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GAMMA-RAY COMPTON SCATTERING OF GERMANIUM AND SELENIUM IN SOLID AND
LIQUID STATE
F. Itoh, T. Honda, K. Suzuki
To cite this version:
F. Itoh, T. Honda, K. Suzuki. GAMMA-RAY COMPTON SCATTERING OF GERMANIUM AND
SELENIUM IN SOLID AND LIQUID STATE. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-
418-C8-421. �10.1051/jphyscol:19808103�. �jpa-00220198�
JOURNAL DE PHYSIQUE Col Zoque C8, suppZ5ment au n08, Tome 41, aofit 1980, page Cg-418
GAMMA-RAY COMPTON SCATTERING OF GERMANIUM AND SELENIUM I N S O L I D AND L I Q U I D STATE
F. Itoh, T. Honda and K. Suzuki
The Research I n s t i t u t e for Iron, S t e e l and Other Metals, Tohoku U n i v e r s i t y , Sendai-980, Japan.
INTRODUCTION
y-ray Compton scattering measurements have been so far successfully performed to elucidate the electronic structure of not only the solid state[l] but also the
liquid state[2-51 of metals. These studies have shown that the volume chanqe upon melting plays an important role in the modification of the Compton profile between the sclid and liquid states of metals such as Li[2,3], Na[2,3], A1[4] and Ga[5].
Ge and Se have typical semiconducting properties in the solid state. In the liquid state, however, Ge is known to show a metallic character; the electrical conductivity[6] has a negative temperature coefficient and the number of carrier is estimated to be about 4 electrons per atom by Hall coeffecient measurement[71. Se takes gradual changes in various electron- ic properties upon melting and still remains as a semiconductor even in the liquid state [ 8 ]
.
The purpose of this study is to examine directly what happens in the electronic structure of Ge and Se through the solid-liquid transition by means of the Compton scattering method.
EXPERIMENTAL
Compton scattering measurements were carried out using 59.54 keV y-rays emitted from 1 Ci 2 4 1 ~ m annular source. The y-ray spectrum scattered by the sample through an scattering angle of 165O was measured with a pure Ge solid state detector. The resolution of the detector at 59.54 keV was 340 eV(FWHM) in the energy scale, or 0.53 a.u. in the momentum scale.
The specimen Ge of 99.99 % purity was contained in the carbon vessel of 26 mm inner diameter and 3.5 mm depth which was located in a vaccum chamber(5xl0-~ Torr) with an aluminum window(O.l mm in thick- ness). Details of the experimental set up used have been described in the previous papers[2,3]. Both of the opening sides of the carbon vessel were sealed with thin carbon foils of 0.17 mm in thickness.
Firstly, the Compton profile of Ge was measured for the liquid state(at 970°C) and then for the solid state(at 24OC) solidified in-situ in the vessel without alteration of the initial arrangement of the detector and the sample. The measur- ing duration required about 10 days to accumulate 39,000 counts at the Compton peak.
The same experimental techniques were applied to measure the Compton profiles of Se in the liquid and solid(trigona1 and amorphous) states. In these cases, how- ever, the stainless steel vessel of 26 mm inner diameter and 2 mm depth was used instead of the carbon vessel. The opening sides of the stainless steel vessel were sealed with stainless steel foils of 5 .am in thickness. The measurement of the Compton profiles of Se was performed under 1 atmosphere of pure argon gas to suppress the vaporization from liquid Se(at 277OC).
Trigonal Se crystal was obtained by
in-situ annealing the solidified specimen at 200°C for 36 hours. Amorphous solid of Se was prepared by quenching molten Se into ice water. The Compton profile of amorphous Se was measured without using the vessel in the vacuum chamber (5xl0-~
Torr) mentioned above. Trigonal and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808103
amorphous phases of S r ..=?-.! i 3c;lt'fied by X-ray diffraction.
RESULTS AND DISCUSSION
The Compton profile J(q) was obtained by the generalized least squares method of the Fourier analysis after subtracting background contributions due to the carbon
(or stainless steel) foils, gas-atmosphere and cosmic rays, and performing the
multiple scattering correction and various energy dependent corrections. Details of the present data processing procedures have been fully described elsewhere[3].
Fig.1 shows the differential Compton profile of Ge between the liquid and solid state*, AJ(q), defined as follows,
AJ ( q ) = JliR (g) -Jsol ( 4 )
.
