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Submitted on 1 Jan 1978
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REFLECTION OF HIGH FREQUENCY PHONONS
AT FREE SILICON SURFACES
D. Marx, S. Buck, K. Lassmann, W. Eisenmenger
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-1015
REFLECTION OF HIGH FREQUENCY PHONONS AT FREE SILICON SURFACES
D. Marx, J. Buck, K. Lassmann and W. EisenmengerUniversit&t Stuttgart, Physikalisches Institute Teilinstitut 1
7000 Stuttgart 80, Federal Republic of Germany
Résumé.- Nous avons fait des expériences de réflexion des phonons par des surfaces libres de Sif^lOO^dans lesquelles on pouvait distinguer phonons réfléchis et phonons diffusés, les réfléchis se propageant selon < 110 > . La proportion phonons diffusés sur phonons spéculairement réfléchis est une fonction croissante de la fréquence. Abstract.- In reflection experiments at free silicon [TOOT- surfaces we could distin-guish between specularly and diffusely reflected transverse phonons propagated along <100^> - directions. With increasing phonon frequency the number of diffusely scattered phonons increase relative to that of specularly reflected phonons.
Our experiments are motivated by two pro-blems connected with the passage of high frequency phonons through boundaries : The Kapitza resis-tance /]/ between solids and helium and also the large phonon losses at the interfaces between substrate and evaporated metal films found by Trumpp 111 in phonon generation and detection ex-periments with superconducting tunnelling junctions as phonon generators and detectors.
The geometry of our reflection experiment (see inset of figure 1) differs from that of expe-riments carried out by other authors /3-6/, giving some more specific conditions : ]) The angle of incidence is oblique for specularly reflected phonons so that incident and reflected phonons propagate in <II0> directions which are pure mode directions for all phonon polarizations (Path 1 of the inset). 2) By a slight misalignment of the generator-detector direction from Q O O ] (about 4°) fast transverse phonons propagating along Path 3 (in [010] and [210], s e e i-nset °f Figure 1) are strongly focused resulting in a large signal of these diffusely scattered phonons. 3) The polari-zation vector of the fast transverse phonons lies in the scattering plane.
As with the earlier experiments the scat-tering surface was part of a vacuum chamber allo-wing changing surface conditions (vacuum or helium coverage), whilst all other surfaces have been in contact with liquid helium. The high purity Si-crystals (25 mm diameter, 5 mm thick) were mecha-nically polished. Constantan heaters (0.4 x 0.4 mm2) and superconducting Sn-tunnelling
junc-tions have been used.
Fig. 1 : Typical detector signal for a scattering surface in vacuum. Heater power : 3.6 W/mm , pulse duration : 50 ns, bath temperature : 1.8 K. The inset shows the experimental set-up and the propagation paths of the phonons of the individual pulses.
A typical detector signal is shown in figu-re 1. Duration of the generator pulse was about 50 ns. The crystal was misaligned, as mentioned above. The detector signal consists mainly of four pulses. The propagation paths of the phonons of
the individual pulses are indicated in the inset of figure 1. Due to their propagation time the first three pulses can be ascribed to specularly reflected phonons : longitudinal (it), mode
conver-ted (mc), and fast transverse (ft) phonons. The specularly reflected slow transverse phonons were defocused and could not be detected.
