215579�

JOURNAL DE PHYSIQUE Colloque C3, supplement au n° 4, Tome 35, Avril 191 A, page C3-215

OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT IN GaSb

D. B l M B E R G

Hochfeld-Magnetlabor des Max-Planck-Instituts fur Festkorperforschung, BP,- 166, Centre de Tri, F-38042 Grenoble, France

W. R U H L E

Physikalisches Institut, Teil 4, D-7 Stuttgart and Hochfeld-Magnetlabor

des Max-Planck-Instituts fur Festkorperforschung, BP 166, Centre de Tri, F-38042 Grenoble, France

Resume. — On demontre que les experiences de luminescence sont un moyen direct et sur pour etudier des proprietes des bandes de donneurs en champ magnetique fort. Les changements de leur energie d'ionisation, de leurs fonctions d'ondes et du recouvrement de celles-ci sont observes d'une maniere plus directe que dans les experiences de transport, par exemple, les experiences d'effet Hall ou Ton observe seulement de « magnetic freezeout » des charges conductrices.

Les echantillons de GaSb du type-p, non dopes, possedent des accepteurs avec des energies d'ionisation comprises entre 13 et 100 meV. Les spectres de luminescence des differents accepteurs sont presentes a basse temperature. Ces spectres ont ete obtenus en fonction de l'intensite d'exci- tation et du champ magnetique jusqu'a 100 kG. Les lignes d'accepteurs se deplacent vers les plus hautes energies sous Faction du champ magnetique et se dedoublent avec un ecart de 4 meV a 100 kG. Ce deplacement est presque le meme pour les differents accepteurs dans le meme echan- tillon, mais depend de la quantite de donneurs et accepteurs. Lorsqu'on augmente l'excitation, les lignes se deplacent vers les plus hautes energies.

Toutes les transitions d'accepteur etudiees, qu'on nomme les lignes A, B, C, E et F, sont des transitions donneur-accepteur. Le splitting des bandes paires, sous champ magnetique, est traite a l'aide du spin-splitting des donneurs et une relocalisation de la bande des donneurs qui recouvre la queue de la bande de conduction.

On sait que cet efFet entraine le « magnetic freezeout » des charges conductrices dans les expe- riences du transport. Le deplacement, avec le champ magnetique, de la composante la plus forte des lignes de luminescence est explique par ces deux effets et par la th6orie de Larsen des niveaux de donneurs dans un champ magnetique.

Abstract. — It is demonstrated here, that luminescence experiments provide a direct and reliable tool to investigate the properties of donor bands in very high magnetic fields. The change of their binding energy, wavefunction and overlap is much more directly reflected in these experiments than in transport measurements, as e. g. Hall effect experiments, where only the magnetic freezeout of charge carriers can be observed.

Undoped p-type GaSb exhibits acceptors with ionization energies between 13 and 100 meV.

Low temperature luminescence spectra are reported involving transitions to the different acceptors.

The excitation intensity dependence and magnetic field dependence up to 100 kG of these spectra were investigated. With increasing magnetic field the acceptor lines shift to higher energies and split by about 4 meV at 100 kG. The shift is nearly independent of the acceptor ionization energy and depends only on the concentration of the impurities. With increasing excitation the lines shift to higher energies.

The A, B, C, E and F lines are identified to be donor-acceptor transitions. The splitting of the lines in a magnetic field is discussed in terms of spin-splitting of the donors and a relocalization of the donor-impurity band which has merged with conduction band tails.

This effect is known to cause the magnetic freezeout of charge carriers in transport experiments.

The magnetic field shift of the dominating low energy component of the recombination lines is explained by these two effects and by Larsen's theory of donor levels in a magnetic field.

1. Introduction. — N o t intentionally doped GaSb is always p-type, independent of the growth condi- tions. Therefore the most prominent features of the radiative recombination of GaSb are associated with different residual acceptor levels [l]-[4]. Three types of recombination processes are believed to be res-

ponsible for the pronounced structure of the lumi- nescence. These are transitions of photocreated electrons to neutral acceptors, the annihilation of excitons bound to acceptors, and the annihilation of free excitons. The free and one of the bound excitons have been investigated by means of wavelength-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974331

modulated reflectivity [5] and stress-modulated magne- toreflectivity [6] and a set of band parameters was determined. The impurity transitions themselves are believed to be a reliable and simple source of infor- mation about the depth of the different acceptor states, much more reliable and comprehensive than, for example, Hall effect measurements.

