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Gap states in a-Si:H by photoconductivity and absorption
Journal of Non-Crystalline Solids 55 (1983) 191-201 North-Holland Publishing Company
191
G A P S T A T E S I N a-Si : H BY P H O T O C O N D U C T I V I T Y A N D ABSORPTION F. E V A N G E L I S T I , P. F I O R I N I , G. F O R T U N A T O , A. F R O V A , C. G I O V A N N E L L A and R. P E R U Z Z I ]stituto di Fisica "G. Marconi", Universitd di Roma, Rome, Italy
Received 2 August 1982 Revised manuscript received 10 December 1982
The spectral dependence of photoconductivity in a series of a-Si : H samples has been analyzed in order to derive the absorption coefficient a. It has been found that the exponent fl which relates photoconductivity and generation rate varies with photon energy and chopping frequency. Its critical influence upon the value of a is established. The Urbach tail in the region 1.4-1.8 eV has been studied and found to be independent of extrinsic gap states and hydrogen content. Finally an inverse correlation has been determined between the photoconductivity lifetime and the extrinsic gap-state density, as measured from the corresponding integrated area of the absorption coefficient.
I. Introduction A great deal of research has been devoted recently to the problem of states localized in the pseudo-gap of a-Si : H, due to its remarkable interest from both fundamental and applied point of view [1]. Optical absorption spectroscopy is in principle the most straightforward m e t h o d of analysis. However, when one deals with states lying deep into the gap, the very low value of the absorption coefficient calls for more elaborate techniques than the conventional transmission method. One possibility is to perform high-sensitivity spectral measurements of the photoconductivity Ao. It has been shown that, in order to extract a from these data, a detailed knowledge of the dependence of photocurrent A I u p o n the pair generation rate G is required [2]. For a-Si: H such dependence can be expressed as A I ~x G a, where fl takes values between 0.5 and 1.0. N o detailed analysis of fl for different defect concentrations and excitation wavelengths is available, although it would itself provide useful information on recombination mechanisms and on the distribution of gap centers [3]. Near-gap optical data, from various sources in the literature, all have in c o m m o n an exponential tail whose extension is remarkably consistent a m o n g samples grown in different laboratories [4,5]. This behavior, suggestive of a state distribution which is intrinsically present in a - S i : H , deserves further 0 0 2 2 - 3 0 9 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
192
F. Evangelisti et al. / Gap states in a-Si: H
investigation. The situation is quite different for absorption associated with deeper states, those usually attributed mainly to dangling bonds [6]. In this case a strong dependence on growth conditions is found. Due to the role that these states play as recombination centers for nonequilibrium carriers, a correlation between their density and photoconductivity must be sought. Aim of the present experiment was to analyze the above mentioned features in a systematic manner. To this purpose, spectral photoconductance was measured over four decades in a number of intrinsic a-Si : H samples, differing by their concentration of gap states as a result of varying growth conditions. Among other results, the intrinsic origin of the Urbach absorption tail was confirmed and analysed; moreover, a direct correspondence between nonequilibrium carrier lifetime and the integrated density of extrinsic gap states was established.
2. Experimental All samples investigated in the present experiment were grown by rf glow-discharge in a capacitive reactor in pure silane or in a silane plus argon mixture. Different gap-state concentrations were obtained by varying the deposition parameters around the values appropriate to get the best material. Details on growth conditions are reported in table 1. Notice that this variation of growth parameters as well as the inclusion of argon in the gas mixture produce samples with an absorption coefficient due to gap states lower than 10 3 cm-1 (see fig. 4 and discussion below). Film thickness ranged typically between 0.5 and 1 /tm and hydrogen content between 9 and 17%, as shown by IR absorption. Hydrogen appeared to be dominantly incorporated as Si-H.
Table 1 Deposition conditions for the samples investigated in the present work. The rf power is 1 W, throughout. T and d are the substrate temperature and the electrode distance. P and O are the pressure and the flow of the gas mixture, respectively. Sample 10 was grown with a modified version of the apparatus; therefore the corresponding values of growth parameters are not strictly comparable to those of the other samples Sample
T(°C)
P(Torr)
O (s.c.c./min.)
