Journal of Non-Crystalline Solids 50 (1982) 139-148 North-Holland Publishing Company
PHOTOLUMINESCENCE OF HYDROGENATED AMORPHOUS SILICON
** a n d F e r d W I L L I A M S
Physics Department, University of Delaware, Newark, Delaware 19711, USA Received 5 June 1981 Revised manuscript received 30 December 1981
Photoluminescence has been proven to be a powerful technique in the characterization of a-Si:H. In particular, it has contributed to the elucidation of some aspects of the electronic structure. However, there is a set of controversial topics still under discussion including the identity of the luminescent transition and the origin of broadening of the emission spectrum. In this paper we study these problems and show that the specified width has its origin in both disorder and electron-phonon interaction. Luminescent decay at low temperature has been studied and lifetimes from 10 -s to 10-2s have been confirmed. Photoconductivity and photoluminescence are shown to behave in a complementary way and activation energies for both processes are obtained. Also, the photoluminescence quenching and photoconductivity enhanced under an applied electric field have been measured and interpreted.
1. Emission width: temperature broadening T h e b r o a d e m i s s i o n p e a k at 1 . 2 0 - 1 . 3 0 eV is well e s t a b l i s h e d in a-Si: H . S i n c e this m a t e r i a l has b e e n s t u d i e d , the i n c r e a s e in e m i s s i o n w i d t h w i t h t e m p e r a t u r e a b o v e 100 K has also r e c e i v e d a t t e n t i o n . S t r e e t  was the first to i d e n t i f y a n e l e c t r o n - p h o n o n i n t e r a c t i o n g i v i n g a S t o k e s shift of 0 . 4 - 0 . 5 eV d u e to the s e l f - t r a p p i n g of e x c i t o n s b o u n d to b a n d tail l o c a l i z e d states. W e s t u d i e d the p h o t o l u m i n e s c e n c e e m i s s i o n b r o a d e n i n g w i t h t e m p e r a t u r e a n d f o u n d a S t o k e s shift of 0.95 eV. I n a d d i t i o n to t h e e f f e c t o f the e l e c t r o n p h o n o n i n t e r a c t i o n , t h e r e is e v i d e n c e t h a t d i s o r d e r c o n t r i b u t e s to the e m i s s i o n b a n d w i d t h . Fig. 1 s h o w s e m i s s i o n w i d t h v e r s u s t e m p e r a t u r e . If the e l e c t r o n - p h o n o n i n t e r a c t i o n is p r e s e n t , the l i n e s h a p e in t h e e m i s s i o n
* Based on the PhD dissertation of Fernando Atvarez; supported in part by a grant from the Department of Energy to the Institute for Energy Conversion, University of Delaware and in part by a grant from the Army Research Office, Durham to the Physics Department, University of Delaware. ** Present address: Universidade Estadual de Campinas, Instituto de Fisica, 13100 Campinas, S.P., Brazil. 0022-3093/82/0000-0000/$02.75
© 1982 N o r t h - H o l l a n d
F. Alvarez, F. Williams / Photoluminescence of a-Si: H
AT HALF MAXIMUM
i~ EXPERIMENTAL • FITTED eo75K
• FITTED 0o=350K eo='tl ~o/2k
Fig. 1. Width versus temperature.
is a gaussian. The temperature dependence of the e x p [ - - ( E / % ) 2 ] , is given by the H u a n g - R h y s equation 
% ( T ) / % ( 0 ) = coth'/2( Oo/kT),
where 00 = hf~o/2k, %(T) is the emission width at T K, %(0) is the emission width at T = 0 K, and hf~ 0 is the phonon energy. It was pointed out by Austin et al.  that the attempt to fit eq. (1) to experimental data, using A(0) = 0.26 eV (extrapolating fig. 1 to T = 0) produces the curve represented by the small triangles. Here A is the full width at half maximum in the emission spectrum and is, of course, simply related to the Gaussian width: A = 2o(1n2)1/2. The difference with experiment is evident. The associated phonon energy is: h~ o = 60 meV. However, the broadening is also produced by disorder. Assuming independent gaussian distributions in energy due to disorder and due to electron-phonon interaction, the total width is approximately  72 = Op2+ odz ,
where oe is the gaussian width due to disorder. With this idea in mind, we can interpret the experimental width A(T) as the full width at half maximum due to electron-phonon interaction and disorder. Using a computer program the open squares are fitted to the experimental points (fig. 1). The resulting curve gives Ap(0).~ 0.20 eV and a phonon energy hf~o = 14.6 meV. Substituting this value and A(0) = 0.26 eV in eq. (2): A~ = A2 -- AZp= 0.0276 eV. From the relation between the gaussian width and the half width, we find: oa .~ 0.098 eV. On the other hand, the relation between the gaussian width op and the Stokes
F Alvarez, F Williams / Photoluminescence ofa-Si." H
shift is : O'p---- (Wsh~'~0) 1/2,
where Ws is the energy displacement between emission and absorption spectra (Stokes shift) and h~20 is the phonon energy. Thus, the Stokes shift is: Ws = 0.95 eV. This value is larger than that estimated by other workers as noted earlier. The explanation for the discrepancy may be that Street  used absorption and emission data in his analysis and we estimated the Stokes shift from the temperature dependence of the width of the emission spectra. From these results the fractional parts of the experimental band width A(0) from phonon broadening and from disorder are found to be 0.55 and 0.45, respectively.
