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Occupancy of dangling bond defects in doped hydrogenated amorphous silicon
Solid State C o m m u n i c a t i o n s , P r i n t e d in Great Britain.
Occupancy
Vol.62,No.3,
of
pp.153-157,
1987.
Dangling Bond Defects in Amorphous Silicon Martin
0 0 3 8 - I 0 9 8 / 8 7 $3.00 + .00 P e r g a m o n Journals Ltd.
Doped
Hydrogenated
Stutzmann
Max-Planck-Institut f~r F e s t ~ d r p e r f o r s c h u n g Heisenbergstrasse I, D - 7 0 O O S t u t t g a r t 80, F e d e r a l R e p u b l i c of G e r m a n y and Warren Xerox Palo Received
B.
Jackson
Palo Alto Research Alto, CA 9 4 3 0 4 , U.
December
22,
1986
by
Center S. A.
Manuel
Cardona
Abstract The occupancy of d a n g l i n g b o n d d e f e c t s in d o p e d h y d r o g e n a t e d amorphous s i l i c o n is e x a m i n e d u s i n g a c o m b i n a t i o n of e l e c t r o n spin resonance, sub-bandgap absorption, and t r a n s p o r t measurements. A corrected v a l u e of U = + 0 . 2 eV (±0.1 eV) is obt a i n e d for the d a n g l i n g bond correlation e n e r g y in s t a t e - o f the-art material. The importance of p o t e n t i a l fluctuations c a u s e d by i n h o m o g e n e o u s defect distributions is d e m o n s t r a t e d for the c a s e of b o r o n d o p i n g in n o n - o p t i m i z e d samples.
A question of f u n d a m e n t a l importance for the u n d e r s t a n d i n g of the e l e c t r o n i c properties of h y d r o g e n a t e d amorphous silicon (a-SI:H) is t h e p o s i t i o n of the m a i n d e f e c t c e n t e r of t h i s material, the silicon dangling bond, in the m o b i l i t y gap. B e c a u s e the d a n g l i n g b o n d d e f e c t has t h r e e p o s s i b l e c h a r g e s t a t e s (+, O, and -, corresponding to the o c c u p a t i o n w i t h 0, I, or 2 electrons), the question concerning the p o s i t i o n of t h e s e d e f e c t s l e v e l s in the gap is equivalent to the problem of locating the demarcation energies E(+/O) and E(O/-) for w h i c h the o c c u p a t i o n of t h e l e v e l s c h a n g e s by one electron. Alternatively, one c a n f o r m u l a t e the s a m e p r o b l e m in t e r m s of the d e n s i t y - o f states distribution, g(E), and the s t a t i s t i c a l functions fo, f,, f 2 ( E - E F, T, U) w h i c h d e s c r i b e the t h e r m a l e q u i l i b r i u m occupancy of t h e d e f e c t l e v e l s w i t h 0, I, a n d 2 e l e c t r o n s as a function of the Fermi-level position, the temperature, a n d the m e a n effective correlation energy, U, of t h e d e f e c t s , Microscopically, the c o r r e l a t i o n energy c a n be d e f i n e d as t h e d i f f e r e n c e E(0/-) - E ( + / 0 ) b e t w e e n the demarcation levels mentioned a b o v e and d e p e n d s on the l o c a l i z a t i o n , the e l e c t r o n i c screening, a n d on p o s s i b l e s t r u c t u r a l relaxation energies of the d e f e c t u n d e r c o n s i d e r a t i o n .
energy of U +0.4 eV. The difficulty with this, however, is that so far no g e n e r a l l y accepted v a l u e for the d a n g l i n g bond correlation energy in a - S i : H has e m e r g e d . The spectrum of p r o p o s e d values for U e x t e n d s from U ~ -0.2 eV s u g g e s t e d by r e c e n t theoretical calculations to U = +0.4 eV d e r i v e d from a variety of e x p e r i m e n t s [I-4, and references therein]. Among the many attempts to d e t e r m i n e a meaningful v a l u e for the d a n g l i n g bond correl a t i o n e n e r g y in a - S i : H , the a p p r o a c h t a k e n by Dersch, Stuke, and Beichler [2] is p r o b a b l y the m o s t p r o m i s i n g . T h e i d e a of t h e s e I n v e s t i gators was to determine the density N S of singly occupied, paramagnetic dangling bond defects in a - S i : H as a f u n c t i o n of the F e r m i level position in the s a m p l e s , w h i c h in t u r n was altered by doping with phosphorus or boron. Conceptually, this method is v e r y m u c h suited f o r the p r e s e n t problem. The absolute concentration of s i n g l y o c c u p i e d , p a r a m a g n e t i c dangling bond defects c a n be d e t e r m i n e d accurately by electron spin resonance (ESR) techniques [5]. T h e o b t a i n e d s p i n d e n s i t y , NS, is r e l a t e d to the m i c r o s c o p i c quantities g(E) and U by: Ns(EF,T)
Thus, the problem of placing the diff e r e n t c h a r g e s t a t e s of d a n g l i n g bond defects within the a - S i : H mobility gap is I n t i m a t e l y related to a s e c o n d question of c o n s i d e r a b l e i n t e r e s t for t h e p h y s i c s of a m o r p h o u s silicon, namely the sign and magnitude of the e f f e c t i v e correlation e n e r g y , U, of t h e s i l i c o n d a n g l i n g bond states. In f a c t , as r e c e n t l y r e v i e w e d by LeComber and Spear [I], the common experimental procedure is to d e t e r m i n e e i t h e r the D ° (singly occupied) or D(doubly occupied) d a n g l i n g b o n d l e v e l and to I n f e r t h e p o s i t i o n of t h e o t h e r l e v e l by a s s u m i n g a correlation
=
[ g(E)fI(E-EF,T,U)dE
(I)
where f, is the p r o b a b i l i t y for a dangling b o n d d e f e c t to be o c c u p i e d by a s i n g l e e l e c tron. 'fl = 2 e x p Here, given
the by
[-(E-EF)/kT]/Z
grand
Z = I + 2exp + exp
153
(2a)
partition
function,
Z,
is
[-(E-EF)/kT ]
[-(2E-2EF+U)/kT
]
(2b)
OCCUPANCY_ O F D A N G L I N G
154