d(cm)
10 21 24 25 27 30 33 34 35
260 120 270 270 270 240 220 205 205
0.70 0.70 0.70 0.70 0.70 0.36 0.18 0.59 0.59
6.3 6.3 6.1 6.1 6.1 3.4 1.4 6.3 6.3
3.5 3.5 3.5 3.5 3.5 4.5 4.5 7.5 6.0
F. Evangelisti et aL / Gap states in a - S i : H
193
The presence of some oxygen is evidenced by the appearance of the S i - O stretching mode at 950 c m - 1. R a m a n and R H E E D analysis were performed to ascertain the amorphicity of the material. To enable photoconductivity measurements, two planar Cr electrodes were evaporated onto the substrate, prior to film deposition. Their spacing was about 1 mm. It was checked that these contacts were ohmic in the whole range of the experiment (applied electric field between 20 and 500 V / c m ) . Photoexcitation was produced with monochromatic photons in the region 0.9-1.8 eV, with flux varying from 1012 to 1016 per c m 2 per second. The light was focused so as to produce a uniform illumination in the gap between the two electrodes, without appreciably touching them. Special care was taken in checking the absence of instabilities associated with such effects as Staebler-Wronski, fatigue, aging, etc. The photoconductivity appeared to be stable over a period of months, and so did its dependence on excitation level. In addition to photoconductivity, each sample was analyzed in transmission by means of a Cary spectrometer. In the photon range where the optical density was sufficiently high, the absorption coefficient a was derived by standard formulas for an absorbing film in contact with a transparent substrate [7]. These data were used to normalize the absorption coefficient deduced from photoconductivity, in the photon range where the two spectra overlapped. The relationship between photoconductivity Ao and absorption coefficient a, for transport due to free electrons (as is the case for a-Si : H) and in the limit a d << 1, is given by Ao = eF(1 - R ),lal~.r,
(1)
where F is the incident photon flux per unit area, R the reflectivity, 71 the quantum efficiency, # the mobility and z the free lifetime. The validity of eq. (1) will be discussed later on. Depending on the recombination kinetics, r is usually a function of the generation rate, implying Ao o~ ( a r ) 1~,
(2)
where fl is found to vary between 0.5 and 1 depending on samples. In eq. (2), fl itself can be a function of the generation rate and also of the photon energy h u. Moreover, due to the very long response time of the photoconductor and to its dependence on generation rate, the measurement of fl can be affected by the modulation frequency of the light. If these factors are not taken in due account, large errors can be introduced in the determination of ct, and in turn of the gap-state density and recombination kinetics. The effect of response time is shown in fig. 1, where Ao is plotted versus excitation intensity for different light chopping frequencies in the range 0 to 130 Hz. Consistently with a response time getting shorter for higher excitation, the slope fl readily increases with frequency to reach a supralinear behavior. The supralinearity effect, if it were not spurious, would be suggestive of a
194
F. Evangelisti et al. / Gap states in a- Si: H
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F. Evangelisti et al. / Gap states in a - S i : H
195
recombination kinetics involving two kinds of levels [8]. To avoid such ambiguities, all our measurements were performed under steady-state excitation.
3. Results and discussion Fig. 2 shows a typical behavior of Ao in our samples versus photon flux F. Different curves correspond to different photon energies. We want to stress the following features: (i) if G = F(1 - R)~la is the generation rate, each curve shows a proportionality between Ao and G ~, with fl independent of light intensity (even though in some samples a slight reduction in slope is found at low excitation levels, similar to that reported in ref. 2). (ii) for hv > 1.8 eV, fl takes values between 0.75 and 0.90 in different samples (see table 2). (iii) for lower hv, fl gets smaller, tending to a value 0.5 at hv - 1 eV. This behavior is somewhat dependent on samples: there are cases where fl remains appreciably above 0.5. The effect of these experimental findings on the determination of the absorption coefficient will be discussed in the following, whereas the consequence on the recombination kinetics will be the subject of a different paper. The determination of a would be readily made from eq. (2), as long as fl were not a function of F and hr. If there is a point where Ao0, c%, and F 0 can be separately measured (e.g. at high hu values), eq. (2) can be rewritten as follows:
(Ao(h ) =---k- t
/
This is not the case for our data and we cannot afford to approximate fl to a constant because this would lead to very serious errors in the evaluation of the gap-state density (see fig. 3 and discussion below). We took therefore another approach, based on the fact that fl is a slowly varying function of hr. fl was measured at a suitable number of fixed photon energies and intermediate values were obtained by linear interpolation. The absorption coefficient was then evaluated by means of the following recurrent expression:
F(hv) ( A o ( h v + A ) ) '/B'h~) a( hv + A ) = a( hP ) F( hv + A ) Zlo(hp) where A was chosen to be 30 meV, to warrant a change of fl in such an interval less than 2%. The starting value for a was provided by transmission measurements, as previously mentioned. In fig. 3, values of the absorption coefficients a for a typical sample, as derived by this procedure, are plotted and compared with those that would be obtained in the constant-fl approximation. It is apparent that both the absolute value of et and its hv-dependence are critically
196
F. Evangelisti et al. / Gap states in a - S i : H
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ENERGY (eV)
Fig. 3. A b s o r p t i o n coefficient versus p h o t o n energy derived with the procedure described in the text (solid line), and by using three c o n s t a n t values of ft. fl = 0.85 dashed line, fl = 0.7 d a s h e d - d o t t e d line, fl = 0.5 dotted line.
