- Email: [email protected]
Photo-induced complex permittivity measurements of tellurium at 9 GHz
~
Solid State Communications, Vol.46,No.l, p p . 1 7 - 1 9 , Printed in Great Britain.
1983.
0038-I098/83/130017-03~03.00/0
Pergamon Press Ltd.
PHOTO-INDUCED COMPLEX PERMITTIVITY MEASUREMENTS OF TELLURIUM AT 9 GHz L. Ding*, L Shih, C.H. C h a m p n e s s and T.J.F. Pavlnsek Dept. of E l e c t r i c a l Engineering, McGill University, 3480 University S t r e e t , M o n t r e a l , P.Q., H3A ZAT, Canada.
(Received by M. F. Collins, November 29, 1982)
A microwave transmission m e t h o d to d e t e r m i n e the photo-induced c o m p l e x relative permittivity of semiconductors (photodielectric effect and photoconductive effect) has b e e n i n v e s t i g a t e d . M e a s u r e m e n t s have b e e n made on single crystal tellurium samples a t a t e m p e r a t u r e of 100 K, at a m i c r o w a v e f r e q u e n c y o f 9 GHz in o p t i c a l f r e q u e n c i e s b e t w e e n about 0.Tx1014 and Z . 0 x l 0 1 4 Hz (i.e. w a v e l e n g t h s b e t w e e n 1.5 and 4.Z pro). From t h e m e a s u r e d data, t h e relaxation t i m e of t h e f r e e c a r r i e r s in t h e tellurium s a m p l e s was calculated.
Introduction
--
=
Cr M e a s u r e m e n t s of t h e c h a n g e of complex relative p e r m i t t i v i t y u n d e r illumination can provide i n f o r m a t i o n on t h e c a r r i e r t r a n s p o r t process in semiconductors. If t h e s e a r e c a r r i e d out a t microwave f r e q u e n c i e s , t h e r e are two experimental a d v a n t a g e s to be gained. F i r s t l y , the samples under study need no c u r r e n t e l e c t r o d e s which are o f t e n the source of unwanted resistance and increased recombination. Secondly, while microwave f r e q u e n c i e s are still o f t e n s m a l l c o m p a r e d with the r e c i p r o c a l of the c a r r i e r c o n d u c t i o n r e l a x a t i o n time (r), t h e r e is s o m e t i m e s f r e q u e n c y dispersion o b s e r v e d in s e m i c o n d u c t o r s arising from spacial inhomogeneity in p h y s i c a l properties; thus m e a s u r e m e n t s at m i c r o w a v e f r e q u e n c i e s may be more r e p r e s e n t a t i v e of t h e bulk m a t e r i a l . Except for work done by Ionov [1], who made p h o t o - i n d u c e d m e a s u r e m e n t s of complex relative p e r m i t t i v i t y on s e v e r a l s u b s t a n c e s using a resonant cavity m e t h o d a t ? GHz, no o t h e r e x p e r i m e n t a l work appears to have b e e n p u b l i s h e d in this area. The present work r e p o r t s m e a s u r e m e n t s on single crystal undoped tellurium at 100 K. The m e t h o d used seems to be simpler for m e a s u r i n g p e r m i t t i v i t y changes t h a n t h a t used by Ionov. The r e s u l t s r e p o r t e d here e n a b l e t h e c o n d u c t i o n r e l a x a t i o n t i m e to be determined for tellurium and provide confirmation of the energy gap.
UT
'
O
[¢rl
] -
G
j[
e (I+~2T 2) o
O
m~ (I+~2T 2) o
],
(i)
!
=
~
3e r
-
r
where Co(=ne~, ~ is t h e mobility) is the dc conductivity in the dark, • is t h e r e l a x a t i o n time of t h e free c a r r i e r s , £o t h e p e r m i t t i v i t y of free s p a c e and (0 is the angular f r e q u e n c y of the e.m. wave.
When l i g h t is i n c i d e n t on the sample, an i l l u m i n a t e d c o n d u c t i v i t y c i = ~o + A c is obtained. The i n c r e m e n t in c o n d u c t i v i t y , A~ , will give rise t o an i l l u m i n a t e d c o m p l e x p e r m i t t i v i t y , ~ri' which is e x p r e s s e d as, !
~ri
=
t
-
(¢r
Aer)
tl
-
!
