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ULTRASONIC ATTENUATION AND VELOCITY IN
Cd0.55 Mn0.45Te+
P. Maheswaranathan, R. Sladek, U. Debska
To cite this version:
P. Maheswaranathan, R. Sladek, U. Debska.
ULTRASONIC ATTENUATION AND
JOURNAL D E PHYSIQUE
Colloque
CIO,
supplémentau n o
12, Tome46,
décembre 1985 page CIO-513ULTRASONIC ATTENUATION AND VELOCITY IN Cd,.,5Mn,.,5Te'
p . MAHESWARANATHAN, R.J. SLADEK AND U. DEBSKA Purdue University, West Lafayette, IN 47907, U.S.A.
Abstract
-
We deduce t h e electromechanical coupling f a c t o r , piezoelectric con-
stant(e14),
and e l e c t r i c a l conductivity of Cdo.55Mno.k5Te from t h e attenua-
t i o n maximum and veloci ty change of piezoelectrical ly-active [ I l 0 1 [O011 u l t r a -
sonic shear waves which occur a s a function of temperature,
T.Electro-
mechanical coupling and e14 are much l a r g e r in Cdo.55Mno.45Te than in CdTe
due t o l e s s bond charge t r a n s f e r in the former because, we believe, of hybrid-
i z a t i o n of Mn 3d o r b i t a l s i n t o the tetrahedral bonds. The dc r e s i s t i v i t y was
measured and found to be an exponential function of 1/T in accord with the
e l e c t r i c a l conductivi t y deduced from
O u rul trasonic data. The conductivi t y
a c t i v a t i o n energy we i d e n t i f y with the ionization energy of centers which
provide mobile charge c a r r i e r s ( h o l e s ) .
1
-
INTRODUCTION
The d i l u t e d magnetic semiconductor CdlmxMnxTe has been t h e subject of extensive
s t u d i e s
/1/because of i t s important semiconducting, optical and magneto-optic prop-
e r t i e s and the growth of CdTe
-
CdMnTe s u p e r l a t t i c e s by molecular beam epi taxy
/2/.Ultrasonic velocity measurements on Cdl-,MnxTe have been made down to low tempera-
tures /3/ and as a function of hydrostatic pressure
/4/i n t h i s laboratory.
In
addition recent ultrasonic attenuation and velocity s t u d i e s on Cdl-xMnxTe by us /5/
have revealed a maximum in t h e attenuation and a concomittant change in velocity as
a function of temperature f o r piezoelectrical l y active ul t r a s o n i c waves because of
d r a s t i c temperature dependence of the e l e c t r i c a l conductivi ty.
In t h i s paper we present 10 MHz f a s t shear wave velocity data not reported prev-
iouslÿ and dc r e s i s t i v i t y data f o r cornparison with t h e e l e c t r i c a l conductivity de-
duced from our ul trasonic resul t s . We analyze these velocity data and Our prev-
iously obtained /5/ 30 MHz attenuation data t o obtain a value f o r the e l e c t r o -
mechanical coupling f a c t o r and suggest an i n t e r p r e t a t i o n of the l a t t e r . The defect/
impurity ionization energy deduced from O u r ultrasonic and dc r e s i s t i v i t y r e s u l t s
are reported and discussed.
C10-514 JOURNAL
DE
PHYSIQUEI I
-
EXPERIMENTAL DETAILS
The ultrasonic sample and the experimental d e t a i l s f o r
O u r ultrasonic attenuation
and velocity measurement have been described i n r e f .
5.A rectangular parallelo-
piped of Cdo.55Mno.45Te was prepared from the ultrasonic sample and i t s dc r e s i s -
t i v i t y was measured by means of a standard four-probe technique.
I I I
-
RESULTS
ANDDISCUSSION
The attenuation of 30 MHz p i e z o e l e c t r i c a l l y a c t i v e ultrasonic waves as a function of
inverse temperature i s shown in Fig. 1 f o r O u r Cdo-55Mno.45Te sample. Use of
1 / Ta s
the abscissa allows one to note t h a t a f t e r the background attenuation i s subtracted
the peak i s symmetric a s would be expected f o r a thermally acti'vated relaxation
process. As will become evident the peak depends on the relaxation of the e l e c t r i c a l
conductivity and t h e a v a i l a b i l i t y of mobile charge c a r r i e r s (holes) t o respond t o the
piezoelectric f i e l d associated with t h e ultrasonic s t r a i n .