For an i l l u s t r a t i o n of Eqs. (I) a n d (2) we consider the c a s e of a s a m p l e at l o w t e m p e r a tures, s u c h t h a t kT << U. T h e n Eq. (2a) j u s t states that all defect levels within the energy interval [EF-U, E F ] w i l l be s i n g l y occupied and c o n t r i b u t i n g to the E S R s i g n a l , whereas defect levels for E < EF-U (E > EF) w i l l be d o u b l y (un-) o c c u p i e d and, t h e r e f o r e , diamagnetic. According to Eq. (I), the i n t e g r a t e d d e n s i t y of p a r a m a g n e t i c states observed in ESR w i l l be g i v e n by t h e c o n v o l u t i o n of t h e defect density of s t a t e s , g(E), w i t h t h e o c cupational w i n d o w d e f i n e d by f,. In t h e l i m i t U >> kT, Eq. (I) c a n be a p p r o x i m a t e d by:
Ns(EF)
~
E IF EF-U
g(E)dE
(3)
Thus, as t h e F e r m l - e n e r g y is s h i f t e d t h r o u g h a d e f e c t b a n d by d o p i n g , the o b s e r v e d d e p e n d e n c e of t h e s p i n d e n s i t y , N S , on E F c a n be d e c o n voluted in t e r m s of t h e d e f e c t distribution, g(E), and the e f f e c t i v e correlation e n e r g y , U. In particular, N S will have a maximum for E F = E M + U/2, w h e r e E M is the p o s i t i o n of t h e maximum in g ( E ) , a n d t h e F W H M of N s ( E F) w i l l provide an e s t i m a t e e i t h e r for U or the F W H M of g(E), w h i c h e v e r is l a r g e r . In p r i n c i p l e , this scheme should provide a v e r y d i r e c t m e t h o d f o r the d e t e r m i n a t i o n of the d a n g l i n g b o n d c o r r e l a t o n e n e r g y in a - S i : H , since both, the microscopic nature and the occupancy of the defects can be positively identified via the E S R r e s p o n s e , without disturbing the thermal equilibrium in the s a m p l e . In practice, however, there are two major problems. The first difficulty is that d o p i n g in a - S i : H c h a n g e s the d e n s i t y of d a n g l i n g b o n d defects [6]. T h u s , as E F is s h i f t e d through the d a n g l i n g b o n d b a n d by d o p i n g w i t h b o r o n or phosphorus, g(E) is no l o n g e r independent of EF, as a s s u m e d in Eq. (3). A s e c o n d p r o b l e m is t h a t d o p i n g of a - S i : H , especially wlth boron, can i n t r o d u c e structural inhomogeneities in a given sample. Then, of c o u r s e , the r e l a t i o n ship between the microscopic quantities, g(E) and U, a n d the m a c r o s c o p i c observables, N S and EF, c a n be v e r y c o m p l i c a t e d . Both complicat i o n s h a v e n o t b e e n t a k e n i n t o a c c o u n t in t h e early measurements by D e r s c h et al. [2], so t h a t the v a l u e of U 0.4 eV g i v e n in t h i s r e f e r e n c e n e e d s to be r e e x a m i n e d . To t h i s end, we h a v e c o m b i n e d ESR e x p e r i ments with measurements of t h e d a n g l i n g bond optical absorption for two d i f f e r e n t s e t s of doped a-Si :H s a m p l e s . Subgap absorption obtained with photothermal deflection spectroscopy (PDS) [ 7 J has b e e n shown to g i v e reliable estimates for t h e t o t a l d a n g l i n g bond d e n s i t y in d o p e d a n d u n d o p e d a-Si:H, ~ndepend e n t of t h e d e f e c t occupancy. Thus, by c o m b i n i n g PDS a n d E S R d a t a o b t a i n e d f o r t h e s a m e samples, the problem posed by the dopinginduced enhancement of the d a n g l i n g bond density c a n be o v e r c o m e . F o r an e x a m i n a t i o n of the e f f e c t of d o p i n g - i n d u c e d inhomogeneities, we h a v e r e p e a t e d s u c h e x p e r i m e n t s for two sets of doped samples prepared under different deposition conditions. Samples belonging to set I were obtained by r f - g l o w discharge of undiluted SiH~ under the s t a n d a r d conditions used for high quality material (substrate temperature 230°C, rf-power density 20 m W / c m Z ) . For set il, the s i l a n e was d i l u t e d in Ar ( v o l u m e r a t i o I : I ) , and the p o w e r d e n s i t y was i n c r e a s e d to 200 m W / o m z . P D S a n d ESR samples were always deposited in t h e s a m e run,
BOND D E F E C T S
Vol.
62, No.
3
u s i n g 7 0 5 9 g l a s s a n d AI as t h e s u b s t / a t e materials, respectively. The thickness of a ~ l s a m p l e s was k e p t a b o v e 3 pm, in o r d e r to s u p press surface effects. Where applicable, we have also included data from ref. [2] for comparison. Deposition conditions for these samples (III) w e r e s o m e w h a t intermediate betw e e n t h o s e for set I a n d set II, in t h a t t h e same Ar-dilution, but a l o w e r p o w e r l e v e l t h a n for set II w e r e e m p l o y e d . In Fig. I, the neutral dangling bond density, NS, o b t a i n e d w i t h ESR for t h e t h r e e s e t s of s a m p l e s has b e e n c o m p i l e d as a f u n c t i o n of t h e d o p a n t gas c o n c e n t r a t i o n in t h e deposition plasma. High quality a-Si:H (I) exhibits a dangling bond density of = 5 x I 0 Is cm -3 in t h e u n d o p e d case, which decreases strongly even for small phosphorus d o p i n g l e v e l s and b e c o m e s u n d e t e c t a b l e f o r PH s concentrations above 10 -5 . D o p i n g with dlborane, however, first increases the densit~ of n e u t r a l danKling b o n d s to a b o u t 10 16 cm at [ B , H , ] / [ S i H , ] = 10-". O n l y for h i g h e r b o r o n concentrations a corr@sponding d e c r e a s e of t h e spin signal is o b s e r v e d . The earlier results of D e r s c h et al. (III) s h o w a n e a r l y i d e n t i c a l doping dependence of t h e s p i n d e n s i t y , h o w e v e r with a five times larger defect density. On the o t h e r hand, t h e b e h a v i o r of the n o n - o p t i mized samples (II) is c o m p l e t e l y different. Although the defect density in t h e undoped c a s e (2xI0 ~6 cm -+) is q u i t e low, d o p i n g w i t h boron increases the concentration of n e u t r a l dangling bonds to n e a r l y 1 0 ' ' cm -~ at a I % doping level. For phosphorous doping, the d a n g l i n g b o n d s p i n d e n s i t y r e m a i n s at a n e a r l y constant level up to [ P H , ] / [ S I H , ] " 10-'.
