PHYSICS

F. P. Kesamanly, S. G. Kroitoru, Yu. V. Rud’,
V. V. Sobolev, N. N. Syrbu

ENERGY BAND STRUCTURE OF SOME CRYSTALS OF THE GROUP \(A^{II}B^{IV}C_2^{V}\)

(Presented by Academician B. P. Konstantinov, 21 I 1965)

The discovery of a great analogy in the nature of the chemical bond in semiconductors with the sphalerite, wurtzite, and chalcopyrite structures made it possible in a number of works \((^{1,2})\) to assume the presence of many common features also in the energy band structure. In \((^2)\), by group-theoretical methods and by the method of equivalent orbits, under the assumption that the extrema of the valence bands and of the conduction band are located at the point \(K=(0,0,0)\), the band structure of semiconductor compounds of type \(A^{II}B^{IV}C_2^{V}\) with the chalcopyrite structure was calculated: the lowest conduction band is simple, while the uppermost valence band consists of three bands; the two upper valence bands are due to the anisotropy of the crystal-lattice field \((\Delta_{\mathrm{cr}})\), and the third band to spin-orbit splitting \((\Delta_{\mathrm{co}})\). According to rough estimates of \((^2)\), at the point \(K=(0,0,0)\) for CdSnAs\(_2\), \(\Delta_{\mathrm{co}}\approx 0.45\) eV, and \(\Delta_{\mathrm{cr}}\approx 0.01\text{--}0.03\) eV.

In recent years, owing to the intensive development of the theory of the energy bands of crystals in \(\vec{k}\)-space and the establishment of a direct connection between reflection spectra in the region \(E>E_g\) and the band structure, studies of the reflection spectra of crystals in the region of intrinsic absorption have begun to develop successfully \((^{3-7})\).

In the reflection spectra of crystals of groups \(A^{IV}\) and \(A^{III}B^{V}\) in the region 1–6 eV, as a rule, an intense short-wavelength band is observed in the region 4–6 eV and a less intense doublet band in the region 1–4 eV \((^{3-7})\). The structure of the reflection spectra of crystals of groups \(A^{IV}\) and \(A^{III}B^{V}\) is explained in good agreement with theory from the point of view of direct allowed interband transitions: the short-wavelength band at the point \(X\) \([K=(1,0,0)]\), and the doublet long-wavelength band at the point \(L\) \([K=(1,1,1)]\), the doublet character of the reflection bands being due to spin-orbit splitting of the upper valence band at the point \(L[\Delta_{\mathrm{co}}(L)]\), and the value \(\Delta_{\mathrm{co}}(L)\approx 0.67\Delta_{\mathrm{co}}(\Gamma)\).

Fig. 1. Reflection spectrum of a ZnSnAs\(_2\) crystal

In the present work we have undertaken a study of reflection spectra in the region 1–6 eV at \(T=293^\circ\) K of ZnSnAs\(_2\), ZnSiP\(_2\), and ZnSiAs\(_2\) crystals. In the spectral distribution of the reflection coefficient we found two intense maxima in each crystal: \(\lambda\) 265 and \(\sim 600\) mµ (ZnSnAs\(_2\)); \(\lambda\) 280 and 330 mµ (ZnSiP\(_2\)); \(\lambda\) 275–295 and 370 mµ (ZnSiAs\(_2\)), with the peak at \(\lambda 600\) mµ in ZnSnAs\(_2\) having a doublet structure in the form of two maxima at \(\lambda 550\) and \(\lambda 650\) mµ (Figs. 1 and 2).

By analogy with the considerations of \((^2)\), we have made an estimate of the quantities \(\Delta_{\mathrm{co}}(L)\) (see Table 1): according to our qualitative estimates, \(\Delta_{\mathrm{co}}(L)\) for

$ \mathrm{ZnSnAs_2} $ proved to be 5–10 times larger than for $ \mathrm{ZnSiP_2} $ and $ \mathrm{ZnSiAs_2} $; therefore, in the reflection spectra, because of the comparatively large half-width of the reflection peaks, the doublet structure of the long-wavelength reflection maximum of $ \mathrm{ZnSiP_2} $ and $ \mathrm{ZnSiAs_2} $ crystals may also fail to appear. In the character of the spectral distribution of the reflection coefficient and in the positions of the bands of the reflection spectrum, the crystals $ \mathrm{ZnSnAs_2} $, $ \mathrm{ZnSiP_2} $, $ \mathrm{ZnSiAs_2} $, on the one hand, and crystals of the groups $ \mathrm{A^{IV}} $, $ \mathrm{A^{III}B^V} $, on the other hand, these semiconductor substances proved to be very similar. Therefore it may be considered that the structure of the reflection spectra of the crystals of the group $ \mathrm{A^{II}B^{IV}C_2^V} $ studied by us is due to direct allowed interband transitions at points of the Brillouin zone analogous to the points $L$ and $X$ of crystals of the groups $ \mathrm{A^{IV}} $ and $ \mathrm{A^{III}B^V} $—$L'$ and $X'$, respectively (see Table 1).

Fig. 2. Reflection spectrum of crystals $ \mathrm{ZnSiP_2} $ and $ \mathrm{ZnSiAs_2} $

Table 1

Values of the interband separations at the points $X'$ and $L'$ ($E_{X'}$ and $E_{L'}$),
$\Delta_{\mathrm{CO}}(L)$ and $E_g$ (in eV)

Thus, the great overall and detailed similarity of the reflection spectra of the crystals $ \mathrm{ZnSnAs_2} $, $ \mathrm{ZnSiP_2} $, $ \mathrm{ZnSiAs_2} $ and of the groups $ \mathrm{A^{IV}} $, $ \mathrm{A^{III}B^V} $ convincingly testifies to the validity of the assumptions of work $^{(1)}$ concerning the very great similarity of the structures of the energy bands and of the nature of the chemical bond of compounds of the groups $ \mathrm{A^{II}B^{IV}C_2^V} $ and $ \mathrm{A^{IV}} $, $ \mathrm{A^{III}B^V} $.

The authors express their gratitude to Prof. D. N. Nasledov for his support of the present work.

Physicotechnical Institute
named after A. F. Ioffe
Academy of Sciences of the USSR

Institute of Applied Physics
Academy of Sciences of the MSSR

Received
15 I 1965

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