Only recently it was shown for the case of high- purity GaAs [7] that these transitions show a much more complex behaviour than believed before and one has to be very cautious before extracting detailed information from such experiments. In particular, effects of the banding of shallow impurities and of the screening of the binding potentials by free and bound carriers have been observed [7].

The band structure of GaSb is much more favou- rable for observing such effects. The lower effective mass of the conduction band (m:

0.042 mo) [6]

and the larger dielectric constant (8,

14.4) [8]

give rise to a binding energy of ED = 2.75 meV for the ground state of the effective mass donor. The Bohr radius of the ground state is 180 A. This means that for a donor concentration of n, > 1.6 x 1017 cm-3 an overlap of the donor ground state wave functions already has to be taken into account (a: nD > 1).

In addition, these band parameters are most favou- rable to apply Larsen's theory on the magnetic field dependence of the donor states [9], [lo]. A measure for the influence of the field is the factor y = ho,/2 E,.

Our maximal field of 100 k G corresponds to y = 5 (for comparison : in GaAs a field of 330 kG would be necessary to reach y = 5).

In this paper first results of magnetoluminescence experiments on GaSb with an unintentional donor concentration in this region are reported. We concen- trate here on transitions involving impurities. The behaviour of bound excitons will be reported elsewhere.

2. Experimental. - The luminescence was excited by a krypton laser with a maxima1 power output of 500 mW. The samples were immersed in liquid helium inside a 100 kG, split-coil superconducting magnet with an aperture offl2.8 in Voigt configuration.

The light was dispersed by a 60 cm Jobin-Yvon spectrometer and detected by a cooled (190 K) PbS-cell.

Undoped samples grown in the crystal growth laboratories of the physical institute of the univer- sities of Stuttgart and of Montpellier were used.

They were grown from either Sb-rich, stoichiome- tric, or Ga-rich melts. The electrical properties of some of the samples are given in Table I. The Hall effect data given there were taken from unpublished data of Dzievior (University of Stuttgart) and the thesis of D'Olne Campos (University of Montpellier, 1972).

3. Results. - In all samples which we investigated, different acceptor recombination bands were present.

According to reference [2] they are labelled A, B, C and E. For simplicity also the labelling used in refe- rence [I] is given. In Table I1 we show their approxi- mate spectral position and the estimated binding energy of the hole. It should be noted that :

a) The spectral position of all lines depends on the excitation intensity as discussed later.

b) Not one of the observed lines corresponds to a free electron-acceptor transition but all of them are due to donor-acceptor pair transitions, and the exact size of the Coulomb term is not known.

c) The value of the band-gap used to evaluate the hole binding energy is 812 meV 121 (1 meV ⁼ 1.239 551 mm).

The most intense of all the different acceptor recombination lines is the A-line. In some crystals this line is even stronger than the bound exciton line at

795 meV. Figure 1 shows the A-line at zero field and at 100 kG for different crystals. The same excitation-intensity was always used. It can be seen

Energetic positions of dzferent transitions to acceptors in GaSb and the estimated hole binding energies

Spectral position Line at 4.2 K (meV)

-

E

F

A

B

C 710

Binding energy Label acc. to ref. [l]

of the hole (Benoit B la G . (mev) et al.)