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ESR s p i n d e n s i t i e s of n e u t r a l d a n g l i n g bond defects (g = 2 . 0 0 5 5 ) in d o p e d a - S i : H as a f u n c t i o n of t h e g a s p h a s e doping level (I: high quality material, II: non-optimized samples, III: r e s u l t s of ref. [ 2 ] . )
Vol.
62, No.
OCCUPANCY
3
OF D A N G L I N G
The corresponding results for the t o t a l dangling bond density obtained from the P D S measurements a r e s ~ o w n in Fig. 2. In v i e w of the large differences b e t w e e n the E S R data, it is q u i t e remarkable t h a t the P D S e x p e r i m e n t s show a nearly identical dependence of the defect densities in s a m p l e s b e l o n g i n g to set I a n d II on t h e d o p a n t gas c o n c e n t r a t i o n . Note also the close agreement between E S R and P D S defect densities for the b o r o n doped samples of set II. Before we c a n a t t e m p t an i n t e r p r e t a t i o n of t h e e x p e r i m e n t a l results in Figs. I a n d 2, it is n e c e s s a r y to t r a n s l a t e the dopant gas concentration used as the abscissa in the previous figures into a parameter more appropriate for a macroscopic description of t h e deposited d o p e d a - S i : H f i l m s [8]. A c c o r d i n g to Eq. (3), the m o s t adequate parameter is the position of t h e F e r m l - l e v e l , EF, w i t h i n the a-Si:H mobility gap. To a g o o d a p p r o x i m a t i o n , this Fermi-level p o s i t i o n c a n be o b t a i n e d f r o m the activation energy of the d a r k conductivity, and results for t h e p r e s e n t s a m p l e s are summarized in Fig. 3. U n d o p e d s a m p l e s c o m m o n l y show n-type conduction with an activation energy between 0 . 7 5 a n d 0 . 8 5 eV. A q u i t e r e markable f e a t u r e of Fig. 3 is the v e r y s i m i l a r (to w i t h i n b e t t e r t h a n 100 meV) d e p e n d e n c e of the Fermi-level position on the dopant gas concentration for t h e t h r e e d i f f e r e n t s e t s of samples. The only exception is h i g h - q u a l i t y n-type a-Si:H, for which already small dopant concentrations l e a d to a s a t u r a t i n g s h i f t of E F into the conduction b a n d tail. A p o s s i b l e explanation for thls difference c o u l d be t h e asymmetry between the valence and conduction b a n d tail, w h i c h w o u l d b e c o m e m o r e n o t i c e a b l e for small mldgap defect densities. The results in Figs. I, 2, a n d 3 c a n n o w be c o m b i n e d to obtain the occupancy of the dangling bond d e f e c t l e v e l s as a f u n c t i o n of t h e F e r m i - l e v e l position in a - S i : H . T h i s is s h o w n in Fig. 4.
155
BOND DEFECTS I
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4:
Fraction Ns/N D of singly occupied dangling bonds as a f u n c t i o n of t h e Fermi-level shift, AE F, f r o m m l d g a p . (I: high quality a-Si:H, II: nonoptimized material).
156
OCCUPANCY
OF D A N G L I N G
T h e o r d i n a t e of t h i s f i g u r e is the r a t i o N s / N D of the E S R s p i n d e n s i t i e s a n d the t o t a l d e f e c t densities calculated f r o m t h e PDS s p e c t r a . TO the extent that only dangling bond defects contribute significantly to the s u b g a p a b s o r p tion spectra, t h i s r a t i o is e s s e n t i a l l y equal to the p r o b a b i l i t y of s i n g l e o c c u p a n c y for t h e dangling bond levels in t h e r m a l equilibrium. The abscissa in F i g . 4, A E F , is t h e d o p i n g i n d u c e d s h i f t of the F e r m i - l e v e l away from the m l d g a p p o s i t i o n in u n d o p e d a - S i : H . In the case of high quality material ( c u r v e I), the p e a k e x p e c t e d f r o m Eq. (3) is clearly observed. N o t e t h a t f o r the c o r r e c t e d occupancy data in Fig. 4 maximum occupancy occurs f o r t h e m l d g a p p o s i t i o n of EF, w h e r e a s the u n c o r r e c t e d ESR d a t a in Fig. I w o u l d h a v e suggested a position closer to the valence band. T h e peak p o s i t i o n in Fig. 4 a g r e e s w i t h the notion that the Fermi-level in u n d o p e d material is pinned between the D ° and Dlevels of the d a n g l i n g bond defects, i.e. at E F = D ° + U/2 = E C 0 . 8 5 eV, w h e r e E C is the conduction b a n d m o b i l i t y edge. T h e F W H M of t h e p e a k in Fig. 4 allows us to d e d u c e an u p p e r l i m i t of 0.3 eV for the d a n g l i n g bond correlation energy, U. It has to be s t r e s s e d that t h i s is o n l y an u p p e r l i m i t , b e c a u s e the F W H M of 0.3 eV m a y a l r e a d y be c l o s e to the i n t r i n sic width of the density-of-state distribution, g(E), a n d b e c a u s e b r o a d e n i n g by i n h o m o geneities m a y be a p p r e c i a b l e (see b e l o w ) . On the o t h e r hand, a lower limit for U c a n be obtained from the temperature dependence of the d a n g l i n g b o n d s p i n s i g n a l . T h i s d e p e n d e n c e f o l l o w s the C u r l e - b e h a v l o r for a c o n s t a n t s p i n d e n s i t y up to t e m p e r a t u r e s of at l e a s t 150°C, w h i c h is o n l y p o s s i b l e if U >> kT = 35 meV. A reasonable lower limit for U is, therefore, U > 100 meV. Combining t h e s e two l i m i t s , we obtain for the correlation energy: U = +0.2 (+_0.1) eV. This, then, places the m a x i m a of t h e D ° a n d D- d e n s i t i e s of s t a t e s at E C - 0 . 