Suppression of D'yakonov-Perel spin relaxation in InAs and InSb by ntype doping at 300K
P. Murzyn1, C. R. Pidgeon1 and P. J. Phillips1
1
Department of Physics, Heriot-Watt University, Edinburgh EH14 4AS, UK.
M. Merrick2, K. L. Litvinenko2 J. Allam and B. N. Murdin2
2
Advanced Technology Institute, University of Surrey, Guildford GU2 7XH, UK.
T Ashley3 and J H Jefferson3
3
QinetiQ, St Andrews Road, Malvern, Worcs WR14 3PS, UK.
L F Cohen4
4
Blackett Laboratory, Imperial College, London SW7 2BW, UK.
We have made direct pump-probe measurements of spin lifetimes in intrinsic and
degenerate n-InAs at 300K. In particular, we measure remarkably long spin lifetimes, s ~
1ns, for near-degenerate epilayers of InAs. For intrinsic material we determine s ~ 20ps in
agreement with other workers. There are two main models that have been invoked for
describing spin relaxation in narrow gap semiconductors: the D'yakonov-Perel (DP) model
and the Elliott-Yafet (EY) model. For intrinsic material the DP model is believed to dominate
in III-V materials above 77K, in agreement with our results. We show that in the presence of
strong n-type doping, the DP relaxation is suppressed both by the degeneracy condition and
by electron-electron scattering, and that the EY model then dominates for the n-type material.
We show that this same process is also responsible for a hitherto unexplained lengthening of
s with n-type doping in our earlier measurements of n-InSb.
PACS: 72.25.Fe, 72.25.Rb
Utilisation of the electron spin has become a focus of interest in semiconductor
electronics, or spintronics, in recent years, and it is important to realise a sufficiently long spin
lifetime, s, to process information stored in the form of the polarisation of spin ensembles.
To find a way to control s it is necessary to understand the spin relaxation mechanisms in
both bulk and low dimensional semiconductor structures which are designed so that spins can
be appropriately confined and/or transferred. In contrast to GaAs-based systems, relatively
little attention has been paid to InAs, even although it may be important in future spintronics
applications. We previously measured spin lifetimes in narrow gap semiconductors (NGS),
Hg1-xCdxTe and InSb, at wavelengths between 4 and 10m and from 4 - 300K8. We have
now extended those measurements to include bulk epilayers of InAs as a function of doping at
300K.
The InAs samples were grown at Imperial College by MBE on GaAs substrates with
the following 300K Hall effect characteristics. IC313: n = 3.8x1016cm-3, mobility  =
3x104cm2V-1s-1; IC311: n = 1x1017cm-3,  = 2.5x104cm2V-1s-1. The InSb samples used in
our previous work8 were as follows:
ME1654:
n = 1.5x1016,  = 6.9x104cm2V-1s-1;
ME1629: n = 2.3x1017cm-3,  = 4.5x104cm2V-1s-1. To measure the spin lifetimes, we used
the standard polarization pump-probe method7,8,14, which excites spins in the semiconductor
with above-bandgap, circularly polarized light, and probes the induced bleaching with either
the same or the opposite circularly polarized light (SCP or OCP respectively). The pump and
probe beams are pulsed, and by changing the time delay between the pump and probe and
comparing the SCP and OCP results we measure the spin decay lifetime. The optical pulses
for the experiment, carried out at the University of Surrey, were generated with a solid-state
laser system (DFG 9850, Coherent Inc., Santa Clara CA, USA) that produces ~40 fs pulses
from 2.5 to 11 m wavelength, with a repetition rate of 250kHz and typical average power of
5mW. The beams were focused on to the sample with spot sizes of approximately 100m,
and the transmitted probe light was detected with a liquid nitrogen cooled InSb photodiode.
Results for the transmission change in the probe due to the pump are shown for
sample IC313 in Fig. 1 for SCP and OCP configurations. The data are characterised by three
features and are in extremely good agreement with the results of other workers7. In both
cases there is a transient increase in transmission that is initiated and decays in less than 2ps.
We attribute this to thermalisation of the optically injected carriers, hole spin relaxation and
coherent artifacts of the system7. The second feature is a clear distinction between the SCP
and OCP data that occurs during the first 40ps and is caused by the spin polarisation
relaxation. Finally, there is a long decay of both SCP and OCP that occurs on a longer,
nanosecond scale. Following ref 7, we plot the fractional difference in transmission between
SCP and OCP, Popt = (TSCP - TOCP)/(TSCP + TOCP) shown in the inset. This, when fitted
with a monoexponential decay, yields a time constant of = 20ps. The error in the fitting due
to noise in the data is estimated to be ±10 ps.
Because of the different transition strengths associated with heavy hole and light hole
to conduction band transitions from a complex (spin-orbit mixed) valence band, a partially
spin-polarised distribution is created by pumping with circularly polarised radiation. If we
take the case of (e.g.) a left circularly polarised pump pulse (-), the relative concentration of
optically generated spin up (n) to spin down (n) electrons is 3:1, leading to a maximum spin
polarisation of Ps = 0.5, where Ps = (n - n)/( n + n)7,8,14 . The actually measured probe
transmission is proportional to the absorption change, . A - probe will experience - 
3nopt+ nopt, while a + probe will experience +  3nopt+ nopt.
Thus the optical
polarisation signal becomes: Popt = (- - +)/(- + +) = 0.5 Ps , which has a maximum
value 0.25. In practice our polarisers were not fully optimised for these long wavelengths, so
the maximum polarisation we achieve is somewhat less than 25%.
In order to test the effect of n-type doping the measurements were repeated for the
near degenerate sample, IC311, and the results are shown in Fig. 2. Although the change in
polarization Popt from SCP to OCP is quite large, the decay times of each are similar to each
other and also to the electron-hole recombination rate. We therefore show in this figure the
SCP and OCP data normalized to the peak so that the difference in slope is more apparent.
Clearly the decay of the spin polarisation is substantially lengthened, and the decay time of
Popt, plotted in the inset, is now = 1.6±0.5 ns. Similar, and hitherto uninterpreted, results
were obtained for InSb in our earlier work8: ME1654 ( = 16ps) and ME1629 ( = 300ps).
In bulk semiconductors three main spin relaxation processes have been found to be
important in optical orientation experiments: the Elliott-Yafet (EY)1,4,5,6, D'yakonov-Perel
(DP)2,5,6 and the Bir-Aronov-Pikus (BAP)3 mechanisms. The BAP mechanism is thought to
be particularly important in p-type wide gap materials and is based on the electron-hole
exchange interaction. By contrast with the other two processes, it depends directly on the
concentration of holes, and is not thought to be important in n-type NGS.
The EY mechanism results from the fact that in real crystals Bloch states are not spin
eigenstates because of the strong spin-orbit coupling induced by the lattice ions. In the
presence of strong spin-orbit coupling, the valence band states have mixed spin character. In
NGS the conduction electron states, in turn, are strongly mixed with the valence states
through the k.p interaction across a narrow energy gap.
In this case spin-independent
interactions with impurities, boundaries, phonons etc., can connect spin up and down
electrons, leading to spin flip transitions whose rate 1/s is proportional to 1/p where p is the
orbital momentum (mobility) scattering time. This process has been shown to be important at
low temperatures in NGS4,5,6. The EY spin relaxation rate for ionised impurity scattering and
degenerate statistics is:
1 32  E F 



