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Electronic structure of the Au-Mn pair complex in silicon
~
Solid State Communications, Printed in Great Britain.
ELECTRONIC
Vol.58,No.9,
STRUCTURE
L.V.C. I n s t i t u t o de CP 2 0 5 1 6 ,
(RECEIVED
pp.577-580,
OF
THE
|986.
Au-Mn
Assall
and
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
PAIR
J.R.
COMPLEX
IN
SILICON
Lelte
F [ s i c a da U n i v e r s i d a d e de Sao P a u l o , Sao P a u l o , C E P 0 1 4 9 8 , SP, B r a z i l .
MARCH
7 th
1986
BY
R,C.C.LEITE)
The e l e c t r o n i c s t r u c t u r e of the s u b s t i t u t i o n a l goldin-terstitial-manganese p a i r c o m p l e x in s i l i c o n has been s t u d i e d u s i n g the m u l t i p l e - s c a t t e r i n g Xs m o l e c u l a r cluster model. A 25Si + Au Mn. c l u s t e r is a d o p t e d and the boundary c o n d i t i o n p r o b l e m w~s ~ o l v e d a c c o r d i n g to the W a t s o n ~ p h e r e terminated c l u s t e r m o d e l . The c a l c u l a t i o n s indicate that the A u - M n c o m p l e x has a spin S=2 in the n e u t r a l c h a r g e s t a t e and S = 3 / 2 in the p o s i t i v e and n e g a t i v e c h a r g e s t a t e s . T h e s e v a l u e s are c o m p a r e d w i t h the r e s u l t s o b t a i n e d f r o m EPR experiments.
INTRODUCTION
G o l d is one of the m o s t s t u d i e d i m p u r i t y in s i l i c o n due to its i m p o r t a n c e u n d e r both scientific and t e c h n o l o g i c a l p o i n t of view I The b a s i c problem related to the amphoteric b e h a v i o r of gold in s i l i c o n has b e e n o b j e c t of v a r i o u s investigations2, 3 The practical i m p o r t a n c e of gold derives from its use as a m i n o r i t y carriers lifetime c o n t r o l i m p u r i t y and as a c o n v e n i e n t m a t e r i a l for o h m i c c o n t a c t s w i t h s i l i c o n 4-6 A t t e m p t s h a v e b e e n m a d e to use first p r i n ciples theoretical m o d e l to d e s c r i b e the electronic s t r u c t u r e of this c e n t e r I However, the c o m p a r i s o n w i t h the e x p e r i m e n t a l data has been hindered by the fact that gold forms c o m p l e x e s w i t h o t h e r d e f e c t s and i m p u r i t i e s in s i l i c o n . U n l i k e gold i s o l a t e d impurity, c o m p l e x e s such as s u b s t i t u t i o n a l - g o l d - i n t e r s t i t i a l - t r a n s i t i o n m e t a l (TM) pairs have been observed in silicon by electronic paramagnetic r e s o n a n c e (EPR) experiments 7 Recently, a microscopic model of the A u - F e pair c o m p l e x in s i l i c o n was p r o p o s e d I . The m o d e l , which was b a s e d on rigorous self-consistent-field (SCF) calc u l a t i o n s was able to e x p l a i n the m a i n features of the EPR and diode capacitance measurements t a k e n on a g o l d - r e l a t e d defect in s i l i c o n a s c r i b e d to the AusFe i pair. In this commu~ i c a t i o n we s h o w that the previous m~croscopic m o d e l u s e d to d e s c r i b e the p h y s i c a l p r o p e r t i e s of the A u - F e comp l e x in s i l i c o n r e m a i n s v a l i d for the A u - M n pair. This conclusion is supported by r i g o r o u s SCF c a l c u l a t i o n s c a r r i e d out on a 27-atom molecular c l u s t e r s i m u l a t i n g a substitutional-gold-interstitial-manganese pair c o m p l e x in s i l i c o n , The m o d e l leads to the c o n c l u s i o n that the s p i n s S = 2 , S = 3/2 and S = 3/2 are a s c r i b e d to the c o m p l e x in the neutral, po-
s i t i v e and n e g a t i v e c h a r g e s t a t e s , respectively. The c e n t e r has b e e n o b s e r v e d by E P R in the p o s i t i v e and n e g a t i v e c h a r g e stateS7o A l t h o u g h our p r e d i c t i o n s are a c c o r d i n g to the m e a s u r e d spin S = 3/2 for the p o s i t i v e c h a r g e state, an e x p e r i m e n t a l v a l u e S = 5/2 has b e e n r e p o r t e d for the n e g a t i v e charge s t a t e of the c o m p l e x Previous interpretation of the E P R experimental data for the positive charge s t a t e of the A u - M n c o m p l e x was b a s e d on the o r i g i n a l Ludwig and Woodbury (LW) m o d e l 7. The spin of the c e n t e r is o b t a i n e d by a s s u m i n g a s t r o n g m a g n e t i c coupling bet w e e n the spins of two m a g n e t i c centers, determined by the LW rule, one c e n t e r e d on the Auion (S = ]) and the o t h e r on the Mn 2+ i m p u r i t y (S = 5/2)° A strong antiferromagnetic c o u p l i n g leads to the v a l u e s S = = 3/2 for the c o m p l e x . Our c a l c u l a t i o n s do not s u p p o r t such i n t e r p r e t a t i o n of the E P R s i g n a l o b s e r v e d for the A u - M n complex.