- -

1 3 f 2 -

27 f 2 -

35 + ²

52

2 I2

102 f 3 E

Impurity concentrations of the samples. These values were determined by Dziewior (University of Stuttgart) for the W samples and by D'Olne Campos (University of Montpellier) for the 1 samples

Sample nA (cm -

nD (cm

( n ~ - n ~ ) (cm-

~ D I ~ A Melt

-

- - -

W4 4 x 1018 3.8 x loi8 2 l0l7 0.95 stoichiometric

W7 2.9 x 10'' 2.7 x 10'' 2 x lox7 0.93 Sb-rich

W9 3 x l o r 7 2.4 x loz7 6 x 1016 0.8 Sb-rich

1 A 2.1 x l0l7 5 lo15 2 x loi7 0.025 stoichiometric

1 A' 3.1 x l0l7 1 x loi6 3 l0l7 0.033 stoichiometric

1 C 7 x 10l6 5 x lot5 6 x loi6 0.08 Ga-rich

OPTICAL OBSERVATION OF THE MAG ;NETIC FREEZEOUT EFFECT I N GaSb C3-217

Photon Energy

-

770 775 780 785 790 795 800

I I I I

01 I 1 I I I I

1.60 1.59 1.58 1.57 1.56 1.55

Wavelength h I91

FIG. I.

The A-line at zero field and at 100 kG in crystals with different impurity concentrations. In W4 the high energy line represents an unresolved doublet. Therefore the splitting

of the two lower components is somewhat larger.

that in the crystal W9 with the lower impurity concen- tration the half-width is smaller. The low energy component of the line shifts to higher energy by about 11 meV in a magnetic field of 100 kG.

In the crystals with the lower impurity concen- tration the line seems to show a somewhat more pronounced shift than the line in sample W4. This can be due to a simple experimental reason : in all three cases there seems to appear a splitting in at least three components. But only in the purer crystals can the two higher energy components be well resolved.

Figure 2 shows the magnetic field dependence of the peak energy of the line. The values of the low energy component are normally more accurate than the values of the higher energy components because

7g51

A Sample W L

6 1 ^{. t X}

E

Sample W 9 1

FIG. 2. - Magnetic field dependence of the peak energy of line A in three different samples.

these latter are less intense and therefore not so well resolved.

In W4 the energetic distance between the lower two components always seems to be somewhat larger than in W9 and W7. This is due to the unresolved overlap of the two high energy components in W4 which causes a shift as is shown in figure I. It can be clearly seen that the two low energy components originate from a splitting of the A-line with magnetic field. The third high-energy-component does not seem to have anything to do with the A-line. A crude extrapolation to zero field results in a spectral posi- tion of 785 meV. The line could be due to another acceptor with a somewhat lower hole binding energy of about 27 meV as assumed by Gouskov 141. It is labelled as F in Table I. The error in determining the energetic position of the peak is, in the case of the lower component, only 0.3 meV. In the case of the higher components the error is about 1 meV.

Figure 3 shows the split A-line at a magnetic field of 100 kG at three different excitation levels. With increasing excitation all components shift to higher energy. The low energy component broadens and gains intensity relative to the others. At the highest excitation level the two high energy components have merged with each other. It should be noted that the relative intensity of the different components depends strongly on the location of the laser spot on the crystal and changes if another point is irradiated, as can easily be seen by comparing W9 in figure 3 with W9 in figure 1.

We mentioned already that in almost every sample different acceptors and therefore acceptor recombi- nation lines are present but only line A is intense

Photon Energy hv [ meV

1

- .

7 r 715 790 7?5 8y

,

. 280mW

\. .*

I Sample W 9.1 I H = 100

k G

I

I T =

L . 2 K

I

FIG. 3. - Intensity dependence of the A-line at a magnetic field of 100 kG and a temperature of 4.2 K. In our case 1 mW is

approximately equal to

x

photons/cmz s.

enough to detect the splitting at different fields. The dominating low energy component of the B, C and E lines could be well resolved. The field dependence of this component of the B-line is shown in figure 4 and compared with the A-line in the same sample (W4). The B-line shows exactly the same shift as the A-line. No difference is detectable. The low energy peaks of the C and E-lines show the same behaviour.

In figure 5 the half-width of the A-line is given as a function of the magnetic field. To show the trend of the half-width the experimental points for sample W4 are connected with a line. At low fields up to about 25 kG the half-width decreases with increasing field. With further field increase the half-width also increases. This is due to the splitting of the band. At fields higher than 60 kG the half-width once more seems to decrease slowly or at least to remain constant.

