Solid State Communications, Vol. 64, No. 8, pp. 1167-l 169, 1987. 00381098/87 $3.00 + .OO Printed in Great Britain. 0 1987 Pergamon Journals Ltd.

FAR-INFRARED QUASI-LOCAL MODES OF ZnTe IN CdTe

Lu Wei, Ye Hongiuan, Yu Zhiyi, Zhang Suying, Fu Ying, Xu Wenlan and Shen Xuechu

Lab for Infrared Physics, Shanghai Institute of Technical Physics, Academia Sinica, China

(Received 24 June 1987 by M. Cardona)

We report the very far-infrared absorption spectra of the mixed-crystals Cd,_,Zn,Te for small x in the temperature range of 4.2 K-l 50 K and the wavenumber region of 20cm- -lOOcm-‘. The quasi-local mode induced by ZnTe in CdTe and CdTe-like 2TA two-phonon creations are observed, to be best of our knowledge, for the first time. The frequencies of the modes are estimated by using the mass-defect model combined with Green’s functions calculations. Besides, the temperature dependence of the absorption peak is well explained in the light of the characteristics of the modes. _

ALTHOUGH THERE HAS BEEN quite a lot of work on the electrical properties and the behavior of the optical phonons for the bulk material and thin layers in superlattice and MQW structures, as well as the mixed crystals Cd,_,Zn,Te [l-4], detailed infor- mation about the dynamic properties of Zn in the mixed crystals Cd,_,Zn,Te in the very far infrared region is not available in the literature. Study of mixed crystals with very small concentrations of ZnTe should act as a bridge between the theory of the mixed crystals and that of the impurity in the binary com- pound semiconductors which have made big progress in recent years [5-71. We report here the induced phonon modes of Zn and ZnTe in CdTe with very small concentration of ZnTe in the very far infrared region, and interpret them by means of defect lattice dynamics. The temperature effect of the phonon absorption is also explained and used for the analysis of the transitions.

The samples used in the experiments were cut from pure mixed crystals Cd, _,Zn,Te with the nomi- nal compositions of x = 0.01 and 0.02 and mechanic- ally polished. The far infrared transmission spectra were measured in the wavenumber region of 20 to lOOcm-’ with a resolution of 2cm-’ in the tempera- ture region from 4.2 to 150 K with a Nicolet NIC- 200SXV Fourier transform spectrometer.

We plot in Fig. 1 the absorption spectra and their temperature dependence for sample Cdo,99ZQ.oo, Te. They were calculated from the measured transmission spectra by the formula T = (1 - R)2 exp (- ad)/(l - R2 exp (- 2ad)). It is seen from the figure that there are two absorption peaks located at 54 cm-’ (A) and 72 cn- ’ (B), respectively, below the optical phonons of the mixed crystal. In addition, the lower frequency

5- iB 72 cm-’

1 I

4- I I

3-

T E 2- ,o

a

I-

150k

IOOk

50k

4.2 k , 80 100

w (cm-‘)

Fig. 1. The far-infrared absorption spectra of the quasi-local mode and the 2TA(A) transition for the sample Cd,,99Z~.0, Te at different temperature norma- lized to the values at 4.2K.

peak A is much narrower than peak B. While peak B (72cm-‘) is associated with the CdTe-like 2TA phonon process, which occurs also in pure CdTe with lower intensity, peak A (54crn-‘) is observed, to our knowledge, for the first time in Cd,_,Zn,Te. We attri- bute it to the quasi-local mode of ZnTe in CdTe by comparison with similar behavior observed for Si in Ge [8], B and Li in Si [9, lo], B in GaAs [ll, 121 and MnTe in CdTe [13, 141, and also according to the

1167

1168 QUASI-LOCAL MODES OF ZnTe IN CdTe Vol. 64, No. 8

following discussion. We did not see the disorder and defect induced TA band mode absorption probably due to the low concentration of ZnTe and the isoelec- tronic substitution of Cd by Zn.

