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p-a-Si:H interface
Journal of Non-Crystalline Solids 262 (2000) 99±105
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The eect of surface states at the SnO2=p-a-Si:H interface J.S.C. Prentice * Department of Physics, Rand Afrikaans University, P.O. Box 524, Auckland Park 2006, South Africa Received 2 July 1999; received in revised form 3 November 1999
Abstract A one-dimensional photovoltaic cell simulation has been used to model a SnO2 =p-a-Si:H interface, in thermodynamic equilibrium. Central to the study is the eect that acceptor-like surface states in the p-a-Si:H have on the contact potential at this interface. Such surface states were assumed to have a Gaussian distribution. It was found that in order to maintain a constant negative contact potential in the p-layer, the surface state concentration needed to be increased as the distribution was shifted towards the conduction band edge. It was found that, for a given surface state concentration, the contact potential became more negative as the distribution was shifted towards the conduction band edge. It was also found that, when the surface states were located at a ®xed position in the gap, increasing their concentration resulted in a decrease in the magnitude of the contact potential, with the contact potential eventually becoming positive for large concentrations. Increases in the dopant concentration also caused the contact potential to become more negative. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 02.60.Cb; 61.43.Dq; 68.35.Dv; 73.40.Lq
1. Introduction We have developed a one-dimensional photovoltaic (PV) cell simulation (designated RAUPV2), which solves the semiconductor equations numerically, assuming a drift-diusion model [1]. In the course of simulating an a-Si:H p-i-n PV cell, using RAUPV2, it was found that a contact potential of approximately ÿ0:19 eV needed to be implemented at the front surface of the cell, which was in contact with a layer of SnO2 (in this paper, the contact potential in the p-layer is the dierence between the electron potential energy W at the interface and in the p-layer bulk). Following the study by Smole et al. [2], in which the eect of *
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surface states on the contact potential at a SnO2 or ZnO and p-a-Si:C:H interface was studied, this paper will study the eect of acceptor-like surface states on the contact potential at a SnO2 /p-a-Si:H interface. Experimentally, it is known that the contact potential (in the p-layer) at this interface is negative [3], implying band-bending towards the valence band edge.
2. Simulation of the SnO2 =p interface Here, the simulation RAUPV2 will be used to simulate the eect of acceptor-like surface states at the SnO2 =p interface, in thermodynamic equilibrium. The simulation considers two bulk layers, each of thickness 400 nm, of SnO2 and p-a-Si:H.
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The input parameters for the p-layer are given in Table 1 and include a donor-like dangling-bond defect concentration of D 3:6 1018 cmÿ3 , located at 1.00 eV above the valence band edge EV . These defects are Gaussian distributed, with standard deviation r 0:15 eV. The parameters in Table 1 and the dangling-bond parameters, have been obtained by determining average values from a large variety of literature sources and so are considered to be generally representative of a-Si:H. The input parameters for the SnO2 layer were taken from Smole et al. [2]. The most important parameter for the SnO2 layer is the eective doping. This is the parameter that determines the Fermi level position in the SnO2 layer which, in turn, in¯uences the Fermi level mismatch at the SnO2 =p-a-Si:H interface. The parameters used by Smole et al. suggest a conduction electron concentration of about 1020 cmÿ3 . Such a concentration is supported experimentally [4,5]. Simulating this junction without incorporating any acceptor-like surface states in the p-layer, yields a contact potential of ÿ0:47 eV, which is much larger than the required ÿ0:19 eV. However, incorporating a surface state concentration of 7:56 1012 cmÿ2 (which corresponds to 2:0 1019 cmÿ3 ) in the ®rst 6.25 nm of the p-layer at 0.4 eV above EV , yields a contact potential of ÿ0:19 eV. Clearly, it is necessary to include surface
states at this interface because of their eect on the contact potential. The surface states implemented here have been assumed to follow a Gaussian distribution, also with standard deviation r 0:15 eV. The carrier capture cross-sections for these surface states were taken to be rn 9:0 10ÿ16 cm2 and rp 1:0 10ÿ14 cm2 , the same as used for the dangling-bond states. 2.1. Surface state concentrations Fig. 1 shows a plot of surface state concentration NSS cmÿ2 vs. ESS ÿ EV , which denotes the separation of the peak of the surface states distribution and the valence edge, for a surface layer thickness dS of 6.25 nm. Also shown are curves for dS 2:75 nm and dS 9:75 nm, the signi®cance of which will be discussed later. These values of NSS are such that, for each value of ESS ÿ EV , the contact potential is ÿ0:19 eV. It is clear that as NSS is moved away from the valence edge, so it must increase in order to preserve the contact potential of ÿ0:19 eV. This is easily explained. Since NSS is a concentration of acceptor-like states, these states capture electrons from both the conduction- and valence bands. When NSS is close to the valence band, it is electron capture from the valence band that dominates. As NSS moves away from the
