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ELECTRONIC BEHAVIOR OF LIQUID
SEMICONDUCTING ALLOYS My (Se.5Te.5)1-y WITH MONOVALENT DOPING ELEMENTS
H. Radscheit, R. Fischer, M. Cutler
To cite this version:
H. Radscheit, R. Fischer, M. Cutler. ELECTRONIC BEHAVIOR OF LIQUID SEMICONDUCTING
ALLOYS My (Se.5Te.5)1-y WITH MONOVALENT DOPING ELEMENTS. Journal de Physique
Colloques, 1981, 42 (C4), pp.C5-1051-C5-1054. �10.1051/jphyscol:19814230�. �jpa-00220861�
JOURNAL DE PHYSIQUE
CoZZoque C4, suppZ6ment au nOIO, Tome 4 2 , octobre 1981 page C4-1051
ELECTRONIC BEHAVIOR OF L I Q U I D SEPIICONDUCTING ALLOYS M ~ ( s ~ . 5 ~ e - 5 ) l-y WITH MONOVALENT DOPING ELEMENTS
H. Radscheit
* ,
R. F i s c h e r and M. C u t l e rPhysics Departmdnt, Oregon S t a t e U n i v e r s i t y , CorvaZZis, OR 97331, U.S.A.
A b s t r a c t . - Results o f measurements o f t h e magnetic s u s c e p t i b i l i t y , e l e c t r i c a l con- d u c t i v i t y and thermopower a r e i n t e r p r e t e d w i t h t h e h e l p o f bond e q u i l i b r i u m theory.
It i s found t h a t an a t t r a c t i v e i n t e r a c t i o n enhances f o r m a t i o n o f diatomic molecules c o n t a i n i n g o n e f o l d bond d e f e c t atoms a t t a c h e d t o \l atoms. Transport occurs i n an acceptor band a t y 0.02, and t h e temperature dependence o f t h e c o n d u c t i v i t y o f t h i s band i n d i c a t e s t h a t a l a r g e f r a c t i o n o f t h e i o n p a i r s a r e i n b i n a r y c l u s t e r s .
I n t r o d u c t i o n . - I n a study o f t h e e f f e c t o f doping l i q u i d Se-5Tea5 w i t h monovalent elements, measurements have been made o f t h e magnetic s u s c e p t i b i l i t y X, t h e e l e c t r i - c a l c o n d u c t i v i t y o and t h e thermopower S i n a l l o y s M (Se 5Te.5)1-y w i t h M = Cu, T1,
Y .
Ag, o r Na and 0 < y
2
0.10.X
was measured up t o T = 900°C. The paramagnetic con- t r i b u t i o nxn
was determined as described i n e a r l i e r papers ( 1 ) . Except a t h i g h T where t h e l r q u i d i s m e t a l l i c , X f o l l o w s a C u r i e l a w f o r s p i n centers whose d e n s i t y ds obeys t h e Arrhenius law (2). d, vs y i s p l o t t e d i n Fig. 1 a t several tempera- t u r e s f o r T1 a l l o y s . I n t h e S and-o measurements as w e l l as these, r e s u l t s f o r Na, Cu and Ag were s i m i l a r t o T1, w i t h almost q u a n t i t a t i v e agreement between Ag and T1.a and S were measured simultaneously up t o 500°C f o r Ag, T1, and Na, and up t o 650°C f o r Cu. The behavior o f t h e undoped l i q u i d has been analyzed i n terms o f t r a n s p o r t a t t h e m o b i l i t y edge o f t h e valence band (3). According t o t h i s model
,
t h e c o n d u c t i v i t y oc a t t h e energy Ec a t which t r a n s p o r t occurs and t h e d i s t a n c e o f t h e Fermi energy EF from Ec can be determined f r o m the experimental values o f o and S by
oc = U exp[Se/k)
-
a],
(1 )EF
-
Ec = T ( s ~ - a k ) (2)a = 1 i n t h e m o b i l i t y - e d g e model. T h i s i s a s p e c i a l case f o r a type o f a n a l y s i s ( 4 ) which has general v a l i d i t y f o r s i n g l e band t r a n s p o r t i n t h e Maxwell Boltzmann l i m i t . The behavior o f oc and EF
-
E, as a f u n c t i o n o f y and T f o r t h e T l a l l o y s i s shown i n Figs. 2 and 3. The decrease i n oc a t low T when y i s increased t o .02 can o n l y be e x p l a i n e d by t r a n s p o r t i n new s t a t e s between EF and t h e valence band.We b e l i e v e these s t a t e s a r e i n an acceptor band. For y $ 0 . 2 , t h e p l o t s o f I n oc vs T-l a r e p a r a l l e l and s h i f t upward w i t h y. T h i s i n d i c a t e s t h a t t r a n s p o r t i s i n - t i r e l y i n t h e acceptor band f o r y