Shen and Cardona have explained the quasi-local mode associated with the TA phonon band of Si in Ge [8] and B-Li in Si [9] from the view point of the nearly two dimensional critical point of the TA phonons at the K-W-U line of the Brillouin zone and with the calculation of the frequency [15] and amplitude 1 Uj’ for the impurity induced vibration. We continue to discuss here the physical origin of the mode in some different way. We start from the eigenequation of the lattice vibration

H(u) = w2]u),

where

(1)

ukx = &&

H kk’xx‘ = $kk’xx’ imk mk

ub is the component of vibrational amplitude in x direction at k-th atom, &Kxx’ is the xx’ element of the interaction matrix between k’-th and k-th atoms, mk the mass of k-th atom, w the frequency. The Green’s function related to matrix H is defined as

G(o’)(H - 02Z) = I, (2)

where Z is the unit matrix. By constructing a new set of normalized orthogonal basis with the recursion method [ 16, 171 one can transform the matrix H into a tri-diagonal matrix H’ and calculate the imaginary part of the diagonal elements of the Green’s function which is actually the local density of the states (LDOSs) for lattice vibrations [16, 171.

As an approximation, the Zn atoms in Cd,_,Zn,Te can be regarded as isolated impurities since x < 0.02 in our case, thus we can write the interaction matrix for the zincblende structure with only two parameters v0 and a,. Here 2v, + ~1~ is the central force constant for the interaction between atoms if only the nearest neighbour interaction is considered. Using of the method described in refe- rence [15] for building the lattice and adjusting the force parameters to fit the critical points of the density-of-states for CdTe with a recursion calcula- tion, we get the force parameters ~1~ = 2.10 x 1 O4 dyn cm-’ and v,, = 1.57 x 104dyn cm-’ for CdTe. The calculated LDOS of atom Cd in CdTe is shown in Fig. 2 as curve 1. Substituting an atom Cd by Zn and making use of the same force parameters for Zn-Te as that for Cd-Te, i.e, with the mass-defect equal-force- constant model, we have obtained now the LDOS of atom Zn in CdTe, which is also shown in Fig. 2 as

curve 2. This figure demonstrates that there is a peak for the LDOS of atom Zn in CdTe at 53.2cm-’ which is just above that of that for the critical point W of the TA phonon states for pure CdTe. In addition, the calculated LDOS at 53.2cm-’ for the atoms around the impurity Zn in Cd’_,Zn,Te with small x decays with the increase of distance measured from the impu- rity center and approaches quickly that of Cd in pure CdTe. It is known that the LDOS of an atom is proportional to the square of the amplitude for the vibration of the atom, thus the curves shown in Fig. 2 represent virtually the vibrational behavior of the lat- tice and the mode at 53.2 cm-’ is partially localized. In addition, the calculated frequency agrees well with the experimental value of 54 cm-‘. Hence we attribute the absorption peak at 54cm-’ shown in Fig. 1 to the quasi-local mode induced by Zn or ZnTe in CdTe. As a justification of our interpretation and calculation, we get also a local mode for Zn in CdTe at 170.9 cm-’ which is again in good agreement with the experimen- tal result of 172.8 cm-’ observed in the reflection spec- trum of the same sample. Furthermore, the central force constant derived from ~1~ and v,, 10.5 x 104dyn cm-’ also agrees with the value of 9.9 x 104dyn cm-’ obtained by fitting the experimental reflection spec- trum to the theoretical one as calculated with a ran- dom element isodisplacement model.

In order to understand further the physical origin of peaks A and B, we plot the temperature dependence of the relative integrated strength for the peaks of the sample Cdo,99Zn,,,l Te in Fig. 3, where “+” and “0”

170.9 cm-’

c

53 2cm-’

1

,Al,r- ! 150 200

L 50 100

w (cm-‘)

Fig. 2. The local density of states for Cd in pure CdTe (curve 1) and Zn (curve 2) in Cd, _,Zn,Te for very small x.

