Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range

Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range

Based on the experimental data obtained, we performed the theoretical investigation of the external reflectance coefficients of uniaxial optically anisotropic polar ZnO single crystals subjected to the action of a high uniform magnetic field that is parallel to the crystal axis С and the surface...

Повний опис

Збережено в:
Бібліографічні деталі
Дата:2008
Автори: Venger, E.F., Evtushenko, A.I., Melnichuk, L.Yu., Melnichuk, O.V.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2008
Назва видання:Semiconductor Physics Quantum Electronics & Optoelectronics
Онлайн доступ:http://dspace.nbuv.gov.ua/handle/123456789/118594
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range / E.F. Venger, A.I. Evtushenko, L.Yu. Melnichuk, O.V. Melnichuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 6-10. — Бібліогр.: 11 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-118594
record_format dspace
spelling irk-123456789-1185942017-05-31T03:09:29Z Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range Venger, E.F. Evtushenko, A.I. Melnichuk, L.Yu. Melnichuk, O.V. Based on the experimental data obtained, we performed the theoretical investigation of the external reflectance coefficients of uniaxial optically anisotropic polar ZnO single crystals subjected to the action of a high uniform magnetic field that is parallel to the crystal axis С and the surface under the condition that E⊥B (the Voigt configuration, Fig. 1). For the first time, we have found the regions in the external reflection spectra of ZnO single crystals, where new oscillations appear which are due to the effect of a high uniform magnetic field. A possibility of solving the direct and inverse problems in such a case is demonstrated. 2008 Article Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range / E.F. Venger, A.I. Evtushenko, L.Yu. Melnichuk, O.V. Melnichuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 6-10. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS 78.40.-q http://dspace.nbuv.gov.ua/handle/123456789/118594 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 Based on the experimental data obtained, we performed the theoretical investigation of the external reflectance coefficients of uniaxial optically anisotropic polar ZnO single crystals subjected to the action of a high uniform magnetic field that is parallel to the crystal axis С and the surface under the condition that E⊥B (the Voigt configuration, Fig. 1). For the first time, we have found the regions in the external reflection spectra of ZnO single crystals, where new oscillations appear which are due to the effect of a high uniform magnetic field. A possibility of solving the direct and inverse problems in such a case is demonstrated.
format Article
author Venger, E.F.
Evtushenko, A.I.
Melnichuk, L.Yu.
Melnichuk, O.V.
spellingShingle Venger, E.F.
Evtushenko, A.I.
Melnichuk, L.Yu.
Melnichuk, O.V.
Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet Venger, E.F.
Evtushenko, A.I.
Melnichuk, L.Yu.
Melnichuk, O.V.
author_sort Venger, E.F.
title Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
title_short Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
title_full Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
title_fullStr Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
title_full_unstemmed Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range
title_sort investigation of zno single crystals subjected to a high uniform magnetic field in the ir spectral range
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/118594
citation_txt Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range / E.F. Venger, A.I. Evtushenko, L.Yu. Melnichuk, O.V. Melnichuk // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2008. — Т. 11, № 1. — С. 6-10. — Бібліогр.: 11 назв. — англ.
series Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv AT vengeref investigationofznosinglecrystalssubjectedtoahighuniformmagneticfieldintheirspectralrange
AT evtushenkoai investigationofznosinglecrystalssubjectedtoahighuniformmagneticfieldintheirspectralrange
AT melnichuklyu investigationofznosinglecrystalssubjectedtoahighuniformmagneticfieldintheirspectralrange
AT melnichukov investigationofznosinglecrystalssubjectedtoahighuniformmagneticfieldintheirspectralrange
first_indexed 2025-07-08T14:17:38Z
last_indexed 2025-07-08T14:17:38Z
_version_ 1837088646223626240
fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 6-10. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 6 PACS 78.40.-q Investigation of ZnO single crystals subjected to a high uniform magnetic field in the IR spectral range E.F. Venger1, A.I. Evtushenko2, L.Yu. Melnichuk2, O.V. Melnichuk2 1V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine 41, prospect Nauky, 03028 Kyiv, Ukraine Phone: (380-44) 525-25-93; e-mail: venger@isp.kiev.ua 2Mykola Gogol State Pedagogic University 2, Kropyv’yans’kogo str., 16600 Nizhyn, Ukraine E-mail: mov310@mail.ru Abstract. Based on the experimental data obtained, we performed the theoretical investigation of the external reflectance coefficients of uniaxial optically anisotropic polar ZnO single crystals subjected to the action of a high uniform magnetic field that is parallel to the crystal axis С and the surface under the condition that E B⊥ r r (the Voigt configuration, Fig. 1). For the first time, we have found the regions in the external reflection spectra of ZnO single crystals, where new oscillations appear which are due to the effect of a high uniform magnetic field. A possibility of solving the direct and inverse problems in such a case is demonstrated. Keywords: Voigt configuration, ZnO, reflection spectra. Manuscript received 23.01.08; accepted for publication 07.02.08; published online 31.03.08. 1. Introduction Zinc oxide ZnO is one of the binary compounds that belong to the wide class of II−VI semiconductors. It crystallizes in the wurtzite structure (space group 4 6vC (P63mc)). Zinc oxide has unique physico-chemical properties which make it potentially applicable in metallurgy, space engineering, acousto-, micro-, and optoelectronics, as well as in some other areas of science, engineering, and medicine [1]. ZnO single crystals demonstrate a great anisotropy of the properties of their phonon subsystem, while the anisotropy of their plasmon subsystem is small [2]. The spectra of external reflection from the surface of ZnO single crystals (with electron concentrations from 1016 up to 5·1019 cm−3) were studied experimentally in [3], and the consistent bulk parameters were obtained. In [4], the reflectance coefficient of ZnO single crystals in IR was studied for the first time with allowance made for vibrations of three coupled subsystems: electromagnetic waves, optical vibrations of the crystal lattice, and plasma oscillations of free charge carriers (for the orientations Е⊥С and Е||С). In [5, 6], it was shown that zinc oxide is a typical optically anisotropic semiconductor. Many its properties have been investigated. However, there are no data in the literature on the effect of high uniform magnetic fields on the reflectance coefficient of this optically anisotropic single crystal. The objective of this work was the investigation of the external reflectance coefficients of optically aniso- tropic polar ZnO single crystals subjected to a high uniform magnetic field that is parallel to the crystal axis С and the surface under the condition that BE rr ⊥ (the Voigt configuration, Fig. 1), as well as the determination of regions where the external reflectance coefficient varies in IR under the action of a uniform magnetic field. 2. Experimental It is known that if a semiconductor is subjected to the action of a magnetic field, then a number of effects appear, in particular, the Zeeman effect, diamagnetic shifting and transitions between the Landau levels, etc. (see, e.g., [7]). A comprehensive analysis of the latter was made in [8] by using CdSe as an example. The spectral curves in a cubic magnetic semiconductor, the Cotton-Mouton effect quadratic in a magnetic field (the Voigt effect), nonreciprocal birefringence linear in a magnetic field, and the Faraday effect were investigated in [9]. It was shown that the Voigt effect is anisotropic in Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 6-10. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 7 B r E r k r С cubic magnetic semiconductors. The propagation of electromagnetic waves in uniaxial semiconductors subjected to a magnetic field which is not parallel to the crystal axis was considered in [10]. It was shown, in particular, that the effect of cyclotron and plasma resonance shifting is related to their transformation to the combined cyclotron-plasma resonances. The Faraday effect in cubic and hexagonal crystals was considered in [11] (without comprehensive analysis of expressions for the Faraday rotation). We do not know about inves- tigations of the external reflectance coefficients in uniaxial optically anisotropic single crystals subjected to a uniform magnetic field. As an example, we consider optically anisotropic n- ZnO single crystals (with gap Eg ≤ 3.43 eV) obtained using the hydrothermal technique. Their optical and electrophysical parameters (determined by us in [3, 6]) are presented in Tables 1 and 2, respectively. Here, we consider the case where BE rr ⊥ (Fig. 1) (the Voigt configuration), i.e., the magnetic bire- fringence which is as follows. A linear polarized radiation directed along a normal to the magnetic field becomes elliptically polarized after having passed a layer of an isotropic matter subjected to the magnetic field. This is due to the optical anisotropy of the matter which appears in the magnetic field and is oriented along this field. We consider the case where the magnetic field induced by the current flowing through the semi- conductor is insignificant. In the system of coordinates with the z-axis oriented along the external magnetic field B r (which lies in the xz-plane and makes an angle φ with the crystal axis), the components of the permittivity tensor of a ZnO single crystal are of the following form [10]: ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎧ µ µ Ω−ωω µΩω =ε=ε Ω−ωω µµΩω =ε=ε Ω−ω ωµ −ε=ε=ε ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ µµ µµ − Ω−ω Ω + ω ω µ−ε=ε Ω−ω ωµ −ε=ε Ω−ω ωµ −ε=ε ⊥ ⊥ ∞ ⊥∞ ⊥∞ ⊥ ∞ . )( , )( , ,11 , , 22 2 0* 22 2 0* 22 2 0 || 22 2 2 2 0 22 2 0 22 2 0 xx xz zyyz xx yxxy xz xxzxxz zzxx zzzzzz yy xx xxxx i i (1) Table 1. Parameters of the ZnO bulk. ZnO 0ε ∞ε Tν , cm−1 Lν , cm−1 E ⊥ C 8.1 3.95 412 591 E ׀׀ C 9.0 4.05 380 570 Fig. 1. Voigt configuration. Here, xxmc eB µµ=Ω ⊥ is the cyclotron frequency, and the components of the dimensionless tensor of inverse effective mass µij are expressed in terms of the principal values µ⊥ and µ||: ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ =µ=µ=µ=µ θθµ−µ=µ=µ θµ+θµ=µ µ=µ θµ+θµ=µ ⊥ ⊥ ⊥ ⊥ .0 ,cossin)( ,cossin , ,sincos || 2 || 2 2 || 2 zyyzyxxy zxxz zz yy xx (2) where θ is the angle between the crystal axis and the z- axis. Similar expressions exist also for the components of the high-frequency permittivity tensor of the crystal lattice ∞ε ij . By solving the dispersion equation ( ) ω ===δ−+ε ck n k k sssn ijjiij ,,02 r r , (3) one obtains that an extraordinary (longitudinal- transverse) wave with BE rr ⊥ , BH rr can propagate across the magnetostatic field E r . At θ = 0, the refractive index of such a wave obeys the equation )( ))(( 222 2222 2 p n ω−ωω ω−ωω−ω ε= −+∞ ⊥ , (4) where ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Ω ω +± Ω +ω=ω ⊥ ⊥± 2 2 0 2 2 0 2 411 2 and 2 0 22 ⊥ω+Ω=ω p . Since BE rr ⊥ in electromagnetic waves, the external reflectance coefficient can be written as 2 1 1 n nR + − = . (5) The frequency dependence of the permittivity in the region of plasmon-phonon interaction is [3] x z y Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 6-10. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 8 [ ] [ ] ( ) [ ].)