dependent on ft. A smaller fl than real, leads to an underestimate of the density of gap states which are responsible for the absorption below 1.5 eV. The opposite is true for fl larger than real. Moreover, the slope of the exponential tail above 1.5 eV is also very sensitive to fl and serious errors can be entailed in the determination of its value. From our earlier considerations, this implies that experiments done in chopped light conditions are bound to yield an unrealistically high value of the gap-state density. Fig. 4 compares the behavior of samples grown under different conditions of deposition. All samples have in common an exponential tail below 1.8 eV, with very similar decay behavior. Expressing a in this region in the Urbach form a = a0exp[ ( E - E l)/E0], our values of the decay energy E 0 are consistent with earlier findings [4,5] and are spread for different samples within 13 meV (see table 2). This suggests that we are dealing with an intrinsic property of a-Si:H. This will be further substantiated in the following by the lack of correlation between E 0 and the density of extrinsic states in the pseudo-gap. E 0 is also found to be independent of hydrogen content, at least over the range available in our samples (9-17%). This result agrees with the analysis of Cody et al. [9] on the influence of thermal and structural disorder upon the optical absorption edge. The extension of the Urbach tail is limited by the taking over of the low-energy absorption plateau, which varies considerably from sample to sample. For this reason, we attribute this added absorption to levels of extrinsic origin, lying deeper in the gap. An estimate of the density of these
F. Evangelisti et a L /
Gap states in a - S i : H
lo,l
197
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2.2
ENERGY (eV)
Fig. 4. Absorption coefficient as a function of photon energy for three typical samples, a = sample 21, b = sample 33, c = sample 24 of table 1.
extrinsic states can be made from the integral of the absorption coefficient in the plateau region, after extrapolation and subtraction of the exponential tail (which, on the other hand, becomes soon negligible: notice the logarithmic scale in fig. 4). The results of this operation for the various samples investigated are given in the last column of table 2. Ng, representing the total density in arbitrary units, does not seem to affect the decay energy E 0, as earlier anticipated. The analysis of photoconductivity in a-Si : H is made simple by the commonly accepted notion that at room temperature the phototransport takes
Table 2 Values of the exponent/3 at 1.8 eV, of the Urbach energy E0(meV ), and of the number of gap states Ns (arbitrary units) for the samples investigated in the present work Sample
/3
E0
Ng
10 21 24 25 27 30 33 34 35
0.75 0.78 0.79 0.87 0.76 0.83 0.81 0.86 0.89
63.0 71.0 60.0 65.0 65.0 58.0 63.0 68.0 56.0
5.3 110. 0.4 2.7 0.8 0.9 2.4 1.5 1.3
198
F. Evangelisti et al. / Gap states in a-Si: H
place only in extended states of the conduction band [10,1 1]. This justifies the use of eq. (1) and also the assumption of a photon-energy independent mobility. As for the photon-energy dependence of ~-, R and 7/in that equation, we should say the following. ~-, which can also be a function of light intensity, is taken care of by our preliminary analysis of fl, which is the experimental parameter reflecting all variations of z. Since the uncertainty concerning the behavior of z represents the major obstacle in the evaluation of a starting from Aa, it follows that our procedure permits us to eliminate the main source of error. The reflectance coefficient R can be estimated from transmission measurements: its variation of a few percent in the photon range explored is negligible within the limits of accuracy in our determination of a. The assumption of a constant quantum efficiency ~/might be somewhat questionable. In principle at low photon energy one might have transitions that do not contribute to photoconducticity. This would lead to an underestimate of a. However, Jackson and Amer [12] have recently shown that this is not the case, since a-values measured at low hu's by the photothermal deflection technique, match rather well with those deduced from photoconductivity measurements (as long as the hu-dependence of fl is taken into account). We now correlate the absorption coefficient with the distribution of levels in the pseudo-gap. The behavior reported in fig. 4 can be quantitatively reproduced starting from the density of states versus energy dependence and the
Ee
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? w
B
!
I i
,1
I
I I
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Fig. 5. Scheme of the density of states which accounts for the absorption spectra. Transitions A and A' give rise to the exponential tail, transitions B to the low-energyplateau.
