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Defect-pool model parameters for amorphous silicon derived from field-effect measurements
Journal of Non-Crystalline Solids 164-166 (1993) 323-326 North-Holland
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Defect-Pool Model Parameters for Amorphous Silicon Derived from Field-Effect Measurements S.C. Deane and MJ. Powell Philips Research Laboratories, Redhill, Surrey, RH1 5HA, U.K. Field-effect conductance measurements are analysed using a new defect-pool model and an energy-dependent density of states for amorphous silicon is derived. We determine the key defect-pool parameters and in particular we find that the energy separation (A) between the D - states in n-type a-Si:H and the D + states in p-type a-Si:H is 0.44 eV. This result implies that the equilibrium density of states in bulk intrinsic amorphous silicon must contain about four times more charged defects than neutral defects. 1. INTRODUCTION There has been a great deal of interest in field-effect conductance measurements on hydrogenated amorphous silicon (a-Si:H) for more than 20 years [1, 2]. However, all work to date has assumed that the density of states is spatially homogeneous, i.e. the density of states measured was the true bulk density of states, We now believe this assumption is not generally true. The defect-pool model [3-5] proposes that the density and energy spectrum of defects in a-Si:H can be derived from thermal equilibrium arguments, and thus depends on the Fermi level at freeze in. Experimental evidence for the defect-pool model was demonstrated by high temperature thermal bias annealing of Tb-Ts [6-10], which results in a modification of the density of states. The equilibrium density of states depends on the Fermi level at freeze in, so an implication of the defect-pool model is that the density of states after bias annealing is inhomogeneous. In TFTs fixed charge in the gate insulator causes band-bending, leading to the same effect, so a homogeneous density of states only exists if bias annealing is carried out to cancel the effect of the fixed charge, In previous work we recognised this effect, but still used a homogeneous density of states model [6-9], where the result represents an average density of states weighted towards the interface. In this paper we use a new modelling method which uses an inhomogeneous density of states, as defined by our defect-pool model [5]. We use the fit of this model to experimental data to determine the key defect-pool model parameters. 2. THEORY In the field-effect experiment, measurement of both the electron and hole branches of the sheet conduc-
lance allows the determination of the density of states throughout the energy gap; the higher the density of states at the Fermi level the slower the increase of the sheet conductance with an increase in surface charge. To remove geometry dependences we normalise the T F r characteristics, to sheet conductance and surface charge [9], G = I,d/[V,dW/L], (1) Q~ ~- Vg~ i n s / q d i n s - Q I , (2) where G is the sheet conductance, I,d is the sourcedrain current, V~a is the source-drain voltage, W/L is the width to length ratio of the device, Q, is the surface charge density (cm-~) in the semiconductor, QI is the insulator fixed charge, Vg is the gate voltage, ein, is the insulator dielectric constant, q is the electronic charge, and din, is the insulator thickness. Our new computer program calculates both electron and hole branches of the field-effect conductance, before and after high temperature thermal bias annealing, using a single set of defect-pool model input parameters. The program fully accounts for the inhomogeneous density of states, and fitting the experimental transfer characteristics allows determination of the defect-pool parameters. The defect-pool model [3-5] proposes that there is a large pool of potential defect sites, and that the formation energy of a defect depends on the defect energy and the Fermi energy. If the Fermi level is raised towards the conduction band, by electron accumulation or n-type doping, then at equilibrium most defects will be negatively charged, and this will favour the formation of defects in the lower half of the band gap. Similarly, if the Fermi energy was lowered towards the valence band, by hole accumulation or p-type doping, then most defects would be positively charged and
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers R.V. All rights reserved.