Vol. 64, No. 8 QUASI-LOCAL MODES OF ZnTe IN CdTe 1169

044 T (k)

Fig. 3. The integrated strength of the absorption peaks vs. temperature. Solid line represents the calculated curve, “ + ” and “0” are the experimental results for peak A and B, respectively.

indicate the experimental strengths for peaks A and B, respectively. It can be seen that the strength of the peak A does not change appreciably with temperature while that of the higher frequency peak B increases clearly with rising temperature. Therefore, the absorp- tion peak A has to be assigned to one phonon tran- sition and B to multiphonon processes. Supposing the peak B is caused by the CdTe-like 2TA transition, the strength S(T) should be a function of temperature as follows:

S(T) 1 + 2F(o, T) - = S(4.2) 1 + 2F(o, 4.2K)’

(3)

with

F(o, T) = 1

exp @o/kT) - 1.

The calculated S(T)/S(4.2 k) is shown in Fig. 3 as a solid line which indicates that the dependence of the absorption strength on the temperature for peak B agrees with the behavior expected for the 2TA tran- sition. Besides, the frequency of the peak, 72cm-’ = 2 x 36 cm-’ as given by the experiment, corresponds

to the critical point A of TA phonon band, which confirms the attribution of the peak B to 2TA(A) transition. Furthermore, it is also worthwhile to point out the composition dependence of the absorption strength of the peaks, the integrated strength of peak A increases one and a half times and that of peak B about 100% for increase of x from 0.01 to 0.02. This shows that they are really related to the existence of Zn or ZnTe, which, in other words, means that they are induced by or associated with the impurity Zn.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

REFERENCES

D.L. Olego, L.P. Faurie, S. Sivananthan & P.M. Raccah, Appl. Phys. Lett. 47, 1172 (1985). D.L. Olego, P.M. Raccah & J.P. Faurie, Phys. Rev. B33, 3819 (1986). D.L. Peterson, A. Petrou, W. Giriat, A.K. Ramdas & S. Rodriguez, Phys. Rev. B33, 1160 (1986). S. Perkowitz, R. Sudharsanan & S.S. Yom Bull. Amer. Phys. Sot., 32, 727 (1987). M. Vandevyver & D.N. Talwer, Phys. Rev. B21, 3405 (1980). D.N. Talwar, M. Vandevyver, K. Kunc & M. Zigone, Phys. Rev. B24, 741 (1981). L. Genzel, T.P. Martin & C.H. Perry, Phys. Status Solidi B62, 83 (1974). S.C. Shen & M. Cardona, Solid State Commun. 36, 327 (1980). M. Cardona, S.C. Shen & S.P. Varma, Phys. Rev. B23, 5329 (1981). J.F. Angress, A.K. Goodwin & S.D. Smith, Proc. R. Sot. London, A308, 111 (1968). J.F. Angress, G.A. Gledhill & R.C. Newman, J. Phys. Chem. Solids 41, 341 (1980). G.A. Gledhill, S.S. Kudhail, R.C. Newman & G.Z. Zhang, Intern. J. Infrared and Millimeter Wave 2, 849 (1981). S.C. Shen, H.J. Ye, L.X. Kang & F.X. Tao, Acta Physica Sinica 34, 1573 (1985) (in Chinese); Chin. Phys. Lett. 2, 209 (1985). S.C. Shen, J.H. Chu & H.J. Ye, 17th Znternat. Conf on Physics of Semicond., San Francisco, p. 1189 (1984). S.C. Shen, C.J. Fang, M. Cardona & L. Genzel, Phys. Rev. B22, 2913 (1980). Y. Fu, W.L. Xu 8z Z.B. Zheng, Solid State Com- mun. 62, 163 (1987). S.Y. Wu & Zheng Zhaobo, Acta Physica Sinica 32, 46 (1983).