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 2 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 g 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- 2 ing solid PbTe and SnT e sources. The growth tem- o 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 1 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 op temp erature co ecientofE is much smaller than the g exp ected value of dE =dT . The temp erature where this g op minimum in E o ccurs coincides with the temp erature g of minimum resistivity for all samples in the band inver- sion region. Fig. 4 plots the temp erature of minimum op resistivity and minimum E as a function of Sn con- g 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 op dE =dT =0 . The solid line is the band crossing tem- g 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- g III Conclusion cause the E value taken from the transmission sp ectra g op is the \optical energy gap" E , which takes into ac- The Burstein-Moss shift in the PbSnTe system, due to g 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.