ELECTRONIC
STRUCTURE
OF
THE
Au-Mn
PAIR
The s u b s t i t u t i o n a l - g o l d - i n t e r s t i t i a l manganese pair c o m p l e x is s i m u l a t e d by the cluster 25Si + A u s M n i , the same m o d e l ass u m e d in our ~ r e v i o u s i n v e s t i g a t i o n s o f t h e A u - F e c o m p l e x I. The c a l c u l a t i o n s were carried out w i t h i n the f r a m e w o r k of the W a t s o n sphere-terminated molecular cluster model and the m u l t i p l e - s c a t t e r i n g X~ t h e o r y 8 - | 3 The r e l e v a n t f e a t u r e s of the s t r u c t u r e of the A u - M n c o m p l e x are s h o w n in Fig. ] Some selected one-electron energy levels r e l a t i v e to the c r y s t a l band edges are s h o w n for the 25Si + A u s M n i cluster~ Only the l e v e l s w h i c h are d e r i v e d f r o m the 5d a t o m i c o r b i t a l s of gold and from 3d of manganese are shown~ The percentage of charge, normalized to one e l e c t r o n , w i t h i n
577
578
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
25 Si + Au s Mni 3,0
--
54=
2,0 --
CONDUCTION I.O-
': = : Mn ] ... ~ 4o1(42%) L-e-'-e---e--'e- 7e (28%)Ev
,,, O . O _J
VALENCE
O -I,O
-
BAND Ec 9e (25%) : 8e(50%)
[
~-] 34,
( t4~
IJJ
_> I---
<=: ...J
-
2,0
-
ILl n.."
>
-3,0
-
>cO
n"'
4e (15%
-8,C
LIJ
-9,0
Au"
3e(~%', 2e(56% Iai(76%',
-I0,0
le(53%) -II.O
-
i - One-electron energy spectrum of the 2 5 S i + Au Mn. c l u s t e r r e l a t i v e to t h e s i l i c o n b ~ n d Z e d g e s . O n l y the e n e r g i e s w h i c h are d e r i v e d f r o m the gold 5d- and manganese 3 d - a t o m i c orbitals are shown. The numbers in p a r e n t h e s i s indicate the p e r c e n t a g e of c h a r g e , normalized to one e l e c t r o n , within the gold and manganese atomic spheres~adius =2.22 a,u.).The full circles indicate the o c c u p a n c y of the gap l e v e l s . FIGURE
the atomic s p h e r e s of g o l d and manganese (radius = 2.22 a u ) are indicated in p a renthesiSo According to the r e s u l t s d e p i c t e d in F i g . ] the g o l d 5d d e r i v e d states appear as s h a r p r e s o n a n c e s at the lower p a r t of the v a l e n c e band. F o u r o t h e r resonant levels are f o u n d b e l o w the top of the v a l e n c e band w h i c h are d e r i v e d from the hybridization between the 3d o r b i t a l s of Mn w i t h the 3p orbitals of the silicon host atom° The most interesting feature of the c l u s t e r energy spectrum s h o w n in Fig~ i is t h a t the 3d a t o m i c o r b i t a l s of M n g i v e r i s e to f o u r impurity levels within the c r y s t a l b a n d gap. These levels are important to d e f i n e the b a s i c o p t i c a l , electrical and m a g n e t i c properties of the c e n t e r ° T h e g o l d 5d d e r i v e d resonances in the lower part of the v a l e n c e b a n d are o r i g i -
Vol.
58, No. 9
h a t e d f r o m the s p l i t t i n g of the t2(d) and e(d) resonant l e v e l s f o u n d in o u r p r e v i o u s calculations for the i s o l a t e d substitutional gold impurity |0-12 These splittings are c a u s e d by the l o w e r i n g of the c r y s t a l field symmetry f r o m T d for the i s o l a t e d impurity to C 3 v for the c o m p l e x . It is i n t e r e s t i n g to p o i n t out t h a t the c o m p a c t a n d l o c a l i z e d character of the g o l d 5d derived states i n f e r e d for the isolated impurity remains practically the same as the complex is formed We compare now the results obtained for the Au-Mn complex with those obtained from other calculations for an isolated interstitial manganese a t o m in s i l i c o n 1 4 - 1 7 S u c h an impurity placed at a t e t r a h e d r a l interstitial p o s i t i o n in s i l i c o n g i v e s r i s e to r e s o n a n t levels just below the top of the v a l e n c e b a n d and to a t w o f o l d (e) and a threefold (t 2) degenerate levels within the c r y s t a l b a n d gap. The r e s o n a n c e s and the g a p s t a t e s have a strong contribution f r o m the 3d a t o m i c o r b i t a l s of m a n g a n e s e . The i n t e r a c t i o n s w i t h the n e a r e s t n e i g h b o r g o l d a t o m l o w e r s the s y m m e t r y from Td to C3v a n d s p l i t s the t 2 and e l e v e l s g i v i n g r i s e to the 7e , 4a I and 8e gap levels s h o w n in Fig. ] for the c o m p l e x . The perc e n t a g e of c h a r g e i