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THE DIFFUSION OF HEAVY ALKALI ATOMS IN AMORPHOUS SILICON
M. Reinelt, S. Kalbitzer
To cite this version:
M. Reinelt, S. Kalbitzer. THE DIFFUSION OF HEAVY ALKALI ATOMS IN AMORPHOUS SILI- CON. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-843-C4-847. �10.1051/jphyscol:19814186�.
�jpa-00220812�
THE D I F F U S I O N OF HEAVY A L K A L I ATOMS I N AMORPHOUS S I L I C O N
M. Reinelt and S. Kalbitzer
Max-PZanck-Institut fiir Kemphysik, 0-6900 Heidelberg, F. R. G.
Abstract.- The diffusion of K, Rb, and Cs has been studied by implantation of low energy ions into a-Si and using high-resolution Rutherford backscattering for measurement of the resulting profiles. The diffusion is many orders of magnitude slower than in c-Si. Trapping and detrapping effects have been ob- served. Trap depth and average distance have been estimated. a-Si appears as an inhomogeneous solid consisting of a disordered bulk with voids embedded
Introduction.- There is little information on atomic transport processes in-a-Si.
Except for the effusion of H from a-Si:H (1,2) no quantitative data have been re- ported so far. To the best of our knowledge, diffusivities of a few elements, such as B and P, have been quoted for a single temperature (3) only. Thermodynamic quan- tities, such as activation energies and entropies, are not known for any system other than H/a-Si.
Besides the need of knowing the thermal stability of dopants for device produc- tion, e.g., of ion-implanted contacts in amorphous solar cells ( 4 ) , there is basic interest In atomic transport processes in amorphous semiconductors. Diffusing atoms probe the latt~ce potential and yield information on the structure. In particular, by comparison with the corresponding data on a crystalline system, the specific dif- ferences due to the disordered arrangement of the lattice constituents should be re- vealed.
For this study, we have chosen the heavy alkali atoms, in particular K, for the following reasons. K is known to be a fast interstitial diffusor in c-Si with an activation energy of about 0.8 eV and a "normal" prefactor of cm2/s ( 5 , 6 )
.
Incontrast to substitutional impurities like B and P, whose diffusion mechanism is still a matter of debate, this system constitutes the possibly best understood case.
Consequently, a comparison of K/c-Si and K/a-Si should be subject to less uncertainty than any of the other systems.
On the experimental side, the diffusion of K in a-Si can be measured very accu- rately by employing high-resolution Rutherford backscattering techn~ques. If, as first qualitative investigations have shown, diffusivities are rather low, then depth resolutions of the order of 10 are required. In this way diffusion constants as low as cm2/s can be measured.
Experimental.- The majority of our measurements was performed on H-free a-Si prepared by ~ i + irradiation of pure monocrystalline Si. By using a dose of 3 x lo1' si+/cm2 at 50 keV an amorphous layer about 1000
a
thick formed on top of the thick crystal- line substrate. SubseqGently the desired atomic species was implanted into the amor- phous top layer. Here typically an areal dose of 10~%~f/cm~ at 5 keV was implanted.The resulting Gaussian-like profile peaks at about 100 depth with a distribution of about 100 fi wldth (FbJHM). By varying the implanted dose a possible concentration de- pendence could be ruled out. Elore generally, no indication of deviations from regu- lar diffusion behavior has been observed, so that the use of the mathematical solu- tions to Fick's second law is justified.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814186
C4-844 JOURNAL DE PHYSIQUE
I
0 a s implanted
o anneaied a1 375'C 209h
--theory ~ z 1 . 3 x 1 0 " ~ crn2/s
0 0
V
-
m
#
m
*
0
-
Fig. 1 : Initial implanted pro- file and diffused profile; the diffusion length is about 60 corresponding to a diffusion co- efficient of about lo-'' cm2/s.The computer fit to the measured diffused profile is shown by the solid line.
0 100 200 300
DEPTH (1)
Figure 1 shows one example of an implanted and subsequently diffused K profile.