324
S.C. Deane, M.J. PoweU / Defect pool model parameters for amorphous silicon
would form in the upper part of the band gap. When the Fermi level is in mid-gap, as in intrinsic material, then defects of all three charge states will be formed, and the relative density °fcharged and neutral defects depends on the defect-pool parameters. The states formed as D - , D °, and D +, at equilibrium, we label as De, Oz, and Oh respectively. At high temperatures, equilibrium is maintained on experimental time scales, giving a temperature and Fermi level dependent density of states. A s w e c o o l , the density of states becomes effectively fixed. The temperature at which this happens is called the freeze in temperature, T*, which we take as 500 K. Below T* the density of states is constant, but the electronic occupancy of the states can change as the Fermi level moves. Thus, for example, D + states are those formed as negatively charged states which have subsequently lost two elecIrons. The defect-pool model leads to the result that D O/- transitions can occur at lower energy than D +/° transitions, even though each defect has a positive correlation energy, Recently, we presented an improved defect-pool model [5, 11 ], with an analytical expression for the density of states, D(E), in terms of the defect-pool parameters: tr, the gaussian width of the defect-pool; /~,~0, the characteristic energy of the valence band tail, which we take as temperature dependent [121; U, the defect correlation energy, and i, the number of Sill bonds mediating the weak bond breaking event, The key new result was an analytic expression for the energy-dependent density of states which depends on i, and we derived a simple expression for the energy separation, A, between D O/- and D +/° transition energies, A =
2~r2 -- U. ~7~o*+ -~kTi.
(3)
It is useful to represent the density of states D(E) in the form of a one electron density of states, g(E). For defects with a positive correlation energy U > 3kT, g(E) = D ( E + k T In 2 ) + D ( E - U - k T In 2), where the k T In 2 terms arise due to the spin degeneracy of the neutral defect. The first term comes from the +/0 transitions, the second from the 0/- transitions. The apparent correlation energy is U,f! = U + 2kTln 2, and g(E) is temperature dependent, even when D(E) is not. On a one electron density of states the energy
102° 10TM ~." ]01a ~ 7 ~ 10v
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Figure 1. One electron density of states in intrinsic a-Si:H with components shown. separation D°~I- - D +1° is A' = LX- 2kT In 2. The field-effect effectively measures A t and the integrated density of states (cm-2). The latter is mainly determined by E~0 [5, 11, 13], and so ~r is determined from equation (3), since we fix U--0.2 eV and i=2 [5, 11]. Figure 1 shows the one electron density of states (at 313 K), for our defect-pool model of bulk intrinsic a-Si:H [5, 11]. E,~0=56 meV (E~0--45 meV at room temperature) and A'=0.4 eV (A=0.44 eV). Both transitions are shown for each component (D,, D,, and Dh). The D +/° (D ° / - ) transition is only accessible after the D O/- (D +/°) transition has occurred. In the field-effect technique, the sum of all six peaks (and the band tails) is observed as the Fermi level is swept through a frozen in density of states. 3. EXPERIMENTS
Experiments were performed on two types of devices using either a thermal oxide for the gate insuiator or PECVD silicon nitride deposited sequentially with the a-Si:H layer. We refer to these devices as THOX2 and SIN2 respectively, and fabrication details are given elsewhere [10]. Figure 2(a) shows the measured normalised transfer characteristics of a THOX2 device which has been bias annealed both positively and negatively. Qb~ is the value of Q, which is maintained, via a constant Va, during the bias annealing process. Figure 2(b) shows the modelled characteristics with E*0=74 meV (E~o=66 meV at room temperature) and A--0.44 eV. We have also performed the same fitting process for a SIN2 device. In this case we used E~0=56 meV
S.C. Deane, M.J. Powell I Defect pool model parameters for amorphous silicon
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Figure 2. Measured (a) and modelled (b) characteristics for bias annealing of THOX2 device. Dotted line, bias annealing surface charge Qba = -16.5 x 10 z1cm-2; solid line Qb~ = -6.5 x 10ncm -2, dashedline Qb,~ = -t-3.5 × 10 zz cm -2, chain line Qb,~ = +13.5 x 1011cm -2.
Figure 3. (a) One electron densities of states for the THOX2 device, in the bulk and at the interface after the extremes of bias annealing. (b) One electron densities of states showing the variation fi'om the bulk to the interface after positive bias annealing in SIN2 device.
