Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs

Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs

The electrical field dependencies of current I and its variation under phonon pulses - ΔIph, were measured in δ-doped GaAs with n = 5*10¹¹ nm⁻². It was shown that if E< 1 V/cm and T = 2 K, E/I, and E/Iph linearly increase with E, and while the change in the first value was less than 5%, the secon...

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Опубліковано в: :Semiconductor Physics Quantum Electronics & Optoelectronics
Дата:2004
Автор: Slutskii, M.I.
Формат: Стаття
Мова:English
Опубліковано: Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2004
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/118116
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Цитувати:Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs / M.I. Slutskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 68-71. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-118116
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spelling Slutskii, M.I.
2017-05-28T17:43:52Z
2017-05-28T17:43:52Z
2004
Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs / M.I. Slutskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 68-71. — Бібліогр.: 15 назв. — англ.
1560-8034
PACS: 73.20. Fz, 73.20. Jc, 73.50. Fq
https://nasplib.isofts.kiev.ua/handle/123456789/118116
The electrical field dependencies of current I and its variation under phonon pulses - ΔIph, were measured in δ-doped GaAs with n = 5*10¹¹ nm⁻². It was shown that if E< 1 V/cm and T = 2 K, E/I, and E/Iph linearly increase with E, and while the change in the first value was less than 5%, the second one increased by more than 3 times. The proposed explanation of experimental results is based on the nearness of the studied structure to a metal-insulator transition.
I wish to thank Professor К.Н. Ploog for permission to use the samples prepared in his laboratory and Professor O.G. Sarbey for useful discussions.
en
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
Semiconductor Physics Quantum Electronics & Optoelectronics
Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
spellingShingle Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
Slutskii, M.I.
title_short Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
title_full Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
title_fullStr Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
title_full_unstemmed Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs
title_sort linear field dependencies of conductivity and phonon-induced conductivity of 2d gas in δ-doped gaas
author Slutskii, M.I.
author_facet Slutskii, M.I.
publishDate 2004
language English
container_title Semiconductor Physics Quantum Electronics & Optoelectronics
publisher Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
format Article
description The electrical field dependencies of current I and its variation under phonon pulses - ΔIph, were measured in δ-doped GaAs with n = 5*10¹¹ nm⁻². It was shown that if E< 1 V/cm and T = 2 K, E/I, and E/Iph linearly increase with E, and while the change in the first value was less than 5%, the second one increased by more than 3 times. The proposed explanation of experimental results is based on the nearness of the studied structure to a metal-insulator transition.
issn 1560-8034
url https://nasplib.isofts.kiev.ua/handle/123456789/118116
citation_txt Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δ-doped GaAs / M.I. Slutskii // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 68-71. — Бібліогр.: 15 назв. — англ.
work_keys_str_mv AT slutskiimi linearfielddependenciesofconductivityandphononinducedconductivityof2dgasinδdopedgaas
first_indexed 2025-11-27T02:19:05Z
last_indexed 2025-11-27T02:19:05Z
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fulltext Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 1. P. 68-71. © 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine68 PACS: 73.20. Fz, 73.20. Jc, 73.50. Fq Linear field dependencies of conductivity and phonon-induced conductivity of 2D gas in δδδδδ-doped GaAs M.I. Slutskii Institute of Physics, NAS of Ukraine, 46, prospect Nauky, 03680 Kyiv, Ukraine Fax: 380 (44) 2651589, phone: 380 (44) 2651432, E-mail: sarbey@iop.kiev.ua Abstract. The electrical field dependencies of current I and its variation under phonon pulses � ∆Iph, were measured in δ-doped GaAs with n = 5×1011 ñm�2. It was shown that if E< 1 V/ñm and T = 2 K, E/I, and E/Iph linearly increase with E, and while the change in the first value was less than 5%, the second one increased by more than 3 times. The proposed explanation of experimental results is based on the nearness of the studied structure to a metal-insulator transition. Keywords: quantum well, quantum localization. Paper received 10.10.03; accepted for publication 30.03.04. 