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Electron spin resonance in n-type GaAs
Volume 7, number 1
PHYSICS
ELECTRON
SPIN
LETTERS
RESONANCE
IN n-TYPE
15 October 1963
GaAs
W. DUNCAN a n d E. E. SCHNEIDER Department of Physics, University of Newcastle upon Tyne, England Received 20 September 1963
I n t h i s note we r e p o r t e l e c t r i n s p i n r e s o n a n c e e x p e r i m e n t s on n - t y p e GaAs. One of the r e s o n a n c e s o b s e r v e d h a s the low g - v a l u e e x p e c t e d f r o m the t h e o r y of Roth et al. 1) for l o o s e l y bound or conduction electrons. Most of the e x p e r i m e n t s w e r e c a r r i e d out with a s e n s i t i v e 300 M c / s s p e c t r o m e t e r u s i n g a c o a x i a l h y b r i d r i n g and a s u p e r h e t e r o d y n e r e c e i v e r . T h e dc m a g n e t i c f i e l d i s p r o d u c e d by a w a t e r cooled s o l e n o i d w h i c h g i v e s a m a x i m u m f i e l d of 800 g a u s s . T h e s a m p l e s a r e l o c a t e d at the s h o r t c i r c u i t end of ½k c o - a x i a l c a v i t y . A s t a b i l i s a t i o n s y s t e m l o c k s the f r e q u e n c y to the s a m p l e c a v i t y so that the p h a s e s e n s i t i v e d e t e c t e d s i g n a l is the d e r i v a t i v e of the true absorption signal. T h e r o o m t e m p e r a t u r e c h a r a c t e r i s t i c s of the c r y s t a l s , which w e r e s u p p l i e d by S . E . R . L . , a r e l i s t e d i n t a b l e 1. The c a r r i e r c o n c e n t r a t i o n w a s e s t i m a t e d f r o m E h r e n r e i c h ' s 2) d a t a on m o b i l i t y versus concentration.
.I
"\..I /
Fig, 1. Spin resonance signal (derivative of absorption) of n-type GaAs at 300 Mc/s. Full line is the experimental curve. Broken line is the residual curve after subtraction of g= 1.2 line.
D = 4 5, showed no s i g / i i f i c a n t change in the l i n e shape. It ~suggested i t s e l f that the s p e c t r u m was c o m Table 1 p o s e d of o v e r l a p p i n g r e s o n a n c e s . In o r d e r to check p RH n t h i s , the s p e c t r o m e t e r was adapted for u s e at the (cm2(V.sec) -1) (~cm) (cm3cou1-1) (cm 3) s e c o n d h a r m o n i c of the h y b r i d r i n g , 600 M c / s , at 6300 0.06 378 5xlo 1~ the c o s t of s o m e s e n s i t i v i t y . In a d d i t i o n it w a s A. Single crystal 4 000 2.75 11 000 5×1017 n e c e s s a r y to u s e a n e l e c t r o m a g n e t which m e a n t B. Single crystal 103 C. Polycrystalline that the o r i e n t a t i o n of the dc field w a s p a r a l l e l to the p l a n e of the m i c r o w a v e m a g n e t i c field, c o n s e Fig. 1 shows the s p e c t r u m o b t a i n e d at 4.2OK q u e n t l y the effective s a m p l e v o l u m e w a s s u b s t a n f r o m s p e c i m e n A, s i m i l a r r e s u l t s w e r e o b t a i n e d tially reduced. f r o m s a m p l e B, but no r e s o n a n c e w a s o b s e r v e d The 600 M c / s s p e c t r u m , shown in fig. 2, c o n with s a m p l e C. The s h a r p l i n e n e a r 500 g a u s s s i s t s of two i n c o m p l e t e l y r e s o l v e d l i n e s , c o r r e c o r r e s p o n d i n g to g ~ 0.4 w a s thought to be a s s o s p o n d i n g to g - f a c t o r s of 0.52 + 0.05 and 1.1 ± 0.2. c i a t e d with