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GEOMETRICAL DEPENDENCE OF TRANSIENT NONLINEARITIES IN MULTIPLE QUANTUM
WELL STRUCTURES
R. Manning, A. Miller, D. Crust, K. Woodbridge
To cite this version:
R. Manning, A. Miller, D. Crust, K. Woodbridge. GEOMETRICAL DEPENDENCE OF
TRANSIENT NONLINEARITIES IN MULTIPLE QUANTUM WELL STRUCTURES. Journal de
Physique Colloques, 1988, 49 (C2), pp.C2-237-C2-240. �10.1051/jphyscol:1988256�. �jpa-00227673�
JOURNAL DE PHYSIQUE
Colloque C2, Supplement au n06, Tome 49, juin 1988
GEOMETRICAL DEPENDENCE OF TRANSIENT NONLINEARITIES IN MULTIPLE QUANTUM WELL STRUCTURES
R.J. MANNING, A. MILLER, D.W. CRUST(^)^^^ K. WOODBRIDGE*
Royal Signals and Radar Establishment, St Andrews Road.
GB-Great Malvern WR14 3PS. Worcestershire, Great-Britain
'philips Research Laboratory, Cross Oak Lane, GB-Redhill RHI 5HA, Surrey, Great-Britain
Abstract
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The transient grating technique has been used with sub-picosecond pulses to study the magnitude, dynamics and saturation of the excitonic nonlinear refraction in roomtemperature GaAs/Al~aAs multiple quantum wells. The dependence of grating decay time with sample orientation in the phase conjugate geometry, was measured and interpretted in terms of intra-well and cross-well contributions to the highly anisotropic carrier diffusion.
1
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INTRODUCTIONRefractive optical nonlinearities associated with excitonic features in semiconductors can be very sensitive, and may be usefully employed in all-optical switching devices if sufficient refractive index change can be induced before the exciton absorption is completed saturated. For GaAsIAlGaAs multiple quantum wells (MQW), the room temperature excitonic nonlinear refraction is apparent at
less than a milliwatt of incident cw optical power 111. Larger refractive index changes are possible through the band filling mechanism, at the expense of higher powers 121. Band gap renormalisation from many body effects will also contribute. The studies reported here concentrate on the excitonic contributions to the nonlinearity, but the carrier dynamics and consequent response times will be the same for other band gap resonant optical nonlinearities in MQWs
.
Spatial confinement plays a double role in the experiments reported here. Firstly, exciton confinement in MQWs leads to clearly resolved absorption features at room temperature which serve to enhance the size of the nonlinearity for photon energies close to resonance with the exciton.
On the time scales encountered in these experiments, this nonlinearity arises from saturation of the exciton absorption associated with the heavy hole valence band by phase space filling 131.
Secondly, spatial confinement of optically generated carriers within the quantum wells produces highly anisotropic carrier diffusion. This will affect the relaxation times associated with four wave mixing. Two different transient grating configurations were employed. A forward travelling geometry determined the magnitude of the room temperature excitonic nonlinear refraction, its saturation, and its dynamics via the decay of the diffracted signal through intrawell carrier diffusion. A counterpropagating (phase conjugate) geometry was used to study a short period grating established perpendicular to the wells. Short period gratings are not normally observed in bulk semiconductors because they are rapidly washed out by carrier diffusion (-10-13s in bulk GaAs). However, this grating is observed in semiconductor doped glasses, because carrier
diffusion is inhibited in these materials. Quantum wells provide the unique situation whereby the short period grating can be observed as a consequence of confinement and the grating decay
constant can be controlled by sample rotation because of the highly anisotropic diffusion associated with the wells.