(Ev0--45 meV at room temperature), a lower value than for the oxide, which we believe corresponds to a higher quality interface [10], and A=0.44 eV, the same as before, Figure 3(a)shows the oneelectron densities of states for the a-Si:H in the THOX2 device in the bulk and near the interface for the extremes of positive and negative bias anneal. Figure 3(b) shows how the one electron density of states varies from the bulk to the interface of the positively bias annealed SIN2 device, demonstrating the extent of the spatial inhomogeneity of the density of states,
states, and A, which affects the energy spectrum. The variation in E~o for different devices we attribute to variations in interface strain, or perhaps impurity tailing [10]. The value we use for the SIN2 device is the same as we would expect in good quality bulk a-Si:H, E~0=56 meV (E~0--45 meV at room temperature). We take this as evidence of the high quality of this interface. Note that there are no interface states in our model. The density of states peaks at the interface as the band bending is at its most extreme, giving a high density of states due to the defect-pool model, but there are no states of different microscopic origin, located only at the interface. We find A=0.44 eV for both devices, even though E~o changes significantly. Other experimental techniques find similar values of A in bulk material [11]. We take this as evidence that this value of A isafunda-
4. DISCUSSION Our new modelling program achieves a very good fit with experimental data. The only free parameters are E~0, which affects the integrated density of
S.C.Dearie,Md. PowellI Defectpoolmodelparametersfor amorphoussilicon
326
mental property of a-Si:H. Figure 4 shows how the ratio of charged to neutral defects would change with A, according to our defect-pool model [11]. A=0.44 eV corresponds to there being about four times as many charged defects compared to neutral defects in intrinsic a-Si:H. For a fixed A, E~0 has little effect on the ratio of charged to neutral defects, even though the total density of states will change significantly [111. If U were increased to 0.4 eV (from 0.2 eV), there would still be more charged than neutral defects in intrinsic a-Si:H for A=0.44 eV, but the quality of fit of our model would be reduced. 10
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Figure 5. Modelledtransfer characteristics, as figure 2(b)
butwithA=O.leV, forwhich(D,+Dh)/D=,~,l.
defect-pool parameters which allow neutral defects to dominate in intrinsic material do not lead to a good fit with experimental data.
,bf~/~ .~z~
REFERENCES 1. W.E. Spear and P.G. LeComber, J. Non-Cryst. Solids 8-10 (1972) 727. 2. M.J. Powell, Phil. Mag. B 43 (1981) 93. 3. Y. Bar-Yam, D. Adler, and J.D. Joannopoulos, Phys. Rev. Lett 57 (1986) 467. 4. K. Winer, Phys. Rev. Lett. 63 (1989) 1487; Phys. Rev. B 41 (1990) 12150. 5. S.C. Deane and MJ. Powell, Phys. Rev. Lett. 70 (1993) 1654. 6. S.C. Dearie, MJ. Powell, J.R. Hughes, I.D. French, and W.I. Milne, Appl. Phys. Lett. 57
~
1 0.0
~
¢,%,,~ ~ " .~.%~/~
~
+
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, i , 0.4 0.6 0.8 A (eX0 Figure 4. The ratio of charged to neutral defects as a function of A. Thick line Evo=56 meV, U--0.2 eV; thin lines vary one parameter,each as labelled. 0.2
In figure 5 we show the modelled characteristics of the THOX2 device using A--0.1 eV, for which the densities of charged and neutral defects are roughly equal. All other parameters are identical to those used in figure 2(b). The quality of fit is much poorer, with large discrepancies in the prethreshold slopes. This demonstrates that our TbT experiments can not be modelled with a density of states which would give more neutral than charged defects in bulk intrinsic a-Si:H. 5. CONCLUSIONS We have determined that the key defect-pool parameter A--0.44 eV in a-Si:H. This value of A implies that there are about four times more charged than neutral defects in intrinsic a-Si:H. Combinations of
(1990) 1416. 7. MJ. Powell, S.C. De'me, J.R. Hughes, I.D. French, and W.I. Milne, Philos. Mag. B 63 (1991) 325. 8. M.J. Powell, C. van Berkel, and S.C. Dearie, J. Non-Cryst. Solids 137&138 (1991) 1215. 9. M.J. Powell, C. van Berkel, A.R. Franklin, S.C. Deane, and W.I. Milne, Phys. Rev. B 45 (1992) 4160. 10. S.C. Deane, FJ. Clough, W.I. Milne, and M_I. Powell, J. Appl. Phys. 73 (1993) 2895. 11. M.J. Powell and S.C. Dearie, Phys. Rev. B, (in press). 12. M. Stutzmann, Phil. Mag. Lett. 66 (1992) 147. 13. M. Stutzmann, Phil. Mag. B 60 (1989) 531.
