- Email: [email protected]
Dispersive transport and trap saturation in doped hydrogenated amorphous silicon
Sol{d State Communications, Vol. 50, No. 9, pp. 845-848, 1984. Printed in Great Britain.
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
DISPERSIVE TRANSPORT AND TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON I.K. Kristensen and J.M. Hvam Fysisk Institut, Odense Universitet, DK-5230 Odense, Denmark
(Received 26 January 1984 by N.I. Meyer) Transient photocurrent measurements in arsenic-doped hydrogenated amorphous silicon show trap-controlled dispersive transport interrupted by trap saturation in an exponential band tail. A nonlinear temperature dependence of the dispersion parameter a is observed at low temperatures, indicating that the density of shallow traps (~ O. 1 eV below the mobility edge) is only weakly energy dependent.
The demarcation level Eu(t) [8], or quasi-Fermi level [9], specifying the relaxation of the carrier packet, sinks into the band tail logarithmically with time t according to
RECENTLY, a number of investigations [1-5] on transient photocurrents (TP) in hydrogenated amorphous silicon (a-Si : H) have provided evidence for dispersive transport [6] controlled by multiple trapping in an exponential distribution of trapping states below the mobility edge. The main features of the experiments are accounted for by the simple models, developed by Tiedje and Rose [7] and by Orenstein and Kastner [8]. They describe the relaxation of excess carriers after a short-pulse excitation by a distribution of localized carriers sinking deeper and deeper into the band tail states, and with recombinations only from extended states. One consequence of such a model is that trap saturation may occur in the deep band tail states [8, 9] if recombination is negligible on the time scale of carrier relaxation into these states. In the previous experiments, saturation effects were not reported. Specifically in relation to the experiments of Hvam and Brodsky [ 1], the nonobservation of saturation led Schiff [9] to question the validity of the generally accepted assumptions incorporated in the simple multiple trapping model. In the present work, we report measurements of TP in arsenic-doped a-Si: H which in the temperature range 1 7 5 - 3 0 0 K, show saturation effects that are in nice agreement with the model of Schiff [9]. At lower temperatures, saturation is not observed on the time scale of our experiment and furthermore the dispersion parameter deviates from the linear temperature dependence observed at higher temperatures [1, 2]. The simplest model, on the basis of which we shall discuss our results, assumes an exponential distribution of localized trapping states below the mobility edge (at E = Ee = 0): g(E) = go exp {E/kTo}
Ea(t) = -- kT in (rot),
(2)
where T is the temperature and Vo is an attempt to escape frequency. In the absence of recombination, the total excess electron density N
g(E) dE F(t) f~ J exp { [E-- Ea(t)]/kT} + 1
(3)
is conserved, determining at the same time the occupancy factor F(t) ~< 1 [9]. When F(t) ~ 1, standard dispersive transport is observed with a time dependent drift mobility given by Nc sin (an) p(t) = Po - - (rot) -I+c~, k Togo an
(4)
where go is the extended state electron mobility, N e is the effective density of states at the mobility edge, and a = T/To is the dispersion parameter. Saturation occurs when F(t) approaches unity and the time, ts, it takes is determined from equations ( 1 ) -
(3): = (Nsin(an)t-i/'x
(1)
with a width of ~ kTo. 845
Of course, recombination does take place and may interfere with the complete saturation of equation (5) - or even prevent saturation. This will depend on the relative rates of recombination and relaxation, i.e. on density (for bimolecular recombination) and temperature. We shall see in the present experiments that, when the temperature is not too low, saturation occurs prior to recombination, except at the highest densities. The experiments were performed on a 1 pm thick
846
TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON 10 3