I l I 20
-
Cdg.uMn0.4sTe
-
-
30 uiir Cirol Cwil > 1.864 t_-
COIC. V O , J---
backqrwnd z W " > E 1.858a
W W " l---
I O u> 1'
0.5
t- u>3.0
4.05.0
1.852
IOOO/T ( K I 200 250 300Fig.
1-
Attenuation of 30 MHz
[ I I 0 1 TEMPERATURE ( K 1[O011 waves in Cdo.,5Mno-45Te versus
inverse temperature. The sol id
Fig.
2-
Fast shear velocity of 10 MHz
curve was calculated using the back-
[1101[0011 waves in C d ~ . ~ ~ M n o . ~ ~ T e
versus tem-
ground attenuation given by the
perature. The solid curve was calculated using
dashed line.
unstiffened values oiven
bythe dashed line.
In order t o analyze t h e attenuation maximum and velocity changes (shown in Fig. 2)
we use the theory of Hutson and White /6/ f o r e l a s t i c wave propagation i n piezo-
e l e c t r i c semiconductors. When t h e r e are negligible c a r r i e r diffusion and small con-
ductivity modulation a s a r e t r u e
i nO u r
case, t h e piezoelectric attenuation
ccpzand
the velocity of shear waves propagating i n the [Il01 crystallographic direction and
polarized i n the [O011 direction a r e given by /6/
and eq.(l) w i t h w = UC, we deduce t h a t t h e electromechanical c o u p l i n g f a c t o r e 1 4 2 / ~ C 4 4 has a value o f 0.0049 2 0.0005 f o r Our Cdo. 55Mno.45Te sample.
Fig. 2 shows the v e l o c i t y o f 10 MHz u l t r a s o n i c f a s t shear waves as a f u n c t i o n o f tem- p e r a t u r e f o r Cdo.55Mno.45Te. I t can be seen t h a t t h e r e i s an e x t r a increase i n ve- l o c i t y w i t h decreasing temperature below 250 K. This i s due t o t h e presence o f p i e z o e l e c t r i c f i e l d s which are n o t screened o u t by t h e charge c a r r i e r s . The s t i f f - ened and unstiffened values o f t h e f a s t shear v e l o c i t y shown i n Fig. 2 and eq. (2) gives e 1 4 2 / ~ C 4 4 = 0.0047 i 0.0005. This value i s w i t h i n experimental e r r o r o f t h a t
obtained from t h e 30 MHz a t t e n u a t i o n r e s u l t s shown i n Fig. 1 (see Table 1 ) . The u n s t i f f e n e d values i n F i g . 2 a r e obtained from a l i n e a r e x t r a p o l a t i o n o f t h e f a s t shear v e l o c i t y above 270 K.
Table 1
-
Values o f e142/~C44 deduced f o r Cdo. 55Mno. 45Te f r o m [ I l 0 1 [O011 u l t r s o n i c waves.
e142/~C44 Frequency Method
0.0049 c 0.0005 30 MHz a t t e n u a t i o n
The dc r e s i s t i v i t y i s shown as a f u n c t i o n o f i n v e r s e temperature i n Fig. 3. Also shown i n F i g . 3 i s t h e c a l c u l a t e d r e s i s t i v i t y u s i n g o u r 10 MHz a t t e n u a t i o n versus temperature r e s u l t s /5/. The agreement i s very good a t a l 1 temperatures except perhaps a t temperatures which a r e w e l l above t h a t o f the peak a t t e n u a t i o n .
From Table 1 i t can be seen t h a t the values o f t h e electromechanical coup- l i n g f a c t o r deduced from v a r i o u s u l t r a - sonic data a r e w i t h i n experimental e r r o r except f o r t h e 10 MHz a t t e n u a t i o n value being somewhat l e s s than t h e o t h e r s . The reason f o r t h e l a t t e r i s 0.0047
+
0.0005 10 MHz v e l o c i t ya 0 . ~ 0 4 2 I 0.0004 30 MHz v e l o c i t y
a0.0037 MHz attenuation
afrom r e f . 5.