9 5 eV a n d E C - 0 . 7 5 ev, r e s p e c t i v e l y . Again, these energy positions of t h e d a n g l i n g bond maxima have an uncertainty of approximately ± 50 meV, d u e to the e r r o r in the determination of the correlation energy and the estimation of the true Fermi-level p o s i t i o n f r o m the t r a n s p o r t data. Thus, the present results suggest that the dangling bond correlation energy is a c t u a l l y by a b o u t a f a c t o r of two s m a l l e r t h a n the v a l u e of 0.4 eV o r i g i n a l l y deduced from ESR m e a s u r e m e n t s and c o m m o n l y e m p l o y e d for m o d e l l i n g the m l d g a p d e n s i t y of s t a t e s in a - S i : H [I ]. W i t h o u t going into further details, we would like to mention that such a smaller v a l u e for U in m a n y c a s e s w l l l b r i n g a p p a r e n t controversies between different experimental approaches b a c k to w i t h i n the l i m i t s of r e a sonable experimental e r r o r bars. Our l a s t c o m m e n t c o n c e r n s the i m p o r t a n c e of s t r u c t u r a l inhomogenities for t h e i n t e r p r e tation of e x p e r i m e n t a l data, which too o f t e n is n e g l e c t e d in t h e d e r i v a t i o n of m o d e l s for a~Si:H. However, such inhomogeneities (or potential fluctuations) may actually dominate the electronic properties of a particular
BOND DEFECTS
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62, No.
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sample. F o r the c a s e of b o r o n - d o p e d a-Si:H, t h i s is s h o w n q u i t e d r a s t i c a l l y by c o m p a r i n g high quality and non-optlmized material (curve I and II) in Fig. 4. E v e n for f a i r l y low doping levels, the comparison of ESR a n d PDS d a t a i n d i c a t e s t h a t t h e o c c u p a n c y of d a n g l i n g b o n d (and o t h e r ) d e f e c t l e v e l s m a y d i f f e r by some orders of magnitude, although the Fermi-level position obtained from electronic transport seems to be similar for the two t y p e s of s a m p l e s . N o t e a l s o t h a t t h e s e d i s c r e p a n c i e s do not o n l y o c c u r b e t w e e n r a t h e r e x o tic s a m p l e s but, a c c o r d i n g to Fig. 2, for t w o sets of s a m p l e s having very similar overall defect densities in the e n t i r e doping range. For an e x p l a n a n t i o n of the d i f f e r e n c e between curves I and II in Fig. 4, we o b v i o u s l y have to assume the existence of spatial inhomogeneitles in the defect distribution. For example, the b e h a v i o r of b o r o n - d o p e d samples belonging to set II i n d i c a t e s the e x i s t e n c e of dangling bond-rlch regions, in w h i c h the Fermi-leVel remains pinned close to m i d g a p , apd of effectively doped regions which are responsible for the changes in electronic transport. Since the conductivity depends exponentially on the F e r m i - l e v e l position, in fact only a very small, interconnected fract i o n of e f f e c t i v e l y doped material is n e c e s s a r y to e x p l a i n our e x p e r i m e n t a l results for t y p e II s a m p l e s . Finally, a comparison of the left and r i g h t h a n d s i d e of Fig. 4 s h o w s t h a t d i f f e r e n t dopants react quite differently, when deposition conditions are changed. Thus, there Is very little difference b e t w e e n the two s e t s of samples in the case of doping with phosphorous. This, however, is no garanty that s i m i l a r e f f e c t s as s e e n f o r b o r o n - d o p i n g will not a p p e a r for o t h e r d e p o s i t i o n conditions. In s u m m a r y , we h a v e examined the o c c u p a n c y of d a n g l i n g b o n d d e f e c t l e v e l s in d o p e d a-Si:H by a c o m b i n a t i o n of e l e c t r o n spin resonance, photothermal deflection spectroscopy, and t r a n s p o r t measurements. It is s h o w n t h a t for a c o r r e c t i n t e r p r e t a t i o n of ESR r e s u l t s it is important to include the doping-lnduced increase of the defect density in t h i s m a terial. We obtain a corrected value of U = + 0 . 2 eV (±0.I eV) f o r the a v e r a g e d a n g l i n g bond correlation energy, and a position for the n e u t r a l and d o u b l y o c c u p i e d dangling bond levels at E C - 0 . 9 5 eV a n d E C - 0 . 7 5 eV, respectively. By c o m p a r i n g r e s u l t s for s t a t e - o f the-art a-Si:H samples with non-optlmlzed material, it is d e m o n s t r a t e d that large potential fluctuations c a u s e d by s p a t i a l i n h o m o geneities in t h e d e f e c t distribution c a n be present, especially in the case of boron doping.
Acknowledgements We w o u l d l l k e to t h a n k C.C. Tsai a n d R. Thompson for s a m p l e p r e p a r a t i o n . M. St. g r a t e fully acknowledges the h o s p i t a l i t y of the c o l leagues in the Xerox Palo Alto Research Center.
Vol. 62, No. 3
OCCUPANCY OF DANGLING BOND DEFECTS
157
References
[I] P.G. LeComber, W.E. Spear, Phil. Mag. B 53, LI (1986). [2] ~ Dersch, J. Stuke, J. Beichler, phys. star. sol. (b) 105, 265 (1981). [3] W.B. Jackson, Solid State Commun. 44, 477 (1982). {4] Y. Bar-Yam, J.D. Joannopoulos, Phys. Rev. Lett. 56, 2203 (1986). [5] M. Stut---zmann, Z. Phys. Chem. Neue Folge, in print.