~
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Defect-Pool Model Parameters for Amorphous Silicon Derived from Field-Effect Measurements S.C. Deane and MJ. Powell Philips Research Laboratories, Redhill, Surrey, RH1 5HA, U.K. Field-effect conductance measurements are analysed using a new defect-pool model and an energy-dependent density of states for amorphous silicon is derived. We determine the key defect-pool parameters and in particular we find that the energy separation (A) between the D - states in n-type a-Si:H and the D + states in p-type a-Si:H is 0.44 eV. This result implies that the equilibrium density of states in bulk intrinsic amorphous silicon must contain about four times more charged defects than neutral defects. 1. INTRODUCTION There has been a great deal of interest in field-effect conductance measurements on hydrogenated amorphous silicon (a-Si:H) for more than 20 years [1, 2]. However, all work to date has assumed that the density of states is spatially homogeneous, i.e. the density of states measured was the true bulk density of states, We now believe this assumption is not generally true. The defect-pool model [3-5] proposes that the density and energy spectrum of defects in a-Si:H can be derived from thermal equilibrium arguments, and thus depends on the Fermi level at freeze in. Experimental evidence for the defect-pool model was demonstrated by high temperature thermal bias annealing of Tb-Ts [6-10], which results in a modification of the density of states. The equilibrium density of states depends on the Fermi level at freeze in, so an implication of the defect-pool model is that the density of states after bias annealing is inhomogeneous. In TFTs fixed charge in the gate insulator causes band-bending, leading to the same effect, so a homogeneous density of states only exists if bias annealing is carried out to cancel the effect of the fixed charge, In previous work we recognised this effect, but still used a homogeneous density of states model [6-9], where the result represents an average density of states weighted towards the interface. In this paper we use a new modelling method which uses an inhomogeneous density of states, as defined by our defect-pool model [5]. We use the fit of this model to experimental data to determine the key defect-pool model parameters. 2. THEORY In the field-effect experiment, measurement of both the electron and hole branches of the sheet conduc-
lance allows the determination of the density of states throughout the energy gap; the higher the density of states at the Fermi level the slower the increase of the sheet conductance with an increase in surface charge. To remove geometry dependences we normalise the T F r characteristics, to sheet conductance and surface charge [9], G = I,d/[V,dW/L], (1) Q~ ~- Vg~ i n s / q d i n s - Q I , (2) where G is the sheet conductance, I,d is the sourcedrain current, V~a is the source-drain voltage, W/L is the width to length ratio of the device, Q, is the surface charge density (cm-~) in the semiconductor, QI is the insulator fixed charge, Vg is the gate voltage, ein, is the insulator dielectric constant, q is the electronic charge, and din, is the insulator thickness. Our new computer program calculates both electron and hole branches of the field-effect conductance, before and after high temperature thermal bias annealing, using a single set of defect-pool model input parameters. The program fully accounts for the inhomogeneous density of states, and fitting the experimental transfer characteristics allows determination of the defect-pool parameters. The defect-pool model [3-5] proposes that there is a large pool of potential defect sites, and that the formation energy of a defect depends on the defect energy and the Fermi energy. If the Fermi level is raised towards the conduction band, by electron accumulation or n-type doping, then at equilibrium most defects will be negatively charged, and this will favour the formation of defects in the lower half of the band gap. Similarly, if the Fermi energy was lowered towards the valence band, by hole accumulation or p-type doping, then most defects would be positively charged and
0022-3093/93/$06.00 © 1993 - Elsevier Science Publishers R.V. All rights reserved.
