Saturation of optical absorption in CdS single crystals

The absorption saturation of CdS single crystals was investigated in the Urbach region. It was shown that the threshold behaviour of the absorption coefficient is caused by recharging of the shallow acceptors, and the absorption edge has exponential character both at low and high pumping intensities...

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Дата:	1999
Автори:	Malysh, N. I., Kunets, V. P., Valiukh, S. I., Kunets, Vas. P.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 1999
Назва видання:	Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/117859
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Saturation of optical absorption in CdS single crystals / N. I. Malysh, V. P. Kunets, S. I. Valiukh, Vas. P. Kunets // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 31-34. — Бібліогр.: 9 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	irk-123456789-1178592017-05-28T03:03:02Z Saturation of optical absorption in CdS single crystals Malysh, N. I. Kunets, V. P. Valiukh, S. I. Kunets, Vas. P. The absorption saturation of CdS single crystals was investigated in the Urbach region. It was shown that the threshold behaviour of the absorption coefficient is caused by recharging of the shallow acceptors, and the absorption edge has exponential character both at low and high pumping intensities. The calculation method of nonlinear transmission dependencies was proposed. Using the known formulae one can minimize the value of root mean square deviation of the measured data from the calculated ones in the whole region of the light intensities. 1999 Article Saturation of optical absorption in CdS single crystals / N. I. Malysh, V. P. Kunets, S. I. Valiukh, Vas. P. Kunets // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 31-34. — Бібліогр.: 9 назв. — англ. 1560-8034 PACS 78.66.H http://dspace.nbuv.gov.ua/handle/123456789/117859 535.34,621.315.592 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The absorption saturation of CdS single crystals was investigated in the Urbach region. It was shown that the threshold behaviour of the absorption coefficient is caused by recharging of the shallow acceptors, and the absorption edge has exponential character both at low and high pumping intensities. The calculation method of nonlinear transmission dependencies was proposed. Using the known formulae one can minimize the value of root mean square deviation of the measured data from the calculated ones in the whole region of the light intensities.
format	Article
author	Malysh, N. I. Kunets, V. P. Valiukh, S. I. Kunets, Vas. P.
spellingShingle	Malysh, N. I. Kunets, V. P. Valiukh, S. I. Kunets, Vas. P. Saturation of optical absorption in CdS single crystals Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Malysh, N. I. Kunets, V. P. Valiukh, S. I. Kunets, Vas. P.
author_sort	Malysh, N. I.
title	Saturation of optical absorption in CdS single crystals
title_short	Saturation of optical absorption in CdS single crystals
title_full	Saturation of optical absorption in CdS single crystals
title_fullStr	Saturation of optical absorption in CdS single crystals
title_full_unstemmed	Saturation of optical absorption in CdS single crystals
title_sort	saturation of optical absorption in cds single crystals
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	1999
url	http://dspace.nbuv.gov.ua/handle/123456789/117859
citation_txt	Saturation of optical absorption in CdS single crystals / N. I. Malysh, V. P. Kunets, S. I. Valiukh, Vas. P. Kunets // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 1. — С. 31-34. — Бібліогр.: 9 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT malyshni saturationofopticalabsorptionincdssinglecrystals AT kunetsvp saturationofopticalabsorptionincdssinglecrystals AT valiukhsi saturationofopticalabsorptionincdssinglecrystals AT kunetsvasp saturationofopticalabsorptionincdssinglecrystals
first_indexed	2025-07-08T12:54:46Z
last_indexed	2025-07-08T12:54:46Z