[6] R.A. Street, D.K. Biegelsen, J.C. Knights, Phys. Rev. B 24, 969 (1981). [7] N.M. Amer, W.-B-. Jackson, S e m i c o n d u c t o r s & Semlmetals 21 B, p. 83, ed. by J.I. Pankove, Academic Press, New York (1984). [8] M. Stutzmann, Phil. Mag. B 53, L15 (1986).
Occupancy
Vol.62,No.3,
of
pp.153-157,
1987.
Dangling Bond Defects in Amorphous Silicon Martin
0 0 3 8 - I 0 9 8 / 8 7 $3.00 + .00 P e r g a m o n Journals Ltd.
Doped
Hydrogenated
Stutzmann
Max-Planck-Institut f~r F e s t ~ d r p e r f o r s c h u n g Heisenbergstrasse I, D - 7 0 O O S t u t t g a r t 80, F e d e r a l R e p u b l i c of G e r m a n y and Warren Xerox Palo Received
B.
Jackson
Palo Alto Research Alto, CA 9 4 3 0 4 , U.
December
22,
1986
by
Center S. A.
Manuel
Cardona
Abstract The occupancy of d a n g l i n g b o n d d e f e c t s in d o p e d h y d r o g e n a t e d amorphous s i l i c o n is e x a m i n e d u s i n g a c o m b i n a t i o n of e l e c t r o n spin resonance, sub-bandgap absorption, and t r a n s p o r t measurements. A corrected v a l u e of U = + 0 . 2 eV (±0.1 eV) is obt a i n e d for the d a n g l i n g bond correlation e n e r g y in s t a t e - o f the-art material. The importance of p o t e n t i a l fluctuations c a u s e d by i n h o m o g e n e o u s defect distributions is d e m o n s t r a t e d for the c a s e of b o r o n d o p i n g in n o n - o p t i m i z e d samples.
A question of f u n d a m e n t a l importance for the u n d e r s t a n d i n g of the e l e c t r o n i c properties of h y d r o g e n a t e d amorphous silicon (a-SI:H) is t h e p o s i t i o n of the m a i n d e f e c t c e n t e r of t h i s material, the silicon dangling bond, in the m o b i l i t y gap. B e c a u s e the d a n g l i n g b o n d d e f e c t has t h r e e p o s s i b l e c h a r g e s t a t e s (+, O, and -, corresponding to the o c c u p a t i o n w i t h 0, I, or 2 electrons), the question concerning the p o s i t i o n of t h e s e d e f e c t s l e v e l s in the gap is equivalent to the problem of locating the demarcation energies E(+/O) and E(O/-) for w h i c h the o c c u p a t i o n of t h e l e v e l s c h a n g e s by one electron. Alternatively, one c a n f o r m u l a t e the s a m e p r o b l e m in t e r m s of the d e n s i t y - o f states distribution, g(E), and the s t a t i s t i c a l functions fo, f,, f 2 ( E - E F, T, U) w h i c h d e s c r i b e the t h e r m a l e q u i l i b r i u m occupancy of t h e d e f e c t l e v e l s w i t h 0, I, a n d 2 e l e c t r o n s as a function of the Fermi-level position, the temperature, a n d the m e a n effective correlation energy, U, of t h e d e f e c t s , Microscopically, the c o r r e l a t i o n energy c a n be d e f i n e d as t h e d i f f e r e n c e E(0/-) - E ( + / 0 ) b e t w e e n the demarcation levels mentioned a b o v e and d e p e n d s on the l o c a l i z a t i o n , the e l e c t r o n i c screening, a n d on p o s s i b l e s t r u c t u r a l relaxation energies of the d e f e c t u n d e r c o n s i d e r a t i o n .
energy of U +0.4 eV. The difficulty with this, however, is that so far no g e n e r a l l y accepted v a l u e for the d a n g l i n g bond correlation energy in a - S i : H has e m e r g e d . The spectrum of p r o p o s e d values for U e x t e n d s from U ~ -0.2 eV s u g g e s t e d by r e c e n t theoretical calculations to U = +0.4 eV d e r i v e d from a variety of e x p e r i m e n t s [I-4, and references therein]. Among the many attempts to d e t e r m i n e a meaningful v a l u e for the d a n g l i n g bond correl a t i o n e n e r g y in a - S i : H , the a p p r o a c h t a k e n by Dersch, Stuke, and Beichler [2] is p r o b a b l y the m o s t p r o m i s i n g . T h e i d e a of t h e s e I n v e s t i gators was to determine the density N S of singly occupied, paramagnetic dangling bond defects in a - S i : H as a f u n c t i o n of the F e r m i level position in the s a m p l e s , w h i c h in t u r n was altered by doping with phosphorus or boron. Conceptually, this method is v e r y m u c h suited f o r the p r e s e n t problem. The absolute concentration of s i n g l y o c c u p i e d , p a r a m a g n e t i c dangling bond defects c a n be d e t e r m i n e d accurately by electron spin resonance (ESR) techniques [5]. T h e o b t a i n e d s p i n d e n s i t y , NS, is r e l a t e d to the m i c r o s c o p i c quantities g(E) and U by: Ns(EF,T)
Thus, the problem of placing the diff e r e n t c h a r g e s t a t e s of d a n g l i n g bond defects within the a - S i : H mobility gap is I n t i m a t e l y related to a s e c o n d question of c o n s i d e r a b l e i n t e r e s t for t h e p h y s i c s of a m o r p h o u s silicon, namely the sign and magnitude of the e f f e c t i v e correlation e n e r g y , U, of t h e s i l i c o n d a n g l i n g bond states. In f a c t , as r e c e n t l y r e v i e w e d by LeComber and Spear [I], the common experimental procedure is to d e t e r m i n e e i t h e r the D ° (singly occupied) or D(doubly occupied) d a n g l i n g b o n d l e v e l and to I n f e r t h e p o s i t i o n of t h e o t h e r l e v e l by a s s u m i n g a correlation