F. Evangelisti et al. / Gap states in a- Si: H
199
transition scheme shown in fig. 5, and assuming constant matrix elements. It should be stressed that such a state distribution is virtually equal to that recently determined by DLTS measurements [13]. The sample-dependent plateau below 1.5 eV is due to transitions of type B originating at localized states near midgap and reaching the conduction band continuum. The sampleindependent Urbach tail between 1.5 and 1.8 eV is associated with transitions of type A and A', i.e. involving intrinsic localized-state tails and extended continua. We ruled out localized-to-localized transition on the ground of a lower joined density of states and also of strongly reduced matrix elements due to weak spatial overlap of the wavefunctions. The Urbach energy E 0 does therefore describe the decay of the localized-state density toward the interior of the gap. Jackson and Amer [14] have claimed a remarkable increase of E o (up to 100 meV) when approaching the upper end of the explored density of gap states (a > 102 c m - ~ at 1.4 eV in the plateau region). In our experiment, in the same density range (sample 21 in table 2 and up) we find that the exponential decay is masked by the plateau absorption. This is in part due to our absorption coefficient flattening off above 1.8 eV, while Jackson and Amer detected an exponential behavior to rather higher energies. This discrepancy
605
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•~
.
\ \ \ \ •0
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• \
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\ k
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,
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,
I 100
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Fig. 6. M o b i l i t y - l i f e t i m e product as a function of the n u m b e r of gap states Ns (arbitrary units).
200
F. Evangelisti et al. / Gap states in a - S i : H
between the two experiments is not explained and deserves further inspection. A useful result of Jackson and Amer's experiment is the correspondence they established between the state density Ng, i.e. plateau absorption, and the spin density. From this, we establish an upper limit 1017 cm -3 to the density of spins for E 0 to remain unaffected. It would apply to sample 21 of table 2. The rest of our samples therefore have a lower density of spins and conceivably of extrinsic gap states. In spite of this, the latter directly affect the photoconductivity response. In fig. 6 we have plotted/~- (for hp = 1.8 eV) as a function of Ng. The nearly inverse correspondence found between the two quantities is an important result since it permits recognition of the states that are responsible for the quenching of photoconductivity lifetime. From the previously discussed correlation between spins and extrinsic gap states, we conclude that recombination centers are predominantly associated with dangling bonds.
4. Conclusions
This work contains a careful analysis of photoconductivity spectral behavior, for deduction of the absorption coefficient of a-Si : H at energies appreciably lower than the mobility gap. We have shown that the results are very critically dependent on the exponent /3 that relates photoconductivity and generation rate, so that its determination as a function of photon energy and excitation level is a basic prerequisite to this type of experiments. The integrated density of states lying deep in the gap has been found to depend strongly on sample preparation conditions, so as to appear of extrinsic defect-related origin, but does not affect the Urbach tail associated with near pseudo-gap transitions. The characteristic Urbach energy E 0 is therefore likely to be an intrinsic property of the disordered material. Finally, we have found an inverse correlation between photoconductivity lifetime and extrinsic gapstate density, which is suggestive of a dangling-bond nature for the recombination centers. The skilful technical assistance of R. Generosi, R. Moretto and S. Rinaldi is gratefully acknowledged.
References [1] B.K. Chakraverty, D. Kaplan, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., Grenoble (1981). [2] G. Moddel, D.A. Anderson and W. Paul, Phys. Rev. B22 (1980) 1918. [3] A. Rose, Concepts in Photoconductivity and Allied Problems (Interscience, New York, 1963). [4] B. Abeles, C.R. Wronsky, T. Tiedje and G.D. Cody, Sol. St. Commun, 36 (1980) 537. [5] S. Yamasaki, N. Hata, T. Yoshida, H. Oheda, A. Matsuda, H. Okushi and K. Tanaka, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, D. Kaplan, Grenoble (1981) p. 297. [6] R.A. Street, Adv. Phys. 30 (1981) 593.
F. Evangelisti et al. / Gap states in a - S i : H
[7] [8] [9] [10] [11] [12] [13]
201
E.C. Freeman and W. Paul, Phys. Rev. B20 (1979) 716. P.D. Persans, Sol. St. Commun. 36 (1980) 851. G.D. Cody, T. Tiedje, B. Abeles, B. Brooks and Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. A.R. Moore, Appl. Phys. lett. 31 (1977) 762. D.L. Staebler, J. Non-Crystalline Solids 35-36 (1980) 387. W.B. Jackson and N.M. Amer, Phys. Rev. B 25 (1982) 5559. J.D. Cohen, D.V. Lang, J.P. Harbison and A.M. Sergent, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, and D. Kaplan, Grenoble (1981) p. 371. [14] W.B. Jackson and N.M. Amer, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, D. Kaplan, Grenoble (1981) p. 293.