T - 4 2 K

0 Line A 777LImeVIIH:OI

5 1'1 ⁵

Magnetic F ~ e l d H 1 kG 1

FIG. 4.

Magnetic field dependence of the peaks of the A and B-lines in sample W4.

0 O

r Sample W 4

x Sample W 9 oSarnpie 1 C

I I r I I

-J

GO 80 100

Magnetlc Field H 1 kG1

FIG. 5. - Half-width of the A-line in three different samples.

To show the trend, the experimental points of sample W4 are connected with a line.

4. Discussion. - We first identify the different investigated lines to be caused by pair transitions.

The influence of a magnetic field on an ideal conduc- tion band and on an impurity band is discussed in connection with the observed shift and splitting of the transitions in a magnetic field. Only the dominant low energy component and the central component

are discussed, because they clearly originate from the same transition, whereas the high energy component seems to be separate as already discussed in section 3.

4. I IDENTIFICATION

- Some recent publications [I]-[4] proposed to attribute the A, B, C and E-lines to either free electron acceptor transitions or to donor-acceptor pair transitions.

Our results enable one to decide unambigously between these two possibilities.

If the different dines are due to the recombination of free electrons with holes bound to acceptors they should show in a first approximation a linear shift to higher energies with increasing magnetic field, according to

e 1

= H (! ¹

^f

^g )

^(I)

2 m z c 2

This shift should be doping independent. This has been verified for example in GaAs [ 7 ] .

Not one of the lines investigated in GaSb show a linear shift at low fields and pronounced doping dependence has also been found in this region.

Also the spectral position of the zero field lines depends on the doping. The difference in position of the A-line between the purest sample, lC, (not shown in Fig. 1) and that with the largest amount of impurities, W4, is 1.1 meV. This cannot be explained with a band filling effect of the conduction band, because the Fermi level is pinned by the acceptors in this p-type material.

Therefore we can rule out an electron-acceptor transition. It is concluded that all investigated lines are due to donor-acceptor pair transitions. This agrees very well with the intensity dependence shown in figure 3. At least in the case of the crystals with larger donor concentrations, labelled with W, the initial state of the transition should not be an isolated donor state, but a donor impurity band. Therefore we have to include in the interpretation of our spectra also the effects of impurity banding and of a merging of the donor band with tail states of the conduction band as observed for example in GaAs [ll].

4 . 2 MAGNETIC

- The photon energy of a pair transition can be simply written as

f t ~ = E, - EA

ED + e2 ^-

&r (2) where E, is the band gap energy, EA is the acceptor ionisation energy, ED is the donor ionisation energy and e2/&r is a coulombic energy.

Before discussing in some detail the possible reasons

for the splitting we remember that, as shown in

figure 4, there is no, or almost no, difference between

OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT IN GaSb C3-219 the magnetic field dependence .of transitions due to

different acceptors. Therefore we neglect the influence of the magnetic field on the acceptor states (for line E this should not hold exactly, but for the following discussion we restrict ourselves to line A, which is due to a much deeper acceptor).

Three different reasons can in principle cause the splitting shown in figures 2-4.

a) The donor level is pinned at the conduction band. This. band splits in a magnetic field into a series of equidistant levels, called Landau levels, with a spacing of

GaSb has a very small effective mass of rn: = 0.042 m, 1161. Therefore the Landau splitting at 100 kG is AE,,,,,, (100 kG)

27.4 meV.

A comparison with the experiment shows that this splitting is a factor of 5-6 times larger than the observed one. Landau splitting seems to be unlikely to cause the observed effect.

b) Besides this splitting into different ~ a n d a u levels every Landau level itself splits into two components according to the two different spin states which are possible for an electron in a magnetic field. For GaSb the electronic g-value is g, ⁼ - 7.8 + 0.8 [6]. Taking this value a splitting of g, p, H = 4.5 meV can be calculated for a field of 100 kG. This sounds much more reasonable in comparison with the experimental mean value of the splitting of about 4.7 meV for the three most accurate experiments at 100 kG, as can be determined from figure 6.