=
[ g(E)fI(E-EF,T,U)dE
(I)
where f, is the p r o b a b i l i t y for a dangling b o n d d e f e c t to be o c c u p i e d by a s i n g l e e l e c tron. 'fl = 2 e x p Here, given
the by
[-(E-EF)/kT]/Z
grand
Z = I + 2exp + exp
153
(2a)
partition
function,
Z,
is
[-(E-EF)/kT ]
[-(2E-2EF+U)/kT
]
(2b)
OCCUPANCY_ O F D A N G L I N G
154
For an i l l u s t r a t i o n of Eqs. (I) a n d (2) we consider the c a s e of a s a m p l e at l o w t e m p e r a tures, s u c h t h a t kT << U. T h e n Eq. (2a) j u s t states that all defect levels within the energy interval [EF-U, E F ] w i l l be s i n g l y occupied and c o n t r i b u t i n g to the E S R s i g n a l , whereas defect levels for E < EF-U (E > EF) w i l l be d o u b l y (un-) o c c u p i e d and, t h e r e f o r e , diamagnetic. According to Eq. (I), the i n t e g r a t e d d e n s i t y of p a r a m a g n e t i c states observed in ESR w i l l be g i v e n by t h e c o n v o l u t i o n of t h e defect density of s t a t e s , g(E), w i t h t h e o c cupational w i n d o w d e f i n e d by f,. In t h e l i m i t U >> kT, Eq. (I) c a n be a p p r o x i m a t e d by:
Ns(EF)
~
E IF EF-U
g(E)dE
(3)
Thus, as t h e F e r m l - e n e r g y is s h i f t e d t h r o u g h a d e f e c t b a n d by d o p i n g , the o b s e r v e d d e p e n d e n c e of t h e s p i n d e n s i t y , N S , on E F c a n be d e c o n voluted in t e r m s of t h e d e f e c t distribution, g(E), and the e f f e c t i v e correlation e n e r g y , U. In particular, N S will have a maximum for E F = E M + U/2, w h e r e E M is the p o s i t i o n of t h e maximum in g ( E ) , a n d t h e F W H M of N s ( E F) w i l l provide an e s t i m a t e e i t h e r for U or the F W H M of g(E), w h i c h e v e r is l a r g e r . In p r i n c i p l e , this scheme should provide a v e r y d i r e c t m e t h o d f o r the d e t e r m i n a t i o n of the d a n g l i n g b o n d c o r r e l a t o n e n e r g y in a - S i : H , since both, the microscopic nature and the occupancy of the defects can be positively identified via the E S R r e s p o n s e , without disturbing the thermal equilibrium in the s a m p l e . In practice, however, there are two major problems. The first difficulty is that d o p i n g in a - S i : H c h a n g e s the d e n s i t y of d a n g l i n g b o n d defects [6]. T h u s , as E F is s h i f t e d through the d a n g l i n g b o n d b a n d by d o p i n g w i t h b o r o n or phosphorus, g(E) is no l o n g e r independent of EF, as a s s u m e d in Eq. (3). A s e c o n d p r o b l e m is t h a t d o p i n g of a - S i : H , especially wlth boron, can i n t r o d u c e structural inhomogeneities in a given sample. Then, of c o u r s e , the r e l a t i o n ship between the microscopic quantities, g(E) and U, a n d the m a c r o s c o p i c observables, N S and EF, c a n be v e r y c o m p l i c a t e d . Both complicat i o n s h a v e n o t b e e n t a k e n i n t o a c c o u n t in t h e early measurements by D e r s c h et al. [2], so t h a t the v a l u e of U 0.4 eV g i v e n in t h i s r e f e r e n c e n e e d s to be r e e x a m i n e d . To t h i s end, we h a v e c o m b i n e d ESR e x p e r i ments with measurements of t h e d a n g l i n g bond optical absorption for two d i f f e r e n t s e t s of doped a-Si :H s a m p l e s . Subgap absorption obtained with photothermal deflection spectroscopy (PDS) [ 7 J has b e e n shown to g i v e reliable estimates for t h e t o t a l d a n g l i n g bond d e n s i t y in d o p e d a n d u n d o p e d a-Si:H, ~ndepend e n t of t h e d e f e c t occupancy. Thus, by c o m b i n i n g PDS a n d E S R d a t a o b t a i n e d f o r t h e s a m e samples, the problem posed by the dopinginduced enhancement of the d a n g l i n g bond density c a n be o v e r c o m e . F o r an e x a m i n a t i o n of the e f f e c t of d o p i n g - i n d u c e d inhomogeneities, we h a v e r e p e a t e d s u c h e x p e r i m e n t s for two sets of doped samples prepared under different deposition conditions. Samples belonging to set I were obtained by r f - g l o w discharge of undiluted SiH~ under the s t a n d a r d conditions used for high quality material (substrate temperature 230°C, rf-power density 20 m W / c m Z ) . For set il, the s i l a n e was d i l u t e d in Ar ( v o l u m e r a t i o I : I ) , and the p o w e r d e n s i t y was i n c r e a s e d to 200 m W / o m z . P D S a n d ESR samples were always deposited in t h e s a m e run,
BOND D E F E C T S
Vol.
62, No.