 s 27  E G 
2
2
1  / 2  1


 1   / 3  p
,
(1)
where  = /(EG+), and  is the spin-orbit splitting of the valence band. In the other limit of
lattice scattering and non-degenerate statistics the EY expression becomes:
 kT 
1

 2
s
 EG 
2
2
1  / 2  1


.
 1   / 3  p
(2)
The DP mechanism has been shown to dominate at temperatures above 77K in
intrinsic or lightly n-type NGS6,7, where the lack of inversion symmetry in the presence of a
k-dependent spin-orbit interaction lifts the spin degeneracy even in the absence of a magnetic
field2. Somewhat counter-intuitively, and in contrast with EY, the spin relaxation rate 1/s is
subject to motional narrowing, and is therefore directly proportional to the orbital (mobility)
scattering time, p. In NGS both the EY and the DP mechanisms may be important, as shown
by reports of spin relaxation in InSb at helium temperature4,5 and InAs at room temperature7 the former being interpreted in terms of EY and the latter of DP. Typically spin lifetimes in
the range 1-10ns were obtained from spin resonance in degenerate n-type InSb at helium
temperatures, whereas a spin lifetime of 20ps was reported for lightly n-type InAs at 300K.
The DP relaxation rate for lattice scattering and non-degenerate statistics:
1
(kT) 3
 0.8 2 2
p .
s
 EG
(3)
For the case of degenerate statistics the DP expression becomes:
1
16 2 (E F ) 3