Line A T : L Z K

0 Sample W 7

of 1C is too small to be explained with a g,-value of 7.8 ) 0.8. These two points are not consistent with an explanation of our results by a simple spin splitting.

(There are also other arguments which contradict a quantitative interpretation of the magnetic field shift by this model.)

c) The high donor concentration which is present at least in all samples labelled with W and the low donor ionization energy suggest that there is a strong overlap of conduction band tail states with the donor impurity band [ll]. Increasing the magnetic field from 0 to 100 kG increases the ionization energy of the donors from 2.8 meV to 11.7 meV [9], [lo]. The mean radius of the wavefunction-shrinks to 45 %

of its original size. This drastic change of the binding potential leads to a narrowing of the donor band and is assumed to create a relocalization of this band.

Figure 7 sketches this situation. This explains very well the initial narrowing of the lines up to about 20 kG as shown in figure 5. At fields higher than 100 kG once more a line narrowing should become visible because the different components are sepa- rated from each other.

Sample W 9 1

-Spin Spllttlng

FIG. 7.

Sketch of the density of states of the donor band and the conduction band tail in GaSb at zero field and at 100 kG.

FIG. 6. - Splitting of the A-line in a magnetic field for three different samples. The straight line represents the calculated

spin splitting withg,

- 7.8 & 0.8 (see ref. [6] and [12]).

A more accurate investigation of the experimental results shown in figure 6 shows that each sample has its own mean value of the splitting, which is exact within about 0.2 meV. The splitting seems to increase with increased doping. At least tbe splitting

Unfortunately there is at least one point which is not completely consistent with this explanation.

There should be a difference in the onset of the splitt-

ing between the differently doped samples. It should

start at lower fields in the lower doped ones and at

higher fields in the more heavily doped ones. Only

a reexamination of the Hall effect data and an eva-

luation of the density of states based on these data

together with a measurement of the temperature

and polarization dependence of the luminescence

can remove all doubts.

4 . 3 MAGNETIC

- Independent of the splitting, the shift of the low energy component can be explained quantitatively. Different effects contribute to this shift. Already mentioned are spin splitting of the conduction band which also effects the donor states [6], [12] and the donor ground state shift calculated by Larsen and others [9], [lo]. Besides, the narrowing of the donor impurity band should create a slight enhancement of the shift. The narrowing of the donor wavefunction results in an increase of the Coulomb term [13], [14] in eq. (2) as observed in GaAs [7].

The last two terms should give a minor. contri- bution to the shift in the case of the purest sample 1C.

In figure 8 we compare the experimental shift of the lower component of the A-line in a magnetic field with the calculated one, using the band structure parameters of Reine et al. [6] and taking into account only the shift of the donor ground state as calculated by Larsen [9] and Cabib [lo] and the spin splitting.

LIW A T = L Z K

o Sample 1 C

-Lorsen's Theory - 0 5 I ~ I u,H

P

7 7 5 0 L - - - i o LO I I 60 I I

Maanetic F~eld H I kGl

Indeed, as predicted, there is only a slight deviation of the experimental points to higher energies. All more heavily doped samples deviate more to higher energies, as also is predicted by our model.

In contrast to the results in GaAs no screening should affect the magnetic field shift because in thermal equilibrium no free electrons and neutral donors are present. The Fermi level is pinned by accep- tor states which are relatively deep and no notable thermal ionization is possible at the temperatures at which we worked.

5. Conclusion. - An investigation of the A, B, C and E luminescence lines in GaSb shows unambi- gously for the first time that all these lines are due to so-called pair transitions between a donor impurity band produced by effective mass donors and different neutral acceptors. In magnetic fields up to 100 kG line A shows a splitting into two components and all lines show a shift to higher energy which is almost independent of the ionization energy of the acceptors.

The shift is explained by Larsen's theory of a donor ground state in a magnetic field and the spin splitting of the donors. With increased concentration of impurities larger corrections due t o changes of the Coulomb term and of the broadened impurity band have to be considered.

Acknowledgments. - We thank W. Kottler and H. Krath for their help in preparing and performing the experiments. One of us (W. R.) is very indebted to the Deutsche Forschungsgemeinschaft (Sonder- forschungsbereich 67, Stuttgart) for a travel stipend and the Max-Planck-Institut for their hospitability.

