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BALLISTIC TRANSPORT AND DECAY OF NEAR ZONE-EDGE NON-THERMAL PHONONS IN
SEMICONDUCTORS
R. Ulbrich, V. Narayanamurti, M. Chin
To cite this version:
R. Ulbrich, V. Narayanamurti, M. Chin. BALLISTIC TRANSPORT AND DECAY OF NEAR ZONE-
EDGE NON-THERMAL PHONONS IN SEMICONDUCTORS. Journal de Physique Colloques, 1981,
42 (C6), pp.C6-226-C6-228. �10.1051/jphyscol:1981664�. �jpa-00221600�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppl6ment au nO1 2, Tome 42, de'cembre 1981 page C6-226
BALLISTIC TRANSPORT AND DECAY OF NEAR ZONE-EDGE NON-THERMAL PHONONS IN SEMICONDUCTORS
R.G. ulbrichf, V. Narayanamurti and M.A. Chin
BeZZ Laboratories, Murray H i Z Z , New Jersey 07974, U. S. A.
Abstract.- We present results on the energy transport by near zone-edge transverse phonon pulses generated in the process of non-radiative electron- hole pair recombination at T=1.4 K in GaAs and InP. Depending on orienta- tion and distance, ballistic transport of phonons with frequencies between 1.0 and 2 THz is reported.
Introduction.- There has been a great deal of recent acitivity in high frequency phonon transport 1
.
We recently presented a preliminary report on the propagation of non-thermal, large-wavevector acoustic phonons over macroscopic distances (QJ mm) in GaAs at low temperaturesL. Here we report on the spatial, temporal and directional dependence of the phonon signals in CaAs and present also results on InP.Experimental.- Bulk crystals of GaAs and InP with mechanically lapped and chemically etched surfaces were used. We studied A1 bolometer and Pb junction detector signals in three geometrical configurations: a) "trans" in the plane-parallel samples with photoexcited source region and detector on opposite sides; b) "cis" with source and detector on the same crystal surface; c) "edge on" with the detector close to a sample edge and the source on the adjacent face. In the following, the necessary corrections for Lambert's Law and the cosine of the detector viewing angle have been made.
Results.- Figure 1 shows phonons signals s*=r2*s, where S is the actually measured A1 bolometer signal as a function of t at different fixed distances r, for the three principal directions in a 2.7~6. 5x12mm3 <1,1,0> cut GaAs crystal with <I, 1,1> edge-on detector. S* has been plotted as a function of t/r to reveal the characteristics of ballistic, dispersive transport: linear scaling of pulse shape in time and space.
Close affinity is, indeed, observed in Fig. 1. The peak of the phonon distribution travels with 0.9xl05cm/sec, and the leading and trailing halfpoints with QJ 2 .%lo5, and QJ 0.4xl0~cm/sec. respectively. The detailed shape of the velocity distributions depends on propagation direction.
The signal onset of the TA phonon signals was measured and compared to low- frequency propagation, launched in evaoorated metal film stripes in situ in the sane experiment. The onset edge of the "slow" signals in Fig. 1 exhibited consistently lower velocities, ranging from 88% to 93% of the low-frequency TA (resp. FTA in 1,1,0) velocities in the three directions. We therefore, conclude that all the signals we observe is due to high-frequency, i.e. v L 1 THz phonons. Pb junction experiments in
*Also at Institut fiir Physik, UniversitEt Dortmund, West-Germany.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981664
log v,,, [lo5 ,,IS]
-
F i g , 1.- Phonon s i g n a l s S* ( t ) i n GaAs, T=1.4K, f o r t h r e e d i r e c t i o n s a t f i x e d p r o p a g a t i o n d i s t a n c e s r=0,44? 0.88, 1.76, 2.6 and 5 , 2 ~ (from t o p t o bottom). P u l s e peak, l e a d i n g and t r a i l i n g edge h a l f p o i n t s a r e i n d i c a t e d ( 1 , 0 , * ) .
t h e same c o n f i g u r a t i o n confirmed t h i s z e s u l t . To o b t a i n frequency d i s t r i b u t i o n s we converted t h e measured v e l o c i t i e s according t o t h e known d i s p e r s i o n curves along t h e p r i n c i p a l d i r e c t i o n s 3 . One example i s shown i n F i g . 2a t h e e v o l u t i o n of t h e frequency d i s t r i b u t i o n w i t h i n c r e a s i n g propagation d i s t a n c e along <1,0,0>.
