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ABSORPTION OF BALLISTIC PHONONS BY THE 2D ELECTRON GAS IN A Si MOSFET
J. Hensel, R. Dynes, D. Tsui
To cite this version:
J. Hensel, R. Dynes, D. Tsui. ABSORPTION OF BALLISTIC PHONONS BY THE 2D ELEC- TRON GAS IN A Si MOSFET. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-308-C6-310.
�10.1051/jphyscol:1981689�. �jpa-00221626�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment au n012, Tome 42, d6cembre
1981page
C6-308ABSORPTION OF BALLISTIC PHONONS BY THE 2D ELECTRON GAS IN A Si MOSFET
J.C. Hensel, R.C. Dynes and D.C. Tsui
BeZZ
Laboratories, Murray
H i Z Z ,Hew Jersey 07974,
U.S.A.Abstract.- Measurements of the absorption of ballistic phonons by the two- dimensional electron gas (2DEG) in the inversion layer of a Si MOSFET are presented and compared with theory.
This paper reports measurements of the absorption of ballistic phonons by the 2DEG in the inversion layer of a (100) Si MOSFET at 2K. The rationale is to determine directly the electron-acoustic phonon interaction in 2D vis-a-vis the 3D case considered in ocr earlier work.'
The experimental geometry is pictured in Fig. 1. The sample consists of a Si pr+m upon whose (001) base is fabricated a large (2.5
x2.5
mm2
)MOSFET device
(8000A thick SiOp). A [1111 beam of ballistic phonons generated from a pulsed laser heater positioned on one inclined face reflects from the interface above the gate and is detected by an
Afibolometer on the opposite inclined face. A 5
Ezsquare wave voltage, 0 to VMoD, is applied to the gate and the resulting modula- tion Al in phonon intensity I due to absorption is detected.
Profiles of A111 for LA phonons shown in Fig. 2 were recorded as V140D was varied increm- entally from 0 to
680 volts with excitation
BOLOMETER
power density
P/Aa parameter. This monitors absorption as a function of
2%in accordance with the relationship 2%
=2 &
a($ =
Fermi wavevector and n
=electron areal density).
The heater temperature Th was estimated from P/A
by use of the black-body formula
P/A =5T
4 (Uis Fig. I. Sample geometry.
h a Stephan-Boltzmann constant).
According to theory, the mechanism for absorption of a phonon with wavevector + q by a degenerate electron gas is the scattering of an electron across the Fermi
surface. (See inset in Fig. 3). Such a scattering process in 2D is characterized by a transition probability shown in Fig. 3 which is peaked sharply in the vicinity of q
6 2%'to an even greater degree than in 3D where it is linear in q up to
?.
2%. Thus, the selective absorption near 2kF acts as a "slit" in energy which
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981689
F i g . 2. Experimental a b s o r p t i o n F i g . 3 . Sketch of t h e a b s o r p t i o n p r o f i l e s f o r LA phonons: f u n c t i o n G(q)
.
(0) Th = 12.4K; (.) Th = 8.77K.
can b e scanned by c o n t r o l o f V MOD. T h e o r e t i c a l p r o f i l e s r e p r e s e n t i n g t h e convolu- t i o n of t h e s h a r p a b s o r p t i o n f u n c t i o n w i t h a P l a n c k i a n phonon d i s t r i b u t i o n ( i n c l u - d i n g e f f e c t s of i s o t o p e and umklapp s c a t t e r i n g ) a r e shown i n F i g . 4. (The c a l c u l a - t i o n assunes t h e electron-phonon i n t e r a c t i o n t o b e t h e same a s i n t h e b u l k
c r y s t a l ) .
Comparison of t h e experimental p r o f i l e s w i t h t h e o r y demonstrates g e n e r a l l y good agreement a s r e g a r d t o t h e i r o v e r a l l shape. The p r o f i l e s a r e observed t o have a quasi-Planckian shape and t o e x h i b i t
a
Mien displacement w i t h Th. I t should be noted t h a t t h e p r o f i l e s t r a c e o u t t h e phonon d i s t r i b u t i o n i n d e t a i l , s u g g e s t i n g p o t e n t i a l a p p l i c a t i o n i n phonon spectroscopy. We should mention t h a t w i t h o u t t h e i n c l u s i o n of i s o t o p e s c a t t e r i n g i n t h e c a l c u l a t i o n s t h e peak p o s i t i o n s would have been s u b s t a n t i a l l y o v e r e s t i m a t e d , e.g. a t 2%*
7 xl o 6
cm'l f o rT
h
= 12.4K. (Moreover,
if
t h e a c o u s t i c mismatch model had been used t o e s t i m a t eT
h' t h e r e s u l t i n g T would have been a f a c t o r of*
2 h i g h e r p r e c l u d i n g any p o s s i b l eh agreement).
