Electroreflectance and thermoreflectance spectra of SnS

Solid State Communications, Vol. 45, No. 5, pp. 445--448, 1983. Printed in Great Britain.

0038-1098/83/050445 - 0 4 $03.00/0 Pergamon Press Ltd.

ELECTROREFLECTANCE AND THERMOREFLECTANCE SPECTRA OF SnS F. Luke§, J. Humli~ek and E. Schmidt Faculty of Science, Purkyn~ University, 611 37 Brno, Czechoslovakia (Received 1 April 1982; in revised form 9 September 1982 by M. Cardona) The electroreflectance and thermoreflectance spectra of SnS single-crystals have been studied from 1.2 to 4.8 eV in polarized light for the E IIa and E IIb polarizations. The energy values of critical points have been determined from the experimental curves. TIN SULPHIDE BELONGS to the group of orthorhombic I V - V I semiconductor compounds with a distorted rocksalt structure of the form M X where M is either Sn or Ge and X is either S or Se. This group of materials has been intensively investigated within the last several years. The absorption spectrum of SnS was studied by Lambros et al. [ 1 ] near the absorption edge (indirect transition) in the temperature range of 100-300 K. Reflection spectra were reported by Eymard and Otto [2] in the range 0.5-28 eV at room temperature and by Sobolev and Doneckich [3] in the energy range 1.5-12 eV at 77 and 293 K. Bleckan et al. [4] studied the electroreflectance (ER) spectra of p-type crystal with p ~ 103-104 g2 cm from 1.2 to 4.2 eV in unpolarized light. These measurements were later repeated in polarized light by Tyagai et al. [5] from 1.2 to 2.5 eV. The only known band structure of SnS, especially of its valence band, was published by Parke and Srivastava [6]. In this paper we present the electroreflectance (ER) and thermoreflectance (TR) spectra of p-type singlecrystals of SnS from 1.2 to 4.8 eV. We studied two crystals - C with p ~ 0.26 ~2 cm and D with p ~ 0.08 ~2 cm. All measurements were performed with polarized light. ER spectra were studied with the help of the electrolyte technique at room temperature [ 12]. 0.5 n solution of KC1 served as the electrolyte. TR spectra were studied at 100 and 320K. We use throughout this paper the same notation for the axes of SnS as Eymard and Otto [2], namely a ~> b (both are in the cleavage plane), c being perpendicular to the cleavage plane. Figure 1 shows the ER spectra of the crystal C for both polarizations E IIa and E IIb. Figures 2 and 3 present the ER spectra of the crystal D for both polarizations from 1.2 to 2.0 eV and from 2.0 to 4.8 eV, respectively. In both figures several curves for different values of d.c. bias and a.c. modulation voltages are given.

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Fig. 1. Electroreflectance spectrum of SnS singlecrystal C for the E 11a ( . . . . . ) and E IIb ( - - ) polarizations; d.c. bias -- 0.9 V, a.c. modulation potential 0.8 V. The following conclusions may be drawn from our experimental results. (1) Some structures appear only for certain orientation and practically disappear for the others. Especially the one near 1.30 eV (labeled Eo) is strong for the E IIa polarization and almost disappears for E IIb. It means that the corresponding transition is allowed for the E IIa polarization but forbidden for E IIb, in agreement with previous conclusions [5]. This structure is evidently due to the Franz-Keldysh effect at the Mo critical point and represents the first direct interband transition. Unfortunately, no information is available concerning the modulating electric field in our samples. In particular, we cannot use the spectral shapes to decide whether the transition is at a two- or three-dimensional minimum Mo. Nevertheless, the critical point energy can be determined fairly reliably and precisely using the procedure suggested by Humli~ek and Schmidt [7]. The low-field conditions of Aspnes [8] seem to be well

445

446

ELECTROREFLECTANCE AND THERMOREFLECTANCE SPECTRA OF SnS

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Vol. 45, No. 5

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fulfilled for this structure. Namely, the magnitude of the ER signal is small (AR/R < 10 -4) and depends linearly on the applied voltage, while the spectral shape does not change with voltage. The energy value Eo is given in Table 1 together with other energy values of the critical points. The energies E l , E 2 and E3 were determined in the same way as E0, while the remaining E i values were only estimated as the energies corresponding to the pronounced extrema on the ER curve. We have good reasons to believe that these values do not differ more than by -+ 0.05 eV from the true energies of the critical points. (2) The structure near 1.59eV (Ea) is more

