Some aspects of vacuum ultraviolet thermoreflectance spectra

SURFACE

SCIENCE 37 (1973) 508-514 o North-Holland

SOME ASPECTS

OF VACUUM

THERMOREFLECTANCE G. GUIZZETTI*,

ULTRAVIOLET SPECTRA

L. NOSENZO **, E. REGUZZONI** Istituto

di Fisica dell’llniversitci,

Publishing Co.

and G. SAMOGGIA**

Pavia, Italy

Vacuum ultraviolet thermoreflectance spectra of Ge, GaAs, InSb and CdTe are analyzed. A direct comparison of the measured and calculated reflectivity peaks is made. The Rydberg series of the l-1 exciton is observed in the thermoreflectance spectrum of RbI and KI. The energy gap, the exciton binding energy, and the electron effective masses are then determined.

1. Introduction Modulation spectroscopy has recently reached a high degree of sophlstication for the investigation of the electronic structure of crystals, and it has also clarified the influence of an external perturbation on optical properties. Recently, several calculations of band energies in semiconductors and insulators and of bound and resonant excitonic states for energies above 5 eV have been performed. However experimental results, obtained from derivative spectroscopy, are lacking above 5 eV. We feel that an interesting field of experimental investigation could be opened by studying the vacuum uv region with the aid of modulation spectroscopy in a systematic way. For this reason we have built an optical bench which allows thermoreflectance (TR) measurements up to 9 eV in the temperature range of 4 to 400 K. We present selected spectra from which it is possible to extract information about the electronic and excitonic structure of a number of crystals. First, by using a semiempirical approach, we shall classify some structures observed in semiconductors; at the end of the paper we shall present and discuss the excitonic structure of some alkali halides. 2. Experimental apparatus Details of the experimental technique have been published elsewherel). The samples were either cleaved or chemically etched. Thermal modulation was obtained by indirect heating of the sample. * Istituto Nazionale di Fisica Nucleare, Sezione di Pavia. ** Gruppo Nazionale di Struttura della Materia de1 C.N.R. 508

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ULTRAVIOLET

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509

3. Results and discussion Many problems arise if one wants to correlate the optical structures observed in the modulation spectra (TR) of solids with excitonic or band-toband transitions. In fact, the lineshapes predicted by the one electron theory for critical points are strongly modified by the electron-hole interaction. Besides, many transitions from different regions of the Brillouin zone (BZ) can occur at nearly the same energy. Temperature modulation, on the other hand, changes the reflectivity spectrum by means of a rigid shift accompanied by broadening of the involved structures. If well separated structures are observed and their analytical shapes are known, it could be possible to identify the transitions and to determine the broadening and shift parameters. Since this is very difficult to accomplish, we shall make the following approximation : the broadening effects are assumed to be small compared with the shift. Under this assumption, thermal and wavelength modulation spectra are equivalent, except for scaling factors related to the temperature coefficients of the various gaps. Then, because peaks in reflectivity are usually taken as the position of a transition, the following procedure2) is used to determine the transition energy from the experimental AR/R versus energy curves. Reflectivity peaks correspond to the zero crossings, from positive to negative, whereas inflection points in R(w) are indicated by a nonzero, positive or negative, minimum in the derivative spectrum. These rules however, as will be seen in the following, are violated in some cases where the broadening term is larger than the shift term. We point out that, contrary to many opinions3), TR spectra are rich with information and much more similar to wavelength modulation spectra than previously reported. 3.1. SEMICONDUCTORS TR spectra of Ge, GaAs, InSb, and CdTe taken at 110 K are reported in fig. 1. Instead of analyzing each structure of every crystal separately, we tried to establish a general relation in order to correlate the observed structures with band-to-band transitions. We observe that all spectra show two prominent structures: the well known E, structure and the E; characterized by a temperature independent energy position. Besides E; and E, structures, many other transitions are common to all reported spectra. In table 1 a tentative classification of the observed structures with their energies is given. We shall apply Herman’s semiempirical rules**s) to the isoelectronic sequences Ge-GaAs-ZnSe and Sn-InSb-CdTe in order to verify that structures named with the same letter in different crystals belong to the same