n d i c a t e d in p a r e n t h e s i s s h o w t h a t the m a n g a n e s e 3d a t o m i c o r b i t a l s p l a y an i m p o r t a n t r o l e in the f o r m a t i o n of these levels. There are two interesting features w h i c h e m e r g e f r o m the c a l c u l a t i o n s : first, the p r e s e n c e of an e m p t y s t a t e in the b a n d gap, 9e ; s e c o n d , the a p p e a r a n c e of a r e sonance in the c o n d u c t i o n b a n d , 5a I . T h e s e l e v e l s r e s u l t f r o m the s p l i t t i n g of the t 2 gap level of the v u b s t i t u t i o n a l gold imp u r i t y w h e n the s y m m e t r y is l o w e r e d f r o m T d to C3v o Therefore, the energy spectrum shown in F i g I is q u i t e s i m i l a r to t h a t o b t a i n e d in o u r p r e v i o u s w o r k for the Au-Fe c o m p l e x | However, the i n t e r a c t i o n b e t w e e n Au a n d Mn impurities are f o u n d to be stronger than that observed b e t w e e n Au and Fe impuritieslo The 9e s t a t e , o c c u p i e d by o n e e l e c t r o n in the Au-Fe complex, was interpreted as a dangling bond-like o r b i t a l or as a v a c a n c y like impurity s t a t e ° On the o t h e r h a n d , in the A u - M n p a i r the 9e state has a significative charge concentration in the manganese atomic sphere (25%) This indicates t h a t the 9e state has contribution from the 3d a t o m i c o r b i t a l s of m a n g a n e s e , which determines for this impurity s t a t e a behavior quite different from a dangling bond -like orbital~ Despite the observations made above, the m o d e l p r o p o s e d in Ref. | is a p p l i c a b l e a l s o to the A u - M n complex° However, when making the s e a r c h for the p o s s i b l e values for the s p i n of the c e n t e r we h a v e to b e a r in m i n d t h a t the 9e gap level has contribution f r o m the m a n g a n e s e 3d-atomic orbitalso The most likely spin configurat i o n s for the Au-Mn complex is s c h e m a t i c a l l y s h o w n in F i g 2 T h e e n e r g y l e v e l s in the g a p are l a b e l l e d a c c o r d i n g to F i g I a n d the " u p " (+) and " d o w n " (-) s p i n s a r e in-
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
Vol. 58, No. 9 S=2
S-O
S=2
These considerations leave configurations (c) and (d) as the m o s t p r o b a b l e s p i n c o n figurations for the A u - M n p a i r w h i c h is a h i g h spin c o m p l e x in the n e u t r a l charge state°
S-2
tf./HIIIIIIHHV.IIIIHHIIIHHII~.HIH/II///I/IIH.IIIIh I
Be-
4°,
tt ~
9~ 9e÷
Be- ~ J, Be÷TT
9eBe-
I I
t t ~* " ~,÷ t t
I
Be" tl ,~T t
r
"
e, ÷
~÷tt
CONCLUSIONS
EV'//HH/H/H/~/¢¢/ ....... ..t"...! ........... (a)
8d" 96"
t t
579
(b)
........
(c)
.....
(d)
FIGURE 2 - Most likely spin configurat i o n s for the gap l e v e l s of the A u - M n c o m p l e x in s i l l c o n . T h e " u p " and " d o w n " s p i n s are i n d i c a t e d by the + and-marks, respectively . T h e t o t a l s p i n S for each configuration is a l s o given.
dicated. The gap level 7e , w h i c h r e m a i n s f u l l y o c c u p i e d is not shown. According to Fig 2 three configurations are h i g h spin (S = 2) and one is low spin (S = O) For the (a) c o n f i g u r a t i o n the c o m p l e x is an o p e n shell s y s t e m w h i c h m a y d i s p l a y J a h n - T e l l e r (JT) l a t t i c e d i s t o r t i o n s For c o n f i g u r a tions (b), (c) and (d) no JT e f f e c t s are e x p e c t e d to occur. A l t h o u g h the spin p o l a r i z a t i o n effects as w e l l as l a t t i c e distortions were not t a k e n into a c c o u n t in our c a l c u l a t i o n s , it is p o s s i b l e to i n f e r w h i c h spin c o n f i g u r a tion for the c o m p l e x is m o r e l i k e l y Acc o r d i n g to our r e s u l t s the e n e r g y difference b e t w e e n the 9e and 8e l e v e l s is 0 20 eV. In o r d e r to the c o n f i g u r a t i o n (a) o c c u r it is r e q u i r e d that the exchange s p l i t t i n g of the l e v e l s be such that the 4a~ level lies a b o v e the 9elevel w i t h a s p l i t t i n g of a b o u t 0 . 5 3 eVo Even taking into a c c o u n t the fact that the 4a] level has a s t r o n g c o n t r i b u t i o n from the 3d orb i t a l s , a s p l i t t i n ~ of a b o u t 0 . 5 3 eV is highly unlikelylT-~9o The (b) c o n f i g u r a tion o c c u r s if the e x c h a n g e s p l i t t i n g was less t h a n 0 20 eV. However, due to the significative contribution from the 3d atomic o r b i t a l s to the 9e s t a t e we e x p e c t the exc h a n g e s p l i t t i n g be l a r g e r t h a m 0 20 eV |6