Table 1 Input parameters for p-a-Si:H used in RAUPV2 Mobility gap, EG (eV) Electron anity, v (eV) Relative dielectric permittivity, e Densities of states, NC ; NV cmÿ3 Dopant concentration, NA cmÿ3 Dopant ionization energy (meV)
1.87 3.90 11.8 2:0 1020 4:5 1018 45
Conduction band tail states Amplitude (cmÿ3 eVÿ1 ) Slope, EC0 (meV) Electron capture cross-section, rn cm2 Hole capture cross-section, rp cm2
1:5 1021 40 2:1 10ÿ17 2:5 10ÿ15
Valence band tail states Amplitude (cmÿ3 eVÿ1 ) Slope, EV0 (meV) Electron capture cross-section, rn cm2 Hole capture cross-section, rp cm2
21
1:5 10 59 2:5 10ÿ15 2:1 10ÿ17
Fig. 1. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the surface layer thickness dS . The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
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valence band, this valence electron capture becomes less eective and so the hole concentration in the valence band is reduced. Since np n2i (where ni is the intrinsic carrier concentration) in thermodynamic equilibrium, there is an associated increase in the conduction electron concentration. Thus, the ratio n=p increases as NSS moves away from the valence band. Of course, the ratio n=p gives a measure of the position of EF within the gap (when n=p 1; EF is at midgap). Thus, an increase in n=p implies that EC has moved closer to EF , which corresponds to a negative contact potential that becomes more negative as NSS moves further away from EV . Now, if NSS induces a contact potential of say, ÿ0:19 eV, then, when NSS is moved towards EC , the contact potential it induces will become more negative than ÿ0:19 eV. To ensure that the contact potential remains ®xed at ÿ0:19 eV, NSS must be increased as it is moved towards EC because this will lead to a larger amount of electrons being captured from the valence band, an increase in p, a decrease in n=p; and ®nally, a reduction in the magnitude of the contact potential. In Fig. 2, various surface state concentrations NSS are positioned at various points in the gap and the contact potential as a function of gap position ESS ÿ EV of these states is plotted. It is seen that the contact potential becomes more negative as ESS ÿ EV increases.
Fig. 2. Contact potential at the SnO2 =p interface vs. surface state energy position ESS ÿ EV , for a variety of surface state concentrations.
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Fig. 3. Contact potential as a function of surface state concentration NSS ; when NSS is located at various positions above EV .
In Fig. 3, the contact potential as a function of NSS is plotted, when NSS is at various positions in the gap. As can be seen, the contact potential decreases (in magnitude) for all values of ESS ÿ EV . This is due to the fact that as NSS increases, so more valence electrons are captured, hence p increases, n=p decreases and EC moves away from EF . It is clear that both the energy position and magnitude of NSS in¯uence the contact potential. Figs. 2 and 3 essentially convey the same information, but for the sake of clarity we have presented both. 2.2. Sensitivity to various parameters It is necessary to investigate the eect of variations in certain parameters on the value of NSS required to induce a contact potential of ÿ0:19 eV. Let us refer to this value of NSS as the `target' T value, denoted NSS in the remainder of this paper. T of varying the surface In Fig. 1 the eect on NSS layer thickness dS is shown. It is immediately clear that dS does not exert a particularly strong eect T , particularly for large values of ESS ÿ EV . on NSS We see that increasing dS , at any particular value T to be decreased. This is of ESS ÿ EV , requires NSS due simply to the fact that an increase in dS increases the number of surface states in the surface layer. This means that more electrons can be trapped, the p-layer becomes more p-type, EV moves towards EF and so the contact potential