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Fig. l. Transient photocurrent in arsenic-doped a-Si : H at 225 K for different excitation densities N. The maximum density No = 2 × 1017 cm -3. The arrows indicate the onset of saturation at time ts. film o f a - S i : H prepared by glow discharge decomposition of Sill4 with 0.05% AsH3 added for n-type doping. Deposition took place onto a quartz substrate, heated to 300°C, with predeposited molybdenum electrode stripes 1 mm apart. TP was excited by an Nz-gas laser pumped dye laser (Rh6G) with a pulse width of 5 nsec. The light was focussed to produce a homogeneous excitation density between the electrodes over a length of about 5 ram, and the intensity was controlled by neutral density filters. The maximum intensity was estimated to generate an initial electron density of No "" 2 x 1017 cm -3. Temperature control was obtained by mounting the sample on a copper block in a helium exchange gas of a variable temperature cryostat. The TP signals were processed by a digital signal averager based on a sampling oscilloscope, controlled by a microcomputer [ 10]. With a careful selection of preamplifiers and bias circuitry (bias voltage VB = 90 V), very accurate current transients were recorded covering 4 orders of magnitude in intensity and time, ranging from 50 nsec to 0.5 msec. Figure 1 shows the result of such measurements performed at 225 K and for several illumination intensities. The results are typical for many measurements. At the highest intensity, the TP does not follow any simple power law decay, but can be explained by a combination of dispersive transport and bimolecular recombination [11]. At lower intensities, the TP exhibits an initial power law decay interrupted by an incomplete saturation and a final recombination. The time, ts, for the onset of saturation depends on the illumination intensity, as seen in Fig. 1, and it also depends on the temperature. In Fig. 2, is plotted the saturation time vs excess carrier density for different temperatures. The points are experimental values and
0.1 0Ol
0.I EXCITATION DENSITY N/No
Fig. 2. Saturation time vs excitation density for different temperatures T = 175 K (x), 200 K (o), 225 K (c~), 250 K (e), 275 K (z~), and 300 K (+). The points are experimental and the curves are calculated from equation (5) with go = 10z° cm -3 (eV) -1- Uo = 1012 sec -1 , To = 575 K, andNo = 2 x 1017 cm -3. The points in the brackets are commented on in the text.
the curves are calculated from equation (5) with Uo = 1012 sec -1 ,go = 102o cm -3 (eV) -1 ,No = 2 x 1017 cm -3, a = T / T o and To = 575 K. In view of the different uncertainties involved, there is a satisfactory agreement between the experimental points and the calculated curves. For the latter, the horizontal axis is the initial carrier density N neglecting recombination. For the experimental points, N is assumed proportional to the illumination intensity which does not quite hold at high intensities (points in brackets in Fig. 2), due to the onset of bimolecular recombination. This is obvious from Fig. 1, but is also observed as a sublinear dependence of the initial current on illumination at high intensity. The values of a and To used above are determined independently from the slopes of the initial photocurrent decays (Fig. 1). In Fig. 3 is plotted the dispersion parameter a as a function of temperature from a large number of measurements on TP between 100 and 300 K. Above 170 K, a is seen to vary approximately linearly with temperature (a = T / T o , To = 575 K) in agreement with the simple model of multiple trapping in an exponential band tail. At lower temperatures this does not hold, a decreases stronger than
Vol. 50, No. 9 0.7
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Fig. 3. Dispersion parameter a as a function of temperature. The points are experimental and the line represents a = T/To with To = 575 K. linearly with decreasing temperature and goes to zero around 100 K. In order to analyze this behaviour, it is important to realize what parts of the trap state distribution are probed in our experiments. This is illustrated in Fig. 4 showing, as a function of temperature, the energy range scanned by the demarcation level [equation (2)] from 50 nsec to 0.5 msec after a short pulse excitation. The lowest limit in any TP experiment is set by the Fermi level E F ( T ) , which in Fig. 4 is plotted as E F ( T ) = -- (Eo + 4 k T ) . Here Eo = 0.33 eV is the measured activation energy of the dark conductivity and 4 k T represents the statistical shift of the Fermi level with temperature [12]. It is now obvious from Fig. 4 that at low temperatures only a narrow and rather shallow region of the band tail distribution is probed by the TP. It is therefore tempting to suggest that the deviation from linearity in a(T) at low temperature is caused by a deviation from a purely exponential shape in the shallow parts of the trapping state distribution. Specifically, we suggest that only for energies more than 0.2 eV below the mobility edge is the density of states given by equation (1) with To = 575 K. For shallower states, the energy dependence is weaker and becomes negligibly small for energies around 0.1 eV below the mobility edge. A similar behaviour of ~(T) has recently been reported by Shirafuji et al. [5], only at higher temperatures and associated with a dominant distribution of traps around 0.2 eV below the mobility edge. In principle, the band tail shape should reveal itself in a single TP experiment at low'temperatures provided the dynamical range is sufficiently large. Due to the slower relaxation, however, this requires an extension of the time scale towards shorter as well as towards longer times. This is not trivial since the current sensitivity has
Fig. 4. The hatched region shows, as a function of temperature, the energy range scanned by the demarcation level (equation (2) with Vo = 1012 sec-1). The upper and lower boundaries are set by the experimental time window, 50 nsec-0.5 msec. At high temperatures, though, the lower boundary is set by the Fermi level, plotted as E F ( T ) = -- (Eo + 4 k T ) with Eo = 0.33 eV (see text). to be improved even more because the current decay is faster at low temperatures. We are working on this experimental problem. In the previous TP experiments of Hvam and Brodsky [ 1] on phosphorus-doped a-Si : H, saturation effects were not observed due to a rather high density of trapping states and a loss of carriers by monomolecular recombination for t > 10/~sec. On the other hand, an observed fast decay of TP before the power law sets in [ 1] and the observed activation energy of 0.1 eV of the initial photocurrent amplitude is consistent with a trap state distribution similar to the present suggestion. In [1 ], however, experiments were not performed at sufficiently low temperature to confirm this. In conclusion, we presently report TP measurements in arsenic-doped a-Si:H which, for the first time, show saturation effects and thus yield further support to the simple model [8, 9] of relaxation of excess carriers by multiple trapping in a distribution of band tail states. From the power law decays, the extended state mobility /.to can be determined from equation (4). With N c = 1020 cm -3 we find values in the range/lo = 10-20 cm 2 Vsec -I in good agreement with previous determinations [1, 2]. Low temperature measurements of the dispersion parameter indicate that for shallow traps the distribution is weakly dependent on energy whereas for deeper traps (E < -- 0.2 eV) the distribution is exponential with a width of k T o ~-- 50 meV. A c k n o w l e d g e m e n t s - We are grateful to M.H. Brodsky
for providing the a-Si : H films, grown by R.J. Serino.
848
TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON REFERENCES
1. 2. 3. 4. 5. 6.
J.M. Hvam & M.H. Brodsky, Phys. Rev. Lett. 46, 371 (1981). T. Tiedje, J.M. Cebulka, D.L. Morel & B. Abeles, Phys. Rev. Lett. 46, 1425 (1981). T. Kagawa, S. Furukawa & N. Matsumoto, Phys. Rev. B26, 4714 (1982). C.-Y. Huang, S. Guha & S.J. Hudgens, Phys. Rev. B27, 7460 (1983). J. Shirafuji, H. Matsui & Y. Inuishi, J. Appl. Phys. 54, 3983 (1983). F.W. Schmidlin, Phys. Rev. B16, 2362 (1977).
7. 8. 9. 10. 11. 12.
Vol. 50, No. 9
T. Tiedje & A. Rose, Solid State Commun. 37, 49 (1980). J. Orenstein & M. Kastner, Solid State Commun. 40, 85 (1981). E.A. Schiff, Phys. Rev. B24, 6189 (1981). D.G. Taylor, T.J. Turley, M.L. Rodgers, S.H. Peterson & J.N. Demas, Rev. Sci. Instrum. 51,855 (1980). J. Orenstein, M.A. Kastner & V. Vaninov, Phil. Mag. B46, 23 (1982). W. Rehm, R. Fischer, J. Stuke & H. Wagner, Phys. Status Solidi (b) 79,539 (1977).