1. Introduction Usually, a change in the semiconductor conductivity in the low electric field range is proportional to the square of the field strength, as it is due to electron heating. But there are other mechanisms of the electric field effect on conductivity, which lead to other field dependencies. For example, in a hopping conduction range, the electric field can result in delocalisation of energy states and decrease in activation energy of bond electrons. In this case, the conductivity change is proportional to the field strength [1�3]. It is known [2�3] that this effect increases near the Anderson-Mott transition in dielectric phase. In the metal phase, for 3D states such mechanism of the conductivity change was observed in the only work [4] for Si:P under extreme conditions: T < 40 mK, E < < 15 µV/cm, (n � ncr)/ncr = 3⋅10�2 (ncr � donor concentra- tion at the transition point). In this work, σ(E) = σ(0)+ + Ea the square root dependence of conductivity on electric field was observed. The Anderson-Mott transition is a special case of quan- tum phase transitions (QPT), in which at T = 0 properties of a system change qualitatively, when one of its parame- ter (magnetic field, the electron concentration in 2D gas, the chemical composition of a crystal and so on) achieves the critical value. For our structure, the corresponding parameter is the donor concentration, because at nd > ncr there are free electrons in 2D gas. In 2D gas, the non- heating mechanism near QPT is stronger than in 3D case and, probably, has universal character [5], because it was found in rather different objects such as: quantum Hall effect [6], à-MoGe thin amorphous films near the superconductor-insulator transition [7] and pure Si near the metal-insulator transitions [8], although in the latter case the physics of the transition was not completely un- derstood [9]. In all the cases this effect was observed on the both sides of transitions. Quite formally, this phenomenon may be described by introducing the field-dependent electron effective tem- perature Tel, however, in such case Tel will not be con- nected with the electron average energy [5]. Should the nonheating mechanism be really univer- sal, it must be observed in δ-doped GaAs, where the metal- insulator transition takes place at the doping concentra- tion nd = 3⋅1011 ñm�2 [10]. Our purpose in the present work was to give experimental evidence of this effect in δ-doped GaAs. 2. Experimental results Horizontal transport in δ-doped GaAs containing 7 quan- tum wells with nd = 5⋅1011 ñm�2 was investigated. The distance between the layers was 100 nm. All the layers were parallel to ohmic contacts. The distance between M.I. Slutskii: Linear field dependencies of conductivity and phonon- induced ... 69SQO, 7(1), 2004 them was 0.5 mm, the wide of 2D gas � 0.2 mm. Gold layer covered the opposite side of the sample. Heat pulses in GaAs were generated by Au film heated with 10ns- nitrogen laser beam, focused by lens to the spot with d = 0.3 mm. The sample structure and measurement tech- nique were described in detail in [11,12]. First, the I-V and ∆Iph � V characteristics of 2D gas were measured (where ∆Iph is a change of I under the heat pulse). Then the resistance R = V/I, phonon-induced conductivity σph = ∆Iph/V and its inverse value Rph = 1/σph were calcu- lated. The temperature and field dependencies of these quantities were analysed. Similar experiments were made in [11,12], but the authors of these works did not investi- gate the field dependencies in low field range in detail. Time dependence of phonon-induced current is shown in Fig. 1; where L and T peaks are formed by longitudi- nal and transverse ballistic phonons. The first peak in Fig. 1 is due to laser beam absorption in GaAs sample in the area between ohmic contacts, causing a change of the conductivity of the sample. The peaks were identified from their delays relative to the light pulse. For the first peak this delay must be equal to zero, for others � the time of flight between the source and detector for phonons of corresponding modes. Field dependencies of Rph, measured at 2K< T < 4 K at the moment of T-peak maximum, are shown in Figs 2 and 3 shows field dependencies of resistance R. In Fig. 4 temperature dependencies of Rph and dR/dE in zero field, obtained by extrapolation of Rph(E) and R(E), are shown. The most interesting feature of these results is the lin- ear character of field dependencies of R and Rph, well seen in the Figs 2�3. For the forthcoming analysis, it is important to note some important features: a) One may introduce an effective