Surface Acoustic Waves probe of the p-type Si/SiGe heterostructures

0.17 MB·English

by  G. O. Andrianov

CondMat 2004
Surface Acoustic Waves probe of the p-type Si/SiGe heterostructures
G. O. Andrianov, I. L. Drichko, A. M. Diakonov, and I. Yu. Smirnov
A. F. Ioffe Physicotechnical Institute of RAS, 194021 St.Petersburg, Russia
O. A. Mironov, M. Myronov, T. E. Whall, and D. R. Leadley
4
Department of Physics, University of Warwick, Coventry CV4 7AL, UK
0
(Dated: February 2, 2008)
0
2 The surface acoustic wave (SAWs) attenuation coefficient Γ and the velocity change ∆V/V were
n measured for p-typeSi/SiGe heterostructures in thetemperature range 0.7 - 1.6 K as a function of
a external magnetic field H up to 7 T and in the frequency range 30-300 MHz in the hole Si/SiGe
J heterostructures. Oscillations ofΓ (H)and∆V/V (H)in amagneticfieldwereobserved. Both real
0 σ1 (H)andimaginaryσ2 (H)componentsofthehigh-frequencyconductivityhavebeendetermined.
3 Analysis of the σ1 to σ2 ratio allows the carrier localization to be followed as a function of tem-
perature and magnetic field. At T=0.7 K the variation of Γ, ∆V/V and σ1 with SAW intensity