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Fig. 5. Thermoreflectance of SnS single-crystal C for the E 11b polarization: - - . , 100K; . . . . . , 3 2 0 K . complicated. It is allowed for the E [] b polarization but there appears a small contribution from this transition even for the E [[a direction(Fig. 1). A remarkable difference exists between the form of the ER curves near El obtained at large negative d.c. bias and at a positive one. In the former case the ER curve resembles strongly typical Franz-Keldysh type ER effect probably at an Mo critical point. The curves obtained for the C crystal are almost all (even for slightly positive bias) of this type while for the crystal D there appears a strong positive signal near 1.59 eV which increases with increasing positive bias. On this main broad peak (denoted as A1 in Fig. 2) is clearly superimposed the Franz-Keldysh type ER curve, at least at lower d.c. voltages. We believe that the main positive broad peak characterized the band population (BP) effect described earlier for heavily doped Ge [9] (here denoted as the "electron distribution

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ELECTROREFLECTANCE AND THERMOREFLECTANCE SPECTRA OF SnS

447

Table 1. Critical points energies E i of SnS single-crystal for the E IIa and E II b polarizations determined from the reflectance (R ), electroreflectance (ER ) and thermoreflectance (TR ) spectra Transition

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ER [4]

unpolarized light

ER (this work) E IIa

295K

TR (this work)

E IIb

E IIa

295K

EII b

100K

320K

100K

320K

1.279

1.180

1.339 1.41 ?

1.204 1.279

1.344

1.282 1.617 2.13 2.32

1.562 1.89 2.21

2.92 3.38

2.77 3.46

4.35

4.24

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1.30

1.32

1.30 + 0.005

1.62 2.30

2.30

2.90 (3.7) 4.01 4.36

2.355 + 0.007 2.82

3.81 4.14

3.70 4.15

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2.34 2.69 2.95

2.22

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4.14

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4.50

2.78

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a From the peaks on the reflectivity curve. effect"). This effect occurs for heavily doped n-type (p-type) semiconductor where the transition ends (starts) at the minimum (maximum) of the conduction (valence) band with high concentration of electrons (holes). This conclusion is supported by the following arguments: (a) the BP effect is more pronounced for the crystal D, i.e. the sample with higher free hole concentration, where the Fermi energy has to be close to the maximum of the valence band as estimated according to the parameters of SnS given by Albers et al. [ 10] ; (b) the BP effect increases with increasing positive d.c. bias as should occur for a p-type sample. We may conclude from the above mentioned facts that the E~ transition starts at the maximum of the valence band. According to Parke and Srivastava [6] the maximum of the valence band is situated at the point X of the BZ. Since the band structure of the conduction band is not yet known we cannot make any conclusion about the correctness of this band structure calculation. (3) The small peak near 1.9 eV (denoted as A2 in Fig. 2) which is quite evident on several curves may be attributed to the BP effect characterizing the E2 transition as well. This identification is not as sure as that for the Ej transition, but this structure is well reproducible and it appears at the same conditions as that (A~) near the E1 transition. (4) It follows from Fig. 3 that even in the range

2.0-4.8 eV there appears a very broad "background" in the ER spectrum of the crystal D for both polarizations on which the Franz-Keldysh component is superimposed. This background is according to our estimation expressed by the dotted line for the curve characterizing the EII b polarization in Fig. 3. We assume that this background is due to the BP effect for the same reasons as discussed above in connection with the E1 transition. This BP effect appears for both polarizations with approximately the same amplitude. We conclude that it originates from the E 4 transition. The critical point energies as obtained from our ER curves are summarized in Table 1. The values Eao a n d El1 are not certain -- the ER effect is rather weak. Several values found in the literature are also given in the table for comparison. Figures 4 and 5 demonstrate typical curves AR/R = f ( E ) of the TR spectra obtained for the E 11a and EII b polarizations for the crystal C. The results obtained for the crystal D were practically the same. We found: (1) the sharp minima denoted byA in Figs. 4 and 5 correspond to the steep increase of reflectance caused by multiple reflections in the regions beyond the absorption edge. The energies Ea (Table 1) correspond approximately to the absorption edge. They are only about 0.05 eV for the EII a and 0.12 eV for the EII b