J (¢r
.
+
Agr)"
Here Aer and A£r (generally positive) given by: AE
'
AOT
r
¢ (I+0 2z2) o
Ac r
(2)
Iv
are
the
increments
and,
(3)
(4)
Ao ( l + ~ 2 T 2)
~c O
F r o m e~As. (3) and (4), a s i m p l e expression to r e l a t e to ' and Ae" is shown as follows, r
Theory
r
Aer to
Assume t h a t t e l l u r i u m can be considered as a lossless continuum with a r e l a t i v e d i e l e c t r i c constant e r l to which n f r e e c a r r i e r s p e r unit volume are added [Z,3]. Then t h e c o m p l e x r e l a t i v e p e r m i t t i v i t y
Aer
(5) i!
To d e t e r m i n e values of Aer and Aer, a t e c h n i q u e involving a t r a n s m i s s i o n microwave bridge ( s e e F i g . l(a)) w a s u s e d . The s a m p l e t o b e investigated was p l a c e d at t h e c e n t r e of a waveguide section (see Fig. l(b)). The following expressions for both Acr and A¢r due to the e x t e r n a l illumination o f the s a m p l e shown in Fig. l(b) can be derived using a p e r t u r b a t l o n m e t h o d [4].
e'r is ,[3],
* Visiting s c i e n t i s t from C h o n g q i n g University, China.
17
PHOT0-INDUCED
18
COMPLEX PERMITTIVITY
Phase shi÷ter Atten.
MEASUREMENTS
Vol.
OF TELLURIUM
4 6 , No.
It is s e e n f r o m e q s . (5) a n d (6) t h a t if t h e values of h~s and AA s are known, one can I calculate b o t h AEr and Ae r , a n d t h u s t h e value of •. Experimental
Chopper F///,,'///)/.4 Monochromcltor I - - ]
Lock-in amp.
!I
(a)
SampLe / . ~ //~< %-! . ~ I r t r a n
2
(b) Fig.
1 (a) A s c h e m a t i c d i a g r a m o f t h e m i c r o w a v e b r i d g e , (b) t h e w a v e g u i d e s e c t i o n p a r t i a l l y filled w i t h t h e s a m p l e .
-17
I0
Et//c
•
• EL±c
% I 0 -le
A
•
J <
I I
<3
E//c, lOOK 15
Te-I
Results
I
i
I
I
I
2.0
2.5
3. O
315
4. 0
i0-,9
45
Light wavelength (#m) Fig.
Z The normalized photodielectric function of optical wavelength.
,
AE r =
,, AE r =
2
~
A2a
s
as a
],
(6)
8AA s] ,
(7)
- 0.115 ~ A
s
The real and imaginary relative permittivity v a l u e s o f t h e t w o s a m p l e s in d a ~ k n e s s a r e , , g i v e n in t a b l e 1. It i s s e e n t h a t t h e Cr a n d e r v a l u e s f o r E IIc a r e g r e a t e r t h a n t h o s e f o r E I c , g i v i n g an average anisotropy ratio of about 1.7 f o r i ! " '! er///er± and about Z.0 f o r ,, ¢rfl /er~_" T h e a n i s o t r o p y r a t i o o f Z.0 f o r E . /e'-is consistent • rll" ~Jw,th the dc conductivity ( d/i/rJ± ) a n i s o t r o p y value [9 ]. T a b l e 1 R e s u l t s of d a r k c o m p l e x r e l a t i v e p e r m i t t i v i t y f o r t w o s a m p l e s a t 100 K.
