Overheating effect and hole-phonon interaction in SiGe heterostructures

The effect of the charge carriers overheating in a two-dimensional (2D) hole gas in a Si1–xGex quantum well, where x = 0.13; 0.36; 0.8, 0.95, has been realized. The Shubnikov–de Haas (SdH) oscillation amplitude was used as a «thermometer» to measure the temperature of overheated holes. The tempera...

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Datum:	2008
Hauptverfasser:	Berkutov, I.B., Andrievskii, V.V., Komnik, Yu.F., Myronov, M., Mironov, O.A.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
Schriftenreihe:	Физика низких температур
Schlagworte:	Низкоразмерные и неупорядоченные системы
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Zitieren:	Overheating effect and hole-phonon interaction in SiGe heterostructures / I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, O.A. Mironov // Физика низких температур. — 2008. — Т. 34, № 11. — С. 1192-1196. — Бібліогр.: 14 назв. — англ.

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spelling	irk-123456789-1178822017-05-28T03:03:03Z Overheating effect and hole-phonon interaction in SiGe heterostructures Berkutov, I.B. Andrievskii, V.V. Komnik, Yu.F. Myronov, M. Mironov, O.A. Низкоразмерные и неупорядоченные системы The effect of the charge carriers overheating in a two-dimensional (2D) hole gas in a Si1–xGex quantum well, where x = 0.13; 0.36; 0.8, 0.95, has been realized. The Shubnikov–de Haas (SdH) oscillation amplitude was used as a «thermometer» to measure the temperature of overheated holes. The temperature dependence of the hole–phonon relaxation time was found using analysis of dependence of amplitude of SdH oscillations change on temperature and applied electrical field. Analysis of the temperature dependence of the hole–phonon relaxation time exhibits transition of 2D system from regime of «partial inelasticity» to conditions of small angle scattering. 2008 Article Overheating effect and hole-phonon interaction in SiGe heterostructures / I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, O.A. Mironov // Физика низких температур. — 2008. — Т. 34, № 11. — С. 1192-1196. — Бібліогр.: 14 назв. — англ. 0132-6414 PACS: 72.15.Lh;72.20.Ht;72.20.My http://dspace.nbuv.gov.ua/handle/123456789/117882 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы
spellingShingle	Низкоразмерные и неупорядоченные системы Низкоразмерные и неупорядоченные системы Berkutov, I.B. Andrievskii, V.V. Komnik, Yu.F. Myronov, M. Mironov, O.A. Overheating effect and hole-phonon interaction in SiGe heterostructures Физика низких температур
description	The effect of the charge carriers overheating in a two-dimensional (2D) hole gas in a Si1–xGex quantum well, where x = 0.13; 0.36; 0.8, 0.95, has been realized. The Shubnikov–de Haas (SdH) oscillation amplitude was used as a «thermometer» to measure the temperature of overheated holes. The temperature dependence of the hole–phonon relaxation time was found using analysis of dependence of amplitude of SdH oscillations change on temperature and applied electrical field. Analysis of the temperature dependence of the hole–phonon relaxation time exhibits transition of 2D system from regime of «partial inelasticity» to conditions of small angle scattering.
format	Article
author	Berkutov, I.B. Andrievskii, V.V. Komnik, Yu.F. Myronov, M. Mironov, O.A.
author_facet	Berkutov, I.B. Andrievskii, V.V. Komnik, Yu.F. Myronov, M. Mironov, O.A.
author_sort	Berkutov, I.B.
title	Overheating effect and hole-phonon interaction in SiGe heterostructures
title_short	Overheating effect and hole-phonon interaction in SiGe heterostructures
title_full	Overheating effect and hole-phonon interaction in SiGe heterostructures
title_fullStr	Overheating effect and hole-phonon interaction in SiGe heterostructures
title_full_unstemmed	Overheating effect and hole-phonon interaction in SiGe heterostructures
title_sort	overheating effect and hole-phonon interaction in sige heterostructures
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2008
topic_facet	Низкоразмерные и неупорядоченные системы
url	http://dspace.nbuv.gov.ua/handle/123456789/117882
citation_txt	Overheating effect and hole-phonon interaction in SiGe heterostructures / I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, O.A. Mironov // Физика низких температур. — 2008. — Т. 34, № 11. — С. 1192-1196. — Бібліогр.: 14 назв. — англ.