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would be become less negative than ÿ0:19 eV. To preserve the contact potential of ÿ0:19 eV then, it T , as suggested by Fig. 3. is necessary to decrease NSS In Fig. 1 the width of the surface state distribution r is ®xed at 0.15eV and the eective donor concentration in the SnO2 layer ND SnO2 is ®xed at T is more 1020 cmÿ3 . This ®gure indicates that NSS sensitive to changes in dS when ESS ÿ EV is small. T Fig. 4 shows NSS vs. ESS ÿ EV for three values of the width of the surface state distribution r. It is T must be declear that as r is increased so NSS creased, for each ESS ÿ EV . This is because increasing the width of the surface state distribution brings more surface states closer to EV , resulting in increased eective p-type doping, a shift of EV towards EF and hence, the contact potential becomes less negative. Again, to preserve the contact potential of ÿ0:19 eV, it is necessary to decrease T . In Fig. 4 dS is ®xed at 6.25 nm and ND SnO2 NSS is ®xed at 1020 cmÿ3 . It is important to note that T NSS is particularly sensitive to changes in r for large values of ESS ÿ EV . T vs. ESS ÿ EV for three values of Fig. 5 shows NSS the eective donor concentration in the SnO2 layer ND SnO2 . Increasing ND SnO2 simply enhances the electron concentration in the SnO2 layer. This means that EC in the SnO2 layer moves towards EF . Thus, at the interface, EC in the a-Si:H layer
Fig. 5. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the SnO2 donor dopant concentration ND SnO2 ). The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
also moves towards EF , resulting in the contact potential becoming more negative. We see from Fig. 3 that if the contact potential is more negative than ÿ0:19 eV, for any value of ESS ÿ EV , the surface state concentration must be increased to preserve the contact potential of ÿ0:19 eV. It is T is not particularly interesting to note that NSS sensitive to the changes in ND SnO2 for any values of ESS ÿ EV . 2.3. Parameters for the surface states
Fig. 4. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the surface state distribution width r. The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
One of the goals of this paper is to attempt to ®nd values for the various surface state parameters. Certainly little is known about the surface states in a-Si:H, as may be deduced from the recent review by Balberg et al. [6]. Certainly, there is very little knowledge concerning the nature of the surface state distribution (whether or not it actually is Gaussian, or uniformly distributed throughout the gap) and the carrier capture cross sections of the surface states. Nevertheless, it would appear that an empirical upper limit of 1014 cmÿ2 can be placed on NSS [6]. This is the horizontal line in Figs. 1, 4 and 5. This indicates that if ÿ0:19 eV is an appropriate contact potential, then the position of the surface state concentration that induces this contact potential relative to the valence band has
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an upper bound. The value of this upper bound varies according to the values of other surface state parameters. T is In Fig. 1 we see that the upper limit on NSS breached when ESS ÿ EV is greater than approximately 0.725 eV, for all three values of dS considered here. Similar behaviour is apparent in Fig. 5, T is breached when where the upper limit on NSS ESS ÿ EV is also greater than approximately 0.725 eV, for all three values of ND SnO2 considered. However, in Fig. 4 it is clear that the value of T is breaESS ÿ EV at which the upper limit on NSS ched is strongly dependent on the value of r. When r 0:10 eV the breach value of ESS ÿ EV is about 0.65 eV and when r 0:20 eV it is about 0.825 eV. To begin with, we would like to choose a value for ESS ÿ EV . Fig. 5 indicates that any value less than about 0.725 eV would be suitable, due to the T on the values of lack of sensitivity of NSS ND SnO2 . Fig. 4 indicates that we should steer clear of values near to 0.6 eV and above, because T on r of the apparently strong dependence of NSS for those values of ESS ÿ EV . On the other hand, T is more sensitive to variaFig. 1 shows that NSS tions in dS for low values of ESS ÿ EV . It would seem from these ®gures that a `safe, middle-of-theroad' value, for which there is minimal sensitivity to dS ; ND SnO2 and r would be ESS ÿ EV 0:4 eV. Now, at this value of ESS ÿ EV in each ®gure, T have been determined, giving a three values of NSS total of nine in all. We are tempted to take the T 8:28 1012 cmÿ2 . average, which gives NSS Simple linear interpolation at ESS ÿ EV 0:4 eV in Figs. 4 and 5 allows values for dS and r to be inferred. These are found to be r 0:1435 eV and dS 5:7976 nm. We prefer to retain the value of ND SnO2 1020 cmÿ3 in the light of experimental T is clearly insupport for this value. Besides, NSS sensitive to variations in ND SnO2 . Simulating the interface using these parameter values gives a contact potential of ÿ0:1902 eV, in excellent agreement with the target value of ÿ0:19 eV assumed at the beginning of this paper. In Fig. 6, the contact potential at the SnO2 =p interface as a function of dopant concentration in the p-layer is shown, in the absence of any acceptor-like surface states. Since the eect of ac-
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Fig. 6. Contact potential at the SnO2 =p interface, as a function of dopant concentration NA in the p-layer, in the absence of any surface states. The horizontal line indicates a contact potential of ÿ0:19 eV.