c o n d u c t i o n e l e c t r o n s i n GaAs. The u n The l i n e shape of the r e s o n a n c e of high g - v a l u e usual line shape r e q u i r e d further investigation. w a s shown to be L o r e n t z i a n and is shown a s a O v e r a r a n g e of r f p o w e r 10 -2 to 10 -5 W the b r o k e n l i n e in fig~ 2. No a t t e m p t w a s m a d e to fit a l i n e s h a p e w a s found to be u n a l t e r e d . At t e m p e r a L o r e n t z or G a u s s i a n c u r v e to the l i n e of low g t u r e s a b o v e 4.2OK no r e s o n a n c e w a s o b s e r v e d . v a l u e a s the s i g n a l is quite s m a l l . To c l a r i f y the Skin depth e f f e c t s could be e x c l u d e d ; for s a m 300 M c / s s p e c t r u m , the l i n e of high g - v a l u e was p l e A the s k i n depth at 300 M c / s (5) is 1 m m u s i n g s u b t r a c t e d f r o m the 300 M c / s c u r v e of fig. 1; the O l i v e r ' s 3) c o n d u c t i v i t y data. A c c o r d i n g to D y s o n 4 ) r e s u l t a n t line is shown a s a b r o k e n c u r v e . d i s t o r t i o n of the r e s o n a n c e l i n e s h a p e is n e g l i g i b l e F u r t h e r e x p e r i m e n t s w e r e c a r r i e d out at 8825 if the s a m p l e t h i c k n e s s i s l e s s t h a n 4 5. In m o s t M c / s with a n e l e c t r o m a g n e t which w a s c a p a b l e e x p e r i m e n t s i n c l u d i n g that shown in fig. 1, D ~ 6. of a m a x i m u m field of 15 k i l o g a u s s . The s p e c t r u m An a d d i t i o n a l e x p e r i m e n t in a s p e c i m e n with w a s c o m p l e t e l y r e s o l v e d into two l i n e s of g - f a c t o r 23,
Volume 7, number 1
PHYSICS
LETTERS
15 October 1963
lOt
!
Fig. 2
I0:
I
Fig. 3
I 8
6'
~
", 6 dB
2~
750 500 250 MAGNETIC FIELD ~;AUSS]
I000
0i
0
IZl)00 11,800 MAGNETIC FIELD ~USS~
Fig. 2. Spin resonance of n-type GaAs at 600 M c / s . Full line is the experimental curve and the broken line is the calculated curve for g = 1.2 line.
Fig. 3. High field spin resonance of n-type GaAs at 8825 Mc/ s.
0.5228 ~ 0.0001 a n d 1.2 ± 0.1. T h e i n t e n s i t y of t h e low f i e l d l i n e w a s found to be v e r y w e a k b e i n g a p p r o x i m a t e l y a f a c t o r of 10 s m a l l e r t h a n t h e o t h e r l i n e . T h e high f i e l d l i n e i s shown in fig. 3 and h as b e e n found to h a v e a L o r e n t z i a n s h a p e . T h e g - f a c t o r p r e d i c t e d by Roth is
n e r 10) g i v e v a l u e s of 0.074 and 0.071 f r o m data on t h e m a g n e t i c f i e l d d e p e n d e n c e of s t i m u l a t e d and spontaneous emission respectively. These values were obtained assuming a hydrogenic model; a var i a t i o n a l t h e o r y l e a d s to v a l u e s 10% l o w e r . W e c o n c l u d e that t h e high f i e l d r e s o n a n c e is due to c o n d u c t i o n e l e c t r o n s p o s s i b l y in t h e i m p u r i t y band.. Th e low f i e l d r e s o n a n c e of g = 1.2 i s p o s s i bly due to d e e p l y i n g d o n o r s . T h e s e a r e e x p e c t e d to h a v e a g - v a l u e i n t e r m e d i a t e b e t w e e n that of c o n d u c t i o n e l e c t r o n s and highly l o c a l i s e d e l e c t r o n s , a s in t h e c a s e of e l e c t r o n c e n t r e s a s s o c i a t e d with Mn ++, g = 2.004 11).