3
u s i n g 7 0 5 9 g l a s s a n d AI as t h e s u b s t / a t e materials, respectively. The thickness of a ~ l s a m p l e s was k e p t a b o v e 3 pm, in o r d e r to s u p press surface effects. Where applicable, we have also included data from ref. [2] for comparison. Deposition conditions for these samples (III) w e r e s o m e w h a t intermediate betw e e n t h o s e for set I a n d set II, in t h a t t h e same Ar-dilution, but a l o w e r p o w e r l e v e l t h a n for set II w e r e e m p l o y e d . In Fig. I, the neutral dangling bond density, NS, o b t a i n e d w i t h ESR for t h e t h r e e s e t s of s a m p l e s has b e e n c o m p i l e d as a f u n c t i o n of t h e d o p a n t gas c o n c e n t r a t i o n in t h e deposition plasma. High quality a-Si:H (I) exhibits a dangling bond density of = 5 x I 0 Is cm -3 in t h e u n d o p e d case, which decreases strongly even for small phosphorus d o p i n g l e v e l s and b e c o m e s u n d e t e c t a b l e f o r PH s concentrations above 10 -5 . D o p i n g with dlborane, however, first increases the densit~ of n e u t r a l danKling b o n d s to a b o u t 10 16 cm at [ B , H , ] / [ S i H , ] = 10-". O n l y for h i g h e r b o r o n concentrations a corr@sponding d e c r e a s e of t h e spin signal is o b s e r v e d . The earlier results of D e r s c h et al. (III) s h o w a n e a r l y i d e n t i c a l doping dependence of t h e s p i n d e n s i t y , h o w e v e r with a five times larger defect density. On the o t h e r hand, t h e b e h a v i o r of the n o n - o p t i mized samples (II) is c o m p l e t e l y different. Although the defect density in t h e undoped c a s e (2xI0 ~6 cm -+) is q u i t e low, d o p i n g w i t h boron increases the concentration of n e u t r a l dangling bonds to n e a r l y 1 0 ' ' cm -~ at a I % doping level. For phosphorous doping, the d a n g l i n g b o n d s p i n d e n s i t y r e m a i n s at a n e a r l y constant level up to [ P H , ] / [ S I H , ] " 10-'.
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ESR s p i n d e n s i t i e s of n e u t r a l d a n g l i n g bond defects (g = 2 . 0 0 5 5 ) in d o p e d a - S i : H as a f u n c t i o n of t h e g a s p h a s e doping level (I: high quality material, II: non-optimized samples, III: r e s u l t s of ref. [ 2 ] . )
Vol.
62, No.
OCCUPANCY
3
OF D A N G L I N G
The corresponding results for the t o t a l dangling bond density obtained from the P D S measurements a r e s ~ o w n in Fig. 2. In v i e w of the large differences b e t w e e n the E S R data, it is q u i t e remarkable t h a t the P D S e x p e r i m e n t s show a nearly identical dependence of the defect densities in s a m p l e s b e l o n g i n g to set I a n d II on t h e d o p a n t gas c o n c e n t r a t i o n . Note also the close agreement between E S R and P D S defect densities for the b o r o n doped samples of set II. Before we c a n a t t e m p t an i n t e r p r e t a t i o n of t h e e x p e r i m e n t a l results in Figs. I a n d 2, it is n e c e s s a r y to t r a n s l a t e the dopant gas concentration used as the abscissa in the previous figures into a parameter more appropriate for a macroscopic description of t h e deposited d o p e d a - S i : H f i l m s [8]. A c c o r d i n g to Eq. (3), the m o s t adequate parameter is the position of t h e F e r m l - l e v e l , EF, w i t h i n the a-Si:H mobility gap. To a g o o d a p p r o x i m a t i o n , this Fermi-level p o s i t i o n c a n be o b t a i n e d f r o m the activation energy of the d a r k conductivity, and results for t h e p r e s e n t s a m p l e s are summarized in Fig. 3. U n d o p e d s a m p l e s c o m m o n l y show n-type conduction with an activation energy between 0 . 7 5 a n d 0 . 8 5 eV. A q u i t e r e markable f e a t u r e of Fig. 3 is the v e r y s i m i l a r (to w i t h i n b e t t e r t h a n 100 meV) d e p e n d e n c e of the Fermi-level position on the dopant gas concentration for t h e t h r e e d i f f e r e n t s e t s of samples. The only exception is h i g h - q u a l i t y n-type a-Si:H, for which already small dopant concentrations l e a d to a s a t u r a t i n g s h i f t of E F into the conduction b a n d tail. A p o s s i b l e explanation for thls difference c o u l d be t h e asymmetry between the valence and conduction b a n d tail, w h i c h w o u l d b e c o m e m o r e n o t i c e a b l e for small mldgap defect densities. The results in Figs. I, 2, a n d 3 c a n n o w be c o m b i n e d to obtain the occupancy of the dangling bond d e f e c t l e v e l s as a f u n c t i o n of t h e F e r m i - l e v e l position in a - S i : H . T h i s is s h o w n in Fig. 4.
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Fraction Ns/N D of singly occupied dangling bonds as a f u n c t i o n of t h e Fermi-level shift, AE F, f r o m m l d g a p . (I: high quality a-Si:H, II: nonoptimized material).