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fulltext	31© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 1. P. 31-34. The optical absorption saturation (OAS) in semiconduc- tors was observed in band-to-band [1], exciton [2] tran- sitions and in transitions to band tail states [3]. In the first case OAS was explained by the occupation of the extrema of allowed bands with nonequilibrium charge carriers (the dynamic Burstein-Moss effect), in the sec- ond case, it was a result of competition between several mechanisms, such as the occupation of the states within bands, the multi-body interaction between free carriers, screening of excitons and others. And the third case was attributed to recharging the charged defects responsible for formation of Urbach absorption edge. Previously we have investigated in details the non- linear absorption of CdSe single crystals in a broad spec- tral range of the fundamental absorption edge [3, 4]. In this paper the OAS in CdS was studied in the Urbach part of the absorption edge. Accounting similarity of the physical properties for these semiconductors, it can be assumed that the features of the non-linear absorption in them are also similar. This work is aimed to check this assumption. The samples of intentionally undoped 50-300 µm thick CdS single crystals were investigated. Pumping was PACS 78.66.H; UDK 535.34,621.315.592 Saturation of optical absorption in CdS single crystals N. I. Malysh, V. P. Kunets, S. I. Valiukh, Vas. P. Kunets Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Kyiv, 252028, Ukraine, phone 265 62 82 Abstract. The absorption saturation of CdS single crystals was investigated in the Urbach region. It was shown that the threshold behaviour of the absorption coefficient is caused by recharging of the shallow acceptors, and the absorption edge has exponential character both at low and high pumping intensities. The calculation method of nonlinear transmission dependencies was proposed. Using the known formulae one can minimize the value of root mean square deviation of the mea- sured data from the calculated ones in the whole region of the light intensities. Keywords: absorption, saturation, recharging, acceptor. Paper received 01.12.98; revised manuscript received 31.03.99; accepted for publication 19.04.99. carried out using dye-laser with the spectral range of 450- 750 nm, line halfwidth of 0.5 � and pulse duration 6 ns. The valence band of hexagonal direct-bandgap CdS is split by the crystal field and spin-orbit interaction into three subbands. The transition from the upper subband to the conduction band is allowed in the polarizationr E ⊥Ñ, and the transitions from two lower subbands are allowed in polarizations r E ⊥Ñ and r E Ñ. Hence, inves- tigations both polarizations of the laser light in respect to the crystal optical axis were used. In the whole investigated spectral range of the CdS absorption edge for polarizations r E ⊥Ñ and r E Ñ the dependence of transmission, T, on the light intensity, I, has the form similar to that presented in Fig. 1. It can be seen that at weak light fluxes (section I) T does not de- pend on I up to some critical value, starting from which a sharp increase of transmission is observed (section II) followed by the gradual approach to the saturation at high intensities (section III). In this case, the same as in CdSe single crystals, transmission does not reach the lim- itation level due to Fresnel reflection, which indicates that the residual (non-photoactive) absorption is present. N. I. Malysh et al.: Saturation of optical absorption in CdS single ... 3 2 SQO, 2(1), 1999 In stationary mode of exciting the semiconductor in the region of band-to-band or impurity-to-band transi- tions, OAS can be described in frames of the two-level model [1]. In the Urbach region of the spectrum, howev- er, the two-level model does not provide satisfactory de- scription of OAS. In this case, a satisfactory agreement with the experiment can be achieved by using the phe- nomenological model [5], assuming that at some critical value of the non-equilibrium carrier concentration the step-like reduction of the absorption coefficient K oc- curs from the initial value Ê Í to the final value Ê Â . Un- der these conditions near the illuminated face of the sam- ple the domain of bleached part of the volume is formed, which moves to the opposite face. In this case, with ac- count of Gaussian distribution of intensity across the laser beam cross-section, for three characteristic parts of intensities the non-linear dependence T(I) can be de- scribed analytically by the set of three equations [5]: T R K dH= − −( ) exp( )1 2 , I I≤ l (1) ( )T R K d I I K K I IH l B H l K KH B = − −       × + −               ( ) exp / 1 1 12 0 0 , I I I hl ≤ ≤ (2) ( )T R K d I I K K I IH l B H l K KH B = − −       × + −               ( ) exp / 1 1 12 0 0 , I > I h (3) where R is the reflectivity, I l , I h are intensities related to the beginning and the end of the bleaching process, re- spectively. The two latter magnitudes