324
S.C. Deane, M.J. PoweU / Defect pool model parameters for amorphous silicon
would form in the upper part of the band gap. When the Fermi level is in mid-gap, as in intrinsic material, then defects of all three charge states will be formed, and the relative density °fcharged and neutral defects depends on the defect-pool parameters. The states formed as D - , D °, and D +, at equilibrium, we label as De, Oz, and Oh respectively. At high temperatures, equilibrium is maintained on experimental time scales, giving a temperature and Fermi level dependent density of states. A s w e c o o l , the density of states becomes effectively fixed. The temperature at which this happens is called the freeze in temperature, T*, which we take as 500 K. Below T* the density of states is constant, but the electronic occupancy of the states can change as the Fermi level moves. Thus, for example, D + states are those formed as negatively charged states which have subsequently lost two elecIrons. The defect-pool model leads to the result that D O/- transitions can occur at lower energy than D +/° transitions, even though each defect has a positive correlation energy, Recently, we presented an improved defect-pool model [5, 11 ], with an analytical expression for the density of states, D(E), in terms of the defect-pool parameters: tr, the gaussian width of the defect-pool; /~,~0, the characteristic energy of the valence band tail, which we take as temperature dependent [121; U, the defect correlation energy, and i, the number of Sill bonds mediating the weak bond breaking event, The key new result was an analytic expression for the energy-dependent density of states which depends on i, and we derived a simple expression for the energy separation, A, between D O/- and D +/° transition energies, A =
2~r2 -- U. ~7~o*+ -~kTi.
(3)
It is useful to represent the density of states D(E) in the form of a one electron density of states, g(E). For defects with a positive correlation energy U > 3kT, g(E) = D ( E + k T In 2 ) + D ( E - U - k T In 2), where the k T In 2 terms arise due to the spin degeneracy of the neutral defect. The first term comes from the +/0 transitions, the second from the 0/- transitions. The apparent correlation energy is U,f! = U + 2kTln 2, and g(E) is temperature dependent, even when D(E) is not. On a one electron density of states the energy
102° 10TM ~." ]01a ~ 7 ~ 10v
~(
i
.
~
\
~
~ /~' ~ i.f~ Ef
D~
t
.
J
,
D _ ~3
~ /, / / Dh
~' ~
101e ! ~ ~ " ~--A = ./,'"/~.'i 10ts ,'~ 0.0 O.4 0.8 1.2
"",('"
.
/---4 +~ I ~
""~.!,~
E-E~(eV)
; >'\,"S 1.6
Figure 1. One electron density of states in intrinsic a-Si:H with components shown. separation D°~I- - D +1° is A' = LX- 2kT In 2. The field-effect effectively measures A t and the integrated density of states (cm-2). The latter is mainly determined by E~0 [5, 11, 13], and so ~r is determined from equation (3), since we fix U--0.2 eV and i=2 [5, 11]. Figure 1 shows the one electron density of states (at 313 K), for our defect-pool model of bulk intrinsic a-Si:H [5, 11]. E,~0=56 meV (E~0--45 meV at room temperature) and A'=0.4 eV (A=0.44 eV). Both transitions are shown for each component (D,, D,, and Dh). The D +/° (D ° / - ) transition is only accessible after the D O/- (D +/°) transition has occurred. In the field-effect technique, the sum of all six peaks (and the band tails) is observed as the Fermi level is swept through a frozen in density of states. 3. EXPERIMENTS
Experiments were performed on two types of devices using either a thermal oxide for the gate insuiator or PECVD silicon nitride deposited sequentially with the a-Si:H layer. We refer to these devices as THOX2 and SIN2 respectively, and fabrication details are given elsewhere [10]. Figure 2(a) shows the measured normalised transfer characteristics of a THOX2 device which has been bias annealed both positively and negatively. Qb~ is the value of Q, which is maintained, via a constant Va, during the bias annealing process. Figure 2(b) shows the modelled characteristics with E*0=74 meV (E~o=66 meV at room temperature) and A--0.44 eV. We have also performed the same fitting process for a SIN2 device. In this case we used E~0=56 meV
S.C. Deane, M.J. Powell I Defect pool model parameters for amorphous silicon
10~
325
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................ 'i o 10-" 10-'2
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--.
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10~ 20
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/
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~
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,
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,
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,
,
,
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Figure 2. Measured (a) and modelled (b) characteristics for bias annealing of THOX2 device. Dotted line, bias annealing surface charge Qba = -16.5 x 10 z1cm-2; solid line Qb~ = -6.5 x 10ncm -2, dashedline Qb,~ = -t-3.5 × 10 zz cm -2, chain line Qb,~ = +13.5 x 1011cm -2.
