UDC 548.0:535+535.343

PHYSICS

V. V. SOBOLEV

CONTOUR OF EXCITON ABSORPTION LINES IN A CUPROUS OXIDE CRYSTAL

(Presented by Academician B. P. Konstantinov, 12 IV 1965)

In solid-state spectroscopy the cuprous oxide crystal occupies a place as important as the hydrogen atom in atomic spectroscopy. Many works have been devoted to a comprehensive study of the optical properties of Cu\(_2\)O (see \((^1)\)). However, such fundamental quantities as the absorption coefficient, half-width, oscillator strength, and also the line contour have been studied insufficiently. At the same time, it is precisely for Cu\(_2\)O that the theory of the contour \((^2,^3)\) and the absorption magnitudes \((^4,^5)\) of exciton lines have been developed in greatest detail.

Fig. 1. Contour of exciton lines of the “yellow” series of cuprous oxide:
\(a\)—\(T = 160^\circ\) K; \(b\)—\(T = 4.2^\circ\) K

In the long-wavelength edge region of the fundamental absorption of the Cu\(_2\)O crystal, two groups of hydrogen-like (\(n \ge 2\), \(n\) is the quantum number) absorption lines are observed, which by their position in the spectrum are usually called the “yellow” and “green” series and are located in the regions 6150–5700 and 5500–5400 Å, respectively.

Using a recording spectral setup with dispersion \(D = 3.2\) Å/mm at temperatures \(T\) equal to 160 and 4.2° K, we investigated the spectral distribution of the absorption coefficient of mono- and polycrystals of Cu\(_2\)O (crystal thickness \(d = 5\)–300 \(\mu\)) \((^{6-9})\). The exciton lines rise above the background of continuous absorption of indirect band-to-band transitions; the absorption in the background is approximately the same as in the lines. The monotonic course of the continuous background outside the lines was extrapolated by us into the region of the lines by a smooth curve under the assumption that the lines do not overlap one another. The extrapolation of the continuous background is reliable in the region of the “yellow” series and less reliable (because of the large half-width of the lines) in the region of the “green” series.

In the spectral distribution of absorption of very perfect single crystals of Cu\(_2\)O we have found lines of the “yellow” series with \(n = 1, 2, 3, 4, 5, 6\) at \(T = 160^\circ\) K (Fig. 1a) and with \(n = 1, 2, 3, 4, 5, 6, 7\) at \(T = 4.2^\circ\) K

Fig. 2. Contour of the exciton lines of the “green” series of cuprous oxide: \(a\)—\(T = 160^\circ\) K; \(b\)—\(T = 4.2^\circ\) K

Fig. 3. Dependence of the logarithm of the area of the contour of the lines of the “yellow” series on the square of the quantum number: \(a\)—\(T = 160^\circ\) K; \(b\)—\(T = 4.2^\circ\) K

(Fig. 1b), and also lines of the “green” series with \(n = 2, 3\) at \(T = 160^\circ\) K (Fig. 2a) and with \(n = 2, 3, 4\) at \(T = 4.2^\circ\) K (Fig. 2b) (see Tables 1 and 2; \(K_{\max}\)—absorption at the maximum; \(\Delta \nu\)—half-width; \(\delta = (2\nu_{\max} - \nu_- + \nu_+) : (\nu_+ - \nu_-)\)—asymmetry of the bands, where \(\nu_{\max}\) and \(\nu_-\), \(\nu_+\) are the frequency values at the band maximum and at the half-width level, respectively; \(f\)—oscillator strength).

Table 1

Values of \(K_{\max}\) (cm\(^{-1}\)), \(\Delta \nu\) (cm\(^{-1}\)), \(\delta\), and \(f \cdot 10^6\) for the lines of the “yellow” and “green” series