are connected with each other by the equation: ( )[ ]I AI K K K d Ih l Í Â Â l= = + −       1 1exp . (4) The equations (1)-(4), in principle, make it possible to calculate the T(I) dependencies and to compare them with experimentally measured ones, as it was done in the paper [5]. The method of this calculation is based on the fact that all the intensity interval can be divided condi- tionally into three above mentioned parts: of low, inter- mediate and high intensities (Fig. 1). In this method, in the first section, the only fitting parameter Ê Í is used for the calculation of transmission. In the second and third sections, as far as independent fitting parameters Ê Â and I l are used. The first one (Ê Â ) can be estimated approx- imately from the experimental value of transmission in the third section, that is at high intensities (Fig. 1, sec- tion III). The second one ( I l ) is estimated from the in- tensity corresponding to the intensity change by a factor of å. Then, by variation of these two parameters the fit- ting of the calculated curve to the experimental one is carried out. The fitting quality in this technique is as- sessed by the best visual coincidence of the calculated curve with the experimental dependence. This is a draw- back of the above technique, since the mathematical cri- terion describing the degree of coincidence of the theo- retical curve with the experimental one is absent. The second drawback is the calculation complexity. In this paper another method is suggested for the cal- culation of the T(I) dependence which makes it possible to adjust the calculated curve to the experimentally mea- sured one using the least-mean square technique with the help of modern personal computers. In this method, for every experimental value of transmission the abnor- mality coefficient is calculated and random values are neglected [6]. The essence of this method consists in the following. The measured dependence T(I) is approximated by the function determined by the equations (1)-(3). By anal- ogy with the well-known and widely used least-squares method (LSM) [7, 8] the unknown parameters are deter- mined from the condition of minimization of the weight- ed mean least-square error [6]: ( )( )σ γ2 2 0 = − = ∑ k Í B i k m F K K I y, , l (5) where F(K H , K B , I l ) is a function given by equations (1)- (3), y i is the experimental value of the sample transmis- sion at intensity I i , γ k are set positive weight coefficients. The coefficients γ k should necessarily be introduced because absolute magnitudes of measurement errors de- pend strongly on the intensity of light, I. Unlike the conventional methods for the determina- tion of unknown coefficients based on the approxima- tion of the calculated curve by the polynomial regres- I, W/ñm 2 10 7 10 6 10 5 10 4 T 10 -1 10 -2 10 -3 I II III Fig. 1. Typical dependence of transmission of CdS on the in- tensity of excitation irradiation. Dots represent the experimental curve and the line is the calculation result according to equa- tions (1)-(3). The thickness of the sample is 257 µm, excitation wavelength is 5163 nm, r E ⊥Ñ. N. I. Malysh et al.: Saturation of optical absorption in CdS single ... 33SQO, 2(1), 1999 sion or by the set of orthogonal functions, in this prob- lem some difficulties arise related to a rather cumber- some form of the function F(K H , K B , I l ). In the conven- tional LSM one should take the particular derivatives of the function (1)-(3) in respect to unknown parame- ters and equate them to zero. Then by solving the ob- tained set of equations the sought coefficients should be determined. However, this method is not the best one, since in this case a set is obtained of three nonlinear equa- tions which are very complicated and do not provide a correct solution at wrong setting of initial approxima- tions. In the described method the function σ 2 is con- structed according to the equation (5) depending para- metrically on the values of K H , K B , I l . Then, using the direct search minimization technique [8, 9] and setting the initial approximations for K H , K B , I l , the minimum of σ 2 is found. To obtain the global minimum, the ex- tremum searching procedure is repeated at different val- ues of initial approximations. After that, the minimum value is chosen from all previously obtained values of σ 2 which corresponds to the global minimum. The ad- vantage of this technique is that all unknown fitting pa- rameters are determined from the condition of the low- est value of