We c o n c l u d e that the A u - M n p a i r comp l e x in s i l i c o n in a n e u t r a l c h a r g e state has a s p i n S = 2 If one e l e c t r o n is rem o v e d in o r d e r to c r e a t e a p o s i t i v e c h a r g e s t a t e the o r b i t a l i n v o l v e d is the 9e + and the spin S = 3/2 w i l l be o b t a i n e d for the center As an a c c e p t o r the c o m p l e x captures an e l e c t r o n in the Be- and 9e- s t a t e s acc o r d i n g to the c o n f i g u r a t i o n (c) or (d), respectively Thus, in the n e g a t i v e c h a r g e state a spin S = 3/2 is e x p e c t e d for the complex° The n e u t r a l c h a r g e s t a t e has not b e e n d e t e c t e d by E P R The s i g n a l s for the p o s i t i v e and n e g a t i v e charge states have b e e n o b s e r v e d and the v a l u e s S = 3/2 and S = 5/2 are a s c r i b e d to them, respectivelyTo We a r g u e that it m a y be p o s s i b l e that the spin S = 5/2 , a s c r i b e d to the negative c h a r g e state, corresponds to some other c o m p l e x i n v o l v i n g gold or m a n g a n e s e rather than to the A u - M n complex. As we p o i n t e d out in the i n t r o d u c t i o n of this w o r k , the spin S = 3/2 for the pos i t i v e c h a r g e state of the c o m p l e x was exp l a i n e d 7 by a s s u m i n g an a n t i f e r r o m a g n e t i c coupling between S = | l o c a l i z e d on the A u and S = 5/2 on the Mn2+o It is a s s u m e d that one e l e c t r o n is t r a n s f e r r e d from manganese to gold due to the d i f f e r e n c e of electronegativities between these two elements. Our c a l c u l a t i o n s i n d i c a t e that there is no transference of one e l e c t r o n f r o m m a n g a n e s e to gold. M o r e o v e r , isolated substitutional gold does not lead to gap levels with d character° We c o n c l u d e that the m i c r o s c o p i c model p r o p o s e d in Ref I a c c o u n t s for the p h y s i c a l properties of the Au-Mn c o m p l e x in s i l i con. It is w o r t h m e n t i o n i n g that the m a n ganese 3d a t o m i c o r b i t a l s p l a y a r e l e v a n t role in d e t e r m i n i n g the a c c e p t o r and d o n o r activities of this c e n t e r .
REFERENCES
i. L . V . C . A s s a l i , J . R . L e l t e and A . F a z z i o , P h y s . R e v . B . 3 2 , 8 0 8 5 (1985) and references therein 2. D . V . L a n g , H . G . G r i m m e i s s , E . M e i j e r , and M . J a r o s , P h y s . R e v . B . 2 2 , 3 9 1 7 ( 1 9 8 0 ) 3. R . M . F e e n s t r a and S . T . P a n t e l i d e s , P h y s . Rev. B.31, 4 0 8 3 (1985) 4. A . G . M i l n e s , D e e p Impurities in S e m i c o n d u c t o r s (Wiley,New York,1973) 5. H . G . C r l m m e l s s , A n n . Rev. M a t e r . S c l . 7 , 3 4 1 (1977) 6. J.W.Chen and A . G . M i l n e s , A n n . Rev. M a t e r . S c i . l O , 1 5 7 (1980) 7. G . W . L u d w i g and H . H . W o o d b u r y , S o l l d S t a t e P h y s i c s 1 3 , 2 2 3 (1962) 8. L . V . C . A s s a l l and J . R . L e l t e , P h y s . R e v . Lett. 5 5 ~ 9 8 0 (1985) 9. V . M . S . G o m e s and J . R . L e i t e , A p p l . P h y s . L e t t . 4 7 , 8 2 4 (1985)
580
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
Vol. 58, No.
I0. J . L . A . A l v e s , J . R . L e i t e , L . V . C . A s s a l i , V . M . S . G o m e s and C.E.T.Gon~alves da Silva J.Phys.C. ~ 7 , L 7 7 1 ( 1 9 8 4 ) II. J.L.A.Alves and J.R.LeitetPhys.Rev. B 30,7284 (1984) 12. J . L . A . A l v e s , J . R . L e i t e , V . M . S . G o m e s and L . V . C . A s s a l i , S o l i d State Commun.55, 333 (1985) 13. N.Makiuchi, J.R.Leite and A.Fazzio,J.Phys. C 17,3423 (1984) 14. G.G.DeLeo, G.D.Watkins and W.B.Fowler,Phys.Rev.B 23,1851(1981);25,4962(1982); 25_~ 4972 (1982) 15. A.Zunger and U.LindefeltpPhys.Rev. B 26,5989 (1982) 16. F . B e e l e r , O , K . A n d e r s e n and M.Scheffler,Phys°Rev. Lett.55,1498(1985) 17. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. B 31, 8317 (1985) 18. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. Lett. 53,1256 (1984) 19. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. B 31,7877 (1985)
Solid State Communications, Printed in Great Britain.