series	Физика низких температур
work_keys_str_mv	AT berkutovib overheatingeffectandholephononinteractioninsigeheterostructures AT andrievskiivv overheatingeffectandholephononinteractioninsigeheterostructures AT komnikyuf overheatingeffectandholephononinteractioninsigeheterostructures AT myronovm overheatingeffectandholephononinteractioninsigeheterostructures AT mironovoa overheatingeffectandholephononinteractioninsigeheterostructures
first_indexed	2025-07-08T12:57:40Z
last_indexed	2025-07-08T12:57:40Z
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fulltext	Fizika Nizkikh Temperatur, 2008, v. 34, No. 11, p. 1192–1196 Overheating effect and hole–phonon interaction in SiGe heterostructures I.B. Berkutov, V.V. Andrievskii, and Yu.F. Komnik B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: Andrievskii@ilt.kharkov.ua M. Myronov Musashi Institute of Technology, 8-15-1 Todoroki, Setagaya-ku, Tokyo, Japan O.A. Mironov Warwick SEMINANO R&D Centre,University of Warwick Science Park, Coventry CV4 7EZ, UK International Laboratory of High Magnetic Fields and Low Temperatures, P.O. Box 4714, 50-985 Wroclaw 47, Poland Received June 26, 2008 The effect of the charge carriers overheating in a two-dimensional (2D) hole gas in a Si1–xGex quantum well, where x = 0.13; 0.36; 0.8, 0.95, has been realized. The Shubnikov–de Haas (SdH) oscillation amplitude was used as a «thermometer» to measure the temperature of overheated holes. The temperature dependence of the hole–phonon relaxation time was found using analysis of dependence of amplitude of SdH oscillations change on temperature and applied electrical field. Analysis of the temperature dependence of the hole–pho- non relaxation time exhibits transition of 2D system from regime of «partial inelasticity» to conditions of small angle scattering. PACS: 72.15.Lh Relaxation times and mean free path; 72.20.Ht High-field and nonlinear effects; 72.20.My Galvanomagnetic and other magnetotransport effects. Keywords: quantum well, 2D hole gas, Shubnikov–de Haas oscillation, hole–phonon relaxation time. Introduction The surface of the crystal experiences surface acous- tic waves [1]: Rayleigh and Lamb waves and so on. The interaction of electrons with them differs essentially from the electron–phonon interaction in the bulk of the crystal. The specific features of the electron–phonon interaction are present in thin films of metals and semiconductors be- cause the surface processes more strongly affect the ki- netic properties of these objects. In free thin films with d < λ (d is the film thickness, λ is the phonon wave length) there are bending waves obeying the quadratic dispersion law ω ∝ q 2 (ω and q are the phonon frequency and momentum, respectively) [2]. Films on a substrate can experience Love waves with shear horizontal pola- rization. These waves obey an unusual dispersion law ω ∝ /q1 2 [3]. The specifics of the phonon spectrum of films affect the character of the electron–phonon interac- tion. Besides, the space quantization of the electron spec- trum can be an additional factor of influence in semi- metallic and semiconducting films. The situation is quite simpler at the interface in semiconducting heterostruc- tures. Here the electron occupies the quantum states in the quantum well (QW) and form a two-dimensional (2D) electron gas, whereas the phonons can be thought of as three-dimensional (3D) since the elastic properties of the crystal are identical at the both sides of the interface. The heterostructures in semiconductors offer a possibility of investigating the electron–phonon interaction between 2D electron gas and 3D phonons. The aim of this study is to investigate the hole–phonon interaction in a 2D hole gas in SiGe heterostructures, in particular to obtain information about the time and the temperature dependence of the hole–phonon interaction. The use of the quantum corrections to conductivity cau- sed by the effects of weak localization on interaction can- not provide information about the electron–phonon re- laxation time at very low temperatures because in this � I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, and O.A. Mironov, 2008 condition