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MAGNETOPHONON OSCILLATIONS IN THE LIFETIME OF HOT PHOTOEXCITED CARRIERS
F. Schmitte, G. Bauer, W. Zawadzki
To cite this version:
F. Schmitte, G. Bauer, W. Zawadzki. MAGNETOPHONON OSCILLATIONS IN THE LIFETIME OF HOT PHOTOEXCITED CARRIERS. Journal de Physique Colloques, 1981, 42 (C7), pp.C7-407- C7-412. �10.1051/jphyscol:1981750�. �jpa-00221687�
MAGNETOPHONON OSCILLATIONS IN THE LIFETIME OF HOT PHOTOEXCITED CARRIERS
F.J. Schmitte, G. Bauer*and W. Zawadzki**
I. Physikalisches Institut, RWTH Aachen , D-Sl Aachen, FRG
Institut fttv Physik, Montanuniversitat Leoben, A-8700 Leoben, Austria
* Institute of Physics, Polish Academy of Sciences, Warszawa, Poland
Résumé. - La dépendance en temps de la photoconductivité de n-InSb a été étudiée avec un LASER à "Q-Switch". A basses températures(T=4.2K),
la durée de vie des porteurs libres décroit lorsque le champs magné- tique augmente, et elle présente des oscillations dont la périodicité pourrait être déduite de la fréquence de piégeage de ces porteurs par les impuretés.Ce piégeaqe s'accompagne d'une émission de phonons-LO
(effet d'impureté magnétique)
Abstract. - The time dependent change of photoconductivity of n-InSb has been studied after photoexcitation with Q-switched C02-laser pulses. At liquid He temperatures, the lifetime decreases with the increasing magnetic field but exhibits a superimposed oscillatory- variation. The periodicity of this oscillation is consistent with a resonant capture of the carriers in impurity states, accompanied by LO-phonon emission (magnetoimpurity-effeet).
1. Introduction. - The magnetophononeffeet served for a long time as a simple but powerful tool for the investigation of the band structu- re of semiconductors and of the electron-phonon interaction.' Usually it is observed as an oscillatory magnetoresistance, where oscilla- tions occur due to inelastic scattering of carriers by optical phonons
(htoT_) and corresponding transitions between Landau states (huLO=N-ho) , u being the cyclotron resonance frequency)-At relatively low lattice temperatures,magnetophonon oscillations can only be observed under hot electron conditions.^'2
In this paper,we report about investigations of the magnetic field de- pendence of the lifetime of hot carriers in InSb, which were photo- excited by C02~laser radidation.
2. Experimental. - Photoexcited carriers were produced in InSb
(n=2-10 ...5-10 cm" , at 77K) using Q-switched C02-laser radiation with peak powers below 1 kW and pulse lengths up to 500ns. The samples were immersed in liquid helium in a split-coil magnetsystem.A schema- tic experimental set up is shown in Fig.1. The voltage drop across the sample before, during, and after illumination with the COj-laser pulse was measured using conventional boxcar techniques. The photo- conductivity experiments were performed under constant current
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981750
C7-408 JOURNAL DE PHYSIQUE
conditions, the applied electric fields being well below the impurity breakdown fields for the magnetic field range and temperatures in- vestigated.Thus the increase in conductivity was caused alone by the photoionization of carriers frozen on impurity sites.
Fig. 1: Experimental setup.
- current source
3. Experimental results. - A typical recorder tracing of the time de- pendent photoconductivity is shown in Fig.2.These traces were taken with a wavelength X=10.6pm. Operating the CO2-laser at more than one wavelength, did not change the observed photoconductivity spectra.
Fig. 2: Change of voltage drop AU along the sample during and after illumination.
Since only the carriers in the conduction band,i.e. in the Landau le- vels contribute to the total conductivity,Fig.2 indicates the time de- pendence of generation and recombination of photoexcited carriers.
There are various recombination processes by which the carriers can re- combine and we assume that these processes lead to a total carrier re- laxation time T. It turned out, that after the end of the laser pulse, the time dependent conductivitv is approximately governed by a simple
3 106
g' Fiq. 3: Recombination time as a function of B.Nmbers inzicate resonance conditions for magneto-
2 phonon series.
1
l 1
- t
0 0.5 10 T 1.5
-
-
Ip . 0.6 mA
-
%
- -applied magnetic field B-The depencence of -c-' on B is shown in Fig. 3.
Superimposed on monotonuous decaying background T exhibits an oscilla- tory dependence on B-The maxima of T-' correspond approximately to the magnetophonon resonance condition Nhwc=AwLO when the appropiate non- parabolic corrections are applied.
4.Discussion. - For an explanation of the lifetime of excited carriers the following processes have to be considered in InSb at helium tenpe- ratures (see Fig. 4. 4-8 ) .