ELECTRONIC
Vol.58,No.9,
STRUCTURE
L.V.C. I n s t i t u t o de CP 2 0 5 1 6 ,
(RECEIVED
pp.577-580,
OF
THE
|986.
Au-Mn
Assall
and
0038-1098/86 $3.00 + .00 Pergamon Journals Ltd.
PAIR
J.R.
COMPLEX
IN
SILICON
Lelte
F [ s i c a da U n i v e r s i d a d e de Sao P a u l o , Sao P a u l o , C E P 0 1 4 9 8 , SP, B r a z i l .
MARCH
7 th
1986
BY
R,C.C.LEITE)
The e l e c t r o n i c s t r u c t u r e of the s u b s t i t u t i o n a l goldin-terstitial-manganese p a i r c o m p l e x in s i l i c o n has been s t u d i e d u s i n g the m u l t i p l e - s c a t t e r i n g Xs m o l e c u l a r cluster model. A 25Si + Au Mn. c l u s t e r is a d o p t e d and the boundary c o n d i t i o n p r o b l e m w~s ~ o l v e d a c c o r d i n g to the W a t s o n ~ p h e r e terminated c l u s t e r m o d e l . The c a l c u l a t i o n s indicate that the A u - M n c o m p l e x has a spin S=2 in the n e u t r a l c h a r g e s t a t e and S = 3 / 2 in the p o s i t i v e and n e g a t i v e c h a r g e s t a t e s . T h e s e v a l u e s are c o m p a r e d w i t h the r e s u l t s o b t a i n e d f r o m EPR experiments.
INTRODUCTION
G o l d is one of the m o s t s t u d i e d i m p u r i t y in s i l i c o n due to its i m p o r t a n c e u n d e r both scientific and t e c h n o l o g i c a l p o i n t of view I The b a s i c problem related to the amphoteric b e h a v i o r of gold in s i l i c o n has b e e n o b j e c t of v a r i o u s investigations2, 3 The practical i m p o r t a n c e of gold derives from its use as a m i n o r i t y carriers lifetime c o n t r o l i m p u r i t y and as a c o n v e n i e n t m a t e r i a l for o h m i c c o n t a c t s w i t h s i l i c o n 4-6 A t t e m p t s h a v e b e e n m a d e to use first p r i n ciples theoretical m o d e l to d e s c r i b e the electronic s t r u c t u r e of this c e n t e r I However, the c o m p a r i s o n w i t h the e x p e r i m e n t a l data has been hindered by the fact that gold forms c o m p l e x e s w i t h o t h e r d e f e c t s and i m p u r i t i e s in s i l i c o n . U n l i k e gold i s o l a t e d impurity, c o m p l e x e s such as s u b s t i t u t i o n a l - g o l d - i n t e r s t i t i a l - t r a n s i t i o n m e t a l (TM) pairs have been observed in silicon by electronic paramagnetic r e s o n a n c e (EPR) experiments 7 Recently, a microscopic model of the A u - F e pair c o m p l e x in s i l i c o n was p r o p o s e d I . The m o d e l , which was b a s e d on rigorous self-consistent-field (SCF) calc u l a t i o n s was able to e x p l a i n the m a i n features of the EPR and diode capacitance measurements t a k e n on a g o l d - r e l a t e d defect in s i l i c o n a s c r i b e d to the AusFe i pair. In this commu~ i c a t i o n we s h o w that the previous m~croscopic m o d e l u s e d to d e s c r i b e the p h y s i c a l p r o p e r t i e s of the A u - F e comp l e x in s i l i c o n r e m a i n s v a l i d for the A u - M n pair. This conclusion is supported by r i g o r o u s SCF c a l c u l a t i o n s c a r r i e d out on a 27-atom molecular c l u s t e r s i m u l a t i n g a substitutional-gold-interstitial-manganese pair c o m p l e x in s i l i c o n , The m o d e l leads to the c o n c l u s i o n that the s p i n s S = 2 , S = 3/2 and S = 3/2 are a s c r i b e d to the c o m p l e x in the neutral, po-
s i t i v e and n e g a t i v e c h a r g e s t a t e s , respectively. The c e n t e r has b e e n o b s e r v e d by E P R in the p o s i t i v e and n e g a t i v e c h a r g e stateS7o A l t h o u g h our p r e d i c t i o n s are a c c o r d i n g to the m e a s u r e d spin S = 3/2 for the p o s i t i v e c h a r g e state, an e x p e r i m e n t a l v a l u e S = 5/2 has b e e n r e p o r t e d for the n e g a t i v e charge s t a t e of the c o m p l e x Previous interpretation of the E P R experimental data for the positive charge s t a t e of the A u - M n c o m p l e x was b a s e d on the o r i g i n a l Ludwig and Woodbury (LW) m o d e l 7. The spin of the c e n t e r is o b t a i n e d by a s s u m i n g a s t r o n g m a g n e t i c coupling bet w e e n the spins of two m a g n e t i c centers, determined by the LW rule, one c e n t e r e d on the Auion (S = ]) and the o t h e r on the Mn 2+ i m p u r i t y (S = 5/2)° A strong antiferromagnetic c o u p l i n g leads to the v a l u e s S = = 3/2 for the c o m p l e x . Our c a l c u l a t i o n s do not s u p p o r t such i n t e r p r e t a t i o n of the E P R s i g n a l o b s e r v e d for the A u - M n complex.