electron–electron scattering predominates over other inelastic processes. This relaxation time can, how- ever, be found from the electron overheating effect, where the electron temperature Te increases above the phonon temperature Tph due to a strong electric field (current) or other heating factors. It should be noted that the electron overheating effect in a 2D electron gas is in- duced by the heat transport through the interface. Estima- tion of the electron–phonon relaxation time is possible because the transfer of the excess energy from the elec- tron system to the phonon one is controlled by this time, even under the condition of strong elastic scattering. Ex- perimentally, this problem comes to estimating the elec- tron temperature Te which changes under the influence a strong current. To achieve the electron overheating effect, the phonon should be free to leave the conducting layer and come into the crystal surrounding (i.e. good acoustic coupling is required between the conducting layer and the crystal). This requirement is met in heterostructures. In present study the overheating effect of charge carriers was realized in p-type heterostructures with a Si1–xGex quantum well. The Shubnikov–de Haas oscillation (SdHO) amplitude was used as a «thermometer» to measure the temperature of overheated holes. Sample description Four of the samples studied in this work (labelled A–D, see Table 1) were prepared by the molecular beam epitaxy technique [4]. In samples A and B the layers are arranged as follows: a single crystal Si n-type (100) sub- strate, pure undoped Si epitaxial layer, Si1–xGex quantum well (~10 nm thick), undoped Si spacer (~20 nm), Si sup- ply layer boron-doped at about 2.5·1018 cm–3, pure Si cap (10 nm). In samples Ñ and D the composition of the crys- tal beneath the QW, the spacer and the boron-doped layers were Si0.7Ge0.3 and Si0.37Ge0.63, instead of pure Si. To measure conductivity Hall bars were prepared, shaped as a «double cross», i.e. a narrow (~0.5 mm) strip with two pairs of narrow (0.05 mm) potential bars about 2 mm apart. The diagonal Rxx and off-diagonal Rxy com- ponents of the resistance tensor were measured as func- tions of magnetic field on samples A and C up to 11 T and for samples B and D up to 6 T. The sample parameters: di- agonal resistivity ρxx, hole concentration from Hall pHall and SdHO pShH, mobility μHall and effective mass m, hole diffusion coefficient D measuring at the lowest tem- perature are shown in Table 1. Overheating effect and hole–phonon interaction in sige heterostructures Fizika Nizkikh Temperatur, 2008, v. 34, No. 11 1193 0 1 2 3 4 5 6 0 2 4 6 8 10 1.5 2.0 2.5 3.0 3.5 0 1 2 3 4 5 6 0.3 0.4 0.5 0.6 1 2 3 4 5 60 2 4 6 8 0 1 2 3 4 5 0 c B, T B, T B, T B, T 0 5 10 15 20 25 a 0 d 0.5 1.0 1.5 2.0 ρ Ω x x , k ρ Ω x x , k ρ Ω x x , k ρ Ω x x , k ρ Ω x y , k ρ Ω x y , k 2.5 3.0 3.5 4.0 4.5 5.0 2 4 6 b ρ Ω x y , k ρ Ω x y , k Fig. 1. Magnetoresistance ρxx and ρxy of samples A (a), B (b), C (c), D (d). T = 33 mK for sample A, and T � 0 3. K of the other samples. Table 1. Characteristic parameters of the samples. S am p le Q u an tu m w el l xx , k Ω p H al l, 1 0 1 1 cm – 2 p S d H , 1 0 1 1 cm – 2 H al l, 1 0 4 cm 2 ·V – 1 ·s – 1 m (m 0 ) D , cm 2 ·s – 1 A Si0.87Ge0.13 3.04 1.89 2.0 1.16 0.24 20.7 B Si0.64Ge0.36 4.78 6.42 6.7 0.22 0,24 13.9 C Si0.2Ge0.8 3.17 15.8 14.6 0.11 0.16 29.3 D Si0.05Ge0.95 0.54 17.5 16.2 0.68 0.156 179 The variations in magnetoresistances ρxx B( ) and ρxy B( ) with field, at the lowest temperatures, are illustrated in Fig. 1 (ρ stands for the resistance per square area of a 2D electron system). The curves exhibit pronounced Shub- nikov–de Haas oscillations at B ≥ 1 Tand clear steps of the quantum Hall effect in sample A. Experimental results and discussion Quantum interference effects were used in Ref. 5 to estimate the electron temperature during electron over- heating. Electron overheating becomes more obvious when the SdHO are observed [6–8]. In the cited papers the falloff of the amplitude of the oscillations with in- creasing applied electric field was used to find a relation- ship between the electron temperature and the rate of loss