ceptor-like surface states is to reduce the contact potential, the contact potentials shown in Fig. 6 represent the largest contact potentials that can exist at the SnO2 =p interface for the indicated dopant concentrations. It can be seen that large contact potentials ( ÿ0:47 eV) occur for dopant concentrations greater than about 3:2 1018 cmÿ3 , while for dopant concentrations less than this value the contact potential is small and is, in fact, positive near a dopant concentration of about 2:0 1018 cmÿ3 . This is due to the Fermi level position in the p-layer being in¯uenced by the dopant concentration. The contact potential arises from the misalignment of the Fermi levels in the SnO2 and the p-layer. As the dopant concentration is reduced in the p-layer, the Fermi level in the player moves towards midgap and the misalignment is reduced, thus reducing the contact potential. The eect is compounded by the presence of the large concentration of donor-like dangling-bond defects ( 3:0 1018 cmÿ3 , which serve to enhance the ratio n=p; thus moving the Fermi level towards midgap. It would appear that, for the parameters used here, a dopant concentration of 3:2 1018 cmÿ3 separates two regimes ± one where the eect of the dopants dominates and one where the eect of the dangling-bonds dominates. The horizontal line indicates a contact potential of ÿ0:19 eV, showing that for such a contact potential to exist at the SnO2 =p interface and allowing
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Fig. 7. Electron potential energy for the SnO2 =p-a-Si:H heterostructure, for NSS 0 cmÿ2 and NSS 9:6 1012 cmÿ2 . The contact potentials are indicated.
for the possible presence of surface states, the dopant concentration in the p-layer must be greater than about 3:2 1018 cmÿ3 . Finally, in Fig. 7 the electron potential energy W for the SnO2 =p-a-Si:H heterostructure simulated here is shown, for NSS 0 cmÿ2 and NSS 9:6 1012 cmÿ2 . The dierence in contact potentials is apparent.
3. Discussion It is clear that the parameters for the surface states determined in the manner described above are dependent on the choice of ESS ÿ EV 0:4 eV. What would happen if ESS ÿ EV 0:1 eV, or if ESS ÿ EV 0:6 eV? In the case of the former, we ®nd that r 0:1395 eV, dS extends 5:84 nm into the p-layer and NSS 5:59 1012 cmÿ2 . These parameters yield a contact potential of ÿ0:194 eV. In the latter case, we ®nd that r 0:1483 eV, dS extends 3:95 nm into the p-layer and NSS 2:35 1013 cmÿ2 . These parameters yield a contact potential of ÿ0:185 eV. The parameter values for ESS ÿ EV 0:1 eV are in closer agreement with those for ESS ÿ EV 0:4 eV, than are those for ESS ÿ EV 0:6 eV. This is ostensibly due to the T at ESS ÿ EV 0:6 eV, signi®cant variation in NSS for various r (Fig. 4). The fact that the contact potentials are dierent (albeit only slightly) from the target value of ÿ0:19 eV suggests that we
should be reasonably con®dent in our choice of ESS ÿ EV 0:4 eV. Of course, if one or more of T ; dS and r were known with cerESS ÿ EV ; NSS tainty, then we would be able to determine the others with greater accuracy. It is instructive to compare these results with those presented by Smole et al. [2]. Before doing so however, we should describe the dierences between the two works. Firstly, Smole et al. have considered a-Si:C:H, whereas we have considered a-Si:H. However, the parameters for these two materials are almost identical, so that we would not expect any dierences in the results to be due primarily to material dierences. Secondly, Smole et al. have assumed a uniform distribution of interface states in the gap, whereas our distribution has been Gaussian. Thirdly, their target contact potential was ÿ0:14 eV, as opposed to our ÿ0:19 eV, although Fig. 3 will enable us to make statements regarding a contact potential of ÿ0:14 eV (for the bene®t of readers who wish to consult Smole et al., we should point out that they have used the term `interface state', while we have used the term `surface state'). Despite these dierences, there is an important similarity in the results of the two works: both ®nd the contact potential to become less negative as the surface state concentration is increased. Moreover, they ®nd that to achieve a contact potential of ÿ0:14 eV, an interface state concentration of 2 1013 cmÿ2 is needed. If we had been seeking such a contact potential then, as can be inferred from Fig. 3, we would have required NSS 7 1012 cmÿ2 (for ESS ÿ EV 0:2 eV), NSS 1 1013 cmÿ2 (for ESS ÿ EV 0:4 eV), or NSS 3:5 1013 cmÿ2 (for ESS ÿ EV 0:6 eV). These values of NSS are similar to that obtained by Smole et al., despite the fact that their distribution was uniform, and ours is a fairly narrow Gaussian. 4. Conclusions The essence of this paper is the fact that the contact potential and the nature of the surface state concentration at the SnO2 =p-a-Si:H interface are intimately related. Indeed, if the contact potential is known, then a reasonable attempt at determining the surface state concentration at the
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SnO2 =p interface can be made. On the other hand, if the surface state parameters are known, then the contact potential can be calculated by simulating the SnO2 =p interface. Of course, other TCOs can also be used in these calculations (such as ZnO) provided their input parameters are known. It must be acknowledged that, due to the general lack of knowledge regarding surface states at the SnO2 =p interface, the calculations performed in this paper are somewhat speculative. Nevertheless, we state the following result: if the contact potential at the SnO2 =p interface is ÿ0:19 eV and if the surface states are acceptor-like and may be assumed to have a Gaussian distribution, then the parameter values r 0:1435 eV, dS 5:8 nm, NSS 8:28 1012 cmÿ2 and ESS ÿ EV 0:4 eV could very well be considered for use in a simulation of such an interface.