ELECTRONIC
STRUCTURE
OF
THE
Au-Mn
PAIR
The s u b s t i t u t i o n a l - g o l d - i n t e r s t i t i a l manganese pair c o m p l e x is s i m u l a t e d by the cluster 25Si + A u s M n i , the same m o d e l ass u m e d in our ~ r e v i o u s i n v e s t i g a t i o n s o f t h e A u - F e c o m p l e x I. The c a l c u l a t i o n s were carried out w i t h i n the f r a m e w o r k of the W a t s o n sphere-terminated molecular cluster model and the m u l t i p l e - s c a t t e r i n g X~ t h e o r y 8 - | 3 The r e l e v a n t f e a t u r e s of the s t r u c t u r e of the A u - M n c o m p l e x are s h o w n in Fig. ] Some selected one-electron energy levels r e l a t i v e to the c r y s t a l band edges are s h o w n for the 25Si + A u s M n i cluster~ Only the l e v e l s w h i c h are d e r i v e d f r o m the 5d a t o m i c o r b i t a l s of gold and from 3d of manganese are shown~ The percentage of charge, normalized to one e l e c t r o n , w i t h i n
577
578
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
25 Si + Au s Mni 3,0
--
54=
2,0 --
CONDUCTION I.O-
': = : Mn ] ... ~ 4o1(42%) L-e-'-e---e--'e- 7e (28%)Ev
,,, O . O _J
VALENCE
O -I,O
-
BAND Ec 9e (25%) : 8e(50%)
[
~-] 34,
( t4~
IJJ
_> I---
<=: ...J
-
2,0
-
ILl n.."
>
-3,0
-
>cO
n"'
4e (15%
-8,C
LIJ
-9,0
Au"
3e(~%', 2e(56% Iai(76%',
-I0,0
le(53%) -II.O
-
i - One-electron energy spectrum of the 2 5 S i + Au Mn. c l u s t e r r e l a t i v e to t h e s i l i c o n b ~ n d Z e d g e s . O n l y the e n e r g i e s w h i c h are d e r i v e d f r o m the gold 5d- and manganese 3 d - a t o m i c orbitals are shown. The numbers in p a r e n t h e s i s indicate the p e r c e n t a g e of c h a r g e , normalized to one e l e c t r o n , within the gold and manganese atomic spheres~adius =2.22 a,u.).The full circles indicate the o c c u p a n c y of the gap l e v e l s . FIGURE
the atomic s p h e r e s of g o l d and manganese (radius = 2.22 a u ) are indicated in p a renthesiSo According to the r e s u l t s d e p i c t e d in F i g . ] the g o l d 5d d e r i v e d states appear as s h a r p r e s o n a n c e s at the lower p a r t of the v a l e n c e band. F o u r o t h e r resonant levels are f o u n d b e l o w the top of the v a l e n c e band w h i c h are d e r i v e d from the hybridization between the 3d o r b i t a l s of Mn w i t h the 3p orbitals of the silicon host atom° The most interesting feature of the c l u s t e r energy spectrum s h o w n in Fig~ i is t h a t the 3d a t o m i c o r b i t a l s of M n g i v e r i s e to f o u r impurity levels within the c r y s t a l b a n d gap. These levels are important to d e f i n e the b a s i c o p t i c a l , electrical and m a g n e t i c properties of the c e n t e r ° T h e g o l d 5d d e r i v e d resonances in the lower part of the v a l e n c e b a n d are o r i g i -
Vol.
58, No. 9
h a t e d f r o m the s p l i t t i n g of the t2(d) and e(d) resonant l e v e l s f o u n d in o u r p r e v i o u s calculations for the i s o l a t e d substitutional gold impurity |0-12 These splittings are c a u s e d by the l o w e r i n g of the c r y s t a l field symmetry f r o m T d for the i s o l a t e d impurity to C 3 v for the c o m p l e x . It is i n t e r e s t i n g to p o i n t out t h a t the c o m p a c t a n d l o c a l i z e d character of the g o l d 5d derived states i n f e r e d for the isolated impurity remains practically the same as the complex is formed We compare now the results obtained for the Au-Mn complex with those obtained from other calculations for an isolated interstitial manganese a t o m in s i l i c o n 1 4 - 1 7 S u c h an impurity placed at a t e t r a h e d r a l interstitial p o s i t i o n in s i l i c o n g i v e s r i s e to r e s o n a n t levels just below the top of the v a l e n c e b a n d and to a t w o f o l d (e) and a threefold (t 2) degenerate levels within the c r y s t a l b a n d gap. The r e s o n a n c e s and the g a p s t a t e s have a strong contribution f r o m the 3d a t o m i c o r b i t a l s of m a n g a n e s e . The i n t e r a c t i o n s w i t h the n e a r e s t n e i g h b o r g o l d a t o m l o w e r s the s y m m e t r y from Td to C3v a n d s p l i t s the t 2 and e l e v e l s g i v i n g r i s e to the 7e , 4a I and 8e gap levels s h o w n in Fig. ] for the c o m p l e x . The perc e n t a g e