IT [ ~
27T2dl
effect
8
l~a [ ~ A e 21T2d1
Two samples (Te-1 and Te-Z) were first c h e m i c a l l y c u t [5] f r o m a t e l l u r i u m s i n g l e c r y s t a l grown by the Czochralski method [6]. Two l a r g e surfaces of each sample were then chemically polished using a mixture of HNO3, CrO 3 and H20 (10:5:20 b y w e i g h t ) . The samples were finally cut into a square plate of about lxl cm2. The t h i c k n e s s o f s a m p l e T e - 1 w a s a b o u t 0.98 m m a n d t h a t o f s a m p l e T e - Z a b o u t 0.61 r a m . The s a m p l e w a s t h e n i n s e r t e d i n t o a w a v e g u i d e section (see Fig. l(b)) for the microwave measurements. A Kodak IRTRAN Z window was inserted in t h e s i d e w a l l o f t h e w a v e g u i d e to a c c e p t the chopped monochromatic l i g h t (at a b o u t 90 Hz) supplied from a Perkin Elmer model 13 monochromator w i t h a N e r r ~ t g l o w e r s o u r c e . The monochromatic light intensity was determined using a c a l i b r a t e d InSb d e t e c t o r ( J u d s o n I n f r a r e d , Inc.). The c o m p l e x r e l a t i v e p e r m i t t i v i t y o f t h e s a m p l e in the dark, %-r, w a s f i r s t determined by m e a s u r i n g t h e p h a s e s h i f t a n d a t t e n u a t i o n of t h e propagating e.m. wave due to the presence of the sample [7]. The photo-induced complex relative permittivity was then determined a s follows. T h e m a g n i t u d e c h a n g e s o f t h e e l e c t r i c f i e l d in b o t h Ea n d H - a r m s o f t h e h y b r i d - T in t h e b r i d g e s h o w n in F i g . l(a), d u e to t h e e x t e r n a l i l l u m i n a t i o n of t h e s a m p l e w e r e f i r s t m e a s u r e d u s i n g a c a l i b r a t e d diode [8] • The corresponding phase shift change h~ s and a t t e n u a t i o n change AA s w e r e t h e n calculated f r o m the m e a s u r e d electric field changes. In the present experiments, the typical value of A~ s was about 0.00Z ° and about 0.0005 dB for AA s for the tellurium samples_under an external illumination o f a b o u t 100 p W / c m z . T h e p h o t o d i e l e c t r i c e f f e c t I AEr a n d t h e p h o t o c o n d u c t i v e effect A~r were finally o b t a i n e d from AO s a n d AA s USing eqs. (6) and (7).
A~
+ 0.115 s
where )to is the e.m. w a v e wavelength in free space, a is the width of the waveguide~ d is the thickness and l is the length of the sample, ~ is the attenuation constant and 8 is the phase constant of the waveguide section partially filled with the sample, A~ s is the phase change and hA s is the attenuation change of the propagating wave due to the external illumination on the sample.
Sample No.
Te-1
Sample orien.
E]]c Elc
Te-Z
E][c Elc
, Er
38.7 E4.Z 39.0 ZZ.1
,, er
Z1.0 11.8 19.1 8.3
!
ul
er// , E rl
er//
~ 1.60 ~ 1.76
i, E
r.L
1.78 Z.30
1
Vol. 46, No. 1
F i g s . Z a n d 3 s h o w t h e s p e c t r a l variation ( b e t w e e n 1.5 a n d 4.Z ~ m ) o f t h e n o r m a l i z e d p h o t o d i e l e c t r i c e f f e c t Ae~/(e~Eq) and the photoconductive effect A e : / ( e r E _) (Eq is t h e p h o t o n flux density) w i t h b o t h Eg~/c and E~J.c f o r sample Te-1 (here E~ is e l e c t r i c field v e c t o r of the incident light). Note t h a t for t h e s e r e s u l t s E, the microwave e l e c t r i c field, was m a i n t a i n e d parallel to t h e c - a x i s . It is seen t h a t t h e r e s p o n s e values of ! ! i! ii Aer/e r and Aer/e r for EjJ/c are generally g r e a t e r t h a n t h o s e for E ¢ l c . The variation L~ f ~ , l II II .-, of Cr/Er and ACr/~ r with monochromatic l i g h t i n t e n s i t y a t a w a v e l e n g t h of 3.6 pm is shown in Fig. 4 for b o t h E£//c a n d E £ 1 c for t h e sample Te-1. The v a r i a t i o n w i t h light i n t e n s i t y is almost l i n e a r over t h e r a n g e b e t w e e n a b o u t 10 and I00 ].lW/~:m2 . i(~ 17 Et//c &
r-
O
CL±C
A
"E
/1 A
&
~ O
O
O
O
o
K E / / c , lOOK
Te-I
I 2.5
I 3.0
I &5
I 4.0
4.5
L i g h t wavelength, (/~m)
Fig. 3 The n o r m a l i z e d p h o t o c o n d u c t i v e e f f e c t as a function of o p t i c a l w a v e l e n g t h .