510

G.GUIZZETTI

Fig. 1. Thermoreflectance

ET AL.

spectra of Ge, GaAs, CdTe and InSb at 110 K.

transition (Z&e and Sn data have been obtained from refs. 11 and 12). We used the simplified Herman’s relation E, = E,,, j + aj;1’ ,

(1)

where Ej and EA,j are the jth gaps in the polar and nonpolar compound of the same isoelectronic sequence, respectively, A, which is an index of the degree of polarity, is taken to be 0 for group IV materials, I for III-V materials, 2 for II-VI materials and 3 for I-VII meterials. It can be seen from fig. 2 that eq. (1) is well satisfied: in fact, all the transitions plotted versus L* give a straight line. We assume, then, that the energy of all the structures that satisfy eq. (l), belong to the same type of transition and is associated with the same region of the BZ. In order to assign the observed structures to specific transitions, simultaneous band calculations for all considered crystals are required. Because such calculations are not available, we shall employ the results for CdTe6),

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511

TABLE 1 Experimental

reflectivity structures and their identification for the isoelectronic Ge-GaAs-ZnSe and Sn-InSb-CdTe

sequences

Transitions Ez+6

E2

Crystal

E3

El’+6

El’

X2-& (band 4-5)

&-AI (band 4-6)

volume effect (band 4-6)

/23-k and or volume effect

volume effect (band 3-J)

4.44 5.03 6.63 3.7 4.12 5.26

5.60 5.90 7.25 4.1 + 4.3 4.6 + 4.84 5.86

5.86 6.62 8.3 + 8.46 4.9 5.4 6.67

6.04 6.9 8.85 + 9.2 5.46 5.95

6.76 7.55 9.75 6.3d 6.67 7.85

Gea

GaAs& ZnSeb SnC InSb& CbTea

7.57

The experimental results (a) are due to the authors, (b) appear in ref. 11, (c) appear in ref. 12, (d) are extrapolated in fig. 2.

ZnSe7) and GaAs*), to extend their attributions to tin, germanium, and indium antimonide. Briefly, six sets of transitions are clearly observed in the 4 to 9 eV region: we denote these sets by E,, E, +6, E;, E; +6, E3, Ed: (i) E2 - This prominent peak is caused almost entirely by X2-X1 transitions from band 4 to band 5.

I -10

y /6--9

-a

-7

3-

E*+6 E

-5

-3

21GeGaAs

ZnSe

I

0

Fig. 2.

-6

-4

24f

E’

1

k

4

Sn

0

CdTe 1

InSb 1

12

2

4

Systematic variation of energy gaps for the isoelectronic sequences Ge-GaAsZnSe and Sn-In.%-CdTe. The experimental results of ZnSe appear in ref. 11 and of Sn in ref. 12.

G.GUIZZETTl

512

ET AL.

(ii) E, +6 - This small structure is assigned to AS-A1 (band 4-6) transition. (iii) E; and E; +6 - Different band calculationsa) assigned such structures to spin-orbit split L,-L, transitions. However this last assignement does not agree with our experimental results; in fact: (a) The observed distance between the peaks is in no way correlated with the known spin-orbit splitting of the A bands. (b) Two different temperature coefficients are observed for the two bands. The shift of the first peak with temperature is less than the experimental resolution (+ 1.O x 10m4 eV/K), whereas the second one shifts with dE.JdT= -6 x 10d4 eV/K. On the other hand, M. L. Cohen has calculated that most of the contribution for these two peaks is from volume effects (band 4-6) and (band 3-6) probably broadened by A (band 4-6) transitions. (iv) E, and E4 - At these energies Cohen’s calculations show that volume effects (band 3-7) are the most important. 3.2. ALKALI HALIDES Recent TR spectral) some alkali halides. 4-

have clarified

the excitonic

and band

KI (300

structure

of

K)

:

2.

