HAL Id: jpa-00220804
https://hal.archives-ouvertes.fr/jpa-00220804
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A THEORETICAL STUDY OF HYDROGEN EXODIFFUSION IN a-Si : H, COMPARISON WITH
CONDUCTIVITY MEASUREMENTS
K. Zellama, P. Germain, C. Picard, B. Bourdon
To cite this version:
K. Zellama, P. Germain, C. Picard, B. Bourdon. A THEORETICAL STUDY OF HYDROGEN EX-
ODIFFUSION IN a-Si : H, COMPARISON WITH CONDUCTIVITY MEASUREMENTS. Journal
de Physique Colloques, 1981, 42 (C4), pp.C4-815-C4-818. �10.1051/jphyscol:19814179�. �jpa-00220804�
CoZZoque C4, suppl6rnent au nO1O, Tome 4 2 , octobre 1981 page C4-815
A THEORETICAL STUDY OF HYDROGEN EXODIFFUSION I N a-Si:H,COllPARISON WITH CONDUCTIVITY MEASUREMENTS
K. Zellama, P. Germain, C. Picard and B.
our don*
Groupe de Physique des Solides de Z 'ENS, Universite' Paris V I I , Tour 23, 2, place Jussieu, 7 5 5 2 2 Paris Cedex 05, France
* Laboratoire de Marcoussis, CR/CGE DMT, Route de Nozay, 91460 Pdarcoussis, France
Abstract Hydrogen evolution in a-Si:H prepared by glow discharge
decomposition of silane has been studied previously as a function of annealing temperature, using nuclear reaction, conductivity (0) and Electron
Paramagnetic Resonance (EPR) measurements. Conductivity measurements show the existence of a surface dehydrogenated layer (SDL) for T 3 500 OC. We presented a theoretical kinetic model which takes into account the existence of two kinds of site for hydrogen in the amorphous network: one site is a center from which hydrogen can diffuse, the other is a tightly bound center (corresponding to isolated Si-H bonds). This theoretical model is used here to interpret our conductivity measurements (which are sensitive to the departure of H in the Si-H configuration) for annealing temperatures above 500 'C. This allows us to describe quantitatively the SDL in the same temperature range. We then deduce the thermodynamic parameters which characterize the breaking of the isolated Si-H bond, and the possibility of trapping of a hydrogen by a Si-dangling bond. We obtain the corresponding activation energies respectively equal to 3.3 eV and 4 eV. We thus confirm the value of the Si-H bond energy and give the capture energy of a hydrogen in an isolated Si-dangling bond, which has not been previously determined.
1 INTRODUCTION
Hydrogen evolution and post hydrogenation have been quantitatively studied versus annealing temperature on hydrogenated a-Si:H prepared in various conditions (See review in Ref. 1)
.
In our case, we have studied amorphous silicon films prepared by glow diseharge decomposition of silane. We correlated nuclear profiling measurements,providing the hydrogen atomic concentration C(x) at depth x, with physical measurements
(electrical conductivity o r electron paramagnetic resonance EPR and infrared absorption IR measurements).
Conductivity measurements showed the existence of a surface dehydrogenated layer (SDL) for annealing temperature T > 450 OC.
We showed that our experimental results (EPR and nuclear profiling measurements) can be interpreted using a theoretical kinetic model of exodiffusion, which assumes the existence of two kinds of site for hydrogen in the amorphous network (this will be presented elsewhere). We are mainly interested by the departure of hydrogen for T > 450 OC.
The aim of this paper is then to demonstrate that the theoretical kinetic model allows us to interpret u measurements in the same temperature range and then to describe quantitatively the SDL.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814179
JOURNAL DE PHYSIQUE
2 EXPERIMENTAL RESULTS
In order to minimize or eliminate the Si-Hp and Si-Hg complexes, a high substrate temperature (420 to 450 "C) and low pressure (1.6
.
lo-' to 2.2- lo-'
Torr) were used during sample deposition (1,2,3).
The experimental and depositionconditions are presented in Ref.(1,4). We have measured o during isochronal runs ( 8 = 30 min, AT = 20 "C) for annealing temperatures ranging from 150 to 640 'C.
After each isochronal anneal, the sample temperature was decreased to 60 OC. In Figure 1 we plot loglo o versus reciprocal temperature (limited to TI annealing temperature) measured during this temperature decrease for T ranging from 450 to 640 OC.