(10-18c.m2sec)
(~', x io'l/C
EIIc
Te-Z
Elc E//c
1.3 2.2, Z.6
3.5 6.4 10.Z
0.67 0.70 0.SZ
11.9 1Z.5 9.1
Elc
0.9
1Z.7
0.19
3.4
A simple m i c r o w a v e t e c h n i q u e to d e t e r m i n e the photodielectric and photoconductive e f f e c t s in s e m i c o n d u c t o r s has b e e n i n v e s t i g a t e d . Using this method, m e a s u r e m e n t s h a v e b e e n m a d e on two single crystal tellurium s a m p l e s a t a t e m p e r a t u r e of about 100 K. The r e s u l t s o b t a i n e d show t !h a t !t h e s p e c t r a l r e st Pv- o n ios e v a l u e s f o r b o t h A e r / ( e r E q) and Aer/(erEq) w i t h E £ 11 c a r e g e n e r a l l y larger t h a! n i t h o s e ulf o rlu E £ 1 c . The variation of Aer/e r and AEr/6 r with the monochromatic light intensity was found to be approximately linear. Using the present method, the relaxation time o f .the c a r r i e r s in t e l l u r i u n was d e t e r m i n e d . The v a l u e s o b t a i n e d were l a r g e r t h a n those r e p o r t e d previously.
References o &
g
o
A
A
> o
1.0
0~ Q_
Te - I
0.5
k =3.6/~m lOOK
0~
I I I I I 2 4 6 8 I0 ReLative light intensity
Fig.
i
!
4 Aer/~r
(10-12sec)
4/
o
E
T
Te-1
o ~ A~,xl0 ) ~
4-, 4~
&e; Ae~
A c k n o w l e d g e m e n t - The a u t h o r s wish to acknowledge the Natural Sciences and Engineering Research Council of C a n a d a for f i n a n c i a l support.
10 ,
Ac~ Eqer
Discussion
O
W
.,
Ae; SampleNo. orien.Sample~
A o
o
I 2.0
Table 7 P h o t o - i n d u c e d r e l a t i v e p e r m i t t i v i t y results a t 100 K and a w a v e l e n g t h of 3.6 pro.
A
u IE~8
10-'9 1.5
The r e l a x a t i o n t i m e ~ of t h e f r e e c a r r i e r s can be d e t e r m i n e d using eq. (5). The r e s u l t s obtained f o r samples T e - I and Te-Z w i t h b o t h EI/c and E l c a r e shown in t a b l e Z. The T - v a l u e s o b t a i n e d in the p r e s e n t w o r k a r e b e t w e e n a b o u t 3x10 - 1 2 and IZxl0-12 sec. These v a l u e s a r e l a r g e r t h a n those r e p o r t e d by Grosse and K r a h l - U r b a n [3] of about Z x l 0 - 1 2 sac m e a s u r e d a t a t e m p e r a t u r e of 130 K.
A
A
o
19
PHOTO-INDUCED COMPLEX PERMITTIVITY MEASUREMENTS OF TELLURIUM
and
l!
i,
Aer/e r
as a function
of r e l a t i v e light i n t e n s i t y showing essentially l i n e a r v a r i a t i o n . A A : Ej~He , O O : E~_Lc.
[1] L.N. Ionov, Instrum. Exp. Tech. (USSR), 14, II3Z (1971), t r a n s l a t e d from Prib. Tekh. Eksp., No. 4, 157 (1971). [2] T.S. Benedict and W. Shockley, Phys. Ray., 89, 115Z (1953). [3] P. Grosse and B. Krahl-Urban, Phys. Status Solidi, Z7, K149 (1968). [4] R . F . Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Co., N e w York (1961). [5] M. EI-Azab, C .R. McLaughlin and C . H . Champness, J. Cryst. Growth, Z8, 1 (1975). [6] L Shih and C . H . Champness, J. Cryst. Growth, 44, 493 (1978). [7] G. Nimtz, R. Dornhaus, M. Schifferdecker, I. shih and E. Tyssen, J. Phys. E: Sci. Instrum, 11, 1109 (1978). [8] L Shih and L. DinE, S. Jatar, T.J.F. Pavlasek and C.H. Champness, accepted for Publication in IEEE Trans. Instrum. Meas, Oct. 198Z.
[9] L L. Drichko, L V. M o c h a n and Yu. N. Obraztsov, Soy. Phys. -Solid S t a t e , 4 9 184Z (1963).