By applying the well-known solution for a diffusion system with a surface sink
-1/2 2 2
~ ( x , t ) = (4,rrDt) ~~iV(~,~){exp[-(S-x) /4~t] - [exp - (E+x) /4~t]}dS ( 1 )
the corresponding diffusion constant was evaluated as D = 10-l' cm2/s. This was done by applying equation 1 to each individual data point and by varying D until the re- sulting curve gave an optimum fit to the measured diffusion profile. The advantage of this technique is that any profile shape is tractable. Details on our Rutherford hackscattering setup may be found elsewhere (7).
Results.- It was found from isothermal annealing that the diffusivity slowed down with time and finally saturated at a value of up to 2 orders of magnitude below the initial value. This effect is shown in figure 2. Figure 3 is a compilation of all
Fig. 2 : Apparent diffusion coefficients, as derived from isothermal annealing treat- ments, vs. annealing time for different temperatures.
apparent diffusion coefficients, D*, in an Arrhenius plot. The upper straight line bounds the values of D* obtained for the smallest possible annealing times, whereas the lower one represents the saturation values. The data between were obtained for intermediate points in time and tend toward the lower boundary. The situation is very much the same for a-Si:H. Beyond about 600°C the samples recrystallize (8) and diffusion takes place in a defect-rich crystalline lattice. A comparison with the K diffusion in c-Si is made in figure 4, where the corresponding H data are also in- cluded (M. Reinelt, F.J. Demond, G. Miiller. and S. Kalbitzer, unpublished data).
Discussion.- The explanation of the observed phenomena will be based on the concept of an inhomogeneous amorphous system consisting of disordered bulk material into which voids are embedded. This model has been used before to interpret electronic transport patterns in the same kind of material ( 9 ) . The conclusion was that the material resembles granular disordered systems where striking similarities in the electrical transport parameters exist (10).
K/a-Si and K/a-Si:H. With i n c r e a s - i n g a n n e a l i n g time t h e p o i n t s t e n d from t h e upper t o t h e lower l i m i t - i n g s t r a i g h t l i n e . The dashed l i n e r e f e r s t o Dl ( t + 0 )
.
F i g . 4 : Comparison of t h e d i f f u - s i o n of both K and H i n c-Si and a-Si. The t h i c k p a r t s of t h e l i n e s denote t h e range of t h e measure- ments.
F i g . 5 : Model scheme f o r t h e d i f - f u s i o n i n an amorphous two-phase s o l i d c o n s i s t i n g of a d i s o r d e r e d bulk w i t h f l u c t u a t i n g atomic po- t e n t i a l s i n t o which v o i d s a r e em- bedded. A f t e r d i f f u s i n g a c e r t a i n l e n g t h i n t h e bulk t h e p a r t i c l e s become t r a p p e d a t t h e v o i d s . F i g u r e 5 i s a schematic i l l u s t r a t i o n of t h e assumed model. The numerical v a l - u e s have been d e r i v e d from t h e s e and o t h e r measurements and w i l l be d e a l t w i t h i n t h e following. F i r s t , i n q u i t e g e n e r a l t e r m s , f i g u r e 5 r e p r e s e n t s t h e f r e q u e n t l y encountered c a s e of d i f f u s i o n i n t h e presence of t r a p s which h a s been t r e a t e d theo- r e t i c a l l y (11-13). The d i f f e r e n c e from c r y s t a l l i n e systems i s t h e f l u c t u a t i n g atom- i c d i s o r d e r p o t e n t i a l which may vary from one l a t t i c e p o s i t i o n t o t h e next by some f r a c t i o n . I t w i l l l e a d t o an e f f e c t i v e average a c t i v a t i o n energy ( f o r t h e " f r e e "
d i f f u s i o n o u t s i d e t h e t r a p s ) which i s h i g h e r t h a n f o r t h e p e r i o d i c p o t e n t i a l of a s i n g l e c r y s t a l . By comparing t h e corresponding d i f f u s i o n regimes i n c-Si and a-Si
( f i g u r e 4 ) we n o t e t h a t t h e e f f e c t i v e p o t e n t i a l b a r r i e r i s s u b s t a n t i a l l y h i g h e r i n t h e d i s o r d e r e d m a t e r i a l . C o r r e c t i o n s of Q1 based on t h e e x t r a p o l a t i o n D ( t - + O ) show t h a t 1.3 eV i s a lower l i m i t . Due t o u n c e r t a i n t i e s i n t h i s procedure t h e c o r r e c t e d value cannot be s t a t e d more p r e c i s e l y t h a n Q = 1 . 5 t 0.2 eV. The concomitant changes i n t h e p r e f a c t o r a r e q u i t e l a r g e : D o l = 1 & 6 + 1 . s cm2/s. The p r e f a c t o r becomes understandable i n t h e upper l i m i t a l t h o u g h it i s s t i l l on t h e low s i d e . Entropy changes by S = -6 k , though n o t s o common, have been observed i n a v a r i e t y o f systems, i n p a r t i c u l a r f o r p l a s t i c a l l y deformed and amorphous m e t a l s (18-20).