Although t h e o v e r a l l match of t h e o r y and d a t a i s d e f i n i t e l y encouraging, t h e r e i s one g l a r i n g discrepancy; and t h a t i s t h e a b s o l u t e magnitude of t h e ab- s o r p t i o n is a f a c t o r > 1 0 l a r g e r than c a l c u l a t e d . I f t h e s t r u c t u r e of t h e t h e o r y i s sound, a s t h e c l o s e correspondence of most s p e c t r o s c o p i c f e a t u r e s would a t t e s t t o , then t h e s o u r c e of t h e d i s c r e p a n c y would b e i n t h e s t r e n g t h of t h e e l e c t r o n - phonon i n t e r a c t i o n . Two p o s s i b i l i t i e s a r e : (1) many-body e f f e c t s ( n o t too prom- i s i n g inasmuch a s renormalized deformation p o t e n t i a l s a r e t y p i c a l l y reduced) and (2) e f f e c t s r e l a t e d t o t h e i n t e r f a c e . We have evidence t h a t t h e observed phonons
JOURNAL DE PHYSIQUE
F i g . 4. C a l c u l a t e d a b s o r p t i o n F i g . 5. Experimental a b s o r p t i o n p r o f i l e s f o r LA phonons. p r o f i l e s f o r TA phonons:
(0) Th = 12.4K; ( - ) Th = 8.77K.
r e f l e c t primarily f rom t h e Si-SiOZ i n t e r f a c e and hence may b e s i g n i f i c a n t l y per- t u r b e d i n t h e r e g i o n (% a few phonon wavelengths t h i c k ) where t h e i n t e r a c t i o n occurs. One should n o t e i n t h i s r e g a r d t h a t t h e r e i s a p a r t i a l c a n c e l l a t i o n of terms comprising t h e e f f e c t i v e deformation p o t e n t i a l f o r LA a b s o r p t i o n which might be r a t h e r s e n s i t i v e t o d e t a i l s of t h i s s o r t .
Data f o r TA phonons shown i n Fig. 5 a r e s i m i l a r e x c e p t t h a t t h e TA p r o f i l e s a r e s h i f t e d t o s u b s t a n t i a l l y h i g h e r q-values by v i r t u e of t h e i r s m a l l e r v e l o c i t y . Although s t i l l s k e t c h y , t h e d a t a s u g g e s t t h a t t h e magnitude of t h e peak a b s o r p t i o n i s n e a r l y a f a c t o r of 2 l e s s t h a n LA. Theory, on t h e o t h e r hand, p r e d i c t s a r a t i o
TA/LA
% 1 . 8 dependent e s s e n t i a l l y o n l y on t h e e f f e c t i v e deformation p o t e n t i a l s , which b r i n g s t h e i r c h a r a c t e r i z a t i o n i n t o q u e s t i o n .I n c o n c l u s i o n , d a t a a r e emerging from b a l l i s t i c phonon experiments which demonstrate s u b s t a n t i a l phonon a b s o r p t i o n i n a 2DEG. Although t h e s p e c t r o s c o p i c f e a t u r e s a r e i n r e a s o n a b l e agreement w i t h t h e o r y , t h e a b s o l u t e magnitude of t h e observed a b s o r p t i o n of LA phonons i s more t h a n one o r d e r of magnitude g r e a t e r t h a n t h e o r e t i c a l e s t i m a t e s f o r r e a s o n s t h a t a r e s t i l l obscure.
We thank T. M. R i c e and M. Lax f o r a number of i n f o r m a t i v e d i s c u s s i o n s and G. Kaminsky f o r sample p r e p a r a t i o n . We a r e e s p e c i a l l y i n d e b t e d t o F . C. Unterwald f o r h i s v i t a l r o l e i n t h e e x e c u t i o n of t h e experiments.
REFERENCES
1. See, e.g., J. C. Hensel and R. C. Dynes, Phys. Rev. L e t t e r s