p ,
 s 315  2 E G
(4)
where6 :  
4 m c
.
30 m 0
We note that the spin relaxation in interband optical orientation experiments such as
this will be dominated by electrons, as the fourfold degeneracy of the valence band at k = 0
and the large spin-orbit coupling are expected to result in extremely rapid decay of the hole
spin polarisation.
In our previous work8 we demonstrated that the temperature dependence of the results
for n-type Hg0.78Cd0.22Te could be explained in terms of the EY model. We also showed a
remarkable lengthening of the spin lifetime in InSb from ~16ps for intrinsic material to 300ps
for the degenerate case. The reason for lengthening was not explained in detail, but we
showed that the longer spin lifetime of the degenerate case was consistent with the EY
process dominating as with the HgCdTe.
For intrinsic and lightly doped samples the DP process (equation (3)) dominates for both
InAs and InSb [theoretical/experimental values for DP are obtained as follows: IC313
(20ps/20ps), and ME1654 (10ps/16ps)].
The EY process (equation (2)) gives EY ~ 530ps
and EY ~ 350ps respectively, so that clearly it is not important for this case.
In the presence of significant n-doping two points become extremely important with
regard to the DP process. In the first instance it is obvious from the pre-factor in equation (4)
that the onset of degeneracy considerably suppresses the DP process. Thus, for the more
heavily doped samples in this limit we obtain theoretical values from equations (1) and (4) as
follows:
IC311 (EY ~ 500ps, DP ~ 800ps) and ME1629 (EY ~ 100ps, DP ~ 100ps).
However, in addition to this it has been convincingly demonstrated recently9 that for the DP
process the precession of an electron spin can be as effectively randomised by scattering from
another electron (i.e. electron-electron scattering) via the Coulomb interaction as by scattering
from thermal vibrations or defects, and yet this process can affect the mobility only weakly.
These authors have found in the case of GaAs that for a degeneracy temperature given by
kT/EF ~ 1.0 (approximately our case for the InAs, IC311) the actual time between momentum
scattering events, p*, is an order of magnitude shorter than the mobility time p, thereby
lengthening the value of DP obtained by a further factor of 10. Thus, for both these reasons
we expect the spin relaxation for samples IC311 and ME1629 to be dominated by the EY
process, and in fact this gives reasonable agreement with our measured values of  given the
simplifications of the model (equation (1)) [experiment/theory(EY): IC311, 1.0ns/500ps;
ME1619, 300ps/100ps].
In summary, we have measured remarkably long spin lifetimes (~ 1.6 ns) in neardegenerate n-InAs at 300K. This, together with our earlier results for degenerate n-InSb ( ~
300 ps)8, is explained in terms of the suppression of the DP spin relaxation process by the
degeneracy condition and by electron-electron scattering. We here present new results for
both intrinsic and near-degenerate InAs at 300K, and show that both the InAs results and the
earlier InSb results give direct evidence of the suppression of the DP process by the
degeneracy condition and by electron-electron scattering9,10, in the presence of strong n-type
doping. The EY process then dominates for the n-type material. The long spin lifetimes are
clearly important from the point of view of devices of the spin transistor type11,12,13.
We gratefully acknowledge the support by EPSRC and the Stichting voor Fundamenteel
Onderzoek der Materie (FOM), as part of the UK programme at FELIX. We are also grateful
for partial support from the FENIKS project (EC: G5RD-CT-2001-00535).
References
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G L Bir, A G Aronov and G E Pikus, Sov. Phys. JETP 42, 705 (1976).
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R Bichard, P Lavallard and C Benoit a la Guillaume, Inst. Phys. Conf. Ser. No 43,
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Figure Captions
1. Pump-probe transmission change as a function of probe delay time for pump and probe
having the same circular polarisation (SCP), and the opposite (OCP), for lightly doped nInAs at 300K (sample IC311, n = 3.8x1016.cm-3). The inset shows the difference of the
SCP and OCP signals divided by their sum. The solid curve is a fit of a monoexponential,
giving a measured decay constant of  = 20 ps.
2. As Fig 1 for heavily doped n-InAs at 300K (sample IC313, n = 1.0x1017.cm-3), except that
the SCP and OCP data have been normalized at the peak to make clear the difference in
slope. The inset shows the difference in the un-normalized data, and the decay time of the
fit is  = 1.0 ns.
Transmission change [a.u]
=20ps
P [%]
4
2
0
SCP
0
50
100
Delay [ps]
OCP
0
20
40
60
80
Delay [ps]
100
120
140
Transmission change [a.u]
P [%]
OCP
=1.6ns
SCP
15
10
0
0
500
Delay [ps]
200
400
Delay [ps]
600
800