ULTRASONIC STUDY OF TUNNELLING DEFECTS IN SELENIUM-GERMANIUM GLASSES

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ULTRASONIC STUDY OF TUNNELLING DEFECTS IN SELENIUM-GERMANIUM GLASSES

J. Duquesne, G. Bellessa

To cite this version:

J. Duquesne, G. Bellessa. ULTRASONIC STUDY OF TUNNELLING DEFECTS IN SELENIUM- GERMANIUM GLASSES. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-449-C10-452.

�10.1051/jphyscol:19851099�. �jpa-00225484�

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ULTRASONIC STUDY OF TUNNELLING DEFECTS I N SELENIUM-GERMANIUM GLASSES

J.Y. DUQUESNE AND G. BELLESSA

Laboratoire de Physique des ~olides* Bat. 510, Universite Paris-Sud Centre d'orsay, 91405 Orsay, France

RBsumB - Nous mesurons les variations de la vitesse acoustique dans des verres de Selenium-Germanium, au-dessous de 1 K et vers

100 MHz. Nos resultats s'expliquent bien par l'interaction reso-

nante entre l'onde ultrasonore et des defauts tunnel. 11s mon- trent que les grandeurs caract6ristiques des d6fauts tunnel sont sensibles 2i la rigiditd du r6seau.

Abstract - We measure the variations of the acoustic velocity in Selenium-Germanium glasses, below 1 K and around 100 M H z . Our results are well explained with the resonant interaction between the ultrasonic wave and the tunnelling defects. They show that the characteristic parameters of the tunnelling defects are sen- sitive to the rigidity of the network.

We report sound velocity experiments performed in amorphous Sel-xGex compounds (x = 0 ; 0.1 ; 0.25 ; 0,75 ; 1) below 1 K and around 100 M H z .

In those temperature and frequency ranges, the elastic properties are mainly governed by the so-called "two-levels system" (or "tunnelling d-efects") /I/. Those excitations arise from the tunnelling transitions of groups of atoms between the two lowest eigenstates of a d-ouble-well potential and exhibit a distribution of energies E extending down to very small values (E < eV) /2,3/. Those excitations seem to be a general feature of the amorphous state since they have been discovered in different kinds of amorphous networks : covalent, polymeric:.. metal- lic glasses. Recently, an experiment has established their existence in amorphous germanium and so has definitly raised the doubt about their existence in rigid networks such as tetrahedrally bonded ones / 4 , 5 / . This has also been confirmed by other experiments /6,7/.

Experiments on a-Se I-x Ge x glasses enable to study the relationship between the tunnelling defects and the rigidit) of the network : it is generally assumed that those networks are chemically ordered and that the atoms of germanium merely crosslink the polymeric chains of selenium, increasing then the rigidity of the network. The Ge-Ge bonds remain scarce as long as it is possible (i.e. as long as x is smaller than 0.33) / 8 , 9 / . Nevertheless, it must be mentioned that other struc- tural models have been proposed /10,11/. Experiments about the effects of crosslinking on the low temperature properties of amorphous networks have already been performed. Results on epoxy resins are contradictory since different variations of the density of localized excitations have been reported /12,13/. Results on crosslinked polybutadiene have been

interpretated with a reduction of the density of localized excitations near a crosslink density corresponding to 50 polymer repeat units between crosslinks /14/.

*Laboratoire associe au Centre National de la Recherche Scientifique.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851099

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C10-450 JOURNAL D E PHYSIQUE

The figures ( I ) , ( 2 ) , (3) display our experimental results :

0.3 0.5 1.0 1.5

TEMPERATURE ( K >

0.5

TEMPERATURE Se /

.

^-'--'^%^.^-

.-

&t + * + t *

260 MHz 360 MHz

-

x

180 MHz

I

Ceference temperatures are srbitrary.

Fiq. (1) : Sound velocity in amorphous Se , Se75Ge25 , ^~e~~^G~

4 0 Shear waves / Absolute velocities (10 cm.s-l) 5 : 1 ; 1.24 ; 1.44

TEMPERATURE ( K

Fig. (2) : Sound velocity in amor- Se and SegoGe10 /longitudinal waves/ Absolute velocities

(10 cm.s-l) 5 : 2 ; 2.16

Fig. (3) : Sound velocity in amorphous Ge /Rayleigg wave/ Absolute velocity : 3.2 10 cm.s-l/ Refe- rence temperature is arbitrary.

At the lowest temperatures, the velocity increases because of the resonant scattering of the acoustic wave by the tunneling defects and follows a logarithmic law. As the temperature further increases, the velocity reaches a maximum whose location versus temperature increases with increasing frequency. Then the velocity decreases.