The main features of the line contours are as follows: 1) all lines of the “green” series and many lines of the “yellow” series are strongly asymmetric, with the asymmetry of the lines decreasing sharply with increasing \(n\); according to the theory [2], this indicates that the character of the interaction of excitons with phonons changes with increasing \(n\) from weak to strong, while the exciton energy bands have a maximum at \(K = (0,0,0)\); 2) lowering the temperature from 160 to 4.2° K leads, for the “yellow” series, to a strong, complex, and different change in the absorption intensity for different lines; the regularity empirically found by us, \(\lg f \sim -n^2\), differs sharply from the theoretically predicted \(f \sim (n^2 - 1) : n^5\) [4, 5] (Fig. 3 presents the dependences of the logarithms of the areas of the line contours \(S_n\) on \(n^2\); \(S_n \sim f\)); 3) the values of \(K_{\max}\) upon lowering the tem-

temperatures increase strongly for \(n > 3\) and change little for \(n = 2\) and 3; the small value of \(K_{\max}\) characterizes the optical transitions of the “yellow” and “green” exciton series, respectively, as forbidden and weakly allowed, in agreement with the theory \({}^{(4)}\).

In \({}^{(10–12)}\), at \(T\) equal to 77.3, 20, and 4.2°K, the line contour of the “yellow” series with \(n = 2, 3, 4\) and of the “green” series with \(n = 2, 3\) of polycrystalline Cu\(_2\)O was studied (see also \({}^{(13)}\)). A careful comparison of our results with the data of \({}^{(10–12)}\) shows the following: 1) the values of \(K_{\max}\) coincide in the different works at \(T \ge 77.3^\circ\)K, but at \(T = 4.2^\circ\)K and \(n > 3\) they differ considerably; 2) the values of \(\Delta \nu\) according to \({}^{(11,12)}\) are considerably smaller than our \(\Delta \nu\); asymmetry was found in \({}^{(11,12)}\) only on the lines with \(n = 2\) and 3; 3) the values of \(f\) in \({}^{(11,12)}\) agree with the theory \({}^{(4)}\) owing to the failure in \({}^{(11,12)}\) to detect the asymmetry of many lines. It is necessary to emphasize the great importance, for studies of line contours, of the dispersion of the spectrometer and the quality of the samples*.

Institute of Applied Physics
Academy of Sciences of the MSSR

Received
8 III 1965

REFERENCES

1. E. F. Gross, UFN, 63, 575 (1957); 76, 433 (1962).
2. J. Toyozawa, Progr. Theor. Phys., 20, 53 (1958); Suppl. 12, 111 (1959); Techn. Rep. JSSP, S. A., No. 79 (1963).
3. L. P. Dzhoб, Fiz. tverd. tela, 5, 1577 (1963).
4. R. J. Elliot, Phys. Rev., 108, 1384 (1957); Proc. Intern. Conf. Semicond. Phys., Prague, 408, 1960.
5. D. Dresselhaus, Phys. Rev., 106, 76 (1957).
6. V. V. Sobolev, Tr. I Vsesoyuzn. soveshch. po fotoelektrich. i optich. yavleniyam v poluprovodnikakh. Kiev, November 1957, Publishing House of the Academy of Sciences of the Ukrainian SSR, 1959, pp. 42, 151.
7. E. F. Gross, V. V. Sobolev, Abstracts of the 13th Conference on Spectroscopy, Leningrad, July 1960, Publishing House of the Academy of Sciences of the USSR, 1960.
8. V. V. Sobolev, Abstract of Candidate’s Dissertation, Leningrad, 1962.
9. V. V. Sobolev, Abstracts of the 15th Conference on Spectroscopy, Minsk, July 1963, Publishing House of the Academy of Sciences of the BSSR, 1963.
10. I. S. Gorban, Optika i spektroskopiya, 9, 759 (1960).
11. S. Nikitine, J. B. Grun, M. Siskind, J. Phys. Chem. Solids, 17, 292 (1961); J. Phys. Rad., 22, 176 (1961).
12. J. B. Grun, Thesis, Strasbourg, 1962 (Rev. d’Optique, 218).
13. L. N. Zverev, M. M. Noskov, M. Ya. Shur, Fiz. tverd. tela, 11, 2643 (1960).

* The dispersion of Gorban’s spectrometers \({}^{(10)}\) is smaller than ours by approximately a factor of 10, and that of Nikitine, Grun, and Siskind \({}^{(11,12)}\) by a factor of 5. It is possible that many discrepancies between the results of works \({}^{(10–12)}\) and our data arise because of insufficient dispersion and the polycrystalline nature of the Cu\(_2\)O samples in works \({}^{(10–12)}\).