Solid State Communications, Vol.46,No.l, p p . 1 7 - 1 9 , Printed in Great Britain.
1983.
0038-I098/83/130017-03~03.00/0
Pergamon Press Ltd.
PHOTO-INDUCED COMPLEX PERMITTIVITY MEASUREMENTS OF TELLURIUM AT 9 GHz L. Ding*, L Shih, C.H. C h a m p n e s s and T.J.F. Pavlnsek Dept. of E l e c t r i c a l Engineering, McGill University, 3480 University S t r e e t , M o n t r e a l , P.Q., H3A ZAT, Canada.
(Received by M. F. Collins, November 29, 1982)
A microwave transmission m e t h o d to d e t e r m i n e the photo-induced c o m p l e x relative permittivity of semiconductors (photodielectric effect and photoconductive effect) has b e e n i n v e s t i g a t e d . M e a s u r e m e n t s have b e e n made on single crystal tellurium samples a t a t e m p e r a t u r e of 100 K, at a m i c r o w a v e f r e q u e n c y o f 9 GHz in o p t i c a l f r e q u e n c i e s b e t w e e n about 0.Tx1014 and Z . 0 x l 0 1 4 Hz (i.e. w a v e l e n g t h s b e t w e e n 1.5 and 4.Z pro). From t h e m e a s u r e d data, t h e relaxation t i m e of t h e f r e e c a r r i e r s in t h e tellurium s a m p l e s was calculated.
Introduction
--
=
Cr M e a s u r e m e n t s of t h e c h a n g e of complex relative p e r m i t t i v i t y u n d e r illumination can provide i n f o r m a t i o n on t h e c a r r i e r t r a n s p o r t process in semiconductors. If t h e s e a r e c a r r i e d out a t microwave f r e q u e n c i e s , t h e r e are two experimental a d v a n t a g e s to be gained. F i r s t l y , the samples under study need no c u r r e n t e l e c t r o d e s which are o f t e n the source of unwanted resistance and increased recombination. Secondly, while microwave f r e q u e n c i e s are still o f t e n s m a l l c o m p a r e d with the r e c i p r o c a l of the c a r r i e r c o n d u c t i o n r e l a x a t i o n time (r), t h e r e is s o m e t i m e s f r e q u e n c y dispersion o b s e r v e d in s e m i c o n d u c t o r s arising from spacial inhomogeneity in p h y s i c a l properties; thus m e a s u r e m e n t s at m i c r o w a v e f r e q u e n c i e s may be more r e p r e s e n t a t i v e of t h e bulk m a t e r i a l . Except for work done by Ionov [1], who made p h o t o - i n d u c e d m e a s u r e m e n t s of complex relative p e r m i t t i v i t y on s e v e r a l s u b s t a n c e s using a resonant cavity m e t h o d a t ? GHz, no o t h e r e x p e r i m e n t a l work appears to have b e e n p u b l i s h e d in this area. The present work r e p o r t s m e a s u r e m e n t s on single crystal undoped tellurium at 100 K. The m e t h o d used seems to be simpler for m e a s u r i n g p e r m i t t i v i t y changes t h a n t h a t used by Ionov. The r e s u l t s r e p o r t e d here e n a b l e t h e c o n d u c t i o n r e l a x a t i o n t i m e to be determined for tellurium and provide confirmation of the energy gap.
UT
'
O
[¢rl
] -
G
j[
e (I+~2T 2) o
O
m~ (I+~2T 2) o
],
(i)
!
=
~
3e r
-
r
where Co(=ne~, ~ is t h e mobility) is the dc conductivity in the dark, • is t h e r e l a x a t i o n time of t h e free c a r r i e r s , £o t h e p e r m i t t i v i t y of free s p a c e and (0 is the angular f r e q u e n c y of the e.m. wave.
When l i g h t is i n c i d e n t on the sample, an i l l u m i n a t e d c o n d u c t i v i t y c i = ~o + A c is obtained. The i n c r e m e n t in c o n d u c t i v i t y , A~ , will give rise t o an i l l u m i n a t e d c o m p l e x p e r m i t t i v i t y , ~ri' which is e x p r e s s e d as, !
~ri
=
t
-
(¢r
Aer)
tl
-
!
J (¢r
.