>
.OZ.I m p l i c a t i o n s o f Bond E q u i l i b r i u m Theory (BET).- The BET equations developed f o r Se- Te a l l o y s ( 5 ) can be r e a d i l y extended t o t h e present problem. There a r e t h r e e types o f bond d e f e c t s : o n e f o l d (1 F) n e u t r a l D* atoms, I F n e g a t i v e D- ions, and t h r e e - f o l d (3F) p o s i t i v e D+ ions. The D* centers a r e paramagnetic and t h e i o n s a r e d i a - magnetic. The c o n c e n t r a t i o n s (normalized t o t h e c o n c e n t r a t i o n s o f atoms) a r e
d* = pt e x p ( - ~ g * ) > (3)
"permanent address : U n i v e r s i t a t Heidelberg, 6900 Heidelberg, F.R.G.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814230
C4-1052 JOURNAL DE PHYSIQUE
F i g u r e 1 Dependence o f s p i n d e n s i t y o f F i g u r e 2 Dependence o f l o g o on T-l T1 -doped a1 l oys on composition f o r T1 -doped a1 l oys!
a t v a r i o u s temperatures.
T ( O K )
Figure 3 Dependence o f EF
-
EC on T f o r T1-doped a1 l o y s .U
1.3 1.4 1.5 1 0 0 0 / T (K-')F i g u r e 4 D e n s i t i e s o f c o n s t i t u e n t s i n 3.95% Ag a l l o y s c a l c u l a t e d from Eqs. 10 and 11, assuming t h a t t h e value o f R c o r r e - sponds t o a narrow acceptor band. The v e r t i c a l l e n g t h s o f t h e p o i n t s correspond t o t h e range o f c a l c u l a t e d values.
B =
l/kT, and g*, g- and
g+ are f r e e energies of formation from the normal 2F atom.
(More accurate expressions which take i n t o account the presence of two kinds of chalcogen atoms with d i f f e r e n t bond energies would include another f a c t o r which has some dependence on T
(6).)The polymer f a c t o r s pl and p3 depend strongly on the branch r a t i o
X =2c3/(cl-c3),where cl and c3 a r e the t o t a l concentrations of 1F and 3F c o n s t i t u e n t s , respectively. When
A >>1 , plaX and
p j a1/X.
In the doped a l l o y t h e f u l l y bonded M1 atoms have a concentration ml which i s related t o the fugacity
XMof t h e dopant by
ml = p X 1 M
( 6 )A s t r i k i n g aspect of the magnetic s u s c e p t i b i l i t y r e s u l t s i s the large increase in ds with y shown i n Fig. 1 . I f
ds =d*, Eq. 3 implies t h a t pl increases with y.
B u t a simple view would predict t h a t
Xand hence pl would decrease with y , since cl (=d-+d*+m 1
)increases because of the increase in ml . This leads t o consideration of the p o s s i b i l i t y t h a t d* increases because of a decrease in
g*.I f
q*decreases because of proximity t o an M atom, there should be an enhanced concentration of diatomic molecules MD*. There seems t o be a good reason f o r ex- pecting the energy of formation of MD* t o be smaller than f o r a normal D* center.
The l a t t e r i s known t o contain a positive term due t o overlap between the occupied dangling bond o r b i t a l and a p a r a l l e l lone-pair o r b i t a l on the neighboring chalcogen atom ( 7 ) . Since the
Matom has no non-bonding valence p e l e c t r o n , t h i s term i s missing, and the energy of formation of the D* center should be lower. Enhancement of the entropy of formation as the r e s u l t of hindered rotation of the small MD*
m01 ecul e s may a1 so reduce g* appreciably.
The same f a c t o r s would reduce the f r e e energy of formation of MD- molecules.
The reduction in energy may be even greater because two electrons a r e involved.
Thus we consider the presence of two more constituents designated Df and D i with
concentrations.
d i
=XM exp(-$gi)
( 7 )d i
= XMe x p C - ~ ( g i - EF)I ,
(8)where g i
<g* and g i
<g-.
