high frequency hopping conductivity in semiconductors. acoustical methods of research. i.l.drichko
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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 - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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High- frequency hopping conductivity
• Two-site model
E
2 2E
,
=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
r
1.Resonant (phononless) absorption
2.Relaxation (nonresonant) absorption
kT E
E
Two-site model can be applied if ()>>(0). The hops between different pairs are absent..
12
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Relaxation case
2
2 2~
1p
1 2 2( ) ( ( ) )E t e t r
0n n n
t
M.PollakV.GurevichYu.GalperinD.ParshinA.Efros
B.Shklovskii
n0 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
2
0
1 1( )
( , ) ( )E r E E
0 (E) is the minimum value of the population relaxation time for symmetrical pairs with =0
0<<1 ~hf ~T00>>1, ~hf~1/0(kT)~0Tn
~cos t
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Effect of magnetic field
0 2
cH
e
c
eH
• 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
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Acoustic methods
Sample CABLE
piezotransducer
Setup for 3-dimensional systems
Setup for low dimensional systems
17-400 MHz150-1500 MHz
T=0.3-4.2 K, H=0-8 T
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Dependences of (0) от Т; f=810(1),
630(2), 395(3),336(4), 268(5),207MHz(6) Dependences of оn Н;
1-0.58К, 2-2.15К, 3-4.2К f=810 MHz
Lightly doped strongly compensated (К=0.84) n-InSb, 3-dimensional case
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21
2 22 1
(4 ( ) / )8.68
2 [1 4 ( ) / ] [4 ( ) / ]s
s s
K t q VqA
t q V t q V
A = 8b(q)(1+0) 02sexp[2q(a+d)],
VV
KA
t q V
t q V t q Vs
s s
22
22
122
1 4
1 4 4
[ ( ) / ]
[ ( ) / ] [ ( ) / ]
28.68
2 21 ( )M
M
K q
2- Dimensional case
14M
1 2hf i
3-dimensional case
1= Re hf ~ 2= Im hf ~ V/V
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HF-hopping in 2D case
1 2hf i 2 1Im( ) Re( )hf hf
Re ~hf Im ~hf
A.L.Efros, Sov.Phys.JETP 62 (5),p.1057 (1985)
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21
2 22 1
(4 ( ) / )8.68
2 [1 4 ( ) / ] [4 ( ) / ]s
s s
K t q VqA
t q V t q V
A = 8b(q)(1+0) 02sexp[2q(a+d)],
VV
KA
t q V
t q V t q Vs
s s
22
22
122
1 4
1 4 4
[ ( ) / ]
[ ( ) / ] [ ( ) / ]
28.68
2 21 ( )M
M
K q
2- Dimensional case
14M
1 2hf i
3-dimensional case
1= Re hf ~ 2= Im hf ~ V/V
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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
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Dependences of 1, 2 on H near =2 at different T, n-GaAs/AlGaAs
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Two-site model nonlinearity
0 50 100 150 200 250 300 350
1.0
1.5
2.0
2.5
3.0
3.5
E, a
.u
t, a .u.
kT
2 2( ) ( ( ) )E t e t r
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The systems with a dense (4The systems with a dense (410101111 cm cm–2–2) array of Ge ) array of Ge quantum dots in silicon, doped with B.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 The boron concentration corresponds to the average corresponds to the average QD filling QD filling 2.85 2.852.5 per 2.5 per dotdot
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Linear regime
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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=510-5cm. Right-Frequency dependence of in the
sample 2 at T-4.2 K, a=410-5cm
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Nonlinear regime
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Results of numerical simulations for b (the distance between the dots) Galperin, Bergli
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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 to >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.
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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