2. Luminescence decay Many workers have reported lifetime measurements on a-Si:H. Engemann et al.  have reported lifetimes of 20 ns. Austin et al.  have measured radiative lifetime decay between 2 ns and 20 #s. Extending the studies to longer times, Tsang et al. , showed the existence of a broad distribution of lifetimes from l0 2 to l0 -8 s. Also, they found a correlation between fast and slow decay components and steady-state photoluminescence efficiency (see fig. 2). This relation, I r, is defined by extrapolating the approximately exponential tail decay at 20-50 /~s to t = 0 and then dividing this by intensity for the actual value at t = 0 (see fig. 3A). From fig. 3A, I r = 0.07, and this figure is representative of device grade material. In what follows we derive an equation for the decay of intensity. Assuming monomolecular recombination the number of filled centers after a pulse of T s is : n(z, T ) -- ~z[1 - e x p ( -
where ~ is the incident photon flux, z is the center characteristic lifetime, and T is the width of the excitation pulse. Following Tsang et al. , one can assume
RELATIVE LUMINESCENCE I/I o
AMORPHOUS Si SAMPLE 79-101
Fig. 2. Photoluminescence relative efficiency.
F. Alvarez, F. Williams ,
Photoluminescence of a-Si." H i
T =IOK EXCITATION=5145~,
EMISSION : 133eV
1o5 • %
T=IOK A=5~45~ EMISSION 1 3 3 e V
" .-...v,., (~)
EXCITATION 5145 ~, I
Fig. 3(a). Lifetime decay, log 1 / 1 o versus t.
Fig. 3(b). Lifetime decay, log 1 / 1 o versus log t.
DEC..A¥ PLOT &LY I01 El.= EMI.~SIOH
"l'o~E ('~ec) -8
l lO 3
•.:..o • :.:'...~.. • .... .'.,: .j: •7: . t01 •"".:-..., • ..:..
EL--- ~,. 35 e v
~0 ° o
.:.:° ""c. ...-..
Fig. 3(c). Lifetime decay, log 1 / I o versus log t (extended scale).
F. Alvarez, F. Williams/ Photoluminescenceof a-Si: H
a model of distribution G(r) of radiative lifetimes. From eq. (1) the number of filled centers with lifetimes between r and r + d r is therefore: n ( r , T) d r = ~[G(~') dr] r[1 - e x p ( - T/r)].
The photoluminescence intensity t s after the excitation is switched off will be :
f0 n(~-,T) + e-'/'d~-.
Substituting eq. (5a) in (5b):
If the time, t, is much longer than T, i.e. T i t << 1, eq. (6) can be approximated by:
I(t, T) ~ q,f0°°[G(~')/r] e x p ( - t / r ) dr.
It was pointed out by Searle  that the shortest components can be eliminated provided that T >>~-. Experiments were performed using time scales from 1 #s to 1 ms. Fig. 3b shows results from one such experiment. The excitation pulse in each case was approximately ~0 of the total time scale. The decay covering the total time, from 10 - 2 to 10 8S w a s constructed by matching them on log-log paper. In this fashion, the fast decay components were eliminated and fig. 3C shows the long lifetime components for short excitation pulse. In principle eq. (1) can be numerically inverted and the distribution obtained. Formally, the Laplace transform is: 1
rG(r) =~-~i Ja_i~ I ( t ) e / dt.