] havebeenstudied andcould beattributed to2DHGheatingbytheSAW electric field. Theenergy
l relaxation timeisfound tobedominated byscatteringat thedeformation potential oftheacoustic
l
a phononswith weak screening.
h
-
PACSnumbers: 73.63.Kv,72.20.Ee,85.50.-n
s
e
m
I. INTRODUCTION erostructureswith2DHGsheetdensityp=2 1011cm−2
t. and mobility µ=10500 cm2/Vs2. ×
a
m For the first time an acoustic method has been ap- Fig. 1illustratesthefielddependencesofΓand∆V/V
for the frequency 30MHz at T=0.7 K as well as com-
pliedinastudyofp-typeSi/SiGeheterostructures. Since
-
d Ge and Si are not piezoelectrics the only way to mea- ponents of the magnetoresistance. One can see the ab-
n sure acoustoelectric effects in these systems is a hy- sorption coefficient and the velocity shift both undergo
o SdH-type oscillations.
brid method: a SAW propagates along the surface of
c
a piezoelectric LiNbO while the Si/SiGe sample is be-
[ 3
ing slightly pressed onto LiNbO surface by means of 30
1 a spring. In this case a strain3from the SAW is not 3) 7
v transmittedto the sample andit is only the electric field -10 6 G r 25 )
631 apclecoamnpdacnryeiantgesthceurSreAnWts tthhaatt,pinenteutrrant,espriondtouctehae fseaemd-- V/V ( 45 xy 20 W (kxy
1 back to the SAW. As a result, both SAW attenuation Dd 15 rd
n 3 n
40 oΓfatnhde 2vDelHocGit.ySVAWa-papceoaursttiocsdperpoevneds toonbteheanpreoffpeecrttiivees m) a 2 10 ) a
/0 probe of heterostructure parameters, especially as it is B/c 1 r 5 W(kxx
at contactless and does not require the Hall-bar configura- (d 0 D V/V xx 0 r
tion of a sample. Moreover,simultaneous measurements
m G
0 1 2 3 4 5 6 7 8
of attenuation and velocity of SAW provide a unique
- possibility to determine the complex AC conductivity, H (T)
d
n σxx(ω)=σ1(ω) iσ2(ω), as a function of magnetic field
−
o H and SAW frequency ω. Furthermore, the magnetic
FIG. 1: Dependences of Γ(H) and ∆V/V(H), f=30MHz,
c field dependence of σ (ω) providesinformation onboth
v: the extended and locxaxlized states1. T=0.7 K;ρxx and ρxy vsH, T=0.7 K.
Xi High frequency conductivity σxAxC = σ1 − iσ2 is
extracted from simultaneous measurements of Γ and
r
a II. EXPERIMENTAL RESULTS ∆V/V, using eqs. 1-5 of1.
Itturns out,thatatT=0.7Kandfillingfactorν=2 (H
TheabsorptionΓandvelocityshift∆V/V oftheSAW, = 4.3 T) σ σ (fig.2). At the same time σ σdc.
1 ≃ 2 1 ≫ xx
thatinteractswith2DHGintheSiGechannel,havebeen These facts suggest that only some of holes in the 2D-
measuredattemperaturesT=0.7-1.6Kinmagneticfields channel are localized, and σAC is determined by both
xx
uptoH=7T.DC-measurementsoftheresistivitycompo- localizedanddelocalizedholes. Fortotallocalizationone
nentsρ andρ havealsobeencarriedoutinmagnetic needsσ σ ,σDC=03. Atν=3(H=2.9T)localization
fields uxpxto 11Txyin the temperature range 0.3-1.3 K and effects a1re≪neg2ligixbxle: σ σdc >σ .
1 ≃ xx 2
have shown the integer quantum Hall effect. At T=0.7K we have measured the dependences of
The samples were modulation doped Si/SiGe het- Γ(H), ∆V/V(H) and σ (H) on the SAW intensity at
1
2
10-3 s
a b
1
10-4 n =3 n =2 -1) 2 4.3T -1) 2 4.3T
-1) 10-5 -5W0 2.9T -5W0 2.9T
1 1
W (1,2 10-6 DC s (11 s (11
s
s
10-7 2 0 0
10-8 10-510-410-310-2 0.8 1.2 1.6
1 2 3 4 5 6 7 8 P (W) T (K)
H (T)
FIG. 3: (a) σ1 vs the RF-source power P; (b) σ1 versus
FIG.2: Magneticfielddependencesofσ1 (solid),σ2 (dashed) temperature T in the linear regime. f=30 MHz, H = 4.3T
at f=30MHz and σDC (dotted);all at T=0.7 K. and 2.9T.
xx
We have analyzed the energy losses rate per hole Q=
30MHz. Fig. 3a shows σ versus P (the RF-source
1 Q¯/pasafunctionofT (Fig.4). Intheinset,Qisplotted
power)formagneticfieldsofH=2.9Tand4.3T.Fig.3b c
vs (T5 T5) and a linear dependence is illustrated.
illustratesthetemperaturedependenceofσ1measuredin c −
the linear regime. One can see from these plots that σ
1
increases with increasing temperature and SAW power. 3
3
For delocalized holes in this magnetic field, the ob-
served nonlinear effects (Fig.3a) are probably associated V/s) 2
with carrier heating. One may describe 2DHG heating4 e
by means of a carrier temperature Tc, greater than the V/s) 2 Q (k 1
lattice temperature T, provided that the following con- e
dition is met: k 0
(
Q 1 0 T55-T5 1(0K5)15
c
τ <<τ <<τ . (1)
0 cc ε
0
Here τ , τ and τ are the momentum relaxation
0 cc ε
0.8 1.2 1.6
time, the carrier-carrier interaction time and the en-
ergy relaxation time, respectively. Calculations give T (K)
τ = 1.4 10−12s; τ = 6.4 10−11s5; τ will be dis- c
0 cc ε
× ×
cussed below.
FIG. 4: The energy losses rate per hole Q = Q¯/p plotted vs
theTrhmeomcaertrrieyrbtyemcopmerpaaturirnegTtcheisddepeteenrdmeinnceeds uσsi(nTg)SadnHd Tc. Inset: dependenceof Q on (Tc5−T5).
1
σ (P).
1
For weak heating (∆T = T T T) one
To characterize heating process one needs to extract c − ≪
can estimate the energy relaxation time from τ =
the absolute energy losses as a result of the SAW inter- ε
action with the carriers Q¯ =σ E2 =4ΓW, where W is (πkB)2/(3γAγεFTγ−2)6, where γ=5 in this case, εF is
xx the Fermi energy and A is the slope of the Q(T5 T5)
the input SAW power scaled to the width of the sound 5 c −
track, E is the intensity of the SAW electric field6: dependence. Using this equation we have computed
τ =(3.8 0.4) 10−8s. Thus, relation (1) is satisfied.
ε
± ×
Theobserveddependenceoftheenergylossrateonthe
|E|2 =K23V2π(ε1+ε0)1+z((q4)πqσexA(x−C2tq(aq)))2W, (2) cthaerricearseteomfpeenreartguyrerealsaxQat=ionAv5(iaTc5ca−rrTie5r)sccoartrteesrpinogndfrsotmo
εsV the deformation potential of the acoustic phonons with
weak screening4,7. In which case the slope A is7:
5
K2 is the electromechanical coupling constant of the
lithium niobate (Y-cut), q is the SAW wave vector; ε ,
s
ε and ε are the dielectric constants of semiconductor, 3√2m2ζ(5)D2 k5
0 1 A = ac B, (3)
freespaceandLiNbO3,respectively;aisthewidthofthe 5 π5/2s4~7p3/2ρ
sample-LiNbO clearance; z(q) and t(q) are functions to
3
allow for the electrical and geometrical properties of the where ρ is the mass density, s is the longitudinal sound
sample. velocity, m=0.24m is the effective mass5. Thus, one
e
3
can determine the value of the deformation potential as
D =5.3 0.3 eV. The value of D calculated from DC
ac ac
±
measurementsofphonon-dragthermopowerwasreported
to be 5.5 0.5 eV for the same 2DHG Si/SiGe sample8.
±
Acknowledgments
The work was supported by RFFI, NATO-CLG
979355,INTAS-01-084,Prg. MinNauki ”Spintronika”.
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