Band Crossing Evidence in Pbsnte Observed by Optical Transmission

Brazilian Journal of Physics, vol. 29, no. 4, Decemb er, 1999 771

Band Crossing Evidence in PbSnTe Observed by

Optical Transmission Measurements

1 2 2 2 2

S. O. Ferreira , E. Abramof ,P. Motisuke ,P. H. O. Rappl , H. Closs ,

2 2 2

A. Y. Ueta , C. Boschetti , and I. N. Bandeira ,

1: Dep. F sica, UniversidadeFederal de Vicosa,

36571-000, Vicosa, MG, Brazil

2: Instituto Nacional de Pesquisas Espaciais,

C.P. 515 - 12201-970 S~ao Jos e dos Campos, SP, Brazil

Received February 8, 1999

Using high quality epitaxial layers, wehave obtained direct evidence of the band inversion in

the Pb Sn Te system. The samples, covering the whole comp osition range, were grown by

1x x

molecular b eam epitaxy on 111BaF substrates. A minimum in the resistivity as a function

of temp erature was observed for all samples with Sn comp osition 0:35 x 0:70. In the

same samples and at the same temp erature, temp erature dep endent optical transmission

measurements have revealed a change in signal of the energy gap temp erature derivative,

a direct evidence of the band inversion. However, the temp erature for which the inversion

o ccurs is not the one exp ected by the band inversion mo del. This discrepancy is supp osed to

b e due to the Burstein-Moss shift caused by the relatively high hole concentration observed

in these samples.

band edge states inverted, up to the SnT e value. The I Intro duction

Sn comp osition for which the band inversion should

Lead-tin telluride is a narrow gap semiconductor which

o ccur varies from x 0:35 to x 0:70 as the tem-

have b een investigated for manyyears and applied

p erature increases from 4 to 300 K. However, it is very

mainly in the fabrication of infrared 3-14 m photo

dicult to determine the band edge structure near and

detectors and dio de lasers [1,2]. The growth of epi-

beyond the band inversion region, since only high car-

taxial layers and multi-layer structures like sup erlat-

rier concentration samples can b e obtained due to the

tices and multi-quantum wells of narrow gap IV VI

deviation from the stoichiometry [9]. The energy gap of

comp ounds by molecular b eam epitaxy MBE has im-

Pb Sn Te has b een exp erimentally determined only

1x x

proved the basic research of quantum e ects in these

for the range x<0:25. The Burstein-Moss shift, caused

materials [3,4]. New interesting research p ossibilities

by the high hole concentration, which is observed in

were op ened by alloying the binary and also ternary

the samples with higher tin comp osition x> 0:30,

lead salts with rare-earth elements mainly Eu and Yb

imp oses diculties in the determination of the \real"

to pro duce comp ounds with higher energy gaps and

gap by optical-absorption measurements [10,11]. In this

their resp ectivemulti-layer heterostructures [5]. Re-

comp osition range, the only available E exp erimental

cently, the growth of lead salts on silicon substrates us-

data has b een determined by tunneling measurements

ing uoride bu er layers, in order to obtain the mono-

in Al Al O SnT e structures [12]. The "real" E

2 3 g

20 3

lithic integration of lead salt detector arrays with silicon

of pure SnT e p 10 cm is 0.18 eV [12], while

read-out circuits, has also received much attention [6,7].

the \optical energy gap" was found to b e near 0.5 eV

[10,11].

According to the band inversion BI mo del [8], the

Pb Sn Te energy gap E initially decreases as the Using In doping to reduce carrier concentration,

1x x g

Sn comp osition increases, and vanishes for an inter- Takaoka et al. [13] have determined the e ective masses

mediate alloy comp osition. Further increasing the Sn and energy gap as a function of tin comp osition across

comp osition, the energy gap starts to increase, with the the band-inversion region by the far-infrared magne-

772 S.O. Ferreira et al

the b ehavior observed in the resistivity and mobility. toplasma metho d. They have observed much heavier

e ective masses in these dop ed samples as compared

with the values exp ected for the undop ed Pb Sn Te

1x x

and an energy gap which do es not go to zero. In their

conclusions, they state that it is dicult to say if this

b ehavior is essential for PbSnTe or a result of the In

doping. Although the BI mo del is widely accepted, di-

rect observation for the Pb Sn Te system has not

1x x

b een achieved yet, mainly due to the lack of go o d qual-

ity samples with x> 0:30 and with low carrier concen-

tration.

II Exp erimental

Recently,wehave rep orted on the growth of high

quality PbSnTe samples, covering the whole comp o-

sition range [14]. The PbSnTe layers were grown on

Figure 1. Resistivity as a function of temp erature for two

typical PbSnTe samples in the band inversion region.

111BaF substrates by molecular b eam epitaxy us-

ing solid PbTe and SnT e sources. The growth tem-

p erature was b etween 250 and 300 C and the nal

thickness was ab out 4m. The samples were charac-

terized by high resolution x-ray di raction, temp era-

ture dep endent resistivity, Hall mobility and infrared

transmission. The lms grown using stoichiometric

PbTe and SnT e sources have shown a hole concentra-

17 3

tion b etween p =1 10 cm , for Pb Sn Te,to

0:85 0:15

19 3

p =2 10 cm , for SnT e. This p value, observed

for SnT e, is at least one order of magnitude lower than

the one previously rep orted in the literature. Sucha

lower carrier concentration increases the hall mobilities

of all samples and makes easier their optical character-

ization. Details ab out the electrical characterization of

these layers have b een published elsewhere [15].