of c h a r g e i n d i c a t e d in p a r e n t h e s i s s h o w t h a t the m a n g a n e s e 3d a t o m i c o r b i t a l s p l a y an i m p o r t a n t r o l e in the f o r m a t i o n of these levels. There are two interesting features w h i c h e m e r g e f r o m the c a l c u l a t i o n s : first, the p r e s e n c e of an e m p t y s t a t e in the b a n d gap, 9e ; s e c o n d , the a p p e a r a n c e of a r e sonance in the c o n d u c t i o n b a n d , 5a I . T h e s e l e v e l s r e s u l t f r o m the s p l i t t i n g of the t 2 gap level of the v u b s t i t u t i o n a l gold imp u r i t y w h e n the s y m m e t r y is l o w e r e d f r o m T d to C3v o Therefore, the energy spectrum shown in F i g I is q u i t e s i m i l a r to t h a t o b t a i n e d in o u r p r e v i o u s w o r k for the Au-Fe c o m p l e x | However, the i n t e r a c t i o n b e t w e e n Au a n d Mn impurities are f o u n d to be stronger than that observed b e t w e e n Au and Fe impuritieslo The 9e s t a t e , o c c u p i e d by o n e e l e c t r o n in the Au-Fe complex, was interpreted as a dangling bond-like o r b i t a l or as a v a c a n c y like impurity s t a t e ° On the o t h e r h a n d , in the A u - M n p a i r the 9e state has a significative charge concentration in the manganese atomic sphere (25%) This indicates t h a t the 9e state has contribution from the 3d a t o m i c o r b i t a l s of m a n g a n e s e , which determines for this impurity s t a t e a behavior quite different from a dangling bond -like orbital~ Despite the observations made above, the m o d e l p r o p o s e d in Ref. | is a p p l i c a b l e a l s o to the A u - M n complex° However, when making the s e a r c h for the p o s s i b l e values for the s p i n of the c e n t e r we h a v e to b e a r in m i n d t h a t the 9e gap level has contribution f r o m the m a n g a n e s e 3d-atomic orbitalso The most likely spin configurat i o n s for the Au-Mn complex is s c h e m a t i c a l l y s h o w n in F i g 2 T h e e n e r g y l e v e l s in the g a p are l a b e l l e d a c c o r d i n g to F i g I a n d the " u p " (+) and " d o w n " (-) s p i n s a r e in-
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
Vol. 58, No. 9 S=2
S-O
S=2
These considerations leave configurations (c) and (d) as the m o s t p r o b a b l e s p i n c o n figurations for the A u - M n p a i r w h i c h is a h i g h spin c o m p l e x in the n e u t r a l charge state°
S-2
tf./HIIIIIIHHV.IIIIHHIIIHHII~.HIH/II///I/IIH.IIIIh I
Be-
4°,
tt ~
9~ 9e÷
Be- ~ J, Be÷TT
9eBe-
I I
t t ~* " ~,÷ t t
I
Be" tl ,~T t
r
"
e, ÷
~÷tt
CONCLUSIONS
EV'//HH/H/H/~/¢¢/ ....... ..t"...! ........... (a)
8d" 96"
t t
579
(b)
........
(c)
.....
(d)
FIGURE 2 - Most likely spin configurat i o n s for the gap l e v e l s of the A u - M n c o m p l e x in s i l l c o n . T h e " u p " and " d o w n " s p i n s are i n d i c a t e d by the + and-marks, respectively . T h e t o t a l s p i n S for each configuration is a l s o given.
dicated. The gap level 7e , w h i c h r e m a i n s f u l l y o c c u p i e d is not shown. According to Fig 2 three configurations are h i g h spin (S = 2) and one is low spin (S = O) For the (a) c o n f i g u r a t i o n the c o m p l e x is an o p e n shell s y s t e m w h i c h m a y d i s p l a y J a h n - T e l l e r (JT) l a t t i c e d i s t o r t i o n s For c o n f i g u r a tions (b), (c) and (d) no JT e f f e c t s are e x p e c t e d to occur. A l t h o u g h the spin p o l a r i z a t i o n effects as w e l l as l a t t i c e distortions were not t a k e n into a c c o u n t in our c a l c u l a t i o n s , it is p o s s i b l e to i n f e r w h i c h spin c o n f i g u r a tion for the c o m p l e x is m o r e l i k e l y Acc o r d i n g to our r e s u l t s the e n e r g y difference b e t w e e n the 9e and 8e l e v e l s is 0 20 eV. In o r d e r to the c o n f i g u r a t i o n (a) o c c u r it is r e q u i r e d that the exchange s p l i t t i n g of the l e v e l s be such that the 4a~ level lies a b o v e the 9elevel w i t h a s p l i t t i n g of a b o u t 0 . 5 3 eVo Even taking into a c c o u n t the fact that the 4a] level has a s t r o n g c o n t r i b u t i o n from the 3d orb i t a l s , a s p l i t t i n ~ of a b o u t 0 . 5 3 eV is highly unlikelylT-~9o The (b) c o n f i g u r a tion o c c u r s if the e x c h a n g e s p l i t t i n g was less t h a n 0 20 eV. However, due to the significative contribution from the 3d atomic o r b i t a l s to the 9e s t a t e we e x p e c t the exc h a n g e s p l i t t i n g be l a r g e r t h a m 0 20 eV |6