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
DISPERSIVE TRANSPORT AND TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON I.K. Kristensen and J.M. Hvam Fysisk Institut, Odense Universitet, DK-5230 Odense, Denmark
(Received 26 January 1984 by N.I. Meyer) Transient photocurrent measurements in arsenic-doped hydrogenated amorphous silicon show trap-controlled dispersive transport interrupted by trap saturation in an exponential band tail. A nonlinear temperature dependence of the dispersion parameter a is observed at low temperatures, indicating that the density of shallow traps (~ O. 1 eV below the mobility edge) is only weakly energy dependent.
The demarcation level Eu(t) [8], or quasi-Fermi level [9], specifying the relaxation of the carrier packet, sinks into the band tail logarithmically with time t according to
RECENTLY, a number of investigations [1-5] on transient photocurrents (TP) in hydrogenated amorphous silicon (a-Si : H) have provided evidence for dispersive transport [6] controlled by multiple trapping in an exponential distribution of trapping states below the mobility edge. The main features of the experiments are accounted for by the simple models, developed by Tiedje and Rose [7] and by Orenstein and Kastner [8]. They describe the relaxation of excess carriers after a short-pulse excitation by a distribution of localized carriers sinking deeper and deeper into the band tail states, and with recombinations only from extended states. One consequence of such a model is that trap saturation may occur in the deep band tail states [8, 9] if recombination is negligible on the time scale of carrier relaxation into these states. In the previous experiments, saturation effects were not reported. Specifically in relation to the experiments of Hvam and Brodsky [ 1], the nonobservation of saturation led Schiff [9] to question the validity of the generally accepted assumptions incorporated in the simple multiple trapping model. In the present work, we report measurements of TP in arsenic-doped a-Si: H which in the temperature range 1 7 5 - 3 0 0 K, show saturation effects that are in nice agreement with the model of Schiff [9]. At lower temperatures, saturation is not observed on the time scale of our experiment and furthermore the dispersion parameter deviates from the linear temperature dependence observed at higher temperatures [1, 2]. The simplest model, on the basis of which we shall discuss our results, assumes an exponential distribution of localized trapping states below the mobility edge (at E = Ee = 0): g(E) = go exp {E/kTo}
Ea(t) = -- kT in (rot),
(2)
where T is the temperature and Vo is an attempt to escape frequency. In the absence of recombination, the total excess electron density N
g(E) dE F(t) f~ J exp { [E-- Ea(t)]/kT} + 1
(3)
is conserved, determining at the same time the occupancy factor F(t) ~< 1 [9]. When F(t) ~ 1, standard dispersive transport is observed with a time dependent drift mobility given by Nc sin (an) p(t) = Po - - (rot) -I+c~, k Togo an
(4)
where go is the extended state electron mobility, N e is the effective density of states at the mobility edge, and a = T/To is the dispersion parameter. Saturation occurs when F(t) approaches unity and the time, ts, it takes is determined from equations ( 1 ) -
(3): = (Nsin(an)t-i/'x
(1)
with a width of ~ kTo. 845
Of course, recombination does take place and may interfere with the complete saturation of equation (5) - or even prevent saturation. This will depend on the relative rates of recombination and relaxation, i.e. on density (for bimolecular recombination) and temperature. We shall see in the present experiments that, when the temperature is not too low, saturation occurs prior to recombination, except at the highest densities. The experiments were performed on a 1 pm thick
846
TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON 10 3
Vol. 50, N'o. 9
100
1
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i N/No=I.O
<~ 102 zk
22t5K "", t q
I -I
Z Ld
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£ 0 T