191
G A P S T A T E S I N a-Si : H BY P H O T O C O N D U C T I V I T Y A N D ABSORPTION F. E V A N G E L I S T I , P. F I O R I N I , G. F O R T U N A T O , A. F R O V A , C. G I O V A N N E L L A and R. P E R U Z Z I ]stituto di Fisica "G. Marconi", Universitd di Roma, Rome, Italy
Received 2 August 1982 Revised manuscript received 10 December 1982
The spectral dependence of photoconductivity in a series of a-Si : H samples has been analyzed in order to derive the absorption coefficient a. It has been found that the exponent fl which relates photoconductivity and generation rate varies with photon energy and chopping frequency. Its critical influence upon the value of a is established. The Urbach tail in the region 1.4-1.8 eV has been studied and found to be independent of extrinsic gap states and hydrogen content. Finally an inverse correlation has been determined between the photoconductivity lifetime and the extrinsic gap-state density, as measured from the corresponding integrated area of the absorption coefficient.
I. Introduction A great deal of research has been devoted recently to the problem of states localized in the pseudo-gap of a-Si : H, due to its remarkable interest from both fundamental and applied point of view [1]. Optical absorption spectroscopy is in principle the most straightforward m e t h o d of analysis. However, when one deals with states lying deep into the gap, the very low value of the absorption coefficient calls for more elaborate techniques than the conventional transmission method. One possibility is to perform high-sensitivity spectral measurements of the photoconductivity Ao. It has been shown that, in order to extract a from these data, a detailed knowledge of the dependence of photocurrent A I u p o n the pair generation rate G is required [2]. For a-Si: H such dependence can be expressed as A I ~x G a, where fl takes values between 0.5 and 1.0. N o detailed analysis of fl for different defect concentrations and excitation wavelengths is available, although it would itself provide useful information on recombination mechanisms and on the distribution of gap centers [3]. Near-gap optical data, from various sources in the literature, all have in c o m m o n an exponential tail whose extension is remarkably consistent a m o n g samples grown in different laboratories [4,5]. This behavior, suggestive of a state distribution which is intrinsically present in a - S i : H , deserves further 0 0 2 2 - 3 0 9 3 / 8 3 / 0 0 0 0 - 0 0 0 0 / $ 0 3 . 0 0 © 1983 N o r t h - H o l l a n d
192
F. Evangelisti et al. / Gap states in a-Si: H
investigation. The situation is quite different for absorption associated with deeper states, those usually attributed mainly to dangling bonds [6]. In this case a strong dependence on growth conditions is found. Due to the role that these states play as recombination centers for nonequilibrium carriers, a correlation between their density and photoconductivity must be sought. Aim of the present experiment was to analyze the above mentioned features in a systematic manner. To this purpose, spectral photoconductance was measured over four decades in a number of intrinsic a-Si : H samples, differing by their concentration of gap states as a result of varying growth conditions. Among other results, the intrinsic origin of the Urbach absorption tail was confirmed and analysed; moreover, a direct correspondence between nonequilibrium carrier lifetime and the integrated density of extrinsic gap states was established.
2. Experimental All samples investigated in the present experiment were grown by rf glow-discharge in a capacitive reactor in pure silane or in a silane plus argon mixture. Different gap-state concentrations were obtained by varying the deposition parameters around the values appropriate to get the best material. Details on growth conditions are reported in table 1. Notice that this variation of growth parameters as well as the inclusion of argon in the gas mixture produce samples with an absorption coefficient due to gap states lower than 10 3 cm-1 (see fig. 4 and discussion below). Film thickness ranged typically between 0.5 and 1 /tm and hydrogen content between 9 and 17%, as shown by IR absorption. Hydrogen appeared to be dominantly incorporated as Si-H.
Table 1 Deposition conditions for the samples investigated in the present work. The rf power is 1 W, throughout. T and d are the substrate temperature and the electrode distance. P and O are the pressure and the flow of the gas mixture, respectively. Sample 10 was grown with a modified version of the apparatus; therefore the corresponding values of growth parameters are not strictly comparable to those of the other samples Sample
T(°C)
P(Torr)
O (s.c.c./min.)