("present address : Department of Physics. University of St Andrews. GB-Fife KY16 YSS. Great-Britain
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988256
JOURNAL
DE
PHYSIQUE2
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EXPERIMENTALTwo samples were grown by molecular beam epitaxy (MBE) under slightly different conditions. Both consisted of 120 periods of 601 thick GaAs quantum wells with 2001 A1xGal-xAs (x ' 0.4) barriers, but they possessed different excess carrier recombination rates. The substrates were removed by selective etching and the samples mounted on sapphire. Anti-reflection coatings were deposited on both surfaces. A tunable, synchronously mode-locked Styryl 9 dye laser with intracavity saturable absorber, produced pulses of -600fs duration. In the experiments, the repetition rate of the system was reduced by a factor of five using a cavity dumper to give a pulse separation of -6511s and an average output power of-35mW. From excite-probe measurements, the carrier lifetimes of the two samples were measured as 4ns (KLB257) and 7011s (KLB269) 141.
The four wave mixing configurations are shown in figure 1. Both the three beam, forward
travelling and counter-propagating experiments were performed under resonant excitation with the exciton at 830nm. These geometries allowed creation of gratings either in the plane of the wells or across the wells respectively. The probe pulses were delayed via a stepper motor driven, variable path length stage. First order diffracted light from the probe beams monitored efficiencies and grating lifetimes.
Excite
Diffracted Probe Diffracted Probe
(4 (b)
Fig. I
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Experimental configurations, (a) forward travelling, and (b) counter propagating.3
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RESULTSIn the forward travelling geometry, figure la, two excite pulses, incident at an angle $ either side of the normal, are arranged to fall coincidently in space and time upon the sample. In doing so, they interfere to form a sinusoidal intensity pattern of period, A , determined by $, in the plane of the wells. The excite pulses were focussed to a beam waist,wo of 25um. Measurements of diffraction efficiency were carried out with the probe pulses delayed by 15ps relative to the overlapping excite pulses. The peak diffraction efficiency occurred on the long wavelength side of the heavy hole exciton feature, consistent with a refractive grating; the expected quadratic dependence of the diffraction efficiency on excite pulse energy was observed up to4300vW of average power per excite beam 141. This corresponds to an estimated generated carrier density of -2x1017cm-3, which agrees well with the expected saturation of the nonlinearity through screening.
The low power results :imply a refractive index change per electron hole pair, neb- 0.4x10-~9cm~, slightly lower than measured by Chemla et a1 /I/ from two pulse self-diffraction grating
measurements in similar structures. The maximum diffraction efficiency was measured at- 0.1% from a refractive index change of -0.5~10-2 at an average power of- 3mW per excite arm.
The diffraction efficiency is given by a first order Bessel function. This may be approximated at low levels to efficiencies which are proportional to the square of the modulation depth of the refractive index. Thus, the decay rate of the diffracted signal, r, is twice the rate of relaxation of the carrier density modulation, and is given by,
IiL T~
where Da is the ambipo:lar diffusion coefficient and T R is the carrier recombination time. The grating spacing in this; forward travelling geometry was varied by adjusting 4 . Figure 2 shows the measured grating decays; for both samples, as a function of 8n2/~2. The gradients determine ambipolar diffusion coefficients of 14 and 16.2cm2/s for 4ns and 7011s samples respectively.
Fig. 2
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Observed signal decay rates for forward travelling geometry.In the counterpropagating configuration, figure lb, interference between the two excite pulses set up a modulated carrier density across the wells when they are arranged to overlap in both space and time within the sample. The grating periodah, covers approximately 5 quantum wells. For these measurements, the front excite beam was polarisation modulated at 50kHz for phase sensitive detection of the diffracted probe. The decay of the grating depends on the angle between the grating and the quantum wells. Figure 3 shows the diffracted probe signal as a function of time for several angles of rotation of sample KLB269 about a horizontal axis. The angle, 8 , is a measure of the rotation from the normal position. Any grating relaxation time between about 40 and 500 picoseconds could be readily selected by sample rotation in this way. Simple geometrical considerations of the arrangement would suggest that intra-well diffusion should contribute to the observed decay rate when the grating is angled with respect to the wells.