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Acknowledgements The Foundation for Research Development is thanked for ®nancial support. References [1] J.S.C. Prentice, PhD thesis, Department of Physics, Rand Afrikaans University, 1999. [2] F. Smole, M. Topic, J. Furlan, J. Non-Cryst. Solids 194 (1996) 312. [3] F. S anchez Sinencio, R. Williams, J. Appl. Phys. 54 (1983) 2757. [4] Z. Crnjak Orel, B. Orel, M. Klanjsek Gunde, Solar Energy Mater. Solar Cells 26 (1992) 105. [5] A. Antonaia, P. Menna, M.L. Addonizio, M. Crocchiolo, Solar Energy Mater. Solar Cells 28 (1992) 167. [6] I. Balberg, Y. Goldstein, A. Many, Solid State Phenomena 44±46 (1995) 791 and references therein.
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The eect of surface states at the SnO2=p-a-Si:H interface J.S.C. Prentice * Department of Physics, Rand Afrikaans University, P.O. Box 524, Auckland Park 2006, South Africa Received 2 July 1999; received in revised form 3 November 1999
Abstract A one-dimensional photovoltaic cell simulation has been used to model a SnO2 =p-a-Si:H interface, in thermodynamic equilibrium. Central to the study is the eect that acceptor-like surface states in the p-a-Si:H have on the contact potential at this interface. Such surface states were assumed to have a Gaussian distribution. It was found that in order to maintain a constant negative contact potential in the p-layer, the surface state concentration needed to be increased as the distribution was shifted towards the conduction band edge. It was found that, for a given surface state concentration, the contact potential became more negative as the distribution was shifted towards the conduction band edge. It was also found that, when the surface states were located at a ®xed position in the gap, increasing their concentration resulted in a decrease in the magnitude of the contact potential, with the contact potential eventually becoming positive for large concentrations. Increases in the dopant concentration also caused the contact potential to become more negative. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 02.60.Cb; 61.43.Dq; 68.35.Dv; 73.40.Lq
1. Introduction We have developed a one-dimensional photovoltaic (PV) cell simulation (designated RAUPV2), which solves the semiconductor equations numerically, assuming a drift-diusion model [1]. In the course of simulating an a-Si:H p-i-n PV cell, using RAUPV2, it was found that a contact potential of approximately ÿ0:19 eV needed to be implemented at the front surface of the cell, which was in contact with a layer of SnO2 (in this paper, the contact potential in the p-layer is the dierence between the electron potential energy W at the interface and in the p-layer bulk). Following the study by Smole et al. [2], in which the eect of *
Tel.: +27-11 489 3145; fax: +27-11 489 2616. E-mail address: [email protected] (J.S.C. Prentice).
surface states on the contact potential at a SnO2 or ZnO and p-a-Si:C:H interface was studied, this paper will study the eect of acceptor-like surface states on the contact potential at a SnO2 /p-a-Si:H interface. Experimentally, it is known that the contact potential (in the p-layer) at this interface is negative [3], implying band-bending towards the valence band edge.
2. Simulation of the SnO2 =p interface Here, the simulation RAUPV2 will be used to simulate the eect of acceptor-like surface states at the SnO2 =p interface, in thermodynamic equilibrium. The simulation considers two bulk layers, each of thickness 400 nm, of SnO2 and p-a-Si:H.