2
[1
-
~
,,z
"m*
_
I)
A 3Eg + ~]
"
F o r G a A s , i n f r a r e d a b s o r p t i o n 5) e x p e r i m e n t s h a v e shown that E g = 1.53 ~ 0.01 eV and B r a u n s t e i n 6) h as o b t a i n e d a v a l u e of A = 0.33 eV. Th e e x p e r i m e n t s of M o s s and W a l t o n 7) h a v e s h ow n that m * / m o i s 0.074 + 0.006. In v i e w of t h e c o n s i d e r a b l e u n c e r t a i n t y in thi~ v a l u e , t h e e x p e c t e d g - f a c t o r fo r c o n d u c t i o n e l e c t r o n s in n - t y p e G a A s l i e s in the r a n g e +0.28 to +0.56. T h e high f i e l d r e s o n a n c e w h i c h we find to be 0.5228 ± 0.0001 is w e l l w i t h i n t h i s r a n g e . T h e p o s i t i v e s i g n of the g - f a c t o r has b e e n e s t a b l i s h e d by e x p e r i m e n t s 8) on i n t e r b a n d and o s c i l l a t o r y F a r a d a y e f f e c t 9) in GaAs . C o n v e r s e l y , the e x p e r i m e n t a l l y d e t e r m i n e d g - f a c t o r c a n be u s e d i n d i r e c t l y to d e t e r m i n e m * / m o. A s s u m i n g th e a b o v e v a l u e s of E z and A to be c o r r e c t , we t h u s o b t a i n m * / m o to t~e 0.078 ± 0.001. It is of i n t e r e s t to note that t h e e l e c t r o l u m i n e s c e n c e e x p e r i m e n t s of W r i g h t and G a l e e -
24
R c f c~'CnCCS 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)
L.Roth. Lax and Zwerdling, Phys. Rev. 114 (1959) 96. H. Ehrer~eich, Phys. Rev. 120 (1960) 1951. D . J . Oliver. Phys. Rev. 127 (1962) 1045. F.Dyson. Phys. Rev. 98 (1955) 349. H.Welker and H.Weiss, Solid State Physics 3 (1956) 1. R. Braunstein, J. Phys. Chem. Solids 8 (1959) 280. F . S . M o s s and A.K.Walton. Proc. Phys. Soc. (London) 74 (1959) 131. Private communication. S. D Smith and C.R. Pidgeon. Proc. Fifth Int. Conf. on Semiconductors, Exeter, 1962, p. 301. G.B.Wright and F . L . G a l e e n e r , Phys. Rev. Letters I0 (1963) 472. N.Almelch and B.Goldstein, Phys. Rev. 128 (1962) 1568.
PHYSICS
ELECTRON
SPIN
LETTERS
RESONANCE
IN n-TYPE
15 October 1963
GaAs
W. DUNCAN a n d E. E. SCHNEIDER Department of Physics, University of Newcastle upon Tyne, England Received 20 September 1963
I n t h i s note we r e p o r t e l e c t r i n s p i n r e s o n a n c e e x p e r i m e n t s on n - t y p e GaAs. One of the r e s o n a n c e s o b s e r v e d h a s the low g - v a l u e e x p e c t e d f r o m the t h e o r y of Roth et al. 1) for l o o s e l y bound or conduction electrons. Most of the e x p e r i m e n t s w e r e c a r r i e d out with a s e n s i t i v e 300 M c / s s p e c t r o m e t e r u s i n g a c o a x i a l h y b r i d r i n g and a s u p e r h e t e r o d y n e r e c e i v e r . T h e dc m a g n e t i c f i e l d i s p r o d u c e d by a w a t e r cooled s o l e n o i d w h i c h g i v e s a m a x i m u m f i e l d of 800 g a u s s . T h e s a m p l e s a r e l o c a t e d at the s h o r t c i r c u i t end of ½k c o - a x i a l c a v i t y . A s t a b i l i s a t i o n s y s t e m l o c k s the f r e q u e n c y to the s a m p l e c a v i t y so that the p h a s e s e n s i t i v e d e t e c t e d s i g n a l is the d e r i v a t i v e of the true absorption signal. T h e r o o m t e m p e r a t u r e c h a r a c t e r i s t i c s of the c r y s t a l s , which w e r e s u p p l i e d by S . E . R . L . , a r e l i s t e d i n t a b l e 1. The c a r r i e r c o n c e n t r a t i o n w a s e s t i m a t e d f r o m E h r e n r e i c h ' s 2) d a t a on m o b i l i t y versus concentration.
.I
"\..I /
Fig, 1. Spin resonance signal (derivative of absorption) of n-type GaAs at 300 Mc/s. Full line is the experimental curve. Broken line is the residual curve after subtraction of g= 1.2 line.