Another imp ortant feature is a well de ned mini-

mum in the temp erature dep endent resistivity and a

corresp onding maximum in the mobility of all samples

Figure 2. Optical energy gap as a function of temp erature

with 0:35 x 0:70, as can b e observed in the Fig. 1

for two PbSnTe samples outside the BI region.

for twotypical PbSnTe layers.

According to the BI mo del, this comp osition range

corresp onds to that where band crossing should o ccur.

Since this b ehavior can b e observed only for the samples To clarify this p oint, the temp erature dep endence of

in the band crossing range, it seems that this minimum the energy gap for all samples, mainly that covering the

in the resistivity is related to the band inversion. For BI region, was measured. The energy gap was deter-

the samples in this range, the energy gap should rst mined from the transmission sp ectra, whichwere mea-

reduce with decreasing temp erature, as it happ ens for sured using a Fourier transform infrared sp ectrometer

PbTe. But after the band inversion it should increase in the range from 4500 to 800 cm for temp eratures

with further decrease in temp erature, the b ehavior of between 5 and 300 K . Fig. 2 shows the energy gap as

SnT e. This change in the signal of the energy gap tem- a function of temp erature for two samples outside the

p erature co ecientdE =dT , would b e the reason for BI region. g

Brazilian Journal of Physics, vol. 29, no. 4, Decemb er, 1999 773

shown Fig. 3.

The optical energy gap rst reduces, reaches a min-

imum, and than starts to increase. Again, due to the

relatively high carrier concentration of the samples, the

temp erature co ecientofE is much smaller than the

exp ected value of dE =dT . The temp erature where this

minimum in E o ccurs coincides with the temp erature

of minimum resistivity for all samples in the band inver-

sion region. Fig. 4 plots the temp erature of minimum

resistivity and minimum E as a function of Sn con-

tent for all our MBE samples, together with the band

crossing temp erature predicted from the BI mo del.

Figure 3. Optical energy gap as a function of temp erature

for twotypical PbSnTe samples in the BI region. The lines

are guides to the eye.

Figure 4. Temp eratures of minimum resistivity and of

dE =dT =0 . The solid line is the band crossing tem-

As exp ected, the energy gap increases with tem-

p erature calculated from the BI mo del.

p erature, for the sample with x =0:15, while it de-

creases, for the sample with x =0:82. But, in contrast

to mo del, the absolute value of the temp erature co ef-

cients dE =dT were very di erent. This o ccurs b e-

III Conclusion

cause the E value taken from the transmission sp ectra

is the \optical energy gap" E , which takes into ac-

The Burstein-Moss shift in the PbSnTe system, due to

count the Burstein-Moss BM shift, due to the band

the high hole concentration, pro duces a strong change

lling. For the Pb Sn Te layer the BM shift is

in the temp erature dep endence and absolute value

0:85 0:15

17 3

negligible p =3 10 cm and the measured values

of the optical energy gap. The change in signal of

of E and dE =dT are the ones exp ected from the lit-

dE =dT , for Pb Sn Te samples with 0:35 x

g g

1x x

erature [16]. On the other hand, for the sample with

0:70, is a direct exp erimental evidence of the band in-

19 3

x =0:82 p =1 10 cm , the BM shift is 230

version in this alloy. The coincidence b etween the op-

meV at 80 K, and dE =dT is a combination of the

tical and electrical measurements shown in Fig. 4, in-

changes in the energy gap and in the p osition of the

dicates that the minimum previously observed in the

Fermi level. Preliminary calculations of the absorption

resistivity curves of our samples is related to the band

co ecient, using a mo del prop osed by Anderson [17],

crossing. The discrepancy b etween the measured and

which takes the BM shift into account, explain the re-

predicted temp eratures, which can b e observed in Fig.

=dT observed for samples with high hole duction in dE

4 is not yet clearly understo o d, but we b elieve that it

concentration.

is also related to the e ect of high carrier concentration

for the samples The temp erature dep endence of E of these samples, since the BI mo del do es not takein

in the band inversion region is completely di erent, as account the BM shift.

774 S.O. Ferreira et al

Acknolegments 8. J. Dimmock, I. Melngailis and A.J. Strauss, Phys.

Rev. Lett. 16, 1193 1966.

9. T. C. Harman, J. Nonmetals, 1, 183 1973.

This work has b een partially supp orted by \Con-

10. E.G. Bylander, J.R. Dixon, H.R. Riedl and R.B.

selho Nacional de Desenvolvimento Cient co e Tec-

Scho olar, Phys. Rev. 138, A873 1965.

nol ogico-CNPq" and \Fundac~ao de Amparo APesquisa

11. R.B. Scho olar, H.R. Riedl and J.R. Dixon, Solid

do Estado de S~ao Paulo-FAPESP".

State Commun. 4, 423 1966.

12. L. Esaki and P.J. Stiles, Phys. Rev. Lett. 16,

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