448

ELECTROREFLECTANCE AND THERMOREFLECTANCE SPECTRA OF SnS

polarizations higher than the indirect band gaps found by Lambros et al. [ 1 ]. The interpretation of the peak B for the E [Ib polarization (it is better developed on the curve obtained at 320 K) is not yet clear. Its energy is very close to Eo for the E IJa polarization but this transition which was identified from the ER measurements as the first direct transition is forbidden for the EI[ b polarization as follows from our ER measurements. The preliminary conclusion is that even this peak is caused by the interference of light inside the sample. (2) We have evaluated the TR spectra shown in Figs. 4 and 5 in the same way as those of GeS [ 11 ]. It means that the energy values given in Table 1 denote the negative-going zero crossings of the dependence A R / R = f ( E ) or the position of the estimated pronounced structure in the TR spectra corresponding to the point between the local maximum and subsequent local minimum. Comparing the values of the assumed critical points as found from the analysis of the ER spectra at 295 K with those obtained from the TR spectra at 320 K we may conclude that the agreement between both systems of values is surprisingly good. This conclusion is true especially at low energies where we may expect rather small broadening parameters as really follows from the analysis of our ER spectra. Considering the fact that the E i values determined from the TR spectra were obtained at T = 320K while those obtained from the ER spectra were obtained at T = 295 K (it means that the E i values determined from the ER spectra should be about 0.012 eV higher) we may conclude that the agreement between the ER and TR values for the Eo, E~ and E2 transitions is excellent irrespective to the fact that the TR values were determined according to rather rough rule while the ER values were obtained with the help of the rigorous procedure. This is an important conclusion with respect to the analysis of the TR spectra of other semiconductors at least those belonging to the same family of materials. Since we mentioned already in case of GeS [ 11 ] that it is difficult, if at all possible, to obtain the ER spectra of some layer-type materials of the group under consideration, then the TR spectra represent very important means how to study the band structure of these materials.

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(3) Similarly as in the ER spectra we see small contributions from the E1 and E2 transitions for the E 14a polarization in the TR spectra as well. They are more pronounced at 100 K. (4) The energies E i decrease with increasing temperature and from our results concerning the pronounced E i values we may deduce that the temperature coefficients of all critical point energies are roughly the same within the experimental error and independent of the polarization. The mean value dE~/dT = -- (5 -+ 1) × 10 -4 eVK-x is only slightly higher than that of the indirect band gap according to Lambros et al. [ I] which give-- 4.37 x 10-4eVK -1 for Ella a n d - 4.05 x 10 -4 eVK -1 for EII b, respectively. A more detailed analysis of both ER and TR spectra presented here will only be possible when the optical constants of SnS as well as the complete band structure are known with reasonable accuracy.

REFERENCES 1.

A.P. Lambros, D. Geraleas & N.A. Economou, J.

2.

Phys. Chem. Solids 35,537 (1974). R. Eymard & A. Otto,Phys. Rev. B16, 1616

3. 4. 5. 6. 7.

8. 9. 10. 11. 12.

(1977). V.V. Sobolev & V.I. Doneckich, Neorgani(eskije materialy VIII, 688 (1972) (in Russian). D.I. Bleckan, A.M. Evstigneev, I.F. Kopinec, I.M. Migolinec & V.A. Tyagai, Neorgani(eski/e materialy X, 735 (1974) (in Russian). V.A. Tyagai, V.N. Bondarenko, A.N. Krasiko, D.I. Bleckan & V.I. ~eka, Fizika Tverdogo Tela 18, 1433 (1976)(in Russian). A.W. Parke & G.P. Srivastava, Phys. Status Solidi (b) 101, K31 (1980). J. Humli4ek & E. Schmidt, Phys. Status Solidi (b) 107, K105 (1981). D.E. Aspnes, Surf. Sci. 37,418(1973). F. Luke~ & J. Humli~ek, Phys. Rev. B6, 521 (1972). W. Albers, C. Haas, H.J. Vink & J.D. Wasscher, Appl. Phys. Suppl. 32, 2220 (1961). F. LukeL E. Schrnidt & A. Lacina, Solid State Commun. 39, 921 (1981). M. Cardona, K.L. Shaklee & F.H. Pollak, Phys. Rev. 154, 696 (1967).