RbI 90 K --- 300 K

8

1 &

Fig. 3. (a) Thermoreflectance spectra of KI crystals at RT. (b) Thermoreflectance spectra of RbI at RT (dashed curve) and at 90 K (solid curve). In the inset, the energies of the Al, AZ, As and A4 peaks (at 90 K) are plotted versus nd2 following the Wannier formula (2) (from ref. 1).

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Let us consider the TR spectra at 90 K of RbI. A strong prominent peak (A,) at 5.7 eV is followed by a series of weaker but well resolved peaks (AZ, A,, A4) at 6.05,6.23, and 6.32 eV (fig. 3b). Let us assign all these structures to transitions of the l-r exciton with n from 1 to 4. We observe that the Wannier formula E, = E, -

L

g2n2

= E,

G _

n2

(2)

fits in an excellent

way the A,-A, series (fig. 3b) and allows the determination of the excitonic parameters. Assuming that 6~6, N 2.61, the energy of the interband edge becomes 6.36 eV, and the binding energy for the r1 exciton in the n = 1 state becomes 0.56 eV. The effective mass of the electron (m,%$, p-m,*) in the l-r conduction band is m,* -0.57 rnz. A similar spectrum has been observed in KI (T=200 K), where after the first exciton n= 1 at 5.76 eV, two weak peaks at 6.12 and 6.30 eV are seen and associated with n = 2, 3 excitonic states. By fitting with (2) these two last structures, one obtains for KI: E,=6.44 eV, G=0.68 eV and m:=0.66 mz. It appears evident that, whereas the experimental lines at n=2, 3, 4 display hydrogenic behavior, the exciton for n= 1 is much less bound than it would be according to the effective mass approximation. The reported experimental data are well predicted in a recent work ls). We observe that effective electron masses deduced from our experiments are larger (20%) than those deduced from cyclotron resonance experimentslO). Such discrepancy is acceptable if one thinks that the two sets of values are derived starting from different systems (exciton and polaron) and further effects of nonparabolicity of the conduction band could be present. References 1) L.Nosenzo, E. Reguzzoniand G. Samoggia, Phys. Rev. Letters 28 (1972) 1388; and at Eleventh Intern. Conf. on the Physics of Semiconductors, Warsaw, 1972. 2) M. Welkowsky and R. Braunstein, Phys. Rev. B 5, (1972) 497. 3) R. Zucca and Y. R. Shen, Phys. Rev. B 1 (1970) 2668. 4) F. Herman, J. Electron. 1 (1955) 103. 5) J. C. Phillips, Phys. Rev. Letters 20 (1968) 550. 6) D. J. Chadi et al., Phys. Rev. B 5 (1972) 3058. 7) J. P. Walter et al., Phys. Rev. B 1 (1970) 2661. 8) J. P. Walter and M. L. Cohen, Phys. Rev. 183 (1969) 763. 9) C. W. Higginbotham, F. H. Pollak and M. Cardona, in: Proc. Intern. Conf. on the Physics of Semiconductors, Moscow, 1966, p. 57. 10) J. W. Hodby, J. Phys. C. (Solid State Phys.) 4 (1971) L8. 11) Y. Petroff et al., Solid State Commun. 7 (1969) 459. 12) M. Cardona, K. Shaklee and F. H. Pollak, Phys. Rev. 154 (1967) 696. 13) S. Antoci and G. F. Nardelli, Surface Sci. 37 (1973)

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Discussion Question (by Y. PETROFF): In the calculation of the binding energy of the exciton of RbI, you use the same dielectric constant for the n = 2, 3,4 levels where the exciton radii vary roughly between approximately 10 8, and 40 A. Are you sure that this is valid? Speaker’s reply (by G. SAMOGGIA): We think that the values of effective masses, binding energies, are reliable. In fact using 8 w 8, in eq. (2) is justified when the binding energy of the nth excitonic state is much larger than the energy of the optical phonons. This is the case for levels corresponding to n = 2. 3 exciton states.