I t i s possible t o derive information about the concentrations of the c o n s t i t - upnts without know'n the f r e e energy parameters. The only 3F constituents a r e
D. so t h a t c3
=d'.' Therefore the equation f o r
Acan
bewritten
~(d*+d-+ml
) =(2+X) d +
(9)
In addition, d'
=d-+di and di+di+ml
=y. If d* i s replaced by ds-df one can derive from these equations:
ml
=(y-ds)/2
+(d-+di)/X (10)
d- =
t(y+dS) - (d-/A)
M
l+R
+(l/ X)
I(11 1
where
R =d i / d i .
Eq. 2 provides an upper l i m i t t o the value of
Rsince EF - E,
=kT ln(1/2R) i f
the acceptor band i s narrow, and
EF- Ec i s l a r g e r otherwise. Two values f o r each
of the parameters d i , ml , d i , and d* can be calculated from experimental data using
Eqs. 10 and 11, together with the narrow-band value of R. One i s with
X = mand
C 4 - 1054 JOURNAL DE PHYSIQUE
another uses a value f o r X (which turns out t o be >> 1 ) estimated from the corre- sponding value of d*(y) in comparison with d*(O). The two values a r e generally close toqether. The r e s u l t s f o r 3.95% Ag shown in Fig. 4 a r e typical. Positively charged 1F attached ring molecules, which play a r o l e i n undoped Se-Te alloys (6) a r e neglected here because t h e i r concentrations a r e small compared t o
m l .
The curves in Fig. 2 show t h a t 5, increases with T with an activation energy
E, - 0.4 eV, while the calculations from Eq. 11 indicate t h a t t h e number of s t a t e s
i n
the acceptor band i s nearly constant % y/2. The explanation seems t o be t h a t a
l a r g e f r a c t i o n of the D i
ions a r e in binary c l u s t e r s with D+ ions, so t h a t the cor-
responding acceptor s t a t e s have an energy reduced below Ec
by roughly the dissocia-
t i o n energy Ed. Binary c l u s t e r s have been discussed in r e l a t i o n t o the behavior of
amorphous chalcogenide a l l o y s by Kastner, Adler and Fritzche, who r e f e r t o them a s
intimate valence a l t e r n a t i o n pairs ( 8 ) . Clustering causes a d i s t r i b u t i o n of ac-
ceptor s t a t e s whose width corresponds t o the value of Ed f o r ions in contact.
Dissociation with increasing T r e d i s t r i b u t e s the s t a t e s . Assuming a d i f f u s i v e model f o r transport a t E,, oc
is
proportional t o t h e square of t h e density of f r e eD i
ions, so t h a t Ea
=
2Ed. Preliminary investigation of theoretical models f o r ion c l u s t e r i n g indicates t h a tEd =
0.2 eV corresponds t o a reasonable value f o r the d i s - tance of c l o s e s t approach. As a r e s u l t of t h e width of the acceptor band, the c a l - culated values of d i such a s those shown in Fig. 4 a r e too l a r g e by a f a c t o r > 3, and the values of d* a r e correspondingly l a r g e r .Discussion.- The BET analysis has led t o the surprising conclusion t h a t the spin centers a r e mostly D* r a t h e r than
D i
centers. The increase in ds with y in Fig. 1 i s largely due t o t h e f a c t o r pl in Eq. 3, and i s caused by a novel mechanism. The f r e e energy of formation of D;-
D+
ion p a i r s i s so low t h a t a large f r a c t i o n of the M atoms form D# ions and a correspondingly l a r g e density of D counterions. The+
l a t t e r a r e 3F, so t h a t X and pl a r e increased t o the point where
ml
i s nearly a s l a r g e a s d i , and these two account f o r most of y.The present study has provided f u r t h e r and more d i r e c t evidence of t h e impor- tance of the polymer f a c t o r s in BET. Another i n t e r e s t i n g r e s u l t i s the concept of an a t t r a c t i v e i n t e r a c t i o n between chalcogen 1F bond defects and covalently bonded elements which lack lone p a i r electrons. Since t h i s would apply t o elements of groups I through V ,
i t
should be s i g n i f i c a n t in a large number of chalcogenide alloys.We thank H. Rasolondramanitra f o r technical assistance. This work has been supported by t h e National Science Foundation with grants DMR-77-19035 and DMR 80- 23682.
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G . H . , Phs. Rev.B E
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