Delay Ins)
Fig. 3
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Diffracted signal decays for three different angles of the sample from the vertical in the counter propagating configuration.Under these circumstances, the separation of carrier density maxima along the wells is given by Antsinewhere n is the refractive index. In this case,h is essentially constant with sample
rotation. If we assume that the diffusion of carriers parallel and perpendicular to the wells is independent, then equation 1 becomes,
2 2
8.rr D sin 0
r = 2 2
2 2
+ - + -
A n R
where rl is the grating decay time due to cross-well diffusion. Figure 4 plots the measured decay rates versus sin2(8/n). The solid line is the anticipated relaxation rate due to intrawell diffusion given by figure 2. The intercept at zero angle implies a carrier grating decay rate of -Ins. This timescale arises from a combination of the time taken to promote initially cold
carriers out of the well by phonon heating and the time taken for the carriers to traverse 2 to 3
C2-240 JOURNAL DE PHYSIQUE
w e l l s . We a l s o n o t e a n enhancement of t h e decay r a t e a t s m a l l a n g l e s . T h i s might be e x p l a i n e a i n terms of a d i f f e r e n t i a l e m i s s i o n r a t e o v e r t h e b a r r i e r s f o r e l e c t r o n s and h o l e s ( t h e h o l e s h a v e a lower b a r r i e r t o c r o s s ) . This l e a d s t o some d e g r e e of c h a r g e s e p a r a t i o n which would be r a p i d l y c a n c e l l e d by c a r r i e r movement a l o n g t h e w e l l s .
Fig. 4
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Measured s i g n a l decay r a t e s a s a f u n c t i o n of a n g l e . The s o l i d l i n e g i v e s t h e e q u i v a l e n t r a t e f o r p u r e l y i n t r a - w e l l d i f f u s i o n from f i g u r e 2.4
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CONCLUSIONST r a n s i e n t g r a t i n g measurements w i t h sub-picosecond time r e s o l u t i o n i n m u l t i p l e quantum w e l l s t r u c t u r e s h a v e emphasised t h e e f f e c t s of t h e h i g h l y a n i s o t r o p i c c a r r i e r d i f f u s i o n on t h e o p t i c a l n o n l i n e a r i t y . T h i s becomes a p p a r e n t i n t h e time c o n s t a n t s of g r a t i n g s when t h e c a r r i e r d e n s i t y m o d u l a t i o n i s s e t up a c r o s s t h e w e l l s . A unique c o n d i t i o n is c r e a t e d s u c h t h a t t h e t e m p o r a l r e s p o n s e a s s o c i a t e d w i t h f o u r wave mixing c a n be c o n t r o l l e d s i m p l y by sample r o t a t i o n . T h i s a l s o p r o v i d e s a new t e c h n i q u e f o r s t u d y i n g c r o s s w e l l c a r r i e r t r a n s p o r t i n MQWs. I n t h e p r e s e n t c a s e , c a r r i e r h e a t i n g r a t e s c a n be monitored v i a c r o s s - w e l l d i f f u s i o n .
REFERENCES
/ I / Chelma D S, M i l l e r D A B, Smith P W, Gossard A C and Wiegmann W, IEEE J Quantum E l e c t r o n QE-20
(1984) 265.
/2/ Lee Y H, Chivez-Pirson A, Rhee B K, Gibbs H M, Gossard A C, Wiegmann W, Appl Phys L e t t s (1986) 1505.
131 Knox, W H, H i r l i m a n n C, M i l l e r D A B, Shah J, Chelma D S, Shank C V , Phys Rev L e t t
6,
(1986) 1191.1 4 1 Manning R J , C r u s t D W, C r a i g D W, M i l l e r A, Woodbridge K, J Mod Opt i n p r e s s .
O C o p y r i g h t , C o n t r o l l e r HMSO, London 1988