The d i f f e r e n c e i n t h e a c t i v a t i o n e n e r g i e s f o r K i n a-Si and c-Si amounts t o Q = 0 . 7 5 f 0.25 eV. T h i s v a l u e i s q u i t e l a r g e ; it means t h a t t h e e f f e c t i v e b a r r i e r s i n t h e d i s o r d e r e d system a r e about twice a s h i g h a s t h o s e i n t h e c r y s t a l l i n e materi- a l . From t h e observed time dependence of t h e d i f f u s i v i t y i n t h i s temperature regime it i s concluded t h a t t h e f r e e ( i n t e r s t i t i a l ) m i g r a t i o n of K i s t e r m i n a t e d by t r a p p i n g
C4-846 JOURNAL DE PHYSIQUE
A rough estimate of the corresponding diffusion length L and the average distance of the traps
A$
(figure 5) can be made from Xb- 2L= 2 x 2(Dltb)'/' where D l is the dif- fusion coefficient for free migration and tb a characteristic time for the slowing down of the apparent diffusivity. It follows from our data that, at all temperatures in this regime, Ab-
80-100i.
This is in fairly good agreement with the conclusions from our electronic transport measurements (9) where tunneling of electronic charge carriers between microvoids has been postulated.As indicated in figure 5, the activation energy Q2 is the sum of the trap depth, QT, and the activation energy for free diffusion,
el.
With reference to the assumedinterstitial position of K, the trap depth amounts to about 1.5 eV with an estimated uncertainty of about 0.5 eV. If one uses the results from our electronic transport and swelling measurements (9,16), then the mean void size should be of the order of dT- 2rT
-
30-100f i .
Also, when we use Xb-
90i
fromour diffusion data and AV/V-
1%from the observed swelling for the c + a transition, then again we obtain 25 from the relation d~ = Xb/ ( (V/AV) 1/3 - 1)
.
This size should be sufficient to put the K atoms into an energetic position similar to the vacuum level.The prefactor for the detrapping process assumes the value Do, = 2X 102'1.5 cm2/
s. Theory predicts Do2 = D O l/fT, where fT denotes the fraction of traps (11)
.
Usingthe relation fT= a2/hg (171, with a = 2.35
&
and Xb = 908 ,
we find fT-
lo-', whichcorresponds to an enhancement by 10' in the prefactor. Unfortunately, the uncertain- ties in both Dol and Do2 are rather large, so that a quantitative check is not possi- ble. Thus, we just note that the upper limit D o l = 1 x lo-' cm2/s would give D o 2 = 1 cm2/s, which is the lower limit of the observed value.
A corrparison of the diffusion of K with the heavier alkali elements is given by the table below.