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The input parameters for the p-layer are given in Table 1 and include a donor-like dangling-bond defect concentration of D 3:6 1018 cmÿ3 , located at 1.00 eV above the valence band edge EV . These defects are Gaussian distributed, with standard deviation r 0:15 eV. The parameters in Table 1 and the dangling-bond parameters, have been obtained by determining average values from a large variety of literature sources and so are considered to be generally representative of a-Si:H. The input parameters for the SnO2 layer were taken from Smole et al. [2]. The most important parameter for the SnO2 layer is the eective doping. This is the parameter that determines the Fermi level position in the SnO2 layer which, in turn, in¯uences the Fermi level mismatch at the SnO2 =p-a-Si:H interface. The parameters used by Smole et al. suggest a conduction electron concentration of about 1020 cmÿ3 . Such a concentration is supported experimentally [4,5]. Simulating this junction without incorporating any acceptor-like surface states in the p-layer, yields a contact potential of ÿ0:47 eV, which is much larger than the required ÿ0:19 eV. However, incorporating a surface state concentration of 7:56 1012 cmÿ2 (which corresponds to 2:0 1019 cmÿ3 ) in the ®rst 6.25 nm of the p-layer at 0.4 eV above EV , yields a contact potential of ÿ0:19 eV. Clearly, it is necessary to include surface
states at this interface because of their eect on the contact potential. The surface states implemented here have been assumed to follow a Gaussian distribution, also with standard deviation r 0:15 eV. The carrier capture cross-sections for these surface states were taken to be rn 9:0 10ÿ16 cm2 and rp 1:0 10ÿ14 cm2 , the same as used for the dangling-bond states. 2.1. Surface state concentrations Fig. 1 shows a plot of surface state concentration NSS cmÿ2 vs. ESS ÿ EV , which denotes the separation of the peak of the surface states distribution and the valence edge, for a surface layer thickness dS of 6.25 nm. Also shown are curves for dS 2:75 nm and dS 9:75 nm, the signi®cance of which will be discussed later. These values of NSS are such that, for each value of ESS ÿ EV , the contact potential is ÿ0:19 eV. It is clear that as NSS is moved away from the valence edge, so it must increase in order to preserve the contact potential of ÿ0:19 eV. This is easily explained. Since NSS is a concentration of acceptor-like states, these states capture electrons from both the conduction- and valence bands. When NSS is close to the valence band, it is electron capture from the valence band that dominates. As NSS moves away from the
Table 1 Input parameters for p-a-Si:H used in RAUPV2 Mobility gap, EG (eV) Electron anity, v (eV) Relative dielectric permittivity, e Densities of states, NC ; NV cmÿ3 Dopant concentration, NA cmÿ3 Dopant ionization energy (meV)
1.87 3.90 11.8 2:0 1020 4:5 1018 45
Conduction band tail states Amplitude (cmÿ3 eVÿ1 ) Slope, EC0 (meV) Electron capture cross-section, rn cm2 Hole capture cross-section, rp cm2
1:5 1021 40 2:1 10ÿ17 2:5 10ÿ15
Valence band tail states Amplitude (cmÿ3 eVÿ1 ) Slope, EV0 (meV) Electron capture cross-section, rn cm2 Hole capture cross-section, rp cm2
21
1:5 10 59 2:5 10ÿ15 2:1 10ÿ17
Fig. 1. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the surface layer thickness dS . The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
J.S.C. Prentice / Journal of Non-Crystalline Solids 262 (2000) 99±105
valence band, this valence electron capture becomes less eective and so the hole concentration in the valence band is reduced. Since np n2i (where ni is the intrinsic carrier concentration) in thermodynamic equilibrium, there is an associated increase in the conduction electron concentration. Thus, the ratio n=p increases as NSS moves away from the valence band. Of course, the ratio n=p gives a measure of the position of EF within the gap (when n=p 1; EF is at midgap). Thus, an increase in n=p implies that EC has moved closer to EF , which corresponds to a negative contact potential that becomes more negative as NSS moves further away from EV . Now, if NSS induces a contact potential of say, ÿ0:19 eV, then, when NSS is moved towards EC , the contact potential it induces will become more negative than ÿ0:19 eV. To ensure that the contact potential remains ®xed at ÿ0:19 eV, NSS must be increased as it is moved towards EC because this will lead to a larger amount of electrons being captured from the valence band, an increase in p, a decrease in n=p; and ®nally, a reduction in the magnitude of the contact potential. In Fig. 2, various surface state concentrations NSS are positioned at various points in the gap and the contact potential as a function of gap position ESS ÿ EV of these states is plotted. It is seen that the contact potential becomes more negative as ESS ÿ EV increases.