The numbers of centers with lifetimes between r and r + d r is:
G(r) d r = r G ( r ) d(lg ~'). Thus, the long lifetimes found experimentally justify of G(~-). In order to obtain the most probable r, one approximation . Assuming l ( t ) ~ l / t , (where/3 is of t) the Laplace transform is, eq. (8), (standard edition):
• a(~) = kr'
(9) looking for r G ( r ) instead can make the following a slowly varying function Math tables, CRC, 25th
where k is a constant. Taking the derivative with respect to fl, one can find the value of /3 for which eq. (I0) is maximal and it is unity. Inspection of fig. 3C shows that the region where the slope is minus one lies between 10 - 2 and 10 4 s. Thus, the maximum contribution in the distribution will be about 10 -2 to
F. Alvarez, F. Williams / Photoluminescence of a-Si : H
10 -4 S. The broad distribution of lifetimes and the long lifetime are explained by assuming a model of radiative recombination by the tunneling of electronhole pairs with weak overlap of the wave functions. The recombination rate thus has the following R-dependence : (11)
where R is the carrier separation, R o is the Bohr radius of the larger wave function and % is 10-8s , which shows that the distribution in lg~-/% is given by the distribution in the electron-hole separation. The average distance is obtained substituting • ~ 10-3s for the estimated average lifetime. The distance between carriers that will recombine radiatively is estimated from the activation energy for quenching, as shown in detail in section 3, 50 ~,. Substituting in eq. (11), R 0 ~ 10 ~,. This value is close to that estimated by Tsang et al.  of 12,~. Also this value is the estimated dispersion in the wave functions for carriers in band tails for amorphous materials .
3. Photoluminescence, photoconductivity and electric field quenching In fig. 4 the photoluminescence and photoconductivity for different temperatures are plotted. The photoluminescence is defined relative to the intensity at temperature 4 K and the photoconductivity is that relative to the conductivity at room temperature. It was observed that no change in the shape for different excitation intensities occurred. The excitation radiation was provided by an argon laser, using the green
PHOTOLUMINESCENCE ~p ARB, UNITS
IO5 l i T
- 0.028 (ev) kT • O.060(ev ) 7~p =Bexp kT 7/c=Aexp
Fig. 4. Photoluminescenceand photoconductivityefficiencyversus 1/T.
F. Alvarez, F. Williams / Photoluminescence of a-Si: H INTENSITY
(ARB. UNITS) o-Si SAMPLE 79-t01
50 TEMF~ 77K
Fig. 5. Electric field quenching of luminescence.
5145.~ line. The power impinging on the samples was - 7 5 mW and so the photons flux - 4 × 1017 (photons/s). In fig. 5 both curves show activation energies in the thermal quenching region of ~ 0.060 eV and ~ 01030 eV for photoluminescence and photoconductivity, respectively. They are complementary in the sense that an electron-hole pair (created by the excitation) can contribute to a radiative emission by recombination or they can be separated contributing to conductivity. If the carrier separation is r0, assuming a coulombic interaction, the associated energy with the carriers is: E o = eZ/4~rc%ro,
where e is the electron charge, c is the dielectric constant and c o is the permittivity of free space. Also, assuming a coulombic barrier the Boltzmann factor for the escape probability is Pe = constant × e x p ( - E o / R T ).
From this interpretation and substituting the activation energy 0.030 eV (from fig. 4) in eq. (12), one can obtain the critical distance R c, which is the limit between the radiative and non-radiative recombination. Using c = 10, the result is Rc-~ 50,~. Focusing our attention on the quenching of emission intensity with an applied electric field will help in the understanding of the origin of the photoluminescence in a-Si: H. Fig. 5 is a plot of the integrated intensity versus applied voltage at 77 K. Fig. 6 is the set-up used in this experiment. There is a stronger quenching in the higher energy radiative components of the spectrum (fig. 7).
F. Alvarez, F. Williams / Photoluminescence of a-Si : H
INTENSITY (ARB UNITS) SAMPLE 79-304 V=APPLIED VOLTAGE
VI =0 VOLT //~1 V2 =2.5 [[[~1
II1 \1 IlY..\ & IIIAII
THICKNESS =6000A \GLASS ~ /ALUMINUM
h?2 EXCITATION \ SEMITRANSPARENT CONTACT
v 6 =zo.o
v :2 .o
V8 =30.0 /
Fig. 6. Amorphous silicon sandwich used in the electric field quenching experiments. Fig. 7. Photoluminescence spectra for different applied electric fields.
If in addition to the coulombic potential there is an applied voltage eq. (12) is modified to:
f ( r ) -- ( e2/4crCCo r) + eFr,
where F is the applied electric field. The resultant potential has a m a x i m u m at
E* = ( e3/~rc% ) ' / 2 F '/2
r2m= ( e2/4~r,% ) ( 1 / e F ).
Thus, the coulombic barrier is lowered proportional to F 1/2 and one can expect a change in the Boltzmann factor for the probability to escape as a consequence of it. Eq. (13) is rewritten:
Pe constant × exp(--E0/kT) exp =
It was shown that for an activation energy of E 0 = 0.030 eV for the coulombic attraction energy the radius was R c = 50,&. The electrical field lowers the barrier. F r o m r m = 50,& interpeted as the distance to the m a x i m u m in the barrier we can determine the m i n i m u m electrical field F m which quenches the luminescence. The photoconductivity is thus enhanced. Substituting this value for r m in eq. (16)
F m = (e/4er,,o)(1/r2m) ~ 10' V / c m .