D = 4 5, showed no s i g / i i f i c a n t change in the l i n e shape. It ~suggested i t s e l f that the s p e c t r u m was c o m Table 1 p o s e d of o v e r l a p p i n g r e s o n a n c e s . In o r d e r to check p RH n t h i s , the s p e c t r o m e t e r was adapted for u s e at the (cm2(V.sec) -1) (~cm) (cm3cou1-1) (cm 3) s e c o n d h a r m o n i c of the h y b r i d r i n g , 600 M c / s , at 6300 0.06 378 5xlo 1~ the c o s t of s o m e s e n s i t i v i t y . In a d d i t i o n it w a s A. Single crystal 4 000 2.75 11 000 5×1017 n e c e s s a r y to u s e a n e l e c t r o m a g n e t which m e a n t B. Single crystal 103 C. Polycrystalline that the o r i e n t a t i o n of the dc field w a s p a r a l l e l to the p l a n e of the m i c r o w a v e m a g n e t i c field, c o n s e Fig. 1 shows the s p e c t r u m o b t a i n e d at 4.2OK q u e n t l y the effective s a m p l e v o l u m e w a s s u b s t a n f r o m s p e c i m e n A, s i m i l a r r e s u l t s w e r e o b t a i n e d tially reduced. f r o m s a m p l e B, but no r e s o n a n c e w a s o b s e r v e d The 600 M c / s s p e c t r u m , shown in fig. 2, c o n with s a m p l e C. The s h a r p l i n e n e a r 500 g a u s s s i s t s of two i n c o m p l e t e l y r e s o l v e d l i n e s , c o r r e c o r r e s p o n d i n g to g ~ 0.4 w a s thought to be a s s o s p o n d i n g to g - f a c t o r s of 0.52 + 0.05 and 1.1 ± 0.2. c i a t e d with c o n d u c t i o n e l e c t r o n s i n GaAs. The u n The l i n e shape of the r e s o n a n c e of high g - v a l u e usual line shape r e q u i r e d further investigation. w a s shown to be L o r e n t z i a n and is shown a s a O v e r a r a n g e of r f p o w e r 10 -2 to 10 -5 W the b r o k e n l i n e in fig~ 2. No a t t e m p t w a s m a d e to fit a l i n e s h a p e w a s found to be u n a l t e r e d . At t e m p e r a L o r e n t z or G a u s s i a n c u r v e to the l i n e of low g t u r e s a b o v e 4.2OK no r e s o n a n c e w a s o b s e r v e d . v a l u e a s the s i g n a l is quite s m a l l . To c l a r i f y the Skin depth e f f e c t s could be e x c l u d e d ; for s a m 300 M c / s s p e c t r u m , the l i n e of high g - v a l u e was p l e A the s k i n depth at 300 M c / s (5) is 1 m m u s i n g s u b t r a c t e d f r o m the 300 M c / s c u r v e of fig. 1; the O l i v e r ' s 3) c o n d u c t i v i t y data. A c c o r d i n g to D y s o n 4 ) r e s u l t a n t line is shown a s a b r o k e n c u r v e . d i s t o r t i o n of the r e s o n a n c e l i n e s h a p e is n e g l i g i b l e F u r t h e r e x p e r i m e n t s w e r e c a r r i e d out at 8825 if the s a m p l e t h i c k n e s s i s l e s s t h a n 4 5. In m o s t M c / s with a n e l e c t r o m a g n e t which w a s c a p a b l e e x p e r i m e n t s i n c l u d i n g that shown in fig. 1, D ~ 6. of a m a x i m u m field of 15 k i l o g a u s s . The s p e c t r u m An a d d i t i o n a l e x p e r i m e n t in a s p e c i m e n with w a s c o m p l e t e l y r e s o l v e d into two l i n e s of g - f a c t o r 23,
Volume 7, number 1
PHYSICS
LETTERS
15 October 1963
lOt
!
Fig. 2
I0:
I
Fig. 3
I 8
6'
~
", 6 dB
2~
750 500 250 MAGNETIC FIELD ~;AUSS]
I000
0i
0
IZl)00 11,800 MAGNETIC FIELD ~USS~
Fig. 2. Spin resonance of n-type GaAs at 600 M c / s . Full line is the experimental curve and the broken line is the calculated curve for g = 1.2 line.