d(cm)
10 21 24 25 27 30 33 34 35
260 120 270 270 270 240 220 205 205
0.70 0.70 0.70 0.70 0.70 0.36 0.18 0.59 0.59
6.3 6.3 6.1 6.1 6.1 3.4 1.4 6.3 6.3
3.5 3.5 3.5 3.5 3.5 4.5 4.5 7.5 6.0
F. Evangelisti et aL / Gap states in a - S i : H
193
The presence of some oxygen is evidenced by the appearance of the S i - O stretching mode at 950 c m - 1. R a m a n and R H E E D analysis were performed to ascertain the amorphicity of the material. To enable photoconductivity measurements, two planar Cr electrodes were evaporated onto the substrate, prior to film deposition. Their spacing was about 1 mm. It was checked that these contacts were ohmic in the whole range of the experiment (applied electric field between 20 and 500 V / c m ) . Photoexcitation was produced with monochromatic photons in the region 0.9-1.8 eV, with flux varying from 1012 to 1016 per c m 2 per second. The light was focused so as to produce a uniform illumination in the gap between the two electrodes, without appreciably touching them. Special care was taken in checking the absence of instabilities associated with such effects as Staebler-Wronski, fatigue, aging, etc. The photoconductivity appeared to be stable over a period of months, and so did its dependence on excitation level. In addition to photoconductivity, each sample was analyzed in transmission by means of a Cary spectrometer. In the photon range where the optical density was sufficiently high, the absorption coefficient a was derived by standard formulas for an absorbing film in contact with a transparent substrate [7]. These data were used to normalize the absorption coefficient deduced from photoconductivity, in the photon range where the two spectra overlapped. The relationship between photoconductivity Ao and absorption coefficient a, for transport due to free electrons (as is the case for a-Si : H) and in the limit a d << 1, is given by Ao = eF(1 - R ),lal~.r,
(1)
where F is the incident photon flux per unit area, R the reflectivity, 71 the quantum efficiency, # the mobility and z the free lifetime. The validity of eq. (1) will be discussed later on. Depending on the recombination kinetics, r is usually a function of the generation rate, implying Ao o~ ( a r ) 1~,
(2)
where fl is found to vary between 0.5 and 1 depending on samples. In eq. (2), fl itself can be a function of the generation rate and also of the photon energy h u. Moreover, due to the very long response time of the photoconductor and to its dependence on generation rate, the measurement of fl can be affected by the modulation frequency of the light. If these factors are not taken in due account, large errors can be introduced in the determination of ct, and in turn of the gap-state density and recombination kinetics. The effect of response time is shown in fig. 1, where Ao is plotted versus excitation intensity for different light chopping frequencies in the range 0 to 130 Hz. Consistently with a response time getting shorter for higher excitation, the slope fl readily increases with frequency to reach a supralinear behavior. The supralinearity effect, if it were not spurious, would be suggestive of a
194
F. Evangelisti et al. / Gap states in a- Si: H
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I
it
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0 o
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,
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F. Evangelisti et al. / Gap states in a - S i : H
195
recombination kinetics involving two kinds of levels [8]. To avoid such ambiguities, all our measurements were performed under steady-state excitation.
3. Results and discussion Fig. 2 shows a typical behavior of Ao in our samples versus photon flux F. Different curves correspond to different photon energies. We want to stress the following features: (i) if G = F(1 - R)~la is the generation rate, each curve shows a proportionality between Ao and G ~, with fl independent of light intensity (even though in some samples a slight reduction in slope is found at low excitation levels, similar to that reported in ref. 2). (ii) for hv > 1.8 eV, fl takes values between 0.75 and 0.90 in different samples (see table 2). (iii) for lower hv, fl gets smaller, tending to a value 0.5 at hv - 1 eV. This behavior is somewhat dependent on samples: there are cases where fl remains appreciably above 0.5. The effect of these experimental findings on the determination of the absorption coefficient will be discussed in the following, whereas the consequence on the recombination kinetics will be the subject of a different paper. The determination of a would be readily made from eq. (2), as long as fl were not a function of F and hr. If there is a point where Ao0, c%, and F 0 can be separately measured (e.g. at high hu values), eq. (2) can be rewritten as follows:
(Ao(h ) =---k- t
/
This is not the case for our data and we cannot afford to approximate fl to a constant because this would lead to very serious errors in the evaluation of the gap-state density (see fig. 3 and discussion below). We took therefore another approach, based on the fact that fl is a slowly varying function of hr. fl was measured at a suitable number of fixed photon energies and intermediate values were obtained by linear interpolation. The absorption coefficient was then evaluated by means of the following recurrent expression:
F(hv) ( A o ( h v + A ) ) '/B'h~) a( hv + A ) = a( hP ) F( hv + A ) Zlo(hp) where A was chosen to be 30 meV, to warrant a change of fl in such an interval less than 2%. The starting value for a was provided by transmission measurements, as previously mentioned. In fig. 3, values of the absorption coefficients a for a typical sample, as derived by this procedure, are plotted and compared with those that would be obtained in the constant-fl approximation. It is apparent that both the absolute value of et and its hv-dependence are critically
196
F. Evangelisti et al. / Gap states in a - S i : H
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I
2.2
ENERGY (eV)
Fig. 3. A b s o r p t i o n coefficient versus p h o t o n energy derived with the procedure described in the text (solid line), and by using three c o n s t a n t values of ft. fl = 0.85 dashed line, fl = 0.7 d a s h e d - d o t t e d line, fl = 0.5 dotted line.