of excess energy by the electrons. In Ref. 8 the depen- dence of the energy loss time on the overheating tempera- ture was found, and it was concluded that the main chan- nel of electron energy loss is the emission of acoustic phonons. In the present study, the overheating effect of the charge carriers is used to calculate, straightforwardly, the temperature dependence of the hole–phonon relax- ation time in p-type Si1–xGex quantum wells. In our experiments, the hole temperature Th was found by comparing the SdHO amplitude change with current and with temperature. As an example, the SdHO amplitude observed in sample D at low current and vary- ing temperature (a) and at constant temperature and vary- ing current (b) are shown in Fig. 2. The amplitude variation in these two cases were ana- lyzed for three extrema (with filling factors ν = 18, 20, and 22) in the magnetic field region 0.8–3.5 T. The quan- tum numbers νare found from the off-diagonal compo- nent of the resistance ρxy B( ) using the equation for resis- tance quantization under the condition of the quantum Hall effect (h e/ 2ν). The electron overheating effect was considered in a number of theoretical studies (their results are applicable to hole overheating as well). In Ref. 9 an expression T T E T Te e e e− = − − −ph ph ph ph 2σ γ τ ( ) , (1) was obtained from the heat balance equation, which con- tains the characteristic of our interest, i.e. the time of elec- tron–phonon relaxation τ e−ph at a certain temperature Te−ph , characterizing the electron–phonon interaction un- der the electron overheating condition. The prefactor γ describes the temperature dependence of the electronic specific heat C T Te ( ) = γ . Since this parameter is un- known, it is reasonable to pass on to the equation of Ref. 10 1194 Fizika Nizkikh Temperatur, 2008, v. 34, No. 11 I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, and O.A. Mironov 1 2 3 4 5 6 7 80 50 100 150 10 20 30 400 50 100 150 ba T, K ν = 18 ν = 20 ν = 22 R , Ω R , Ω I, Aμ Fig. 2. Dependence of Shubnikov–de Haas oscillation amplitudes for sample D (à) with temperature and (b) with driving current. Solid lines are guides to the eye. ( ) ( ) ( )kT kT eE De e 2 2 2 26= + ⎛ ⎝⎜ ⎞ ⎠⎟ −ph ph π τ . (2) This follows from Eq. (1) if we write down the heat capacity and conductivity in terms of density of states νds: C k Te ds= /( )π ν2 23 and σ ν= e D ds 2 , besides it is necessary to use expressions for 2D electron gas: ν πds m= /* ( )� 2 , D F= /( )1 2 2 v τ (vF is the Fermi velocity vF m n= / /( )( )� 2 1 2π , n is the concentration of 2D elec- trons). Equation (2) is quite convenient because it in- cludes only one characteristic of the samples, namely the electron diffusion coefficient D. The calculations ac- cording to Eq. (2) gives possibility to obtain dependence τ e eT− −ph ph( ). Temperature Te−ph is taken to be the mean T T Te e− = + /ph ph( ) 2 [11,12], here Tph corresponds to the temperature of the crystal. The temperature dependences of the hole–phonon re- laxation time τ h−ph of all the samples are shown in Fig. 3. The dependences τ h hT− −ph ph( ) above 1 K for sample D and above ~0.5–0.6 K for the other samples can be approximated by the power function τ e T− − −= ⋅ph 1 9 29 10 (Fig. 3, solid lines). It is essential that this function is common despite the different characteristics of the sam- ples. Moreover, the points corresponding to the filling factors ν different for each sample fall on the same curve, which suggests that the τ h−ph — value is independent of the magnetic field. A stronger dependence τ h hT− −ph ph( ) appears below the temperatures specified above. The results obtained must be interpreted in the con- texts of the theoretical studies considering the tempera- ture variations of electron–phonon relaxation for 2D elec- trons interacting with 3D phonons [13,14]. In Ref. 14 these variations are analyzed in a wide range of tempera- tures. The energy is quantized in a QW: E p m p m m L nx x y y z 1 2 2 2 2 2 2 2 2 2 = + + * * π � , where L is the width of the well, n is the quantum number. Electrons occupied the ground state in the QW with the energy E m Lz1 2 2 22= /π � * . The