As a consequence of its propagation time the fourth pulse cannot be ascribed to specularly
r e f l e c t e d phonons. I t s w i d t h i s n o t c o n s i d e r a b l y g r e a t e r t h a n t h a t of t h e o t h e r p u l s e s . I f t h e pho- nons of t h e f o u r t h p u l s e a r e d i f f u s e l y s c a t t e r e d , t h e y must p r o p a g a t e i n a narrow "channel" formed by phonon f o c u s i n g . As mentioned above, s u c h a "channel" e x i s t s i n f a c t f o r t h e c h o s e n o r i e n t a - t i o n ( P a t h 3 i n f i g u r e l ) . The p r o p a g a t i o n time of t h e fiast t r a n s v e r s e phonons o n t h i s p a t h a g r e e s w e l l w i t h t h e d e l a y t i m e of t h e f o u r t h p u l s e . T h i s i n t e r p r e t a t i o n of t h e f o u r t h p u l s e c o u l d b e v e r i f i e d by e v a p o r a t i n g s e l e c t i v e l y i n - dium o n t o t h e s u r f a c e showing t h a t i t o r i g i n a t e s from phonons d i f f u s e l y s c a t t e r e d from s p o t s d i r e c - t l y o p p o s i t e t o t h e d e t e c t o r and t o t h e g e n e r a t o r . S i n c e t h e d i f f u s e s c a t t e r i n g i s p r o b a b l y due t o t h e roughness o f t h e s c a t t e r i n g s u r f a c e , one e x p e c t s t h a t t h e r a t i o o f t h e d i f f u s e l y and
s p e c u l a r l y r e f l e c t e d p a r t s of t h e d e t e c t o r s i g n a l depends on t h e wavelength o f t h e phonons.
Due t o t h e f a c t t h a t w i t h i n c r e a s i n g hea- t e r power t h e maximum energy d e n s i t y o f t h e phonon spectrum s h i f t s t o h i g h e r f r e q u e n c i e s , one can q u a l i t a t i v e l y t e s t t h e d e t e c t o r s i g n a l i n depen- dence o n t h e phonon f r e q u e n c y by u s i n g a h e a t e r a s phonon g e n e r a t o r and v a r y i n g t h e h e a t e r power. F i g u r e 2 shows t h e r e l a t i v e a m p l i t u d e s , i . e . t h e a m p l i t u d e s o f t h e i n d i v i d u a l p u l s e s d i v i d e d by t h e a m p l i t u d e of t h e t h i r d ( f t ) p u l s e v e r s u s t h e hea- t e r power.
Heater Power Density i W l m m 2 l
F i g . 2 : Amplitudes o f t h e d i f f e r e n t p u l s e s d i v i - ded by t h e a m p l i t u d e o f t h e f t - p u l s e v e r s u s t h e h e a t e * power. i n c r e a s i n g h e a t e r power s t r o n g e r t h a n t h e f t - p u l s e . T h i s c o n f i r m s o u r i n t e r p r e t a t i o n t h a t t h e f t and t h e R p u l s e s o r i g i n a t e from t h e same s c a t t e r i n g mechanism (mainly s p e c u l a r ) i n c o n t r a s t t o t h e d i f - f u s e s c a t t e r i n g o f t h e d , r , and mc p u l s e s . Another i n t e r e s t i n g r e s u l t which s o f a r we do n o t u n d e r s t a n d , i s t h e f a c t t h a t t h e f t and t h e d p u l s e s a r e reduced d i f f e r e n t l y by helium covera- ge of t h e s u r f a c e : t h e f t - p u l s e i s reduced by a p p r o x i m a t e l y 45 X, t h e d-pulse by more t h a n 85 %. I n b o t h c a s e s t h e i n c i d e n t phonons a r e t r a n s v e r s e , p o l a r i z e d i n t h e boundary. Using s u p e r c o n d u c t i n g S n - t u n n e l l i n g junc- t i o n s a s g e n e r a t o r s we can compare t h e y i e l d of s p e c u l a r l y r e f l e c t e d p u l s e s t o t h a t of b a l l i s t i c e x p e r i m e n t s / 2 / . We f i n d t h a t a t l e a s t 60 % of t h e phonons a r e s p e c u l a r l y r e f l e c t e d . F u r t h e r m o r e , we d i d n o t g e t an i n d i c a t i o n t h a t e i t h e r t h e f t o r t h e d-pulse i s s c a t t e r e d i n e l a s t i c a l l y by t h e free, m e c h a n i c a l l y p o l i s h e d s u r f a c e . The a u t h o r s g r a t e f u l l y acknowledge v a l u a b l e d i s c u s s i o n s w i t h W. F o r k e l , M. Welte, a l s o w i t h H.P. Haar, who s t a r t e d w i t h t h e e x p e r i m e n t s . R e f e r e n c e s / I / C h a l l i s ,
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