Figure 1 Evolution of the behavior of the conductivity log10 o versus reciprocal temperature 1000/T for one sample after one annealing (30 min) at: A 400 OC,
0
450 OC,+
480 OC, x 500 OC, 0 5 2 0 OC,o
550 OC, A 580 OC, r 600 OC, 0 6 5 0 OC,*
670 OC,4
690 OC,o
710 OC. @ evaporated amorphous sample.Solomon et a1 (5) have demonstrated that in unannealed a-Si:H samples, the room temperature conductivity is controlled by band bending effects. In our annealed samples, we showed that room temperature conductivity is not due to this phenomenon. We showed that in such films, annealed at T > 450 OC, some of the hydrogen has diffused out of the sample from a region near the external surface. The electrical conductivity of this superficial dehydrogenated zone is much greater than the conductivity inside the film where hydrogen atoms have not diffused.
The superficial layer where the conduction mechanism takes place has an electrical conductivity close to that of evaporated amorphous silicon. Figure 1 shows that curves representing loglO o versus 1000/T for temperatures
r-' (lo3 K-I) ranging in the vicinity of room temperature, obtained after
successive isochronal anneals of the sample can be deduced from each other by translation. The behavior of loglo o versus 1000/T is the same for all the curves but the effective thickness egff of the surface
dehydrogenated layer is different and increases with the annealing temperature.
An effective conductivity is measured and given by:
where oa is the conductivity of a hydrogenless amorphous layer. It is close to the conductivity measured at 60 OC of a hydrogenated film annealed at 640 "C for 30 minutes, (Figure 1 shows that oa = 3.4 (Q cm)-I) and e is the thickness of the sample. Values of ezff deduced from room temperature conductivity measure- ments (~igure 1) using equation (1) are given in Table 1, shown versus T in Figure 2.
Table 1
3 THEORETICAL KINETIC MODEL
t d
0
I n o r d e r t o i n t e r p r e t our o r e s u l t s , we use a t h e o r e t i c a l k i n e t i c model which assumes t h a t hydrogen can occupy two k i n d s o f s i t e i n t h e amorphous network. The f i r s t ( s t a t e 1) where hydrogen atoms can d i f f u s e w i t h a d i f f u s i o n c o e f f i c i e n t D, t h e second ( s t a t e 2) i s t h e
i s o l a t e d Si-H bond, where hydrogen cannot d i f f u s e . L e t C1 = C l (x, t ) and C2 = C2 (x, t ) b e t h e hydrogen c o n c e n t r a t i o n s r e s p e c t i v e l y i n s i t e s 1 and 2, a t d e p t h x and time t. These c o n c e n t r a t i o n s obey t h e f o l l o w i n g e q u a t i o n s ( 6 ) :
-
1C
450 , , , ,Lo, ,
, , 5 50,
,, ,
, 600,
= ax2 - K l C l+
K2.2 andT P C ) - = ac2
a t +
KlCl-
K2C2 (2)s :
where K1 and K2 a r e t h e frequencies c h a r a c t e r i z i n g r e s p e c t i v e l y t h e t r a n s i t i o n from s t a t e 1 t o s t a t e 2 and t h e i n v e r s e t r a n s i t i o n . Considering t h e f o l l o w i n g i n i t i a l c o n d i t i o n s Cl(x,t=O) = C1O, C2(x,t=O) = C20 and t h e boundary c o n d i t i o n s of
e x o d i f f u s i o n f o r hydrogen i n t h e d i f f u s i n g s t a t e : f o r t > 0, Cl(x=O,t) = 0,
= 0 t h e s o l u t i o n s f o r t h e d i f f e r e n t i a l _ s y s t e m (2) a r e given by:
x=e ; clth ( x . t . ~ ) = ~ l t h ~ X , K L T ) , K ~ ( T ) , K ~ L T ) ) =
+
L -!-- 51" (2m + 1 )2
f m ( t ) (3' m=O ( 2 W l )c 2 r n ( x , t . ~ ) = c 2 t h ( x , K ( T ) , K~ (TI, K ~ ( T ) ) = =,
C
2 ( 2 m t l ) sm ( 2 m + 1)2
g m ( t ) 141~11th f m ( t ) and g m ( t ) respectively equal to:
f,(t) =
&
{(-Km - h"m) [C1O + C 2 0 ( e i m m tK1
+ ( A 1 m + ~ m ) [ C ~ O + C Z ~ ( h"m ) I eAabmt
K1 1 , and
9 , ( t ) = i K l * = l o + C 2 0 ( - 1 1
K1
1
15)-
K1 [ c l o + c 2 0 ( Xllm+ K1 1 1 eAnnrnt 1w h e r e A'm, A s h and Km are respectively given by: - -tKm + Kzl
' '
'2)2 - 4(KmK2 - KIKZ'X"m - 2
and = K 1 + ~ { ( 2 m + l ) L l ~ = K ~ + K ( ~ ~ + I ) ~
2 e
We t h e n deduce t h e t o t a l c o n c e n t r a t i o n of hydrogen:
We s h a l l u s e t h e s e r e s u l t s t o d e s c r i b e t h e c o n d u c t i v i t y measurements and t h e SDL.