Figure 3. (a) One electron densities of states for the THOX2 device, in the bulk and at the interface after the extremes of bias annealing. (b) One electron densities of states showing the variation fi'om the bulk to the interface after positive bias annealing in SIN2 device.
(Ev0--45 meV at room temperature), a lower value than for the oxide, which we believe corresponds to a higher quality interface [10], and A=0.44 eV, the same as before, Figure 3(a)shows the oneelectron densities of states for the a-Si:H in the THOX2 device in the bulk and near the interface for the extremes of positive and negative bias anneal. Figure 3(b) shows how the one electron density of states varies from the bulk to the interface of the positively bias annealed SIN2 device, demonstrating the extent of the spatial inhomogeneity of the density of states,
states, and A, which affects the energy spectrum. The variation in E~o for different devices we attribute to variations in interface strain, or perhaps impurity tailing [10]. The value we use for the SIN2 device is the same as we would expect in good quality bulk a-Si:H, E~0=56 meV (E~0--45 meV at room temperature). We take this as evidence of the high quality of this interface. Note that there are no interface states in our model. The density of states peaks at the interface as the band bending is at its most extreme, giving a high density of states due to the defect-pool model, but there are no states of different microscopic origin, located only at the interface. We find A=0.44 eV for both devices, even though E~o changes significantly. Other experimental techniques find similar values of A in bulk material [11]. We take this as evidence that this value of A isafunda-
4. DISCUSSION Our new modelling program achieves a very good fit with experimental data. The only free parameters are E~0, which affects the integrated density of
S.C.Dearie,Md. PowellI Defectpoolmodelparametersfor amorphoussilicon
326
mental property of a-Si:H. Figure 4 shows how the ratio of charged to neutral defects would change with A, according to our defect-pool model [11]. A=0.44 eV corresponds to there being about four times as many charged defects compared to neutral defects in intrinsic a-Si:H. For a fixed A, E~0 has little effect on the ratio of charged to neutral defects, even though the total density of states will change significantly [111. If U were increased to 0.4 eV (from 0.2 eV), there would still be more charged than neutral defects in intrinsic a-Si:H for A=0.44 eV, but the quality of fit of our model would be reduced. 10
'
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~' I
#,~'j ~ .
~
~
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~, .~"
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/
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20
30
Q, (lOUelectr°ns/em2)
Figure 5. Modelledtransfer characteristics, as figure 2(b)
butwithA=O.leV, forwhich(D,+Dh)/D=,~,l.
defect-pool parameters which allow neutral defects to dominate in intrinsic material do not lead to a good fit with experimental data.
,bf~/~ .~z~
REFERENCES 1. W.E. Spear and P.G. LeComber, J. Non-Cryst. Solids 8-10 (1972) 727. 2. M.J. Powell, Phil. Mag. B 43 (1981) 93. 3. Y. Bar-Yam, D. Adler, and J.D. Joannopoulos, Phys. Rev. Lett 57 (1986) 467. 4. K. Winer, Phys. Rev. Lett. 63 (1989) 1487; Phys. Rev. B 41 (1990) 12150. 5. S.C. Deane and MJ. Powell, Phys. Rev. Lett. 70 (1993) 1654. 6. S.C. Dearie, MJ. Powell, J.R. Hughes, I.D. French, and W.I. Milne, Appl. Phys. Lett. 57
~
1 0.0
~
¢,%,,~ ~ " .~.%~/~
~
+
10-7
, i , 0.4 0.6 0.8 A (eX0 Figure 4. The ratio of charged to neutral defects as a function of A. Thick line Evo=56 meV, U--0.2 eV; thin lines vary one parameter,each as labelled. 0.2
In figure 5 we show the modelled characteristics of the THOX2 device using A--0.1 eV, for which the densities of charged and neutral defects are roughly equal. All other parameters are identical to those used in figure 2(b). The quality of fit is much poorer, with large discrepancies in the prethreshold slopes. This demonstrates that our TbT experiments can not be modelled with a density of states which would give more neutral than charged defects in bulk intrinsic a-Si:H. 5. CONCLUSIONS We have determined that the key defect-pool parameter A--0.44 eV in a-Si:H. This value of A implies that there are about four times more charged than neutral defects in intrinsic a-Si:H. Combinations of
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