(// /)()()()( 222 22 21 ppfT TL ivvivvv vvvivv γ+γε−γ−− −ε+ε=ε+ε≡ε ∞ ∞∞ (6) Here, ∞ε is the high-frequency permittivity; νL, νT the frequencies of the longitudinal and transverse optical phonons, respectively; γf the optical phonon damping coefficient; νp the plasma resonance frequency; and γp the plasmon damping coefficient. Taking Eq. (6) into account, we obtain the frequency dependence of the refractive index for a low-doped ZnO single crystal (whose parameters are given in Tables 1 and 2) at different values of the magnetic field (Fig. 2). Curve 1 (Figs. 2-5) corresponds to the dependence R(ν) without the effect of a magnetic field. It agrees with the curve R(ν) obtained in [3] for a single-oscillator model of ZnO. Curves 2-4 (Figs. 2 and 3) correspond to the depen- dences R(ν) at high (30−100 kGs) magnetic fields. One can see from Fig. 2 that, in high magnetic fields, the number of minima and peaks of the reflectance coefficient (which shifts towards higher frequencies) increases. Table 3 presents the frequencies of the minimum and the peak at various values of the magnetic field. One can see from Fig. 2 that the resonance frequency of the minimum of the external reflectance coefficient decreases as the uniform magnetic field grows from 30 up to 100 kGs; however, Rmin ≠ 0. In this case, the resonance frequency of the peak of the external reflectance coefficient increases; however, Rmax ≠ 1. One should note that, in the case where BE rr ⊥ , no changes in the external IR reflectance spectra in the 355–1200-cm−1 frequency region occur as the uniform magnetic field grows. Fig. 2. Frequency dependence of the reflectance coefficient R (ν) of a ZnO single crystal (sample ZO2-3) in the uniform magnetic field: 1 – В = 1 Gs; 2 – 30 kGs; 3 – 65 kGs; 4 – 100 kGs. In Fig. 3, we show the R(ν) curves of the sample ZO6-B (for its parameters see Table 2). One can see that there is no effect of a uniform magnetic field in the 370– 640- and 840–1200-cm−1 frequency ranges. The biggest change of the external reflectance coefficient of a heavily doped ZnO single crystal under the action of the uniform magnetic field occurs in the 250–380-cm−1 frequency range (see the inset in Fig. 3). Contrary to the previous case, some new peaks and minima were detected in the IR external reflectance spectra near 300 cm−1 as the magnetic field grew. Our calculations showed, however, that their shifts towards higher IR frequencies with increase in the magnetic field strength were insignificant in this case. Figures 4 and 5 show the R(ν) curves for low- doped ZnO single crystals in a magnetic field of 65 kGs at various values of the optical phonon damping coefficient (the plasma frequency and the damping coefficient of optical plasmons remaining the same). One can see from Fig. 4 that, at νp = 100 cm−1 and γp = 100 cm−1, one more peak (minimum) appears in the reflection spectrum at a frequency of 180 (190) cm−1 in a uniform magnetic field of 65 kGs. In the 390–600-cm−1 frequency range, the reflectance coefficient decreases as the optical phonon damping coefficient grows. Figure 5 presents the reflectance spectra of zinc oxide single crystals (the plasma frequency νp = 500 cm−1 and the plasmon damping coefficient γp = 500 cm−1). One can see from the inset that, in the 250–380-cm−1 frequency range, Rmin(ν) increases from 0.295 up to 0.36, as the phonon damping coefficient γf grows from 11 up to 30 cm−1. At the same time, Rmax(ν) decreases from 0.925 down to 0.875 in the 400–570-cm−1 frequency range. 200 600 1000 ν, cm-1 Fig. 3. As in Fig. 2, but for the sample ZO6-B. Inset: the same in the 250−380-cm−1 frequency range. Table 2. Electrophysical parameters of ZnO single crystals grown with the use of the hydrothermal technique. νp, cm−1 γp, cm−1 γf, cm−1 N Sample n, cm−3 E⊥C E׀׀C E⊥C E׀׀C E⊥C E׀׀C ||m ||m m⊥ ⊥m ||µ ⊥µ 1 ZO2-3 9.3×1016 90 100 150 170 11 11 0.21 1.23 0.258 4.76 3.88 2 ZO1-3 6.6×1017 240 250 280 260 13 13 0.23 1.13 0.260 4.35 3.85 3 ZO6-B 2.0×1018 420 480 406 350 21 21 0.22 1.18 0.260 4.55 3.85 R( ν) ν, cm-1 200 600 1000 0.2 0.6 1.0 1 3 2 4 R( ν) 0.2 0.6 1.0 1 2 3 4 2 1 4 3 R( ν) ν, cm-1 250 380 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 6-10. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 9 Table 3. Frequencies of minima and peaks of the external reflectance coefficient of a low-doped ZnO crystal at various magnetic field strengths. Curve number in Fig. 2 В, kGs νmin, cm−1 νmax, cm−1 2 30 89 98 3 65 115 163 4 100 172 236 200 600 1000 ν, cm-1 Fig. 4. Reflectance coefficient R (ν) of a ZnO single crystal versus the frequency at νp = 100 cm−1 and γp = 100 cm−1, В = 65 kGs; γf = 11 (1), 15 (2), 20 (3), and 30 (4) cm−1. 200 600 1000 ν, cm-1 Fig. 5. As in Fig. 4, but at νp = 500 cm−1 and γp = 500 cm−1. 20 60 B, kGs Fig. 6. Dependence of the minima of reflectance coefficient of ZnO single crystal (sample ZO2-3) on uniform external magnetic field at frequencies ν = 88 (1), 119 (2) and 186 cm-1 (3). By analyzing the obtained external reflectance spectra (Figs. 2-5), one can conclude that the biggest effect of a uniform magnetic field on the reflectance coefficient of an optically anisotropic ZnO single crystal occurs in a low-doped sample (Fig. 2). 20 60 B, kGs Fig. 7. As in Fig. 6, but at the frequencies ν = 104 (1), 177 (2), and 259 (3) cm−1. Figures 6 and 7 show the dependence of the reflectance coefficient on the uniform magnetic field strength measured at the frequencies that correspond to the minima and the peaks of the R(ν) curves of a low- doped ZnO single crystal (sample ZO2-3) presented in Fig. 2 (curves 2-4). 3. Conclusions It follows from the results of our investigations that if ZnO single crystals are subjected to a high uniform magnetic field (B = 1−100 kGs), some anomalies of the external reflection coefficient appear in their IR reflection spectra. One of the considerable results of our work is that, using an optically anisotropic ZnO single crystal as an example, the spectral regions, where the novel oscillations appear in the external reflection spectra under the action of a high uniform magnetic field in the Voigt configuration ( BE rr ⊥ ), are first discovered. This fact seems to be of interest for the establishment of fixed points on the magnetic field scale. In addition, we have detected for the first time that the most essential changes in the IR reflection spectra (the appearance of additional minima and peaks) occur in low-doped single crystals subjected to high uniform magnetic fields. The dependences of the reflectance coefficient and the frequencies of spectral extrema on the strength of a uniform magnetic field are determined. This makes it possible to solve both the direct problem (the investigation of the physical and chemical properties of a semiconductor subjected to the magnetic field of a given strength) and the inverse problem (by getting the information on the external uniform magnetic field from the known optical and electrophysical parameters of a semiconductor). References 1. I.P. Kuz’mina, V.A. Nikitenko, Zinc Oxide. Preparation and Optical Properties. Nauka, Moscow, 1984 (in Russian). R( ν) 0.2 0.6 1.0 3 4 1 2 R( ν) 0.2 0.6 1.0 R( B) 0.4 0.8 3 4 1 2 3 1 2 R( B) 0.4 0.8 3 1 2 Semiconductor Physics, Quantum Electronics & Optoelectronics, 2008. V. 11, N 1. P. 6-10. © 2008, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine 10 2. E.F. Venger, A.V. Melnichuk, L.Ju. Melnichuk, Ju.A. Pasechnik // Phys. status soidi (b) 188(2), p. 823 (1995). 3. A.V. Melnichuk, L.Yu. Melnichuk, Yu.A. Pa- sechnik // Fiz. Tverd. Tela 36(9), p. 2624 (1994) (in Russian). 4. E.F. Venger, L.Yu. Melnichuk, O.V. Melnichuk, Yu.A. Pasichnyk // Ukr. Fizychny Zhurnal 45(8), p. 976 (2000) (in Ukrainian). 5. R.J. Collins, D.A. Kleinman // J. Phys. Chem. Sol. 11(3-4), p. 190 (1959). 6. E.F. Venger, O.V. Melnichuk, Yu.A. Pasichnyk, Residual Rays Spectroscopy. Naukova Dumka, Kyiv, 2001 (in Ukrainian). 7. F.F. Sizov, Yu.I. Ukhanov, Magnetooptical Fara- day and Voigt Effects as Applied to Semiconductors. Naukova Dumka, Kiev, 1979 (in Russian). 8. A.B. Kapustina, B.V. Petrov, A.V. Rodina, R.P. Seisyan // Fizika tverdogo tela 42(7), p. 1207- 1217 (2000) (in Russian). 9. B.B. Krichevtsov, H.-J. Weber // Fizika tverdogo tela 46(3), p. 488-494 (2000) (in Russian). 10. L.E. Gurevich, R.G. Tarkhanyan // Fizika Techn. Poluprov. 6(4), p. 703 (1972) (in Russian). 11. L.E. Gurevich, I.P. Ipatova // Zhurnal Eksperim. Teor. Fiziki 37(5), p. 1324 (1959) (in Russian).

Схожі ресурси