+
Agr)"
Here Aer and A£r (generally positive) given by: AE
'
AOT
r
¢ (I+0 2z2) o
Ac r
(2)
Iv
are
the
increments
and,
(3)
(4)
Ao ( l + ~ 2 T 2)
~c O
F r o m e~As. (3) and (4), a s i m p l e expression to r e l a t e to ' and Ae" is shown as follows, r
Theory
r
Aer to
Assume t h a t t e l l u r i u m can be considered as a lossless continuum with a r e l a t i v e d i e l e c t r i c constant e r l to which n f r e e c a r r i e r s p e r unit volume are added [Z,3]. Then t h e c o m p l e x r e l a t i v e p e r m i t t i v i t y
Aer
(5) i!
To d e t e r m i n e values of Aer and Aer, a t e c h n i q u e involving a t r a n s m i s s i o n microwave bridge ( s e e F i g . l(a)) w a s u s e d . The s a m p l e t o b e investigated was p l a c e d at t h e c e n t r e of a waveguide section (see Fig. l(b)). The following expressions for both Acr and A¢r due to the e x t e r n a l illumination o f the s a m p l e shown in Fig. l(b) can be derived using a p e r t u r b a t l o n m e t h o d [4].
e'r is ,[3],
* Visiting s c i e n t i s t from C h o n g q i n g University, China.
17
PHOT0-INDUCED
18
COMPLEX PERMITTIVITY
Phase shi÷ter Atten.
MEASUREMENTS
Vol.
OF TELLURIUM
4 6 , No.
It is s e e n f r o m e q s . (5) a n d (6) t h a t if t h e values of h~s and AA s are known, one can I calculate b o t h AEr and Ae r , a n d t h u s t h e value of •. Experimental
Chopper F///,,'///)/.4 Monochromcltor I - - ]
Lock-in amp.
!I
(a)
SampLe / . ~ //~< %-! . ~ I r t r a n
2
(b) Fig.
1 (a) A s c h e m a t i c d i a g r a m o f t h e m i c r o w a v e b r i d g e , (b) t h e w a v e g u i d e s e c t i o n p a r t i a l l y filled w i t h t h e s a m p l e .
-17
I0
Et//c
•
• EL±c
% I 0 -le
A
•
J <
I I
<3
E//c, lOOK 15
Te-I
Results
I
i
I
I
I
2.0
2.5
3. O
315
4. 0
i0-,9
45
Light wavelength (#m) Fig.
Z The normalized photodielectric function of optical wavelength.
,
AE r =
,, AE r =
2
~
A2a
s
as a
],
(6)
8AA s] ,
(7)
- 0.115 ~ A
s
The real and imaginary relative permittivity v a l u e s o f t h e t w o s a m p l e s in d a ~ k n e s s a r e , , g i v e n in t a b l e 1. It i s s e e n t h a t t h e Cr a n d e r v a l u e s f o r E IIc a r e g r e a t e r t h a n t h o s e f o r E I c , g i v i n g an average anisotropy ratio of about 1.7 f o r i ! " '! er///er± and about Z.0 f o r ,, ¢rfl /er~_" T h e a n i s o t r o p y r a t i o o f Z.0 f o r E . /e'-is consistent • rll" ~Jw,th the dc conductivity ( d/i/rJ± ) a n i s o t r o p y value [9 ]. T a b l e 1 R e s u l t s of d a r k c o m p l e x r e l a t i v e p e r m i t t i v i t y f o r t w o s a m p l e s a t 100 K.