(1)The J(q) of Ge is normalized to 24.807/2 over the range from q=O.O to 5.0 a. u. using the free atom wave functions by Clementi[9]. The contribution of Is 2 electrons is neglected in this normaliza- tion value because the binding effect appears at q= 0.1 a.u. in the Compton profile. Two experimental runs were done for liquid Ee to confirm the reliability of data. As shown in Fig.1, the experi- mental AJ(q) of Ge has a large negative value in the range of lq1<1.5 a.u. and shows a maximum around q= 2.0 a.u. and then approaches gradually to zero. The dotted line in Fig.1 shows the theoretical AJ(q) for Ge calculated by assuming that four valence electrons per atom behave as the free electron in the liquid state as well as in the solid state. The theoreti- cal AJ(q) thus calculated is very far from the experimental one. This discrepancy is in contrast to the nice agreement between the experimental and the theoretical AJ(q) based upon the free electron model for Li
131, Na[3], A1141 and Gal51.
Hence, the characteristic behavior of the experimental AJ(q) as shown in Fig.1 must be ascribed to the other effects which originate from the semiconductor- metal transition in Ge upon melting. In order to verify this conjecture, we try to construct a model AJ(q) based upon the
F i g . 1 D i f f e r e n t i a l Compton p r o f i l e s o f G e between t h e l i q u i d and s o l i d s t a t e , AJ(q)= Jliq(q)-Jsol (9).
The s o l i d and broken c u r v e s i n d i c a t e t h e experimen- t a l . The b a r s show t h e s t a t i s t i c a l u n c e r t a i n t i e s . The d o t t e d curve i n d i c a t e s t h e t h e o r e t i c a l A J ( ~ ) c a l c u l a t e d from t h e f r e e e l e c t r o n model.
Fig.2 Comparison o f t h e d i f f e r e n t i a l Compton p r o f i l e s f o r Ge between t h e e x p e r i m e n t ( s o 1 i d curve) and t h e t h e o r e t i c a l . The broken curve denotes t h e d i f f e r e n t i a l Compton p r o f i l e between 4sl.54p2.5 c o n f i g u l a t i o n and 4s14p3 c o n f i g u l a t i o n u s i n g C1ementi.s f r e e atom wave f u n c t i o n s [ 9 ] . The d o t t e d curve d e n o t e s t h e d i f f e r e n c e between 4s0.54p3-5 and 4s14p3 c o n f i g u l a t i o n s .
JOURNAL DE PHYSIQUE
LCAO h y b r i d i z a t i o n . The band s t r u c t u r e o f s o l i d Ge i s n a t u r a l l y b e l i e v e d t o c o n s i s t o f t h e c o v a l e n t sp3 h y b r i d i z a t i o n o f 4 s - and 4p-atomic o r b i t a l s . We assume h e r e t h a t t h e 4s4p e l e c t r o n i c c o n f i g u r a t i o n i n 3
s o l i d Ge i s modified upon m e l t i n g i n t o t h e 4s" & 4 p 3 j 6 conf i g u l a t i o n s i n l i q u i d Ge.
For example, t h e t h e o r e t i c a l A J ( q ) i n c a s e s o f 4 ~ ~ and ~4 s 0 . 5 4 p 3 . 5 ~ 4 e l e c t r o n i c ~ ~ ' ~ c o n f i g u l a t i o n s f o r l i q u i d Ge a r e shown i n Fig.2 t o g e t h e r w i t h t h e e x p e r i m e n t a l one.
The former model which d e s c r i b e s t h e e l e c t r o n t r a n s f e r from t h e p - l i k e s t a t e t o t h e s - l i k e s t a t e i s l i k e l y t o r e p r e s e n t t h e f e a t u r e o f t h e e x p e r i m e n t a l AJ(q) e x c e p t f o r around q= 0 a.u. The d i s c r e p a n c y n e a r q= 0 a.u. can b e reduced by t a k i n g i n t o a c c o u n t t h e volume e f f e c t a s shown i n Fig.1. I t i s c o n c l u d e d t h a t s - l i k e e l e c - t r o n s i n c r e a s e w h i l e p - l i k e e l e c t r o n s d e c r e a s e i n l i q u i d Ge upon m e l t i n g and t h a t t h e m e t a l l i c c h a r a c t e r o f l i q u i d Ge comes o u t from t h e e l e c t r o n t r a n s f e r from t h e p - l i k e s t a t e t o t h e s - l i k e s t a t e accompa- n i e d by m e l t i n g .