The v a r i a t i o n of S" w i t h i n c r e a s i n g d i s t a n c e r i s expected t o b e propor- t i o n a l t o l / r exp ( - a r ) , where a i s a phenomenological averaged damping c o n s t a n t . Due t o t h e p u l s e shape v a r i a t i o n s e v i d e n t i n Fig. 1
-
a narrowing of v e l o c i t y spread among t h e h a l f p o i n t s by almost a f a c t o r of 2 i s observed i n a l l t h r e e d i r e c t i o n s i n t h e d i s t a n c e range d i s c u s s e d h e r e-
t h i s p r o p o r t i o n a l i t y i s modified. Evaluating t h e t o t a l i n t e g r a t e d p u l s e s i g n a l we found a<111> 3cm -1 , ci-
10cm-I i n t h e o t h e r d i r e c t i o n s . From t h e narrowing we conclude t h a t b o t h t h e high frequency t h e low frequency p a r t s of t h e i n i t i a l frequency d i s t r i b u t i o n a r e a f f e c t e d by a t t e n u a t i o n . The minimum of damping o c c u r s a t f r e q u e n c i e s of 2.05 THz i n <1,0,0>, <1,1,0> and 1.55 TNz i n t h e <1,1,1> d i r e c t i o n . T h i s i s an i n d i c a t i o n of a n i s o t r o p i c phonon propagation i n t h e d i s p e r s i v e r e g i o n . However, t h e polychromatic e x c i t a t i o n of TA phonons ( v i a t h e LO + LA + TA r e l a x a t i o n cascade) and t h e r e l a t i v e l y l a r g e d e t e c t o r viewing a n g l e t e n d s t o smooth o u t l a r g e v a r i a t i o n s i n t h e d i r e c t i o n a l i t y i n t h e i n t e n s i t y of t h e phonon s i g n a l s , which one would expect f o r monochromatic high- frequency phonon propagation ( i n analogy t o t h e f o c u s s i n g e f f e c t i n non-dispersive t r a n s p o r t a t low f r e q u e n c i e s ) .I n F i g u r e 2(b) we show some r e s u l t s f o r InP on t h e s p a t i a l dependence of t h e phonon s i g n a l s f o r t h r e e d i f f e r e n t e l a p s e d times. T h i s p l o t shows t h a t t h e phonon energy d e n s i t y has a peak which moves w i t h i n c r e a s i n g time away from r = O i n a q u a s i b a l l i s t i c f a s h i o n . T h i s i s c l e a r l y d i f f e r e n t from d i f f u s i v e t r a n s p o r t , where t h e e x c i t a t i o n r e g i o n would always have t h e maximum energy d e n s i t y a f t e r p u l s e d e x c i t a t i o n . These d a t a i n d i c a t e t h a t t h e momentum and enerp,y r e l a x a t i o n time f o r phonons i n t h e 1.5 THz r e g i o n i s microseconds long i n InE'.
I n both m a t e r i a l s boundary s c a t t e r i n g of t h e s e TIIz phonons turned o u t t o b e completely d i f f u s e and caused e f f i c i e n t down conversion i n t o low
3
phonons.JOURNAL DE PHYSIQUE
GaAs
<
1,080)T.1.4K .5
F i g . 2 ( a ) . - Phonon d i s t r i b u t i o n s on t h e lowest /1,0,0> TA branch i n G a A s a f t e r che p u l s e h a s propagated over a d i s t a n c e of r=0.44 mm (1-11, 0.68 mm (---) and 1.76 mm (....). The arrows i n d i c a t e t h e peak; upper and lower ends of t h e l i n e s mark t h e h a l f p o i n t s .
F i g . 2 (b)
. -
Phonon s i c n a l s S* a s a f u n c t i o n of d i s t a n c e f o r t h r e e d i f - f e r e n t e l a p s e d times t. a f t e r pulsed e x c i t a t i o n a t r = O , t = O i n InP.P u l s e sharpening, presumably because of down conversion, was a l s o observed f o r h i g h e x c i t a t i o n l e v e l s (2 1 0 - ~ ~ / m m 2 )
.
I n summary, we have observed t h e propagation of n e a r zone-edge TA phonons a f t e r n o n - r a d i a t i v e e-h p a i r recombination i n bulk GaAs and InP. Such propagation appears t o be a g e n e r a l f e a t u r e f o r zinc-blende semiconductors w i t h high chemical, p h y s i c a l and s u r f a c e p e r f e c t i o n .
References.-
1 ) For a review s e e W. Bron, Rep. Prog. Phys. %, 301 (1980).
2) R. G. U l b r i c h , V. Narayananurti and M. A. Chin, Phys. Rev. L e t t . 43,
1432 ( 1 980).
3 ) J. J. Waugh and G. J. D o l l i n g Phys. Rev.