electron–phonon interac- tion of 2D carriers is limited on variation of the transverse momentum of the electrons in direction of quantization (in z direction). The transverse component of the mo- menta of the emitted (absorbed) phonons is determined by the width of the QW q L⊥ /� 2π . At high temperatures the thermal phonon momentum is q LT > /2π , and the electron–phonon scattering is accompanied by emission (absorption) of phonons with the wave vector mainly per- pendicular of the QW. The process is characterized by the dependence τ e T− − ∝ph 1 . At lower temperatures the mo- mentum of the thermal phonon q k T sT B= / � (s is the sound velocity) is smaller than 2π / L. But if the phonon is capable to change the wave vector of the electron by the maximum value 2k F , the energy exchange between the electron and the lattice can be about k TB . We expect the dependence τ e T− − ∝ph 1 2 in this region of «partial inelas- ticity». At even lower temperatures (q kT F< 2 ) the wave vector of the emitted (absorbed) phonon is limited by temperature and the scattering is similar to the small-an- gle scattering in a 3D metal following the dependence τ e T− − ∝ph 1 5. The obtained dependencies τ h T− − ∝ph 1 2 (Fig. 3) corre- spond to the region of «partial inelasticity» [14]. At low- ering temperatures the dependence becomes stronger. We Overheating effect and hole–phonon interaction in sige heterostructures Fizika Nizkikh Temperatur, 2008, v. 34, No. 11 1195 0.2 1.0 10 –9 10 –8 10 –7 10 –6 0.2 1.0 10 –9 10 –8 10 –7 10 –6 Sample B = 5ν ν = 6 ν = 7 Sample D ν = 18 ν = 20 ν = 22 4.02.0 a 4.02.00.6 Sample A = 8ν ν = 10 Sample C ν = 8 ν = 9 ν = 10 0.6 b τ h p h – , s τ h p h – , s T , Kh ph– T , Kh ph– Fig. 3. Temperature dependence of hole–phonon relaxation times τh−ph found from the overheating effect. Solid line is depen- dence τe T− − −= ⋅ph 1 9 29 10 , doted line is dependence τe T− − −= ⋅ph 1 9 50 6 10. , dash line is dependence τe T− − −= ⋅ph 1 9 51 2 10. , short dash line is dependence τe T− − −= ⋅ph 1 8 515 10. . attribute this to the small-angle mechanism predict in theory [14], which is characterized by the dependence τ e T− − ∝ph 1 5. The temperature of the transition to this dependence obeys qualitatively (to within the numeri- cal coefficient << 1) the condition q kT F� 2 , if we take k nF = /( )2 1 2π for a 2D electron gas, i.e., the temperature grows as the carrier concentration increases. The quanti- tative discrepancy is not clear yet and may be connected with conditional character of the formulas for 2D electron gas to the real situation. 1. I.A. Viktorov, Rayleigh and Lamb Waves: Physical and Application, New York, Plenum Press (1967). 2. I.M. Lifshits, Zh. Eksp. Teor. Fiz. 22, 471 (in Russian) (1952). 3. E.S. Syrkin, Yu.F. Komnik, and E.Yu. Beliaev, Low Temp. Phys. 22, 80 (1996). 4. T.J. Grasly, C.P. Parry, P.J. Phillips, B.M. McGregor, R.J.H. Morris, G. Braithwaite, T.E. Whall, E.H.C. Parker, R. Hammond, A.P. Knights, and P.G. Coleman, Appl. Phys. Lett. 74, 1848 (1999). 5. R. Fletcher, J.J. Harris, C.T. Foxon, and R. Stoner, Phys. Rev. B45, 6659 (1992). 6. P.T. Coleridge, R. Stoner, and R. Fletcher, Phys. Rev. B39, 1120 (1989). 7. K.J. Lee, J.J. Harris, A.J. Kent, T. Wang, S. Sakai, D.K. Maude, and J.C. Portal, Appl. Phys. Lett. 78, 2893 (2001). 8. G. St�ger, G. Brunthaler, G. Bauer, K. Ismail, B.S. Meyer- son, J. Lutz, and F. Kuchar, Semicond. Sci. Technol. 9, 765 (1994). 9. P.W. Anderson, E. Abrahams, and T.W. Ramakrishnan, Phys. Rev. Lett. 43, 718 (1979). 10. S. Hershfield and V. Ambegaokar, Phys. Rev. B34, 2147 (1986). 11. S.I. Dorozhkin, F. Lell, and W. Schoepe, Solid State Com- mun. 60, 245 (1986). 12. V.V. Andrievskii, I.B. Berkutov, Yu.F. Komnik, O.A. Mi- ronov, and T.E. Whall, Fiz. Nizk. Temp. 26, 1202 (2000) [Low Temp. Phys. 26, 890 (2000)]. 13. P.J. Price, Ann. Phys. 133, 217 (1988). 14. V. Karpus, Sov. Phys. Semicond. 20, 6 (1986). 1196 Fizika Nizkikh Temperatur, 2008, v. 34, No. 11 I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, M. Myronov, and O.A. Mironov

Overheating effect and hole-phonon interaction in SiGe heterostructures

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