We are very grateful to M. and Mrs Gouskov and

FIG. 8. - Magnetic field dependence of the A-line in sample IC.

The solid line is the theoretically predicted behaviour, taking W. Jakowetz who provided us with the GaSb crystals.

into account only the donor around state variation with magnetic The support the VO1kswagen-Stiftung is

field [9], [lo] and the spin splitting.

- gratefully acknowledged.

References

[I] BENOIT

GUILLAUME, C. and LAVALLARD, P., Phys.

Rev. B 5 (1972) 4900.

[2] JAKOWETZ, W., RUHLE, W., BREUNINGER, K. and PILKUHN, M., Phys. Stat. Sol. a 12 (1972) 169.

[3] RUHLE, W., JAKOWETZ, W. and PILKUHN, M.,

Lumines- cence of Crystals, Molecules and Solutions

edited by Ferd Williams, p. 444 (Plenum Publishing Corporation, New York) 1972.

[4] D'OLNE CAMPOS, M., GOUSKOV, A,, GOUSKOV, L. and PONS, J. C., Phys. Stat. Sol. a 2 (1970) 779.

[5] POLLAK, F. H., AGGARWAL, R. L., Phys. Rev. B 4 (1971) 432.

[6] REINE, M., AGGARWAL, R. L. and LAX, B., Phys. Rev.

B 5 (1972) 3033.

[7] WILLMANN, F., DREYBRODT, W., BETTINI, M., BAUSER, E.

and BIMBERG, D., Phys. Stat. Sol. b, to be published.

[aj ZWERDLING, s., LAX, B., BUTTON, K. J., ROTH, L. M., J. Phys.

Chem. Sol. 9 (1959) 320.

[9] LARSEN, D. M., J. Phys.

Chem. Sol. 29 (1968) 271.

[lo] CABIB, D., FABRI, E. and FIORI, G., NUOVO Cimento 10B (1972) 185.

[ l l ] POEHLER, T. O., Phys. Rev. B 4 (1971) 1223.

1121 CHERLOW, J. M., Thesis, MIT Boston (1972), unpublished.

It is shown that there is only a minor difference of less than 7 % between the conduction band g-value as taken from spin resonance experiments and a g-value taken from optical experiments including donors, for example in Si.

[13] DOEHLER, G. H., Phys. Stat. Sol. b 45 (1971) 705.

[14] HAGSTON, J. Luminescence 3 (1971) 253.

OPTICAL OBSERVATION OF THE MAGNETIC FREEZEOUT EFFECT I N GaSb C3-22 1

DISCUSSION

P. J. DEAN. - IS it reasonable to indicate a peak in the donor density of states, particularly at zero magnetic fields, shown well resolved from the conduc- tion band edge considering the large value of the product ND a: in your samples ?

D. BIMBERG. - Indeed this figure is only a rough sketch to show the separation of the donor band with increased magnetic field. The question whether there remains a minimum between the donor states and the conduction band tail depends on the donor concentration and has to be answered for every sample separately.

P. J. DEAN. - YOU report shifts in the peak energies of your bands with optical pumping despite the low ED and rather high doping levels in your samples. Do you think that these shifts are better explained by the localised band tail states concepts involved by Red-

field et 01. to explain their data an heavily Si-doped GaAs, rather than by conventional d-a pair concepts ? D. BIMBERG. - The shift of the A-band reported here was determined at 100 kG where the donor binding energy is 11-12 meV. Therefore it can be explained by the conventional change of the Coulomb term with increased excitation intensity. At zero field the intensity dependence of the peak ,is much less pronounced. This could be due to the effect proposed by Redfield.

C. BENOIT

LA GUILLAUME. - A study with circu- larly polarized light in a Faraday configuration would give a good check between the two models you dis- cuss. In addition, it is known that T I > z, a situation that could explain the lack of thermalization between the two components in a magnetic field.

D. BIMBERG. - I agree with this comment ; polari-

sation dependent experiments are in preparation.