Determination of the reduced effective mass in zinc selenide

J. Phys. Chem. Solids

PergamonPress 1967. Vol. 28, pp. 1623-1624.

TECHNICAL Determination

of the reduced effective mass in zinc selenide

(Received 26 January 1967) THE EFFECT of

strong electric fields on the absorption edge of polycrystalline thin films of zinc selenide and zinc telluride has been investigated at room temperature. For ZnSe the value which was obtained for the reduced effective mass is in good agreement with the value calculated from known effective masses of electrons and holes deduced from other measurements. In a number of semiconductors, it has been possible to derive some information on the energy band structure and the reduced effective mass from measurements of the shift of the fundamental optical absorption edge under the influence of strong electric fields.‘r - 3, The theory of this effect has been developed by FRANZ(~)and KELDYSH@) for periodical lattice structures of high crystalline perfection. However, more recently measurements were also carried out on amorphous selenium(e*7) and cadmium selenide.(s) These experiments indicated that thermally evaporated films behave similarly to bulk samples. In this paper is reported an investigation into the effect of strong electric fields on the absorption edge of polycrystalline thin films of zinc selenide and zinc telluride, resulting in a quantitative determination of the reduced effective mass in ZnSe. An explicit expression for the reduced effective mass, m*, as a function of the field-induced shift of the absorption edge, AEo/F2, is given by l/m* = -where p is the logarithmic slope of the absorption edge. By measuring the shift AEQ as a function of the electric field F, the reduced effective mass defined by 1 1 __=-+m* me

1 mh

Printed in Great Britain.

NOTES

can be obtained provided that the value of ,9 is known. From optical transmission measurements on thin films of ZnSe and ZnTe values of the absorption coefficient a as a function of photon energy were derived using the formula exp( - ad) = T/(1 -R)=, where T is the transmittance, R the reflectance, and d the thickness of the sample. Corrections for the reflection losses were calculated for the wavelength range in which the index of refraction was knowr~.(~)Figure 1 shows the absorption coefficient of polycrystalline films of ZnSe and ZnTe as a function of photon energy. Using the function ln a = (j?kv/kT) + constant we obtain j3= 0.207 for ZnSe. This is smaller by a factor of 10 than in bulk material. The determination of j3 in ZnTe films is rather uncertain because of the existence of an absorption band near 5500 A.(lO) The maximum shift of the absorption edge under the influence of an electric field occurs in ZnTe at 5660 8. The measurements of the field-induced change in the optical absorption coefficient a were carried out at room temperature with samples prepared by vacuum evaporating high purity grade ZnSe or ZnTe onto glass substrates. Aluminium electrodes were used, evaporated on the surface of the semiconductor films. The distances between the electrodes varied between 100 and 150 pm for different samples. All measurements were made using a Spexf/6*8 Czemy-Turner monochromator equipped with a Bausch and Lomb grating (7500 A blaze, 1200 grooves/mm) and an EM1 6256 photomultiplier-detector. In order to measure the small changes in light intensity caused by the electric field, a P.A.R. model JB-5 phase-sensitive detector was employed. The high voltage applied perpendicular to the transmitted light beam was in the form of a unidirectional square wave modulated at a frequency of 1 kcs. The highest fields applied to the samples were about 1.3 x lo6 V/cm which was calculated from the applied voltage and electrode distance.

1624

TECHNICAL

NOTES

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FIG 2. Dependence of the absorption edge shift on electric field in polycrystalline films of ZnSe and ZnTe.

(aV)

FIG. 1. Absorption coefhcient of vacuum evaporated films of ZnSe and ZnTe.

The shift of the absorption edge as a function of the applied electric field in polycrystalline films of ZnSe and ZnTe is shown in Fig. 2 from which it will be seen that the shift is proportional to the square of the electric field. With the measured values of AEG/F2 and B the calculated reduced effective mass in ZnSe is m* = 0.13( f O.Ol)mc. Within the limits of experimental error this is in good agreement with m* = O-133 ma obtained from the electron effective mass m, = 0.17 m,, measured by MARPLE(~~) and a value of the hole effective mass mh = 0.6 m,. Because of the uncertainty of j3 we were not able to determine the reduced effective mass in ZnTe. Measurements of the electroabsorption in ZnTe single crystals are now underway. authors would like to thauk B. ROBERTS, A. J. WALDORF and H. WEBER for their technical assistauce in this w&k.

Acknowledgements-The

(V/CM)

Diwision of Applied Physics, National Research Council, Ottawa, Canada

H. D. RICCIUS R. TURNER

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H., Phys. status solidi 4, K21 (1964). 3. hOVA A. and HANDLER P., Phys. Rew. 137, A1857

(1965). 4. FRANZ W., Z. Nuturf. 13a, 484 (1958). 5. %LDYsH L. V., Soviet Phys. JETP 7, 788 (1958). 6. STUKE J. and WEISER G., Phys. Status Solidi 17, 343 (1966). 7. DRKW~ R. E., Appl. Phys. Lctt. 9,347 (1966). 8. POEI-ILERT. 0. and ABRAHAMD.. . Phvs. _ Lett. 23. 523 (1966). 9. MARPLE D. T. F., J. uppl. Phys. 35, 539 (1964). 10. ZHOLKEVICHG. A., Soviet Phys. solid St. 2, 1009 (1960). 11. MARPLE D. T. F., J. appl. Phys. 35, 1879 (1964).