IT [ ~
27T2dl
effect
8
l~a [ ~ A e 21T2d1
Two samples (Te-1 and Te-Z) were first c h e m i c a l l y c u t [5] f r o m a t e l l u r i u m s i n g l e c r y s t a l grown by the Czochralski method [6]. Two l a r g e surfaces of each sample were then chemically polished using a mixture of HNO3, CrO 3 and H20 (10:5:20 b y w e i g h t ) . The samples were finally cut into a square plate of about lxl cm2. The t h i c k n e s s o f s a m p l e T e - 1 w a s a b o u t 0.98 m m a n d t h a t o f s a m p l e T e - Z a b o u t 0.61 r a m . The s a m p l e w a s t h e n i n s e r t e d i n t o a w a v e g u i d e section (see Fig. l(b)) for the microwave measurements. A Kodak IRTRAN Z window was inserted in t h e s i d e w a l l o f t h e w a v e g u i d e to a c c e p t the chopped monochromatic l i g h t (at a b o u t 90 Hz) supplied from a Perkin Elmer model 13 monochromator w i t h a N e r r ~ t g l o w e r s o u r c e . The monochromatic light intensity was determined using a c a l i b r a t e d InSb d e t e c t o r ( J u d s o n I n f r a r e d , Inc.). The c o m p l e x r e l a t i v e p e r m i t t i v i t y o f t h e s a m p l e in the dark, %-r, w a s f i r s t determined by m e a s u r i n g t h e p h a s e s h i f t a n d a t t e n u a t i o n of t h e propagating e.m. wave due to the presence of the sample [7]. The photo-induced complex relative permittivity was then determined a s follows. T h e m a g n i t u d e c h a n g e s o f t h e e l e c t r i c f i e l d in b o t h Ea n d H - a r m s o f t h e h y b r i d - T in t h e b r i d g e s h o w n in F i g . l(a), d u e to t h e e x t e r n a l i l l u m i n a t i o n of t h e s a m p l e w e r e f i r s t m e a s u r e d u s i n g a c a l i b r a t e d diode [8] • The corresponding phase shift change h~ s and a t t e n u a t i o n change AA s w e r e t h e n calculated f r o m the m e a s u r e d electric field changes. In the present experiments, the typical value of A~ s was about 0.00Z ° and about 0.0005 dB for AA s for the tellurium samples_under an external illumination o f a b o u t 100 p W / c m z . T h e p h o t o d i e l e c t r i c e f f e c t I AEr a n d t h e p h o t o c o n d u c t i v e effect A~r were finally o b t a i n e d from AO s a n d AA s USing eqs. (6) and (7).
A~
+ 0.115 s
where )to is the e.m. w a v e wavelength in free space, a is the width of the waveguide~ d is the thickness and l is the length of the sample, ~ is the attenuation constant and 8 is the phase constant of the waveguide section partially filled with the sample, A~ s is the phase change and hA s is the attenuation change of the propagating wave due to the external illumination on the sample.
Sample No.
Te-1
Sample orien.
E]]c Elc
Te-Z
E][c Elc
, Er
38.7 E4.Z 39.0 ZZ.1
,, er
Z1.0 11.8 19.1 8.3
!
ul
er// , E rl
er//
~ 1.60 ~ 1.76
i, E
r.L
1.78 Z.30
1
Vol. 46, No. 1
F i g s . Z a n d 3 s h o w t h e s p e c t r a l variation ( b e t w e e n 1.5 a n d 4.Z ~ m ) o f t h e n o r m a l i z e d p h o t o d i e l e c t r i c e f f e c t Ae~/(e~Eq) and the photoconductive effect A e : / ( e r E _) (Eq is t h e p h o t o n flux density) w i t h b o t h Eg~/c and E~J.c f o r sample Te-1 (here E~ is e l e c t r i c field v e c t o r of the incident light). Note t h a t for t h e s e r e s u l t s E, the microwave e l e c t r i c field, was m a i n t a i n e d parallel to t h e c - a x i s . It is seen t h a t t h e r e s p o n s e values of ! ! i! ii Aer/e r and Aer/e r for EjJ/c are generally g r e a t e r t h a n t h o s e for E ¢ l c . The variation L~ f ~ , l II II .-, of Cr/Er and ACr/~ r with monochromatic l i g h t i n t e n s i t y a t a w a v e l e n g t h of 3.6 pm is shown in Fig. 4 for b o t h E£//c a n d E £ 1 c for t h e sample Te-1. The v a r i a t i o n w i t h light i n t e n s i t y is almost l i n e a r over t h e r a n g e b e t w e e n a b o u t 10 and I00 ].lW/~:m2 . i(~ 17 Et//c &
r-
O
CL±C
A
"E
/1 A
&
~ O
O
O
O
o
K E / / c , lOOK
Te-I
I 2.5
I 3.0
I &5
I 4.0
4.5
L i g h t wavelength, (/~m)
Fig. 3 The n o r m a l i z e d p h o t o c o n d u c t i v e e f f e c t as a function of o p t i c a l w a v e l e n g t h .