dependent on ft. A smaller fl than real, leads to an underestimate of the density of gap states which are responsible for the absorption below 1.5 eV. The opposite is true for fl larger than real. Moreover, the slope of the exponential tail above 1.5 eV is also very sensitive to fl and serious errors can be entailed in the determination of its value. From our earlier considerations, this implies that experiments done in chopped light conditions are bound to yield an unrealistically high value of the gap-state density. Fig. 4 compares the behavior of samples grown under different conditions of deposition. All samples have in common an exponential tail below 1.8 eV, with very similar decay behavior. Expressing a in this region in the Urbach form a = a0exp[ ( E - E l)/E0], our values of the decay energy E 0 are consistent with earlier findings [4,5] and are spread for different samples within 13 meV (see table 2). This suggests that we are dealing with an intrinsic property of a-Si:H. This will be further substantiated in the following by the lack of correlation between E 0 and the density of extrinsic states in the pseudo-gap. E 0 is also found to be independent of hydrogen content, at least over the range available in our samples (9-17%). This result agrees with the analysis of Cody et al. [9] on the influence of thermal and structural disorder upon the optical absorption edge. The extension of the Urbach tail is limited by the taking over of the low-energy absorption plateau, which varies considerably from sample to sample. For this reason, we attribute this added absorption to levels of extrinsic origin, lying deeper in the gap. An estimate of the density of these
F. Evangelisti et a L /
Gap states in a - S i : H
lo,l
197
......-"
/ • ¢ j
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a ' " " .... .. . . . . . . . . . . . .,
•
1.0
, ,.-"/ ,,,"'" / ....... •. / / j
1.4
1.8
2.2
ENERGY (eV)
Fig. 4. Absorption coefficient as a function of photon energy for three typical samples, a = sample 21, b = sample 33, c = sample 24 of table 1.
extrinsic states can be made from the integral of the absorption coefficient in the plateau region, after extrapolation and subtraction of the exponential tail (which, on the other hand, becomes soon negligible: notice the logarithmic scale in fig. 4). The results of this operation for the various samples investigated are given in the last column of table 2. Ng, representing the total density in arbitrary units, does not seem to affect the decay energy E 0, as earlier anticipated. The analysis of photoconductivity in a-Si : H is made simple by the commonly accepted notion that at room temperature the phototransport takes
Table 2 Values of the exponent/3 at 1.8 eV, of the Urbach energy E0(meV ), and of the number of gap states Ns (arbitrary units) for the samples investigated in the present work Sample
/3
E0
Ng
10 21 24 25 27 30 33 34 35
0.75 0.78 0.79 0.87 0.76 0.83 0.81 0.86 0.89
63.0 71.0 60.0 65.0 65.0 58.0 63.0 68.0 56.0
5.3 110. 0.4 2.7 0.8 0.9 2.4 1.5 1.3
198
F. Evangelisti et al. / Gap states in a-Si: H
place only in extended states of the conduction band [10,1 1]. This justifies the use of eq. (1) and also the assumption of a photon-energy independent mobility. As for the photon-energy dependence of ~-, R and 7/in that equation, we should say the following. ~-, which can also be a function of light intensity, is taken care of by our preliminary analysis of fl, which is the experimental parameter reflecting all variations of z. Since the uncertainty concerning the behavior of z represents the major obstacle in the evaluation of a starting from Aa, it follows that our procedure permits us to eliminate the main source of error. The reflectance coefficient R can be estimated from transmission measurements: its variation of a few percent in the photon range explored is negligible within the limits of accuracy in our determination of a. The assumption of a constant quantum efficiency ~/might be somewhat questionable. In principle at low photon energy one might have transitions that do not contribute to photoconducticity. This would lead to an underestimate of a. However, Jackson and Amer [12] have recently shown that this is not the case, since a-values measured at low hu's by the photothermal deflection technique, match rather well with those deduced from photoconductivity measurements (as long as the hu-dependence of fl is taken into account). We now correlate the absorption coefficient with the distribution of levels in the pseudo-gap. The behavior reported in fig. 4 can be quantitatively reproduced starting from the density of states versus energy dependence and the
Ee
\ \\ \\\ ]\N\\ x
? w
B
!
I i
,1
I
I I
Ev Log. N
Fig. 5. Scheme of the density of states which accounts for the absorption spectra. Transitions A and A' give rise to the exponential tail, transitions B to the low-energyplateau.