σ 2 in the whole intensity interval, and not in separate parts of it, as was done previously [5]. Besides, this technique makes it possible to use modern personal computers for fitting, hence the calculation process may be automated and the time of parameter determination can be reduced essentially. To exclude random data from the initial selection the assessment of abnormality of all measured results is car- ried out [6]. The coefficient of abnormality V i is calcu- lated from the equation V y F K K Ik i H B= − ( , , ) /l σ , (6) where the value of function F(K H , K B , I l ) is determined at I = I i , and compared with the reference data [6]. At large values of V i , the y i value is considered as the outli- er and the calculation is repeated with this point being removed. The calculated in such a way curves agrees quantita- tively well with the experimental results (Fig. 1). This fact proves that blooming in CdS, the same as in CdSe, is described by the phenomenological model [5] and is related to recharging of shallow acceptors. In calcula- tions of the dependence Ò(I) for CdS in frames of the two-level model the satisfactory agreement of the calcu- lation with the experiment was not achieved. This fact proves again that the OAS mechanism in the Urbach part of the CdS spectrum is not related to occupation of empty states in the respective band tails with the non- equilibrium charge carriers. Experimental dependencies Ò(I), measured at the set of wavelengths allow us also to determine the values of Ê Í and Ê Â and to establish the spectral dependence of the absorption edge in CdS at low (I < I l ) and high (I > I l ) intensities. In both cases it has an exponential character (Fig. 2) corresponding to the Urbach rule. Thus, in the Urbach region of the spectrum of CdS single-crystal the sharp decrease of the absorption coef- ficient was found at high intensities of laser irradiation. It can be satisfactorily described in frames of the phe- nomenological model of shallow acceptor recharging, when anomalously fast reduction of the absorption co- efficient occur. This is confirmed by the similar charac- ter of absorption saturation processes in both semicon- ductors. Spectral dependencies of linear and non-linear absorption coefficients obey the exponential law. References 1. V. P. Gribkovski, Teoriya pogloshcheniya i ispuskaniya sveta v poluprovodnikakh (Theory of absorption and emission of light in semiconductors), Nauka i Tekhnika, Minsk (1975) (in Russian). 2. I. Broser, J. Gutowsky, Optical nonlinearity of CdS // Appl. Phys. (b), 46, p. 1-17 (1988). 3. N. R. Kulish, M. P. Lisitsa, N. I. Malysh, B. M. Bulakh, Nelinei- nost� kraevogo pogloscheniya CdSe (Nonlinearity of edge absorp- tion in CdSe) // FTP, 24(1), p. 25-28 (1990) (in Russian). 4. B. M. Bulakh, B.R. Djumaev, N. E. Korsunskaya et al., Vliyanie otzhiga v parakh sobstvennykh komponentov na pogloschenie sveta v oblasti Urbakhovskogo kraya CdSe (Influence of anneal- ing in the vapour of intrinsic components on the light absorption in the Urbach edge region of CdSe) // FTP, 25(11), p. 1946-1951 (1991). 5. N. R. Kulish, N. I. Malysh, V. N. Sokolov, Prosvetlenie monokri- stallov CdSe v oblasti kraya sobstvennogo pogloscheniya pri neod- norodnom fotovozbuzhdenii (Blooming in CdSe single crystals near the intrinsic absorption edge at nonuniform photoexcitation) // Kvantovaya Electron., s. 38, p.66-82, Kiev (1991). 6. K. G. Rego, Metrologicheskaya obrabotka rezultatov tekh- nicheskikh izmereniy (Metrological processing of results of tech- nical measurements), Tekhnika, Kiev (1987) (in Russian). 7. A. B. Bartkiv, Ya. T.Grynchishin, A. M. Lomakovich,Yu. S. Ram- skiy, Turbo Pascal: algoritmy i programy: chiselni metody v fizyt- Fig. 2. Spectral dependencies of absorption coefficient in CdS at low (1) and high (2) intensities. r E ⊥Ñ. ln [K , cm -1 ] N. I. Malysh et al.: Saturation of optical absorption in CdS single ... 3 4 SQO, 2(1), 1999 si ta matematytsi (Turbo Pascal: algorithms and programs: nu- merical methods in physics and mathematics), Vishcha Shkola, Kiev (1992) (in Ukrainian). 8. V. P. Dyakonov, Spravochnik po algoritmam i prgrammam na yazyke beisik dlia personalnykh EVM (Manual on algorithms and programs in the Basic language for PC), Nauka, Moscow (1987) (in Russian). 9. H. -I. Kunze. Metody fizicheskikh izmereniy (Methods of physi- cal measurements), Mir (1989) (Russian translation).

Saturation of optical absorption in CdS single crystals

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