4 COMPARISON OF THEORETICAL MODEL WITH EXPERIMENTAL RESULTS (T 3 500 O C ) F i g u r e 1 shows a n i n c r e a s e on two o r d e r s of magnitude o f a measured a t 60 'C f o r a n n e a l i n g t e m p e r a t u r e s r a n g i n g from 450 t o 640 "C. The c o r r e l a t i o n between c o n d u c t i v i t y and EPR measurements (1) allowed u s t o show t h a t i n t h i s t e m p e r a t u r e r a n g e t h e i n c r e a s e o f u i s due t o d e p a r t u r e o f hydrogen r e l e a s e d from i s o l a t e d Si-H bonds ( s t a t e 2)
,
whose c o n c e n t r a t i o n i s C2Th (x, t = O ).
I t i s r e a s o n a b l e t o admit t h e e x i s t e n c e o f a c r i t i c a l c o n c e n t r a t i o n (we s h a l l c a l l t h i s ~ s r i t ) o f t i g h t l y bound H i n t h e l a y e r , below which one b e g i n s t o o b s e r v e an i n c r e a s e i n u . T h i s should b e i n agreement w i t h t h e Brodsky model (71, which assumes t h a t t h e r e i s a p e r c o l a t i o n mechanism between dehydrogenated zones c o n t r i b u t i n g t o t h e conduction.The SDL model i m p l i e s t h a t i f :
JOURNAL DE PHYSIQUE
crit crit
CgTh(x,t) < Cg
,
then a = oa; and CgTh(x,t) > C2,
then o = oSiH, where oSiH is the conductivity of the hydrogenated layer. On the other hand, equation(1) provides an effective thickness ezff of the dehydrogenated layer for each temperature. In Figure 3 we present the variations of C2Th(xrerT) versus X, as well as the straight line csrlt = 0.0135. The physical meaning of this value is discussed elsewhere. The intersection of the line with curves C ~ T ~ ( X ~ ~ , T ) allows one to define a theoretical effective thickness e& = eth for each temperature.
AS CZTh(~,er~) involves three parameters, K (K == D/4e2), KI and Kg, we have to calculate these parameters for annealing temperatures ranging from 500 to 640 "C.
We look for the best agreement between egff and eTh. values of e ~ h are given in Table 1 and presented in Figure 2 versus T. Values of K, K1 and K2 obtained from the comparison between experiments and theory are given in Table 1 and plotted in Fiaure 4 versus reciprocal temperature.
0 0.20 MO OM] 080 1
RELATIVE DEPTH
Figure 3 Variation of C2,h (x, 6 ,T) versus relative depth.
The
dottedline represents chrit = 0,0135
Figure 4 Variations of logl 0 K(x)
,
logl l C 1 ( 8 )and loglo Kp(+) versus reciprocal temperature.
The upper and lower straight lines correspond res- pectively to log10K and log10K2 presented in Ref.(l).
5 DISCUSSION AND CONCLUSION
I " ,
,\,
, ,'<I 1.2 13 14 15 1.6
T-I (lo3 K-I )
Flgure 4 shows that K, K1 and Kg are thermally activated with activation energies respectively equal to 1.32, 4 and 3.3 eV. It appears that the activation energies associated with K and Kg are in correct agreement with those obtained using the simple kinetic model presented in Ref.(l). On the other hand, it seems that the activation energy associated with K1 (corresponding to the capture of H atoms in an isolated Si dangling bond) is slightly higher than that of K2.
The few values of K1 do not allow us to define the activation energy with great accuracy. We shall calculate elsewhere values of K1 by comparing the complete kinetic model presented here with results of nuclear reaction, o and EPR
measurements. These values of K1 will confirm those obtained here by o measurements.
1 ZELLAMA K., GERMAIN P., SQUELARD S., BOURDON B., FONTENILLE J. and DANIELOU R., (in press) Phys-Rev-B (1981)
2 BRODSKY M.H., Thin Solid Films
40
(1977) L23 3 BRODSKY M.H., Thin Solid Films50
(1978) 574 ZELLAMA K., GERMAIN P., SQUELARD S., MONGE J. and LIGEON E., J-Non-Cryst-Solids 35 and
36
(1980) 2255
SOLOMON
I., DIETEL T. and KAPLAN D., J-Physique39
(1978) 12416 SHAW D., Atomic diffdsion in semiconductors edited bv D. Shaw 1st Edition (Plenum Press London and New York) (1973) 273
7 BRODSKY M.H., (in press) Solid State Com.