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Fig. l. Transient photocurrent in arsenic-doped a-Si : H at 225 K for different excitation densities N. The maximum density No = 2 × 1017 cm -3. The arrows indicate the onset of saturation at time ts. film o f a - S i : H prepared by glow discharge decomposition of Sill4 with 0.05% AsH3 added for n-type doping. Deposition took place onto a quartz substrate, heated to 300°C, with predeposited molybdenum electrode stripes 1 mm apart. TP was excited by an Nz-gas laser pumped dye laser (Rh6G) with a pulse width of 5 nsec. The light was focussed to produce a homogeneous excitation density between the electrodes over a length of about 5 ram, and the intensity was controlled by neutral density filters. The maximum intensity was estimated to generate an initial electron density of No "" 2 x 1017 cm -3. Temperature control was obtained by mounting the sample on a copper block in a helium exchange gas of a variable temperature cryostat. The TP signals were processed by a digital signal averager based on a sampling oscilloscope, controlled by a microcomputer [ 10]. With a careful selection of preamplifiers and bias circuitry (bias voltage VB = 90 V), very accurate current transients were recorded covering 4 orders of magnitude in intensity and time, ranging from 50 nsec to 0.5 msec. Figure 1 shows the result of such measurements performed at 225 K and for several illumination intensities. The results are typical for many measurements. At the highest intensity, the TP does not follow any simple power law decay, but can be explained by a combination of dispersive transport and bimolecular recombination [11]. At lower intensities, the TP exhibits an initial power law decay interrupted by an incomplete saturation and a final recombination. The time, ts, for the onset of saturation depends on the illumination intensity, as seen in Fig. 1, and it also depends on the temperature. In Fig. 2, is plotted the saturation time vs excess carrier density for different temperatures. The points are experimental values and
0.1 0Ol
0.I EXCITATION DENSITY N/No
Fig. 2. Saturation time vs excitation density for different temperatures T = 175 K (x), 200 K (o), 225 K (c~), 250 K (e), 275 K (z~), and 300 K (+). The points are experimental and the curves are calculated from equation (5) with go = 10z° cm -3 (eV) -1- Uo = 1012 sec -1 , To = 575 K, andNo = 2 x 1017 cm -3. The points in the brackets are commented on in the text.
the curves are calculated from equation (5) with Uo = 1012 sec -1 ,go = 102o cm -3 (eV) -1 ,No = 2 x 1017 cm -3, a = T / T o and To = 575 K. In view of the different uncertainties involved, there is a satisfactory agreement between the experimental points and the calculated curves. For the latter, the horizontal axis is the initial carrier density N neglecting recombination. For the experimental points, N is assumed proportional to the illumination intensity which does not quite hold at high intensities (points in brackets in Fig. 2), due to the onset of bimolecular recombination. This is obvious from Fig. 1, but is also observed as a sublinear dependence of the initial current on illumination at high intensity. The values of a and To used above are determined independently from the slopes of the initial photocurrent decays (Fig. 1). In Fig. 3 is plotted the dispersion parameter a as a function of temperature from a large number of measurements on TP between 100 and 300 K. Above 170 K, a is seen to vary approximately linearly with temperature (a = T / T o , To = 575 K) in agreement with the simple model of multiple trapping in an exponential band tail. At lower temperatures this does not hold, a decreases stronger than
Vol. 50, No. 9 0.7
TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON I
I
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Fig. 3. Dispersion parameter a as a function of temperature. The points are experimental and the line represents a = T/To with To = 575 K. linearly with decreasing temperature and goes to zero around 100 K. In order to analyze this behaviour, it is important to realize what parts of the trap state distribution are probed in our experiments. This is illustrated in Fig. 4 showing, as a function of temperature, the energy range scanned by the demarcation level [equation (2)] from 50 nsec to 0.5 msec after a short pulse excitation. The lowest limit in any TP experiment is set by the Fermi level E F ( T ) , which in Fig. 4 is