Fiq. 4: Schematic diagram of various recombination proces- ses. I: impurity, ak: acoustic phonon interaction. For
clarity only the impurity states associated with the spin up Landau levels were included.
a) optical phonon emission d) ionized impurity scattering b) acoustical phonon emission e) resonant capture of carriers C) Auger processes from Landau states by impurity
states via LO-phonon emission A determination of the Landau level lifetime of nonequelibrium carriers was recently reported by Kiiller et for InSb and by Bluyssen et al. 6 r 7 for GaAs. Saturation absorption experiments5, observation of transient decay of photoconductivity after pulsed far infrared exi- tation 5 , current decay after electrical impurity breakdown5 and cyclo- tron resonance induced absorption followed by a conductivity change617 were measured by these authors. There is a puzzling difference between n - ~ a A s ~ ' ~ and n-1nsb5 as far as the recombination process from the lowest Landau level to the impurity ground state is concerned: in
6,7,10
n-GaAs this process seems to be about two orders of magnitude faster (10-'s) than in n-InSb. For our n-InSb samples and lattice temperatures below 10K it is typically of the order of several 100ns. Its exact value depends on compensation ratio, B, and T. This process is deter- mined by acoustic phonon scattering. lliiller et a l a 5 have shown that the lifetime in the n=l Landau level in InSb is in the subnanosecond regime and governed for electron concentrations of the order of
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1 0 ' ~ c m - ~ in this level already by an Auger process. Another inter Landau level transition process via LO-phonon scattering also yields Landau level lifetimes in the subnanosecond time scale. However, a possible recombination mechanism which directly influences the life- time of the excited carriers is the magnetoimpurity effect. It is as- sociated with the capture of electrons from Landau levels at donor im- purities, accompanied by optical phonon emission. This process is now considered in some detail:
The initial complete Hamiltonian in one-band effective mass approxima- tion is given by:
A-vector potential of external magnetic field, ss-static dielectric constant I % el-ph -electron-phonon polar interaction, q h - f r e e phonon field.
The initial free-electron state, described by the Landau gauge + A=[ -~y,0,01 is:
Y-Yo Yi = Aiexp (ikxx+ik z) @ (-)
z n L ( 2 )
Where yo=kxL 2 , in which L= (iic/eH) and A . -norm. coef f icient . The ii-
1
nal donor-in-a-magnetic field state isy :
where Af is a normalization coefficient, and al and a l l are variational parameters fixed for a given H. The Frohlich polar interaction is given by :
where a is the coupling constant, + q the phonon wavevector, b the
+ q
phonon destruction-, b the phonon creation operator\.
9
The first term in Eq.(4) describes phonon absorption, the second term phonon emission. The calculation of electron transitions Yi+Yf with optic phonon emission yields to the following result. For the "zWpart of the matrix element we get:
where k f = k -q
Z Z -2-
The "transverse" part of matrix element (assuming that it is the same as for the free electron state for sufficiently high fields, when al?L) is given by
I (Yf l l exp i-iq 1 1 r ) I Y ~ ) I 2--& ,"exp (-X)
where Ei=hwc (n+l/2) + h2ki/2m* 0 phonons
Ef = E ~ + ~ w ~ ~ 1 phonon of energy hwLO is the donor energy (counted from zero and not from the lowest Landau level).
The transition rate is obtained by multiplying Pfli by a statistical factor F ( E ~ , ~ ) [ 1-F ( E ~ ) I =F ( E ~ + ~ w ~ ~ ) [ 1-F (E=) 1 where F (E) is the distri- bution functign of photo-excited carriers (the Auger effect rando- mises the electron energies, so that one deals probably with Fermi- Dirac function for an effective temperature of hot electrons). The summation over electronic band states (n,kx,kz), donor states NI, and phonon states (qxrq ,q,) gives:
Y
where N is determined by the condition ~ ~ + f i ~ ~ ~ 2 R w ~ ( N + Z ) . 1 The recombination time T has zeros for the equality sign. One would need to cut the singularity in (8) to get a "physical" result.
The main process determining the lifetime of excited carriers in our case is still the 0 + +(000) transition (Fig.4). However, superimposed on this capture of free carriers is the magneto-impurity effect at resonant magnetic fields yielding to an oscillatory variation of the limetime of the carriers superimposed on a nonoscillatory background.
We would like to point out that from conductivity experiments under hot electron conditions (impurity breakdown accomplished by the application of high electric fields) this magnetoimpurity effect is well known 4 , whereas the normal magneto-phonon-oscillations (free carrier transitions hwLO=Nhwc) are not observed under hot electron conditions at liquid helium temperatures. 2
Acknowledgment. - The authors thank Prof.P.Grosse for his interest in this work. One of us (G.B.) would like to thank the "Fonds zur FGrderung der wissenschaftlichen Forschung", Vienna, Austria, for support .
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References.
1 R-A-Stradling, in Proc. Int. Conf. Phys. Semiconductors ed. M.Miasek (PWN, Warszawa 1972) p.261
2 W.Racek, G.Bauer, H.Kahlert, Phys.Rev.Lett. 31 301 (1973) 3 F.J. Schmitte, Diploma thesis, RWTH Aachen (1 978)
4 L.Eaves and J.C.Porta1, in the Application of High Magnetic Fields in Semiconductor Physics, ed.J.F. Ryan (Oxford 1978)p.116 5 W.PIiiller, E-Gornik, T.J.Bridges, T.Y.Chang, Solid State Electronics
21, 1455 (1978)
6 H.J.A. Bluyssen, J.C. Maan, P.F7yder, Solid State Commun. 31,
465 (1979)
7 H.J.A. Bluyssen, J.C. Maan, T.B. Tan, P. Wyder, Phys.Rev. S, 749 (1980)
8 0. Matsuda, E.Otsuka, J.Phys.Chem.Solids 40 819 (1979)
9 Y.Yafet, R.W.Keyes, and E.N. Adams, J.Phys.Chem.Solids 1, 137 (1956)
10 However, time-dependent luminescence results on the (e,AO) recombination in GaAs indicate that the lifetime of electrons in the lowest Landau level is of the order of 10-7s:
D.Schulz, Diploma thesis, Dortmund University 1979, R-G-Ulbrich, private communication