It is seen that the apparent diffusion coefficients D* are appreciably smaller for Rb and Cs than for K. In view of the larger atomic dimensions of the heavier s ecies, this is a plausible result. At room temperature a diffusion coefficient of lo-"
cm2 s-' or less will be sufficient to prevent redistribution processes over dis- tances larger than a few atomic spacings over a time span of 10 years. Extrapolation to room temperature shows that all three alkali species may safely be used at ambi- ent temperatures. Processing steps at elevated temperatures, say at maximum 400°C, have to be restricted to less than 1 h for K and 5-10 h for Rb and Cs, if diffusion lengths of about 10 can be tolerated. It rather appears from figure 4 that H, which is of key importance for the electronic quality of the a-Si material, is the more critical species as regards diffusive redistributions.
As regards the lightest alkali species, rough estimates based on literature val- ues (14,15) indicate that Li diffuses more slowly in a-Si than in c-Si by about 5 orders of magnitude. This result follows the trend reported here. Although Li acts as an efficient donor type impurity in gd-a-Si, its use for devices is impractical since the absolute value of its diffusivity is too high to allow for long-term sta- bility.
Conclusions.- The diffusion of K, Rb and Cs in a-Si is reduced by many orders of magnitude as compared to c-Si. Free diffusion, very likely of the interstitial type, is terminated by trapping. Detrapping occurs at higher temperatures. Devices doped with these he'avy alkali elements are expected to have long-term stability. In gen- eral, limitations to temperature treatments set by diffusional motion appear to af- fect hydrogen prior to these impurities.
CARLSON, D.E., and MAGEE, G.W., Appl.Phys.Lett.
2
(1978) 81.ZELmlA, K., GERMAIN, P . , SQUELARD, S., BOURDOPJ, B., FONTAILLE, J., and DANILON, R., Phys.Rev. 1981 (in press).
CARLSON, D.E., LJRONSKI, C.R., PAPJKOVE, J.I., ZANZUCCHI, P.J., and STAEBLER, D.L., RCA Review
3
(1977) 211.SPEAR, N.E., and KALBITZER, S., EEC Report, Naples, Plarch 24-26, 1981;
GIBSON, R.A., YOUNG, D., LeCOMBER, P.G., SPEAR, W.E., MULLER, G., and KALBITZER, S., this conference.
WOLF, H.F., Silicon Semiconductor
Data,
Pergamon Press (1969), p.136.SVOB, L., Solid State Electronics
10
(1967) 991.KALBITZER, S., FEUERSTEIN, A., GRAHhlANN, H., and IJITTNER, J., Proc. IV Conf.
Scientific
and
Industrial Applications of Small Accelerators, Denton 1976, The Institute for Electrical and Electronic Engineers, p.403.PRISSLINGER, R., KALBITZER, S., KFL~~.?CLE, H., GROB, J.J., and SIFFERT, P.,
Proc.
IV Conf. Ion Implantation
%
Semiconductors, Osaka 1974, Plenum Press, p.547.---
PFEILSTICKER, R., KALBITZER, s., and MULLER; G., Proc. 11 Int. Conf. Ion Beam Modificationof
Materials, Albany 1980, Nucl.Instr.flethods 1981, in press.ABELES, B., SHENG, P., COUTHS, M.D., and ARIE, Y., Adv.Physics
2
(1975) 407.NORGETT, M.J., and LIDIARD, A.B., Phil.Mag.
18
(1968) 1193.GAUS, H., Z.f.Naturf. (1968) 985.
ORIANT, R.A., Acta !let.
18
(1970) 147.BEYER, W., and FISCHER, R., Appl.Phys.Lett.
2
(1977) 850.PELL, E.M., Phys.Rev.
119
(1960) 1014.MULLER, G., and KALBITZER, S., Phil.Mag.
41
(1980) 307.MATZKE, Hj., and SPRINGER, F., Rad.Effects
2
- (1969) 11.BOLTAKS, B.I., Diffusion
2
Semiconductors, Infosearch (19631, p.235.ZENER, c., Imperfections in Nearly Perfect Crystals, J. Wiley and Sons (1952), 0.289.
20. DIENES, G.J., J.Appl.Phys.
