ESR spectra of the zinc vacancy in ZnO

Volume 33A, number 1

P H Y SI C S L E T T E R S

ESR

SPECTRA

OF

THE

ZINC

VACANCY

21 September 1970

IN

ZnO

D. GALLAND and A. HERVE Laboratoire de R$sonance Magn$tique, Centre d'Etudes Nucl$aires de Grenobles, Cedex 85 - 38 Grenoble-Gate, F r a n c e Received 8 August 1970

Electron irradiated ZnO single crystals show anisotropic ESR spectra corresponding to a spin ½ and a spin 1 hole centers. Tehy are respectively identified as the negative and the neutral charge states of the zinc vacancy.

We have i r r a d i a t e d single c r y s t a l s of ZnO at r o o m t e m p e r a t u r e with 3 MeV e l e c t r o n s to a t ota l dose of 4× 1018 e l e c t r o n s / c m 2. O b s e r v e d at 90°K with a 35 GHz ESR s p e c t r o m e t e r , they exhibit a c o m p l e x s p e c t r u m belonging to at l e a s t five d i f f e r e n t p a r a m a g n e t i c c e n t e r s , one of which is the F + c e n t e r r e c e n t l y d e s c r i b e d by Smith et al. [1]. In t h i s l e t t e r , we a r e c o n c e r n e d only with two c e n t e r s , which we identify a s two d i f f e r e n t p a r a m a g n e t i c c h a r g e s t a t e s of the zinc vacancy. When the m a g n e t i c field is p a r a l l e l to the c - a x i s of the c r y s t a l , we o b s e r v e an in te n s e line, A, c e n t e r e d at g = 2 . 0 1 5 5 , a w e a k e r one, B, at g = 2.0024 and two l i n e s of equal intensity, C 1 and C2, s e p a r a t e d by 510 g a u s s and c e n t e r e d at g = 2.0165. F o r a g e n e r a l o r i e n t a t i o n of the m a g n e t i c field, the A - l i n e s p l i t s into six equally inte ns e l i n e s c o r r e s p o n d i n g to the six d i f f e r e n t s i t e s a v a i l a b l e in the W u r t z i t e s t r u c t u r e f o r a defect having C S s y m m e t r y . The a n g u l a r v a r i a ti ons a r e well r e p r e s e n t e d by the s p i n - H a m i l tonian 2= fltlo~S

where S = ½

T he z and x a x i s of the j - t e n s o r a r e in a (1210) m i r r o r plane, the z - a x i s making an angle of 69.25o+ 0.25 ° with the c - a x i s , and the y - a x i s is along a (1210) d i r e c t i o n . T h e p r i n c i p a l v a l u e s a r e : g z z = 2.0028 + 0.0002, g x x = 2.0173 ± 0.0002, g y y = 2.0183 + 0.0002. The v a r i a t i o n s of the nonsplitting B - l i n e c o r r e s p o n d to an e q u i v a l e n t s p i n - H a m i l t o n i a n , w h e r e the W-tensor is a x i a l ly s y m m e t r i c about the c - a x i s with g~ = 2.0024, g . = 2.0193. We a t t r i b u t e the A and B s p e c t r a to the zinc v a c a n c y having t r a p p e d a hole on one of the four adjacent 0 2- which f o r m a n e a r l y r e g u l a r t e t r a h e d r o n with one (0001) face. The A - s p e c t r u m is

due to the h o l e s t r a p p e d on the n o n - a x i a l oxygens of the (0001) f a c e , the six m a g n e t i c a l l y i n e q u i v a l e n t s i t e s being p r o v i d e d by the two d i f f e r e n t c o o r d i n a t i o n t e t r a h e d r a of the W u r t z i t e s t r u c t u r e , s e p a r a t e d by a 60 ° r o t a t i o n about c. The B s p e c t r u m is due to h o l e s t r a p p e d on axial o x y gens. On the p a r a m a g n e t i c O- ion, the hole o c c u p i e s the P z o r b i t a l pointing t o w a r d s the c e n t e r of the v a c a n c y . In a p e r f e c t r e g u l a r t e t r a h e d r o n , t h i s must give a ~ - t e n s o r , axially s y m m e t r i c about a (1117 d i r e c t i o n , with (to f i r s t o r d e r in k / A E ) g,t = ge = 2.0023, g± = ge (1 - ~ / A E ) .