Fig. 2. Contact potential at the SnO2 =p interface vs. surface state energy position ESS ÿ EV , for a variety of surface state concentrations.
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Fig. 3. Contact potential as a function of surface state concentration NSS ; when NSS is located at various positions above EV .
In Fig. 3, the contact potential as a function of NSS is plotted, when NSS is at various positions in the gap. As can be seen, the contact potential decreases (in magnitude) for all values of ESS ÿ EV . This is due to the fact that as NSS increases, so more valence electrons are captured, hence p increases, n=p decreases and EC moves away from EF . It is clear that both the energy position and magnitude of NSS in¯uence the contact potential. Figs. 2 and 3 essentially convey the same information, but for the sake of clarity we have presented both. 2.2. Sensitivity to various parameters It is necessary to investigate the eect of variations in certain parameters on the value of NSS required to induce a contact potential of ÿ0:19 eV. Let us refer to this value of NSS as the `target' T value, denoted NSS in the remainder of this paper. T of varying the surface In Fig. 1 the eect on NSS layer thickness dS is shown. It is immediately clear that dS does not exert a particularly strong eect T , particularly for large values of ESS ÿ EV . on NSS We see that increasing dS , at any particular value T to be decreased. This is of ESS ÿ EV , requires NSS due simply to the fact that an increase in dS increases the number of surface states in the surface layer. This means that more electrons can be trapped, the p-layer becomes more p-type, EV moves towards EF and so the contact potential
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would be become less negative than ÿ0:19 eV. To preserve the contact potential of ÿ0:19 eV then, it T , as suggested by Fig. 3. is necessary to decrease NSS In Fig. 1 the width of the surface state distribution r is ®xed at 0.15eV and the eective donor concentration in the SnO2 layer ND SnO2 is ®xed at T is more 1020 cmÿ3 . This ®gure indicates that NSS sensitive to changes in dS when ESS ÿ EV is small. T Fig. 4 shows NSS vs. ESS ÿ EV for three values of the width of the surface state distribution r. It is T must be declear that as r is increased so NSS creased, for each ESS ÿ EV . This is because increasing the width of the surface state distribution brings more surface states closer to EV , resulting in increased eective p-type doping, a shift of EV towards EF and hence, the contact potential becomes less negative. Again, to preserve the contact potential of ÿ0:19 eV, it is necessary to decrease T . In Fig. 4 dS is ®xed at 6.25 nm and ND SnO2 NSS is ®xed at 1020 cmÿ3 . It is important to note that T NSS is particularly sensitive to changes in r for large values of ESS ÿ EV . T vs. ESS ÿ EV for three values of Fig. 5 shows NSS the eective donor concentration in the SnO2 layer ND SnO2 . Increasing ND SnO2 simply enhances the electron concentration in the SnO2 layer. This means that EC in the SnO2 layer moves towards EF . Thus, at the interface, EC in the a-Si:H layer
Fig. 5. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the SnO2 donor dopant concentration ND SnO2 ). The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
also moves towards EF , resulting in the contact potential becoming more negative. We see from Fig. 3 that if the contact potential is more negative than ÿ0:19 eV, for any value of ESS ÿ EV , the surface state concentration must be increased to preserve the contact potential of ÿ0:19 eV. It is T is not particularly interesting to note that NSS sensitive to the changes in ND SnO2 for any values of ESS ÿ EV . 2.3. Parameters for the surface states
Fig. 4. Surface state concentration NSS in the p-layer vs. surface state energy position ESS ÿ EV , for the SnO2 =p interface. Curves have been drawn for three values of the surface state distribution width r. The horizontal line indicates the assumed 1014 cmÿ2 empirical limit for NSS . The values of NSS in this plot are those for which the contact potential is ÿ0:19 eV.