156
OCCUPANCY
OF D A N G L I N G
T h e o r d i n a t e of t h i s f i g u r e is the r a t i o N s / N D of the E S R s p i n d e n s i t i e s a n d the t o t a l d e f e c t densities calculated f r o m t h e PDS s p e c t r a . TO the extent that only dangling bond defects contribute significantly to the s u b g a p a b s o r p tion spectra, t h i s r a t i o is e s s e n t i a l l y equal to the p r o b a b i l i t y of s i n g l e o c c u p a n c y for t h e dangling bond levels in t h e r m a l equilibrium. The abscissa in F i g . 4, A E F , is t h e d o p i n g i n d u c e d s h i f t of the F e r m i - l e v e l away from the m l d g a p p o s i t i o n in u n d o p e d a - S i : H . In the case of high quality material ( c u r v e I), the p e a k e x p e c t e d f r o m Eq. (3) is clearly observed. N o t e t h a t f o r the c o r r e c t e d occupancy data in Fig. 4 maximum occupancy occurs f o r t h e m l d g a p p o s i t i o n of EF, w h e r e a s the u n c o r r e c t e d ESR d a t a in Fig. I w o u l d h a v e suggested a position closer to the valence band. T h e peak p o s i t i o n in Fig. 4 a g r e e s w i t h the notion that the Fermi-level in u n d o p e d material is pinned between the D ° and Dlevels of the d a n g l i n g bond defects, i.e. at E F = D ° + U/2 = E C 0 . 8 5 eV, w h e r e E C is the conduction b a n d m o b i l i t y edge. T h e F W H M of t h e p e a k in Fig. 4 allows us to d e d u c e an u p p e r l i m i t of 0.3 eV for the d a n g l i n g bond correlation energy, U. It has to be s t r e s s e d that t h i s is o n l y an u p p e r l i m i t , b e c a u s e the F W H M of 0.3 eV m a y a l r e a d y be c l o s e to the i n t r i n sic width of the density-of-state distribution, g(E), a n d b e c a u s e b r o a d e n i n g by i n h o m o geneities m a y be a p p r e c i a b l e (see b e l o w ) . On the o t h e r hand, a lower limit for U c a n be obtained from the temperature dependence of the d a n g l i n g b o n d s p i n s i g n a l . T h i s d e p e n d e n c e f o l l o w s the C u r l e - b e h a v l o r for a c o n s t a n t s p i n d e n s i t y up to t e m p e r a t u r e s of at l e a s t 150°C, w h i c h is o n l y p o s s i b l e if U >> kT = 35 meV. A reasonable lower limit for U is, therefore, U > 100 meV. Combining t h e s e two l i m i t s , we obtain for the correlation energy: U = +0.2 (+_0.1) eV. This, then, places the m a x i m a of t h e D ° a n d D- d e n s i t i e s of s t a t e s at E C - 0 . 9 5 eV a n d E C - 0 . 7 5 ev, r e s p e c t i v e l y . Again, these energy positions of t h e d a n g l i n g bond maxima have an uncertainty of approximately ± 50 meV, d u e to the e r r o r in the determination of the correlation energy and the estimation of the true Fermi-level p o s i t i o n f r o m the t r a n s p o r t data. Thus, the present results suggest that the dangling bond correlation energy is a c t u a l l y by a b o u t a f a c t o r of two s m a l l e r t h a n the v a l u e of 0.4 eV o r i g i n a l l y deduced from ESR m e a s u r e m e n t s and c o m m o n l y e m p l o y e d for m o d e l l i n g the m l d g a p d e n s i t y of s t a t e s in a - S i : H [I ]. W i t h o u t going into further details, we would like to mention that such a smaller v a l u e for U in m a n y c a s e s w l l l b r i n g a p p a r e n t controversies between different experimental approaches b a c k to w i t h i n the l i m i t s of r e a sonable experimental e r r o r bars. Our l a s t c o m m e n t c o n c e r n s the i m p o r t a n c e of s t r u c t u r a l inhomogenities for t h e i n t e r p r e tation of e x p e r i m e n t a l data, which too o f t e n is n e g l e c t e d in t h e d e r i v a t i o n of m o d e l s for a~Si:H. However, such inhomogeneities (or potential fluctuations) may actually dominate the electronic properties of a particular
BOND DEFECTS
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sample. F o r the c a s e of b o r o n - d o p e d a-Si:H, t h i s is s h o w n q u i t e d r a s t i c a l l y by c o m p a r i n g high quality and non-optlmized material (curve I and II) in Fig. 4. E v e n for f a i r l y low doping levels, the comparison of ESR a n d PDS d a t a i n d i c a t e s t h a t t h e o c c u p a n c y of d a n g l i n g b o n d (and o t h e r ) d e f e c t l e v e l s m a y d i f f e r by some orders of magnitude, although the Fermi-level position obtained from electronic transport seems to be similar for the two t y p e s of s a m p l e s . N o t e a l s o t h a t t h e s e d i s c r e p a n c i e s do not o n l y o c c u r b e t w e e n r a t h e r e x o tic s a m p l e s but, a c c o r d i n g to Fig. 2, for t w o sets of s a m p l e s having very similar overall defect densities in the e n t i r e doping range. For an e x p l a n a n t i o n of the d i f f e r e n c e between curves I and II in Fig. 4, we o b v i o u s l y have to assume the existence of spatial inhomogeneitles in the defect distribution. For example, the b e h a v i o r of b o r o n - d o p e d samples belonging to set II i n d i c a t e s the e x i s t e n c e of dangling bond-rlch regions, in w h i c h the Fermi-leVel remains pinned close to m i d g a p , apd of effectively doped regions which are responsible for the changes in electronic transport. Since the conductivity depends exponentially on the F e r m i - l e v e l position, in fact only a very small, interconnected fract i o n of e f f e c t i v e l y doped material is n e c e s s a r y to e x p l a i n our e x p e r i m e n t a l results for t y p e II s a m p l e s . Finally, a comparison of the left and r i g h t h a n d s i d e of Fig. 4 s h o w s t h a t d i f f e r e n t dopants react quite differently, when deposition conditions are changed. Thus, there Is very little difference b e t w e e n the two s e t s of samples in the case of doping with phosphorous. This, however, is no garanty that s i m i l a r e f f e c t s as s e e n f o r b o r o n - d o p i n g will not a p p e a r for o t h e r d e p o s i t i o n conditions. In s u m m a r y , we h a v e examined the o c c u p a n c y of d a n g l i n g b o n d d e f e c t l e v e l s in d o p e d a-Si:H by a c o m b i n a t i o n of e l e c t r o n spin resonance, photothermal deflection spectroscopy, and t r a n s p o r t measurements. It is s h o w n t h a t for a c o r r e c t i n t e r p r e t a t i o n of ESR r e s u l t s it is important to include the doping-lnduced increase of the defect density in t h i s m a terial. We obtain a corrected value of U = + 0 . 2 eV (±0.I eV) f o r the a v e r a g e d a n g l i n g bond correlation energy, and a position for the n e u t r a l and d o u b l y o c c u p i e d dangling bond levels at E C - 0 . 9 5 eV a n d E C - 0 . 7 5 eV, respectively. By c o m p a r i n g r e s u l t s for s t a t e - o f the-art a-Si:H samples with non-optlmlzed material, it is d e m o n s t r a t e d that large potential fluctuations c a u s e d by s p a t i a l i n h o m o geneities in t h e d e f e c t distribution c a n be present, especially in the case of boron doping.
Acknowledgements We w o u l d l l k e to t h a n k C.C. Tsai a n d R. Thompson for s a m p l e p r e p a r a t i o n . M. St. g r a t e fully acknowledges the h o s p i t a l i t y of the c o l leagues in the Xerox Palo Alto Research Center.
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References
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