IE Alvarez, F. Williams / Photoluminescence of a-Si." H
From fig. 6 the interception of both asymptotes gave F m ~ 105 V/cm. The results are the same because equal activation energy is involved in field quenching and in thermal quenching of luminescence, and the assumption seems to be correct. For greater values of F m the photoluminescence efficiency is quenched and the photoconductivity is enhanced. Now, we turn to the interpretation of the slopes in the efficiencies. The photoconductivity is an activated process proportional to n, the concentration of electrons in the extended states n = kexp(-Eo/kT
On the other hand, the photoluminescence is proportional to n 2 (bimolecular recombination process) because of the high excitation intensity to be discussed later. The intensity of luminescence will be: L = k n z = k exp( - 2 E o / k T )
and the activation energy for the photoluminescence is twice the activation energy for photoconductivity. The experimental data of fig. 4 are in accord with this interpretation. The bimolecular process is a consequence of the high density of carriers. Otherwise, the recombination process is geminate. We have shown that a distance less than or equal to ~ 50 A is necessary in order to have a geminate radiative recombination, that is, electron-hole creation and annihilation without intervening electron-hole separation. This critical distance represents a density of carriers of ~ 2 × 1018/cm3. Indeed it is the limit where the recombination starts to be bimolecular .
4. Conclusions The photoluminescent spectrum of a-Si: H peaks at 1.3 eV, substantially less than the optical gap of 1.68 eV. The transition energy and spectral width are characteristic of an extrinsic transition between localized states. Analysis of the dependence of emission band width on temperature indicates both homogeneous broadening due to electron-phonon interaction and inhomogeneous broadening due to disorder. Time-resolved spectroscopy also reveals a broad distribution of radiative lifetimes indicative of a distribution of centers, consistent with the inhomogeneous broadening and with tunneling recombination. From these data plus thermal and electrical field quenching measurements, we estimate that the electron-hole distance for recombination is - 50 ,~ and their effective Bohr radii are - 10 ,~. A red shift with electrical field is consistent with the extrinsic character of the luminescent transition and with the distribution of centers responsible for the inhomogeneous broadening. Photoconductivity and photoluminescence complement each other as a function of temperature. The activation energy for the quenching of photoluminescence is found to be twice that for the enhancement of photoconductiv-
F. A Ivarez, F. Williams / Photoluminescence of a-Si: H
ity as a function of temperature. These results can be explained on the basis of photoluminescence being bimolecular recombination, i.e. proportional to n 2, and photoconductivity being proportional to the number of conductive electrons, n. Thus luminescence is quantitatively correlated with photoconductivity, which has recently been emphasized as an important goal . The origin of the inhomogeneous broadening and distribution of decay times may arise from either structural inhomogeneity, i.e. in the intermediate range order, or compositional disorder, e.g. inhomogeneity in the hydrogen concentration. The scale of the recombination distance, ~ 50A, leads us to suggest fluctuations akin to spinodal separation as the origin of the inhomogeneity [ 13]. The authors are indebted to Dr V. Dalai of the Institute for Energy Conversion for supplying the samples and for useful discussions and to Dr M. Martens of the Physics Department for cooperation on the measurements and helpful advice. We also acknowledge the hospitality of Dr. R. Street at Xerox, Palo Alto where the time-resolved measurements were made.
References             [ 13]
C. Tsang and R.A. Street, Phys. Rev. BI9 (1979) 3027. R.A. Street, Phil. Mag. 37 (1978) 35. J.J. Markham, Rev. Mod. Phys. 31 (1959) 956. I.G. Austin, T.S. Nashashibi and T.M. Searle, J. Non-Crystalline Solids 32 (1979) 373. R.A. Street, Adv. Phys. 25 (1976) 397. D. Engemann and R. Fisher, AlP Conf. Proc. No. 31 Eds., Lucovsky and Galeener, (Williamsburg, VA 1976). R.H. Bube, Photoconductivity of Solids (John Wiley, New York, 1960). D. Curie, Luminescence in crystals (John Wiley, New York, 1963) p. 45. T.M. Searle, T.S. Nashashibi and I.G. Austin, Phil. Mag. B39 (1979) 389. D.G. Thomas, J.J. Hopfield and W.M. Augustiniak, Phys. Rev. 140A (1965) 202. N.F. Mott and E.A. Davis, Electronic processes in non-crystalline materials, (Clarendon, Oxford, 1979) p. 83. R.A. Street, Adv. Phys. 30 (1981) 593. F. Williams, J. Non-Crystalline Solids 8-10 (1972) 516.