F i g . 3 shows t h e d i f f e r e n t i a l Compton p r o f i l e s A J ( q ) between v a r i o u s Se p h a s e s
*.
Each Compton p r o f i l e o f Se i s normalized t o 26.054/2 o v e r t h e r a n g e from q= 0 t o 5.0 a . u . , u s i n g c l e m e n t i p s f r e e atom wave func- t i o n s [9]. The c o n t r i b u t i o n from l s 2 e l e c - t r o n s i s o m i t t e d i n t h e n o r m a l i z a t i o n v a l u e b e c a u s e ls2 e l e c t r o n s o f Se can n o t be e x c i t e d i n t h e r a n g e g r e a t e r t h a n q=
-2.4 a . u . under t h e p r e s e n t e x p e r i m e n t a l c o n d i t i o n .
The AJ(q) o f Se between t h e l i q u i d and t r i g o n a l c r y s t a l p h a s e i s t h e l a r g e s t and t h e AJ(q) between t h e l i q u i d and amorphous s t a t e i s t h e s m a l l e s t . The AJ(q) between t h e amorphous and t r i g o n a l c r y s t a l s t a t e i s s i m i l a r t o t h e r e s u l t observed by Bonse e t a 1 [ l o ] .
S i n c e Se h a s l i t t l e c o n d u c t i o n e l e c - t r o n s i n t h e l i q u i d a s w e l l a s i n t h e s o l i d s t a t e , t h e c h a r a t e r i s t i c b e h a v i o r s i n t h e AJ(q) a s shown i n Fig. 3 is l i k e l y t o r e f l e c t t h e v a r i a t i o n i n t h e chemical bonding n a t u r e o f v a l e n c e e l e c t r o n s t h r o u g h
0 L - TI A - T r L - A
F i g . 3 D i f f e r e n t i a l Compton p r o f i l e s AJ(q) of Se between t h r e e s t a t e s w i t h s t a t i s t i c a l e r r o r b a r s . Open and c l o s e d c i r c l e s denote t h e AJ(q) between l i q u i d ( L ) and t r i g o n a l (Tr) Se and between
amorphous ( A ) and t r i g o n a l Se, r e s p e c t i v e l y . T r i - a n g l e s denote t h e AJ(q) between l i q u i d and amorphous Se
.
t h e t r a n s i t i o n from t h e t r i g o n a l c r y s t a l s t a t e t o t h e l i q u i d o r amorphous s t a t e .
I t i s i n t e r e s t i n g t o compare t h e p r e s e n t r e s u l t s w i t h t h e s t r u c t u r a l d a t a o f v a r i o u s Se p h a s e s a s shown i n T a b l e I. The bond a n g l e ( a ) and i n t r a - m o l e c u l a r bond l e n g t h ( d l ) a r e k e p t a l m o s t same v a l u e s i n any Se p h a s e , w h i l e t h e i n t e r - m o l e c u l a r a t o m i c d i s t a n c e ( d 2 ) i s l e n g t h e n e d w i t h d e c r e a s i n g mass d e n s i t y ( p )
.
Table 1. The d e n s i t y ( p 1 , i n t r a - m o l e c u l a r bond l e n g t h ( d l ) , i n t e r - m o l e c u l a r atomic d i s t a n c e f d 2 ) and bond a n g l e ( a ) o f t r i g o n a l , amorphous and l i q u i d Se. The s t r u c t u r a l d a t a f o r t r i g o n a l Se were t a k e n from r e f . [ I l l , amorphous Se from r e f . [11,121 and l i q u i d Se from ref.[13,141.
phase p (g/cm3) d l (A) d2 ( A ) a (degree)
t r i g o n a l 4.819 2.37 3.44 103
amorphous 4.285 2.32 3.72 104-105
l i q u i d 3.912 2.38 3.75 103-106
According t o t h e c a l c u l a t i o n by Joannopoulos e t a 1 [ 1 5 ] , t h e c h a r g e d e n s i t y o f p - l i k e e l e c t r o n s i n t h e i n t e r - m o l e c u l a r r e g i o n d e c r e a s e s a s t h e i n t e r - m o l e c u l a r a t o m i c d i s t a n c e ( d 2 ) i n c r e a s e s w h i l e t h e s - l i k e e l e c t r o n s remain r e l a t i v e l y unchanged. T h i s s u g g e s t s t h a t t h e
c h a r a c t e r i s t i c b e h a v i o r o f AJ(q)>O around q= 0 a.u. a s shown i n F i g . 3 may b e r e l a t e d t o some d e c r e a s e i n t h e c h a r g e d e n s i t y of i n t e r - c h a i n bonding p - l i k e e l e c t r o n s i n amorphous and l i q u i d Se. T h i s c o n c l u s i o n
is consistent with the previous observa- tions by positron annihilation measurements
[16,171.