Fig. 3. High field spin resonance of n-type GaAs at 8825 Mc/ s.
0.5228 ~ 0.0001 a n d 1.2 ± 0.1. T h e i n t e n s i t y of t h e low f i e l d l i n e w a s found to be v e r y w e a k b e i n g a p p r o x i m a t e l y a f a c t o r of 10 s m a l l e r t h a n t h e o t h e r l i n e . T h e high f i e l d l i n e i s shown in fig. 3 and h as b e e n found to h a v e a L o r e n t z i a n s h a p e . T h e g - f a c t o r p r e d i c t e d by Roth is
n e r 10) g i v e v a l u e s of 0.074 and 0.071 f r o m data on t h e m a g n e t i c f i e l d d e p e n d e n c e of s t i m u l a t e d and spontaneous emission respectively. These values were obtained assuming a hydrogenic model; a var i a t i o n a l t h e o r y l e a d s to v a l u e s 10% l o w e r . W e c o n c l u d e that t h e high f i e l d r e s o n a n c e is due to c o n d u c t i o n e l e c t r o n s p o s s i b l y in t h e i m p u r i t y band.. Th e low f i e l d r e s o n a n c e of g = 1.2 i s p o s s i bly due to d e e p l y i n g d o n o r s . T h e s e a r e e x p e c t e d to h a v e a g - v a l u e i n t e r m e d i a t e b e t w e e n that of c o n d u c t i o n e l e c t r o n s and highly l o c a l i s e d e l e c t r o n s , a s in t h e c a s e of e l e c t r o n c e n t r e s a s s o c i a t e d with Mn ++, g = 2.004 11).
2
[1
-
~
,,z
"m*
_
I)
A 3Eg + ~]
"
F o r G a A s , i n f r a r e d a b s o r p t i o n 5) e x p e r i m e n t s h a v e shown that E g = 1.53 ~ 0.01 eV and B r a u n s t e i n 6) h as o b t a i n e d a v a l u e of A = 0.33 eV. Th e e x p e r i m e n t s of M o s s and W a l t o n 7) h a v e s h ow n that m * / m o i s 0.074 + 0.006. In v i e w of t h e c o n s i d e r a b l e u n c e r t a i n t y in thi~ v a l u e , t h e e x p e c t e d g - f a c t o r fo r c o n d u c t i o n e l e c t r o n s in n - t y p e G a A s l i e s in the r a n g e +0.28 to +0.56. T h e high f i e l d r e s o n a n c e w h i c h we find to be 0.5228 ± 0.0001 is w e l l w i t h i n t h i s r a n g e . T h e p o s i t i v e s i g n of the g - f a c t o r has b e e n e s t a b l i s h e d by e x p e r i m e n t s 8) on i n t e r b a n d and o s c i l l a t o r y F a r a d a y e f f e c t 9) in GaAs . C o n v e r s e l y , the e x p e r i m e n t a l l y d e t e r m i n e d g - f a c t o r c a n be u s e d i n d i r e c t l y to d e t e r m i n e m * / m o. A s s u m i n g th e a b o v e v a l u e s of E z and A to be c o r r e c t , we t h u s o b t a i n m * / m o to t~e 0.078 ± 0.001. It is of i n t e r e s t to note that t h e e l e c t r o l u m i n e s c e n c e e x p e r i m e n t s of W r i g h t and G a l e e -
24
R c f c~'CnCCS 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)
L.Roth. Lax and Zwerdling, Phys. Rev. 114 (1959) 96. H. Ehrer~eich, Phys. Rev. 120 (1960) 1951. D . J . Oliver. Phys. Rev. 127 (1962) 1045. F.Dyson. Phys. Rev. 98 (1955) 349. H.Welker and H.Weiss, Solid State Physics 3 (1956) 1. R. Braunstein, J. Phys. Chem. Solids 8 (1959) 280. F . S . M o s s and A.K.Walton. Proc. Phys. Soc. (London) 74 (1959) 131. Private communication. S. D Smith and C.R. Pidgeon. Proc. Fifth Int. Conf. on Semiconductors, Exeter, 1962, p. 301. G.B.Wright and F . L . G a l e e n e r , Phys. Rev. Letters I0 (1963) 472. N.Almelch and B.Goldstein, Phys. Rev. 128 (1962) 1568.