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High frequency hopping conductivity in semiconductors. Acoustical methods of research. I.L.Drichko

High frequency hopping conductivity in semiconductors. Acoustical methods of research. I.L.Drichko Ioffe Physicotechnical Institute RAS Физико-технический институт им. А.Ф.Иоффе РАН, 194021, С.-Петербург, ул.Политехническая, 26. Outline. 1.Two-site model of high frequency hopping conductivity

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High frequency hopping conductivity in semiconductors. Acoustical methods of research. I.L.Drichko

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  1. High frequency hopping conductivity in semiconductors. Acoustical methods of research. I.L.Drichko Ioffe Physicotechnical Institute RAS Физико-технический институт им. А.Ф.Иоффе РАН, 194021, С.-Петербург, ул.Политехническая, 26

  2. Outline • 1.Two-site model of high frequency hopping conductivity • 2. 3-dimensional high frequency hopping • 3. 2-dimensional high frequency hopping • 4. high frequency hopping in system with • dense arrays of Ge –in- Si quantum dots

  3. High- frequency hopping conductivity • Two-site model  =1-2 is the difference between initial energies of impurity sites 1 and 2 (r)= 0e-r/is the overlap integral, where 0EB,  is the localization length 1 2 , • Resonant (phononless) absorption E 2.Relaxation (nonresonant) absorption r Two-site model can be applied if ()>>(0). The hops between different pairs are absent. .

  4. Relaxation case ~cos t M.Pollak V.Gurevich Yu.Galperin D.Parshin A.Efros B.Shklovskii n0 is the equilibrium value of n 0 (E) is the minimum value of the population relaxation time for symmetrical pairswith  =0 The very important point is that it is necessary to take into account the Coulomb correlation (A.Efros, B.Shklovskii) Two regimes 0<<1 ~hf ~T0 0>>1, ~hf~1/0(kT)~0Tn

  5. Effect of magnetic field • An external magnetic field deforms the wave function of the impurity electrons and reduces the overlap integrals . This integral depends on the angle between the magnetic field Н and an arm of pair r. Weak magnetic field Н<H0~H2 ~H2 High magnetic field Н>H0~H-4/3 ~H-2 -(H)=(0)- (H)(H)=- (0)+b/H2

  6. Acoustic methods Setup forlow dimensional systems Setup for 3-dimensional systems piezotransducer Sample CABLE 150-1500 MHz 17-400 MHz T=0.3-4.2 K, H=0-8 T

  7. Dependences of  оn Н; 1-0.58К,2-2.15К,3-4.2К f=810 MHz Dependences of (0) от Т; f=810(1), 630(2), 395(3),336(4), 268(5),207MHz(6) Lightly doped strongly compensated (К=0.84)n-InSb, 3-dimensional case

  8. 3-dimensional case 1= Re hf ~  2= Im hf~ V/V 2- Dimensionalcase A = 8b(q)(1+0) 02sexp[2q(a+d)],

  9. HF-hopping in 2D case A.L.Efros, Sov.Phys.JETP 62 (5),p.1057 (1985)

  10. 3-dimensional case 1= Re hf ~  2= Im hf~ V/V 2- Dimensionalcase A = 8b(q)(1+0) 02sexp[2q(a+d)],

  11. The dependences of real 1 and imaginary 2 parts of high frequency conductivity , T=1.5 K, f=30 MHz; n-GaAs/AlGaAs The absorption coefficient Γ and the velocity shift V/V vs. magnetic field (f=30 MHz)

  12. Dependences of 1, 2 on H near =2 at different T, n-GaAs/AlGaAs

  13. Two-site model nonlinearity

  14. The systems with a dense (41011 cm–2) array of Ge quantum dots in silicon, doped with B. Quantum dots (QD) has a pyramidal shape with the square base 100×100 ÷ 150×150 Ǻ2 and the height of 10-15 Ǻ. The samples have been delta-doped with B with the concentration (1÷1.12)·1012 cm-2. The boron concentration corresponds to the average QD filling 2.852.5 per dot

  15. Linear regime

  16. Left-Temperature dependence of  in the sample 1 for f=30.1 and 307 MHz, a=510-5cm. Right-Frequency dependence of  in the sample 2 at T-4.2 K, a=410-5cm In linear regime the high frequency hopping conductivity looks like hopping predicted by of "two-site model"provided >1 if holes hop between quantum dots. But 1> 2.

  17. Nonlinear regime

  18. Results of numerical simulations for b (the distance between the dots) Galperin, Bergli

  19. Conclusion • Hopping relaxation conductivity • At R>, • where R is the distance betweenpairs of impurity site,  is the localization length • 1. Hopping conductivity in 3-dimensional strongly compensated lightly and heavily doped semiconductors (n-InSb) is successfully • explained by two-site model • In strongly compensated lightly doped n-InSb it was observed crossover from<1to >1. • 2.In two-dimensional structures with quantum Hall effect there is hopping conductivity. This one is observed in minima of conductivity at small filling-factors and it is successfully explained by two-site model too. In this case Im  >Re  • At R • 3. The main mechanism of HF conduction in hopping systems with large localization length (dense arrays of Ge –in- Si quantum dots) is due to charge transfer within large clusters.

  20. Acknowledgments • I am very grateful to my numerous co-authors: • Yu.M.Galperin, L.B.Gorskaya, A.M.Diakonov, I.Yu.Smirnov, A. V.Suslov, V.D.Kagan, D.Leadley, • V. A.Malysh, N.P.Stepina, E.S.Koptev, J.Bergli, B.A.Aronzon, D. V.Shamshur • and ours very good technologists: V.S.Ivleva, A.I.Toropov, A.I. Nikiforov

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