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, , С.- Петербург, ул.Политехническая, 26

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

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

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

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<H 0   ~H 2   ~H 2 High magnetic field Н>H 0   ~H -4/3   ~H -2 -  (H)=  (0)-  (H)  (H)=-  (0)+b/H 2

Acoustic methods Sample CABLE piezotransducer Setup for 3-dimensional systems Setup for low dimensional systems MHz MHz T= K, H=0-8 T

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

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

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

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

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

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

Two-site model nonlinearity

The systems with a dense (4  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 Ǻ 2 and the height of Ǻ. The samples have been delta-doped with B with the concentration (1÷1.12)·10 12 cm -2. The boron concentration corresponds to the average QD filling  2.85  2.5 per dot

Linear regime

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. Left-Temperature dependence of  in the sample 1 for f=30.1 and 307 MHz, a=5  cm. Right-Frequency dependence of  in the sample 2 at T-4.2 K, a=4  cm

Nonlinear regime

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

Conclusion Hopping relaxation conductivity At R> , where R is the distance between pairs 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  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.

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