The 0.36 eV c o n d u c t i v i t y a c t i v a t i o n energy o f Our Cdo.55Mno.45Te, which i s p-type, i s s i m i l a r t o t h a t observed i n Cdl-xMnxTe / I O / (0.05 x 0.20) which had been sub- j e c t e d t o annealing i n t h e presence o f Cd, Au, o r Cu. Such values have been a t t r i b - uted t o complexes c o n t a i n i n g r e s i d u a l chemical i m p u r i t i e s and l a t t i c e defects.
n o t known a t present. I n any case t h e e l ectromechanical coupl i ng f a c t o r s shown i n Table 1 f o r Cdo.55Mno,45Te a r e much l a r g e r than t h a t o f CdTe which has a value o f 0.0007 [ r e f . 51 o r 0.0005
[ r e f . 71. The enhanced electromechan- i c a l c o u p l i n g i n Cdo.55Mno.45Te i s due
I V
-
CONCLUSIONt o e l 4 being l a r g e r s i n c e c [ r e f . 81 has n e a r l y t h e same value i n i t as i n CdTe. The l a r g e r value o f e l 4 can be under- stood as f o l lows. According t o M a r t i n /9/
e14 = e;da2
-
eaQ/a 2 ( 3 )where a i s t h e l a t t i c e parameter, e; i s t h e t r a n s v e r s e macroscopic (Born) e f f e c t i v e charge, 5 i s t h e i n t e r n a l s t r a i n parameter, e i s t h e e l e c t r o n i c charge, and
AQ
i s t h e quadrupolar bond charge t r a n s f e r . Now t h e i o n i c i n t e r n a l s t r a i n component e*q/a2i s o n l y about 1.5% s m a l l e r i n Cdo.5Mno.5Te than i n CdTe [ r e f . 51 so t h a t e14 engance- ment must be due t o Mn reducing t h e bond charge t r a n s f e r term by about 10%. Me suggest t h a t t h e i n f l u e n c e o f Mn on t h e bond charge t r a n s f e r term i s due t o Mn 3d e l ectrons h y b r i d i z i n g w i t h sp3 bonding o r b i t a l s /5/.
To o b t a i n t h e c a l c u l a t e d curves shown i n Figures 1 and 2 we used Equations ( 1 ) and (2) w i t h wc = ~ ~ ( 0 ) exp(-E /kT) o b t a i n e d from t h e 10 MHz, a t t e n u a t i o n versus tem- p e r a t u r e r e s u l t s /5/ and t c e electromechanical c o u p l i n g f a c t o r deduced already. As can be seen from Figures 1 and 2 we o b t a i n very good f i t s t o Our experimental r e s u l t s . This i n d i c a t e s t h a t 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 must be an exponential f u n c t i o n of temperature c h a r a c t e r i z e d by a s i n g l e a c t i v a t i o n energy o f 0.36 eV.
CIO-516 JOURNAL DE PHYSIQUE
associated w i t h t h e r m a l l y a c t i v a t e d e l e c t r i c a l c o n d u c t i v i t y which i n d i c a t e s stronger electromechanical c o u p l i n g i n Cdo.55Mno.k5Te than i n CdTe. The enhanced e l e c t r o - mechanical c o u p l i n g i s due t o a s m a l l e r strain-induced t r a n s f e r o f bond charge, caused by t h e h y b r i d i z a t i o n o f Mn 3d States i n t o t h e t e t r a h e d r a l bonding o r b i t a l s . The c o n d u c t i v i t y a c t i v a t i o n energy, .which gives the d e f e c t i o n i z a t i o n energy, i s s i m i l a r t o t h a t observed by o t h e r s i n Cdl-xMnxTe w i t h various values o f x.
IOOO/T(K)
REFERENCES
T ( K )
*
Supported by NSF-MRL Grant DMR80-20249, Purdue Research Foundation and NSF Grant DMR79-08538A3 a t various times.
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Fig. 3
-
p , the dc r e s i s t i v i t y o f-
Cdo.55Mno.Q5Te versus inverse temperature. E
O
The s o l i d curve snows t h e r e s i s t i v i t y