plotted as E F ( T ) = -- (Eo + 4 k T ) . Here Eo = 0.33 eV is the measured activation energy of the dark conductivity and 4 k T represents the statistical shift of the Fermi level with temperature [12]. It is now obvious from Fig. 4 that at low temperatures only a narrow and rather shallow region of the band tail distribution is probed by the TP. It is therefore tempting to suggest that the deviation from linearity in a(T) at low temperature is caused by a deviation from a purely exponential shape in the shallow parts of the trapping state distribution. Specifically, we suggest that only for energies more than 0.2 eV below the mobility edge is the density of states given by equation (1) with To = 575 K. For shallower states, the energy dependence is weaker and becomes negligibly small for energies around 0.1 eV below the mobility edge. A similar behaviour of ~(T) has recently been reported by Shirafuji et al. [5], only at higher temperatures and associated with a dominant distribution of traps around 0.2 eV below the mobility edge. In principle, the band tail shape should reveal itself in a single TP experiment at low'temperatures provided the dynamical range is sufficiently large. Due to the slower relaxation, however, this requires an extension of the time scale towards shorter as well as towards longer times. This is not trivial since the current sensitivity has
Fig. 4. The hatched region shows, as a function of temperature, the energy range scanned by the demarcation level (equation (2) with Vo = 1012 sec-1). The upper and lower boundaries are set by the experimental time window, 50 nsec-0.5 msec. At high temperatures, though, the lower boundary is set by the Fermi level, plotted as E F ( T ) = -- (Eo + 4 k T ) with Eo = 0.33 eV (see text). to be improved even more because the current decay is faster at low temperatures. We are working on this experimental problem. In the previous TP experiments of Hvam and Brodsky [ 1] on phosphorus-doped a-Si : H, saturation effects were not observed due to a rather high density of trapping states and a loss of carriers by monomolecular recombination for t > 10/~sec. On the other hand, an observed fast decay of TP before the power law sets in [ 1] and the observed activation energy of 0.1 eV of the initial photocurrent amplitude is consistent with a trap state distribution similar to the present suggestion. In [1 ], however, experiments were not performed at sufficiently low temperature to confirm this. In conclusion, we presently report TP measurements in arsenic-doped a-Si:H which, for the first time, show saturation effects and thus yield further support to the simple model [8, 9] of relaxation of excess carriers by multiple trapping in a distribution of band tail states. From the power law decays, the extended state mobility /.to can be determined from equation (4). With N c = 1020 cm -3 we find values in the range/lo = 10-20 cm 2 Vsec -I in good agreement with previous determinations [1, 2]. Low temperature measurements of the dispersion parameter indicate that for shallow traps the distribution is weakly dependent on energy whereas for deeper traps (E < -- 0.2 eV) the distribution is exponential with a width of k T o ~-- 50 meV. A c k n o w l e d g e m e n t s - We are grateful to M.H. Brodsky
for providing the a-Si : H films, grown by R.J. Serino.
848
TRAP SATURATION IN DOPED HYDROGENATED AMORPHOUS SILICON REFERENCES
1. 2. 3. 4. 5. 6.
J.M. Hvam & M.H. Brodsky, Phys. Rev. Lett. 46, 371 (1981). T. Tiedje, J.M. Cebulka, D.L. Morel & B. Abeles, Phys. Rev. Lett. 46, 1425 (1981). T. Kagawa, S. Furukawa & N. Matsumoto, Phys. Rev. B26, 4714 (1982). C.-Y. Huang, S. Guha & S.J. Hudgens, Phys. Rev. B27, 7460 (1983). J. Shirafuji, H. Matsui & Y. Inuishi, J. Appl. Phys. 54, 3983 (1983). F.W. Schmidlin, Phys. Rev. B16, 2362 (1977).
7. 8. 9. 10. 11. 12.
Vol. 50, No. 9
T. Tiedje & A. Rose, Solid State Commun. 37, 49 (1980). J. Orenstein & M. Kastner, Solid State Commun. 40, 85 (1981). E.A. Schiff, Phys. Rev. B24, 6189 (1981). D.G. Taylor, T.J. Turley, M.L. Rodgers, S.H. Peterson & J.N. Demas, Rev. Sci. Instrum. 51,855 (1980). J. Orenstein, M.A. Kastner & V. Vaninov, Phil. Mag. B46, 23 (1982). W. Rehm, R. Fischer, J. Stuke & H. Wagner, Phys. Status Solidi (b) 79,539 (1977).