F. Evangelisti et al. / Gap states in a- Si: H
199
transition scheme shown in fig. 5, and assuming constant matrix elements. It should be stressed that such a state distribution is virtually equal to that recently determined by DLTS measurements [13]. The sample-dependent plateau below 1.5 eV is due to transitions of type B originating at localized states near midgap and reaching the conduction band continuum. The sampleindependent Urbach tail between 1.5 and 1.8 eV is associated with transitions of type A and A', i.e. involving intrinsic localized-state tails and extended continua. We ruled out localized-to-localized transition on the ground of a lower joined density of states and also of strongly reduced matrix elements due to weak spatial overlap of the wavefunctions. The Urbach energy E 0 does therefore describe the decay of the localized-state density toward the interior of the gap. Jackson and Amer [14] have claimed a remarkable increase of E o (up to 100 meV) when approaching the upper end of the explored density of gap states (a > 102 c m - ~ at 1.4 eV in the plateau region). In our experiment, in the same density range (sample 21 in table 2 and up) we find that the exponential decay is masked by the plateau absorption. This is in part due to our absorption coefficient flattening off above 1.8 eV, while Jackson and Amer detected an exponential behavior to rather higher energies. This discrepancy
605
\\ \
•~
.
\ \ \ \ •0
1[) 6
\
\
\
\
\ \
• \
E
\
\ k
\ \ \ \ \ k \ \ \ \ \ \
• \ \ \
I 1
,
I 10
,
I 100
Ng (arb. un.)
Fig. 6. M o b i l i t y - l i f e t i m e product as a function of the n u m b e r of gap states Ns (arbitrary units).
200
F. Evangelisti et al. / Gap states in a - S i : H
between the two experiments is not explained and deserves further inspection. A useful result of Jackson and Amer's experiment is the correspondence they established between the state density Ng, i.e. plateau absorption, and the spin density. From this, we establish an upper limit 1017 cm -3 to the density of spins for E 0 to remain unaffected. It would apply to sample 21 of table 2. The rest of our samples therefore have a lower density of spins and conceivably of extrinsic gap states. In spite of this, the latter directly affect the photoconductivity response. In fig. 6 we have plotted/~- (for hp = 1.8 eV) as a function of Ng. The nearly inverse correspondence found between the two quantities is an important result since it permits recognition of the states that are responsible for the quenching of photoconductivity lifetime. From the previously discussed correlation between spins and extrinsic gap states, we conclude that recombination centers are predominantly associated with dangling bonds.
4. Conclusions
This work contains a careful analysis of photoconductivity spectral behavior, for deduction of the absorption coefficient of a-Si : H at energies appreciably lower than the mobility gap. We have shown that the results are very critically dependent on the exponent /3 that relates photoconductivity and generation rate, so that its determination as a function of photon energy and excitation level is a basic prerequisite to this type of experiments. The integrated density of states lying deep in the gap has been found to depend strongly on sample preparation conditions, so as to appear of extrinsic defect-related origin, but does not affect the Urbach tail associated with near pseudo-gap transitions. The characteristic Urbach energy E 0 is therefore likely to be an intrinsic property of the disordered material. Finally, we have found an inverse correlation between photoconductivity lifetime and extrinsic gapstate density, which is suggestive of a dangling-bond nature for the recombination centers. The skilful technical assistance of R. Generosi, R. Moretto and S. Rinaldi is gratefully acknowledged.
References [1] B.K. Chakraverty, D. Kaplan, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., Grenoble (1981). [2] G. Moddel, D.A. Anderson and W. Paul, Phys. Rev. B22 (1980) 1918. [3] A. Rose, Concepts in Photoconductivity and Allied Problems (Interscience, New York, 1963). [4] B. Abeles, C.R. Wronsky, T. Tiedje and G.D. Cody, Sol. St. Commun, 36 (1980) 537. [5] S. Yamasaki, N. Hata, T. Yoshida, H. Oheda, A. Matsuda, H. Okushi and K. Tanaka, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, D. Kaplan, Grenoble (1981) p. 297. [6] R.A. Street, Adv. Phys. 30 (1981) 593.
F. Evangelisti et al. / Gap states in a - S i : H
[7] [8] [9] [10] [11] [12] [13]
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E.C. Freeman and W. Paul, Phys. Rev. B20 (1979) 716. P.D. Persans, Sol. St. Commun. 36 (1980) 851. G.D. Cody, T. Tiedje, B. Abeles, B. Brooks and Y. Goldstein, Phys. Rev. Lett. 47 (1981) 1480. A.R. Moore, Appl. Phys. lett. 31 (1977) 762. D.L. Staebler, J. Non-Crystalline Solids 35-36 (1980) 387. W.B. Jackson and N.M. Amer, Phys. Rev. B 25 (1982) 5559. J.D. Cohen, D.V. Lang, J.P. Harbison and A.M. Sergent, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, and D. Kaplan, Grenoble (1981) p. 371. [14] W.B. Jackson and N.M. Amer, Proc. 9th Int. Conf. on Amorphous and Liquid Semiconductors, eds., B.K. Chakraverty, D. Kaplan, Grenoble (1981) p. 293.