The slope of-the logarithm& variations is PB2/pv2 where P is the density of tunnelling defects per unit volume, unit asymmetry E

and unit overlapping factor 1 (it is .assumed thar :

P (E I A ) = ConSte = P) , B is the deformation potential relating the changes of asymmetry to the local strain, p is the specific mass and v is the absolute velocity. So our experiment gives a direct measurement of the coupling term PB2 . The figure (4) displays pB2 as a function of the mean coordination number <r>, for shear waves (Se, Se75Ge251

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F)

^:^Density of tunnel- 'ng defects and deformation potential BT (deduced from the velocity data) as a func- -tion of the mean coordina- -tion number <r>. The full

line is the calculated number N of zero frequency modes

(in arbitrary units) (from/l8/) point, it would be certainly very interesting to get the-variations

of both the density P and the

1.5 deformation potential B. Heat

(U

I?

capacity experiments usually provide a direct measure of the density of tunnellinq defects.

Unfortunately, the experiments which have been carried on Se-Ge glasses, down to 100 mK cannot provide any data on the tunnel- -ling defects / 1 6 / . Nevertheless, acoustic experiments can provide an indirect way to obtain a r o u ~ h estimate of P and B. For that

0

X

2 ^t -purpose, we notice that the rela-

xation processes of the tunnel-

< t- > -1ina defects involves two limi- Fig. (4) : coupling term P ^F3' ^as -tinv behaviours of the elastic afunctimof the mean coordina- properties: a low temperature

-tion number <r>. regime ( w ~ >>I) and a high tempe- -rature retime ( w ~ < < I ) . ( w / 2 ~ is the acoustic frequency, T is the shortest relaxation pime of a tunnelling defect, for a g%en splitting). The intermediary regime -

( W T ~ Q 1) occurs around a temperature T depending on R (and not on P).

It has been pointed-out that Ti was &roportionnal to w /17/. We get then : B a p vS w T'". At low frequency ( % lo2 Hz ) Ti can be iden- -tified Twith tge maftimum of velocity T since the low and temperature regimes clearly appears on both sides OF T 1 Pt higher frequen- -cies ( % 10' Hz ) the identification is n8t straightforward since other processes tend to blur out the contribution of the tunnelling defects. Nevertheless, in a-SiO , the extrapolation of the low fre- -quency data ( 484 Fz ) to the gigh frequency range ( 30 MHz ) pro- -vides the right location of the velocity maximum /17/. We will then assume : T.=T, . We can also check that our data are consistent with T! = w.It 'is then possible to extract a rouqht value of BT from the lkcation of the velocity mazirnum and then to extract an estmste of P

fro^ the value of B and of P B ~ . It must be pointed out that tbe values of P and B are only rough estimates but that their variations are significant. The figure (5) displays the values of P and RT that we derive as a function of the mean coordination number <r> ( in the

6'7

z

0

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C10-452 JOURNAL DE PHYSIQUE

c a s e of a-Se O G e 1 0 , w e assumed t h a t F B ~ 1 / 2 PB: which i s v a l i d i n a-Se ) . TWO-2egimes a p p e a r t h e n : when t8ezmean c o o r d i n a t i o n number < r >

i n c r e a s e s , P d e c r e a s e s a n d B k e e p s c o n s t a n t f o r low v a l u e s of < r > and t h e n P k e e p s c o n s t a n t and B i n c r e a s e s f o r h i g h v a l u e s of < r > . I t i s i n t e r e s t i n g t o s t r e s s t h a t b o t h * r e g i m e s a r e r o u g h l y s e p a r a t e d by t h e a p p e a r e n c e of f i r s t n e i g h b o u r s of atoms of germanium. Thorpe h a s

s u g g e s t e d t h a t some of t h e z e r o f r e q u e n c y modes which a r e p r e d i c t e d i n amorphous n e t w o r k s c o u l d p o s s i b l y b O r e l a t e d t o t h e t u n n e l l i n g d e f e c t s

/ 1 5 / . The f u l l l i n e i n f i g . ( 5 ) shows t h e c a l c u l a t e d number N of t h o s e z e r o f r e q u e n c y modes ( i n a r b i t r a r y u n i t s ) ( from / 1 8 / ) . ^{I t}^{i s}

w o r t h w i l e t o stress t h e s i m i l i t u d e s and d i f f e r e n c e s between t h e v a r i a - - t i o n s o f b o t h P and N : I t a p p e a r s t h a n b o t h P a n d N d e c r e a s e a s < r >

i n c r e a s e s . N e v e r t h e l e s s , t h e ~ e d u c t i o n of P i s n o t s o s t r o n g a S f o r M . Moreover, c o n t r a r y t o N , P d o e s n o t t e n d t o z e r o above < r > = 2 . 4 .-

Our e x p e r i m a n t shows t h a t t h e c o u p l i n g f a c t o r F B ~ o f t h e t u n n e l l i n g d e f e c t s i s s e n s i t i v e t o t h e d e g r e e o f c r o s s l i n k i n g of t h e network. A q u a l i t a t i v e a n a l y s i s s u g g e s t s t h a t b o t h t h e d e n s i t y P of d e f e c t s a n d t h e d e f o r m a t i o n p o t e n t i a l B a r e s e n d i t i v e t o t h e d e g r e e o f c r o s s l i n k i n g . Heat c a p a c i t y e x p e r i m e n t s below 100 mK would b e v e r y i n t e r e s t i n g s i n c e t h e y c o u l d p o s s i b l y p r o v i d e a d i r e c t d e t e r p i n a t i o n of P .

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