We c o n c l u d e that the A u - M n p a i r comp l e x in s i l i c o n in a n e u t r a l c h a r g e state has a s p i n S = 2 If one e l e c t r o n is rem o v e d in o r d e r to c r e a t e a p o s i t i v e c h a r g e s t a t e the o r b i t a l i n v o l v e d is the 9e + and the spin S = 3/2 w i l l be o b t a i n e d for the center As an a c c e p t o r the c o m p l e x captures an e l e c t r o n in the Be- and 9e- s t a t e s acc o r d i n g to the c o n f i g u r a t i o n (c) or (d), respectively Thus, in the n e g a t i v e c h a r g e state a spin S = 3/2 is e x p e c t e d for the complex° The n e u t r a l c h a r g e s t a t e has not b e e n d e t e c t e d by E P R The s i g n a l s for the p o s i t i v e and n e g a t i v e charge states have b e e n o b s e r v e d and the v a l u e s S = 3/2 and S = 5/2 are a s c r i b e d to them, respectivelyTo We a r g u e that it m a y be p o s s i b l e that the spin S = 5/2 , a s c r i b e d to the negative c h a r g e state, corresponds to some other c o m p l e x i n v o l v i n g gold or m a n g a n e s e rather than to the A u - M n complex. As we p o i n t e d out in the i n t r o d u c t i o n of this w o r k , the spin S = 3/2 for the pos i t i v e c h a r g e state of the c o m p l e x was exp l a i n e d 7 by a s s u m i n g an a n t i f e r r o m a g n e t i c coupling between S = | l o c a l i z e d on the A u and S = 5/2 on the Mn2+o It is a s s u m e d that one e l e c t r o n is t r a n s f e r r e d from manganese to gold due to the d i f f e r e n c e of electronegativities between these two elements. Our c a l c u l a t i o n s i n d i c a t e that there is no transference of one e l e c t r o n f r o m m a n g a n e s e to gold. M o r e o v e r , isolated substitutional gold does not lead to gap levels with d character° We c o n c l u d e that the m i c r o s c o p i c model p r o p o s e d in Ref I a c c o u n t s for the p h y s i c a l properties of the Au-Mn c o m p l e x in s i l i con. It is w o r t h m e n t i o n i n g that the m a n ganese 3d a t o m i c o r b i t a l s p l a y a r e l e v a n t role in d e t e r m i n i n g the a c c e p t o r and d o n o r activities of this c e n t e r .
REFERENCES
i. L . V . C . A s s a l i , J . R . L e l t e and A . F a z z i o , P h y s . R e v . B . 3 2 , 8 0 8 5 (1985) and references therein 2. D . V . L a n g , H . G . G r i m m e i s s , E . M e i j e r , and M . J a r o s , P h y s . R e v . B . 2 2 , 3 9 1 7 ( 1 9 8 0 ) 3. R . M . F e e n s t r a and S . T . P a n t e l i d e s , P h y s . Rev. B.31, 4 0 8 3 (1985) 4. A . G . M i l n e s , D e e p Impurities in S e m i c o n d u c t o r s (Wiley,New York,1973) 5. H . G . C r l m m e l s s , A n n . Rev. M a t e r . S c l . 7 , 3 4 1 (1977) 6. J.W.Chen and A . G . M i l n e s , A n n . Rev. M a t e r . S c i . l O , 1 5 7 (1980) 7. G . W . L u d w i g and H . H . W o o d b u r y , S o l l d S t a t e P h y s i c s 1 3 , 2 2 3 (1962) 8. L . V . C . A s s a l l and J . R . L e l t e , P h y s . R e v . Lett. 5 5 ~ 9 8 0 (1985) 9. V . M . S . G o m e s and J . R . L e i t e , A p p l . P h y s . L e t t . 4 7 , 8 2 4 (1985)
580
ELECTRONIC STRUCTURE OF THE Au-Mn PAIR COMPLEX IN SILICON
Vol. 58, No.
I0. J . L . A . A l v e s , J . R . L e i t e , L . V . C . A s s a l i , V . M . S . G o m e s and C.E.T.Gon~alves da Silva J.Phys.C. ~ 7 , L 7 7 1 ( 1 9 8 4 ) II. J.L.A.Alves and J.R.LeitetPhys.Rev. B 30,7284 (1984) 12. J . L . A . A l v e s , J . R . L e i t e , V . M . S . G o m e s and L . V . C . A s s a l i , S o l i d State Commun.55, 333 (1985) 13. N.Makiuchi, J.R.Leite and A.Fazzio,J.Phys. C 17,3423 (1984) 14. G.G.DeLeo, G.D.Watkins and W.B.Fowler,Phys.Rev.B 23,1851(1981);25,4962(1982); 25_~ 4972 (1982) 15. A.Zunger and U.LindefeltpPhys.Rev. B 26,5989 (1982) 16. F . B e e l e r , O , K . A n d e r s e n and M.Scheffler,Phys°Rev. Lett.55,1498(1985) 17. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. B 31, 8317 (1985) 18. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. Lett. 53,1256 (1984) 19. H . K a t a y a m a - Y o s h i d a and A.Zunger,Phys.Rev. B 31,7877 (1985)