(10-18c.m2sec)
(~', x io'l/C
EIIc
Te-Z
Elc E//c
1.3 2.2, Z.6
3.5 6.4 10.Z
0.67 0.70 0.SZ
11.9 1Z.5 9.1
Elc
0.9
1Z.7
0.19
3.4
A simple m i c r o w a v e t e c h n i q u e to d e t e r m i n e the photodielectric and photoconductive e f f e c t s in s e m i c o n d u c t o r s has b e e n i n v e s t i g a t e d . Using this method, m e a s u r e m e n t s h a v e b e e n m a d e on two single crystal tellurium s a m p l e s a t a t e m p e r a t u r e of about 100 K. The r e s u l t s o b t a i n e d show t !h a t !t h e s p e c t r a l r e st Pv- o n ios e v a l u e s f o r b o t h A e r / ( e r E q) and Aer/(erEq) w i t h E £ 11 c a r e g e n e r a l l y larger t h a! n i t h o s e ulf o rlu E £ 1 c . The variation of Aer/e r and AEr/6 r with the monochromatic light intensity was found to be approximately linear. Using the present method, the relaxation time o f .the c a r r i e r s in t e l l u r i u n was d e t e r m i n e d . The v a l u e s o b t a i n e d were l a r g e r t h a n those r e p o r t e d previously.
References o &
g
o
A
A
> o
1.0
0~ Q_
Te - I
0.5
k =3.6/~m lOOK
0~
I I I I I 2 4 6 8 I0 ReLative light intensity
Fig.
i
!
4 Aer/~r
(10-12sec)
4/
o
E
T
Te-1
o ~ A~,xl0 ) ~
4-, 4~
&e; Ae~
A c k n o w l e d g e m e n t - The a u t h o r s wish to acknowledge the Natural Sciences and Engineering Research Council of C a n a d a for f i n a n c i a l support.
10 ,
Ac~ Eqer
Discussion
O
W
.,
Ae; SampleNo. orien.Sample~
A o
o
I 2.0
Table 7 P h o t o - i n d u c e d r e l a t i v e p e r m i t t i v i t y results a t 100 K and a w a v e l e n g t h of 3.6 pro.
A
u IE~8
10-'9 1.5
The r e l a x a t i o n t i m e ~ of t h e f r e e c a r r i e r s can be d e t e r m i n e d using eq. (5). The r e s u l t s obtained f o r samples T e - I and Te-Z w i t h b o t h EI/c and E l c a r e shown in t a b l e Z. The T - v a l u e s o b t a i n e d in the p r e s e n t w o r k a r e b e t w e e n a b o u t 3x10 - 1 2 and IZxl0-12 sec. These v a l u e s a r e l a r g e r t h a n those r e p o r t e d by Grosse and K r a h l - U r b a n [3] of about Z x l 0 - 1 2 sac m e a s u r e d a t a t e m p e r a t u r e of 130 K.
A
A
o
19
PHOTO-INDUCED COMPLEX PERMITTIVITY MEASUREMENTS OF TELLURIUM
and
l!
i,
Aer/e r
as a function
of r e l a t i v e light i n t e n s i t y showing essentially l i n e a r v a r i a t i o n . A A : Ej~He , O O : E~_Lc.
[1] L.N. Ionov, Instrum. Exp. Tech. (USSR), 14, II3Z (1971), t r a n s l a t e d from Prib. Tekh. Eksp., No. 4, 157 (1971). [2] T.S. Benedict and W. Shockley, Phys. Ray., 89, 115Z (1953). [3] P. Grosse and B. Krahl-Urban, Phys. Status Solidi, Z7, K149 (1968). [4] R . F . Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill Book Co., N e w York (1961). [5] M. EI-Azab, C .R. McLaughlin and C . H . Champness, J. Cryst. Growth, Z8, 1 (1975). [6] L Shih and C . H . Champness, J. Cryst. Growth, 44, 493 (1978). [7] G. Nimtz, R. Dornhaus, M. Schifferdecker, I. shih and E. Tyssen, J. Phys. E: Sci. Instrum, 11, 1109 (1978). [8] L Shih and L. DinE, S. Jatar, T.J.F. Pavlasek and C.H. Champness, accepted for Publication in IEEE Trans. Instrum. Meas, Oct. 198Z.
[9] L L. Drichko, L V. M o c h a n and Yu. N. Obraztsov, Soy. Phys. -Solid S t a t e , 4 9 184Z (1963).