electron tempera- ture Tef (E,T0), defining it from the conditions Rph(E,T0) = = Rph(0,Tef) or R(E,T0) = R(0, Tef). It is important to know to what extend Tef differs from T0, because our prime interest concerns the range where T0 and Tef are close to each other. Knowing Rph(E,T0), one can get Tef (1 V/cm, 2.0 K) = 3.6 K, and Tef (1 V/cm, 2.5 K) = 3.9 Ê. Then, using R(E, T0) data, we obtain Tef(1 V/cm, 2.0 K) = 3.5 Ê, and Tef (1 V/cm, 2.5 K) = 3.8 K. It means, that at E < < 1 V/cm the condition Tef � T0 < T0 is satisfied. b) The effect markedly decreases, if the temperature increases � Rph increases, dR/dE in zero field becomes smaller, the range of linearity Rph(E) becomes narrower. c) If E < 1 V/cm, the relative change of Rph with field increasing is 30�40 times greater than the change of re- sistance. 3. Discussion Let us assume that R(E) and Rph(E) are due to the grow of the electron temperature Te and try to define, how strong Te changes at E <1 V/cm. In principle, a dependence R(T) in zero field is due to the change of the energy distribu- tions of both electrons and phonons, but for the investi- gated structure one can neglect the phonon contribution. Magnetotransport measurements of the structure simi- lar to investigated in this work were made in magnetic fields up to B = 14T/13/. It was found that 2D gas occu- pies two subbands with electron concentrations n1 = = 4.9⋅1011cm�2, n2 = 0.93⋅1011cm�2 and mobilities 0 1 2 3 4 5 0 10 20 30 40 50 60 70 T L I p h (1 0 � 8 A ) t, ms Fig. 1. Time dependence of phonon-induced current in 2D gas. R , M W p h 0 2 4 6 8 10 0.0 0.1 0.2 0.3 0.4 E , V/cm a R , M W p h 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 E, V/cm b Fig. 2. Field dependencies of inverse phonon-induced conducti- vity in 2D gas, o � T = 4K, ¡ � T = 3.5 K, ¯ � T = 3K, r � T = = 2.5K, l � T = 2K. 70 SQO, 7(1), 2004 M.I. Slutskii: Linear field dependencies of conductivity and phonon- induced ... µ1 = 2.33⋅103 cm2/Vs, µ2 = 1.28⋅104 cm2/Vs, and that these mobilities are determined by electron scattering from ion- ized donors. In this way one can estimate the middle elec- tron mobility as µ = (n1µ1+n2µ2)/(n1 + n2) ≅ 4⋅103 cm2/Vs. In pure GaAs structures, in which phonon scattering domi- nates, the mobility can rise up to 2⋅106 cm2 /Vs at T = 5K [10]. Consequently, a relative change of the mobility, caused by the phonon scattering can not exceed of 0.2%, which is much less than observed value (see Fig. 3). In this case, the temperature Tef, defined previously, is simply equal to Te, and we have Te � T0 < T0 at E < 1V/cm. But at ∆T << T0 we must observe R = R0 + aE2, whereas in Fig. 3 we see the linear dependence. It com- pels us to refuse from the initial assumption and to find an nonheating mechanism to explane R(E). In principle, one can suggest that the quadratic de- pendence takes place at very low values ∆T/T, and in Fig. 3 we observe the transfer between regions of low and high fields, which quite accidentally can be interpolated by a linear dependence. But observation of the same field dependencies for two so different physical values as R and Rph makes this assumption highly improbable be- cause in general case the behaviour of R(E), Rph(E) must be different in middle and strong fields. Now we stand before the question: can these results be connected with the Anderson�Mott transition? In our δ-doped GaAs, this transition takes place at ncr = = 3⋅1011cm�2 [10], so we have ∆ = (n � ncr)/ncr = 0.67. Usually, phase transition can significantly affect on the crystal properties if ∆ << 1. But in 2D case, QPT has strong effect on the same even at rather high values of ∆. In Si:P, field scaling relations were observed near the metal-insulator transition �0.85 < ∆ < 0.25 [8] and tem- perature one � at �0.25 < ∆ < 0.45 [14]. In a-MoGe, temperature scaling relations were observed near super- conductor-insulator transition at �0.4 < ∆ < 0.45 (∆ = (H � Hcr)/Hcr) [7]. This point of view is confirmed by the analysis of electron mobility dependence on the donor concentration in δ-doped GaAs. At ncr < n < < 5⋅1011cm�2, it is due to the transition from hopping con- ductor to the metal one [10]. In Si:P, the temperature scaling relations were observed at 0.2 < T < 3 K [14]. It means that QPT influence can be significant at relatively high temperatures. All these facts give evidence for cor- relation between our results and the nearness of the in- vestigated structure to QPT. Let us analyse the possible mechanisms of such influence. Unfortunately, the mechanism of the conductivity field dependence in Si:P was not discussed in [8], but for other QPTs this effect was always attributed to delocalisation by electric field of elementary crystal excitations such as: electrons localized near the Landau levels, quantum vortex localized in a superconductivity phase and Cooper pairs localized in dielectric phase [6, 7]. Qualitative representation of the Anderson-Mott tran- sition can be outlined by the percolation theory [15], ac- cording to which there are dielectric incorporations in metal phase and vice versa. Near the transition, the typi- cal size of incorporations ξ approaches to infinity and the activation energy Ed of dielectric phase � to zero. From this point of view, the phonon-induced conduc- tivity is due to the absorption of phonons in dielectric incorporations, which leads to transitions of bound elec- trons into the conductivity band. The excitation of elec- trons has been made possible because Ed decreases near the transition and becomes less than the typical phonon energy. On the other hand, the temperature and field dependencies of Rph, and R can be explained by destruc- tion of dielectric incorporations under heating and elec- tric field. It is important to notice that the dependence of resistance on field strength δR = aE/T, which was ob- tained in the 3D case for the hopping conductance range in [1�3], is well agreed with the similar dependencies obtained in the present work. As it can be seen from Figs 2, 3, Rph increases much stronger than R with increase of a field. In the context of the proposed theory, the sensitivity to dielectric incorpo- rations can be due to the weakness of alternative mecha- nism � an electron heating by nonequilibrium phonons, E , V/cm 0.0 0.5 1.0 840 860 880 900 920 Fig. 3. Field dependencies of 2D gas resistance o � T = 4 K , ¡ � T = 3.5 K, ¯ � T = 3K, r � T = = 2.5K, l � T = 2K. R , a rb . u n it s d R d E / , a rb . u n it s dR dE T/ = 300 R p h ph 2 3 4 100 100 = 7.3 T 2.19 �1.11 Fig. 4. The temperature dependencies Rph � o and dR/dE � r. M.I. Slutskii: Linear field dependencies of conductivity and phonon- induced ... 71SQO, 7(1), 2004 because the conductivity of δ-structure is almost inde- pendent of T. Let us estimate the typical size ξ and activation en- ergy Ed of the dielectric incorporations. Should Ed be of the same value for all incorporations, the dependence Rph ~ exp(Ed/T) would be expected. Of course, there is a wide distribution of Ed in QPT, but nevertheless one can estimate its typical value. At T1 = 2K we have Ed = 5K. According to [1], the delocalization occurs at Ed = eEξ. Taking into account, that at T = 2K, the phonon-induced conductivity decreases twice at E = 0.4V/cm, we get ξ = 15 µm. The appearance of such capture centres not related to the QPT is scarcely probable. 4. Conclusions The linear field dependencies of resistance and phonon- induced conductivity of 2D electron gas were observed. The analysis of the given data revealed that it is hard to explain them by electron heating, because at low fields this heating is only proportional to the field squared. The alternative explanation of the results was pro- posed � the delocalisation of electrons with low activa- tion energies by electric fields. The existence of such elec- trons in the sample is related to the nearness of the re- searched structure to the metal-insulator transition. Acknowledgments I wish to thank Professor K.H. Ploog for permission to use the samples prepared in his laboratory and Professor O.G. Sarbey for useful discussions. References 1. B.I. Shklovskii // Fiz. Tech. Pol., 6, p. 2335 (1972). 2. I.N. Timchenko, A.G. Astafurov // Fiz. Tech. Pol. 12, p. 1196 (1978). 3. B.I. Shklovskii // Fiz. Tech. Pol, 10, p. 1440 (1976). 4. T.F. Rosenbaum, R.F. Milligan, M.A. Paalanen, G.A.Thomas, R.N.Blatt and W.Lin // Phys. Rev. B, 27, p. 7509 (1983). 5. S.L. Sondhi, S.M. Girvin, J.P. Garini and D. Shahar // Rev. Mod. Phys., 69, p. 315 (1997). 6. D.G. Polyakov, B.I. Shklovskii // Phys. Rev. B, 48, p. 11167 (1993). 7. Ali Yazdani, Aharon Kapitulnik // Phys. Rev. Let., 74, p. 3037 (1995). 8. S.V. Kravchenko, D. Simonian, M.P. Sarachik, Whitney Mason and J.E. Furneaux // Phys. Rev. Let. 77, p. 4938 (1996). 9. V.M. Pudalov // Usp. Fiz. Nauk. 168, p. 227 (1998). 10. P. M. Koenraad, in Delta-doping of semiconductors, E.E. Schubert (ed) Cambridge, University press, (1996), p 407. 11. M. Asche, R. Hey, M. Horiche et al. // Semicond. Sci. Technol. 9, p. 835 (1994). 12. B. Danilchenko, A. Klimashov, O. Sarbey., Proc. of 23 In- tern. Conf. on the Phys of Semicond., Berlin (1996). 13. Th.Ihn, K.J. Friedland, R.Hey and F.Koch // Phys. Rev. B, 52, p. 2789 (1995). 14. S.V. Kravchenko, Whitney E. Mason, G.E. Bowker, J.E. Furneaux, V.M. Pudalov and M. D�Iorio // Phys.Rev. B, 51, p. 7038 (1995). 15. B.I. Shklovskii, A.L. Efros // Usp. Fiz. Nauk. 117, p. 401 (1975).

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