Furthermore, recent theoretical studies[l8-211 have shown that the Compton profile of amorphous Se deviates from that of the polycrystalline phase into that of the free atom state. This result provides the qualitative explanation for the
experimental AJ (q) of Se shown in Fig. 3.
These theoretical studies, however, depend upon a random distribution of atoms or one-dimensional potential arrays. Hence, it would be of interest to examine the Compton profile of amorphous or liquid Se taking into account the more realistic atomic arrangement.
References
see for example, Compton Scattering, ed. Williams,B.G.(McGraw Hill, New York) 1977.
Suzuki,K., Itoh,F., Kuroha,M. and Honda,T., 1nst.Phys.ConE.Ser.No.~
(1977) 181.
Itoh,F., Honda,T. and Suzuki,K., J.Phys.Soc.Jpn.~(1979)122.
Honda,T., Itoh,F. and Suzuki,K., J.Phys.Soc. Jpn.g(l979) 133.
Itoh,F. and Suzuki,K., Proc. 5th Int.
Conf. Positron Annihilation, ed.
Hasiguti,R.R. and Fujiwara,K.( The Japan Institute of Metals, Sendai) 1979, p865.
Glazov,V.M., Chizhevskaya,S.N. and Glagoleva,N.N., Liquid Semiconductor
(Plenum Press, New York11969.
Bush,G. and Gunterrodt,H.J., Solid State Phys. g(1967) 471.
see for example, Selenium, ed.
Zingar0,R.A. and Cooper,W.C.(reinhold, Mew york) 1974 ; see also ref. [61.
Clementi, E., IBM J.Res.Dev.Suppl.9 (1965) 2.
Bonse,U., Schroder,W. and Schulke,w., Solid State Comm. g(1977) 807.
Unger, P. and Cherin, P., Physics of Selenium and Tellurium, ed. Cooper, W.C.(Pergamon, Oxford)1969, p.223.
12. Hansen,F.Y., Knudesen,T.S. and Carneiro,K., J.Chem.Phys. G(1975) 1556.
13. Suzuki, K. and Misawa, M., Trans.JIM 18 (1977) 427.
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14. Misawa, M. and Suzuki, K., J.Phys.,Soc.
Jpn. fi(1978) 1612.
15. Joannopaulos,~.D., Schulter,M. and Tejeda,J, Phys.Rev.E(1975)2186.
16. Itoh,F., Matsuura,M., Suzuki,K., Miyata,Y. and Noguchi,S., J.Phys.Soc.
Jpn. g(1978) 1622.
17. Matsuura,M., Itoh,F.,Honda,T. and Suzuki,K., Proc. 5th Int. Conf.
Positron Annihilation ed. Hashiguchi, R.R. and Fujiwara,K., (The Japan Institute of MetalsrSendai)1979,p.889 18. Kramer,B. and Krusius,P., Phys.Rev.
916 (1977)5341.
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19. Krusius,P., Kramer,B., Schultz,O. and Treusch,J., Solid Stare Commun.
21 (1977) 1127.
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20. Krusius,P., Isomaki,H. and Kramer,B., Phys.Rev.g(l979) 1818.
21. Krusius,P,, The Physics of Selenium and Tellurium, ed. Gerlach,E. and Grosse,P. (Springer-Verlag,New York) 1979.p.12.
5 e r t i c a l bars in Figs. 1 and 3 show the staristical fluctuation in total counts for A.J(q), i.e. : 2 f i (N : counts number) at several q values. The expe- rimental uncertainty involved in AJ(q) is much less than the statistical uncertainty, because a curve- smoothing procedure has been applied during the data processing as described in the text. Therefore, the characteristic behaviors of AJ(q) in q < 1.5 a.u., which have been intensively discussed in this paper, are qualitatively acceptable.