(1)

AE is the e n e r g y d i f f e r e n c e between P z and P x o r p .y o r b i t a l s , and ~ (negative) is the s p i n - o r b i t coupling for the O- ion. Due to the W u r t z i t e p o l a r field, the s y m m e t r y is l o w e r e d f r o m C3v to C S for h o l e s t r a p p e d on n o n - a x i a l oxygens and the g t e n s o r d e v i a t e s slightly f r o m axial s y m m e t r y , with a tilting of 1.25°+ 0.25 of the p z - o r b i t a l a x i s with r e s p e c t to a (1117 t e t h r a h e d r a l d i r e c tion in the ideal W u r t z i t e s t r u c t u r e . The m e a s u r e d p o s i t i v e g - s h i f t s a r e c o n s i s t e n t with S c h i r m e r ' s r e s u l t [2] on a s i m i l a r hole c e n t e r t r a p p e d by a substitutional Li + impurity. F o r the l i t h i u m c e n t e r , the g - s h i f t s a r e g r e a t e r than f o r the v a c a n c y c e n t e r . T h i s is e x p e c t e d f r o m f o r m u l a (1) si n ce AE is g r e a t e r in the s t r o n g e r e l e c t r i c field of the v a c a n c y . A c o n f i r m a t i o n of the validity of the m o d e l is given by the a n a l y s i s and the i n t e r p r e t a t i o n of the c - s p e c t r u m , the i n t en si t y of which is e n hanced m a n y - f o l d by u v - i l l u m i n a t i o n at 90°K. T h i s is a t t r i b u t e d to a spin one e l e c t r o n i c c e n t e r , having C S s y m m e t r y and is well d e s c r i b e d by the s p i n - H a m i l t o n i a n :

Volume 33A.

number 1

I'HYS1CS

: ~ : ~t'loI~S+D{S; 2 - ½S(S+ 1)}+ E(S ~! -S '2),

(2,

where x', y' and z' a r e the p r i n c i p a l axes of the o r t o r h o m b i e fine s t r u c t u r e t e n s o r / ) . The z - a x i s of the eq-tensor and the z ' axis a r e both p a r a l l e l to a {1210, d i r e c t i o n , i.e., to the d i r e c t i o n j o i n ing two adjacent oxygens in a (0001) plane; The x a n d y axes of the g - t e n s o r and t h e x , 3' axes a r e in a (1210) plane. The y and y ' axes make a n g l e s of r e s p e c t i v e l y 4 0 . 2 5 o • 0.5 ° and 52°± 0.25 ° with the c - a x i s . The p r i n c i p a l v a l u e s of the ~:-tensor are: gzz : 2.0088 • 0.0002, g xx - 2.0132 • 0.0002, gyy : 2.0187 • 0.0002 and the fine s t r u c t u r e c o n s t a n t s are: iD/hi: 1470±5 MHz, !E/h] = 5 8 • 1 MHz. D a n d E have the same sign, but this sign has not been d e t e r mined experimentally. We p r o p o s e that the c - s p e c t r u m is due to the n e u t r a l p a r a m a g n e t i c eharge state of the zinc v a c a n c y , two holes being t r a p p e d on two of the t h r e e n o n - a x i a l oxygens adjacent to the vacancy. The s p i n - H a m i l t o n i a n of the r e s u l t i n g defect is: : ~ : [~Ho~IS1 + f ~ l l o i ~ 2 S 2 + ~ d + j S 1 S 2

(3)

where ' ~ d and J S 1 $2 r e p r e s e n t r e s p e c t i v e l y the dipole m a g n e t i c and exchange couplings between the two O- ions. Within the t r i p l e t state, the H a m i l t o n i a n (3) r e d u c e s to (2) with ~ : ~(~1 ~ g2). F r o m the model and the m e a s u r e d r e s o n a n c e p a r a m e t e r s for the " n o n - a x i a l " spin ~ c e n t e r s ,

LETTEHS

~1 S e p t e m b e r i!i7!)

we can p r e d i c t that g xw: 2.0129, g y v : 2.0176 and gzz : 2.0082. Also the y and y ' axes should be r e s p e c t i v e l y at 41.5 ° and 37.5 ° to the c - a x i s . v" being p e r p e n d i c u l a r to the plane of the two hole p - o r b i t a l s axes, and D and E should have the s a m e sign. The m e a s u r e d p a r a m e t e r s a r e in f a i r a g r e e m e n t with these values. The m a j o r d i s c r e p a n c y c o n c e r n s the tilting of the y ' axis. T h i s can be explained if we a s s u m e that the weak a s y m m e t r y factor of the D t e n s o r can be strongIy affected by the existence of a s m a l l d e l o c a l i s a t i o n of spin density to the two r e m a i n i n g 0 2- anions adjacent to the vacancy. The e x p e r i m e n t a I D value c o r r e s p o n d s to a s e p a r a t i o n of a p p r o x i m a t e l y 3.75 ~ between the two O- ions, i n s t e a d of 3.25 A in the u n d i s t u r b e d lattice. T h i s p o s s i b l y indicates a r e l a x a t i o n of the O- ions along the d i r e c t i o n s joining them to the v a c a n c y site. We wish to thank MM. Cox, Maffeo and Rius for helpful d i s c u s s i o n s . We a r e v e r y g r a t e f u l to Dr. K. F. N i e l s e n for kindly providing the c r y s tals.

Rejerenc'cs [1] J . M . S m i t h and W . E . V e h s e ,

P h y s . L e t t e r s 31A

(1970) 147. ]2] O . F . S c h i r m e r , 14O7.

J, P h y s . (?hem. Solids 29 !1,~)6~!