One of the goals of this paper is to attempt to ®nd values for the various surface state parameters. Certainly little is known about the surface states in a-Si:H, as may be deduced from the recent review by Balberg et al. [6]. Certainly, there is very little knowledge concerning the nature of the surface state distribution (whether or not it actually is Gaussian, or uniformly distributed throughout the gap) and the carrier capture cross sections of the surface states. Nevertheless, it would appear that an empirical upper limit of 1014 cmÿ2 can be placed on NSS [6]. This is the horizontal line in Figs. 1, 4 and 5. This indicates that if ÿ0:19 eV is an appropriate contact potential, then the position of the surface state concentration that induces this contact potential relative to the valence band has
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an upper bound. The value of this upper bound varies according to the values of other surface state parameters. T is In Fig. 1 we see that the upper limit on NSS breached when ESS ÿ EV is greater than approximately 0.725 eV, for all three values of dS considered here. Similar behaviour is apparent in Fig. 5, T is breached when where the upper limit on NSS ESS ÿ EV is also greater than approximately 0.725 eV, for all three values of ND SnO2 considered. However, in Fig. 4 it is clear that the value of T is breaESS ÿ EV at which the upper limit on NSS ched is strongly dependent on the value of r. When r 0:10 eV the breach value of ESS ÿ EV is about 0.65 eV and when r 0:20 eV it is about 0.825 eV. To begin with, we would like to choose a value for ESS ÿ EV . Fig. 5 indicates that any value less than about 0.725 eV would be suitable, due to the T on the values of lack of sensitivity of NSS ND SnO2 . Fig. 4 indicates that we should steer clear of values near to 0.6 eV and above, because T on r of the apparently strong dependence of NSS for those values of ESS ÿ EV . On the other hand, T is more sensitive to variaFig. 1 shows that NSS tions in dS for low values of ESS ÿ EV . It would seem from these ®gures that a `safe, middle-of-theroad' value, for which there is minimal sensitivity to dS ; ND SnO2 and r would be ESS ÿ EV 0:4 eV. Now, at this value of ESS ÿ EV in each ®gure, T have been determined, giving a three values of NSS total of nine in all. We are tempted to take the T 8:28 1012 cmÿ2 . average, which gives NSS Simple linear interpolation at ESS ÿ EV 0:4 eV in Figs. 4 and 5 allows values for dS and r to be inferred. These are found to be r 0:1435 eV and dS 5:7976 nm. We prefer to retain the value of ND SnO2 1020 cmÿ3 in the light of experimental T is clearly insupport for this value. Besides, NSS sensitive to variations in ND SnO2 . Simulating the interface using these parameter values gives a contact potential of ÿ0:1902 eV, in excellent agreement with the target value of ÿ0:19 eV assumed at the beginning of this paper. In Fig. 6, the contact potential at the SnO2 =p interface as a function of dopant concentration in the p-layer is shown, in the absence of any acceptor-like surface states. Since the eect of ac-
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Fig. 6. Contact potential at the SnO2 =p interface, as a function of dopant concentration NA in the p-layer, in the absence of any surface states. The horizontal line indicates a contact potential of ÿ0:19 eV.
ceptor-like surface states is to reduce the contact potential, the contact potentials shown in Fig. 6 represent the largest contact potentials that can exist at the SnO2 =p interface for the indicated dopant concentrations. It can be seen that large contact potentials ( ÿ0:47 eV) occur for dopant concentrations greater than about 3:2 1018 cmÿ3 , while for dopant concentrations less than this value the contact potential is small and is, in fact, positive near a dopant concentration of about 2:0 1018 cmÿ3 . This is due to the Fermi level position in the p-layer being in¯uenced by the dopant concentration. The contact potential arises from the misalignment of the Fermi levels in the SnO2 and the p-layer. As the dopant concentration is reduced in the p-layer, the Fermi level in the player moves towards midgap and the misalignment is reduced, thus reducing the contact potential. The eect is compounded by the presence of the large concentration of donor-like dangling-bond defects ( 3:0 1018 cmÿ3 , which serve to enhance the ratio n=p; thus moving the Fermi level towards midgap. It would appear that, for the parameters used here, a dopant concentration of 3:2 1018 cmÿ3 separates two regimes ± one where the eect of the dopants dominates and one where the eect of the dangling-bonds dominates. The horizontal line indicates a contact potential of ÿ0:19 eV, showing that for such a contact potential to exist at the SnO2 =p interface and allowing
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Fig. 7. Electron potential energy for the SnO2 =p-a-Si:H heterostructure, for NSS 0 cmÿ2 and NSS 9:6 1012 cmÿ2 . The contact potentials are indicated.
for the possible presence of surface states, the dopant concentration in the p-layer must be greater than about 3:2 1018 cmÿ3 . Finally, in Fig. 7 the electron potential energy W for the SnO2 =p-a-Si:H heterostructure simulated here is shown, for NSS 0 cmÿ2 and NSS 9:6 1012 cmÿ2 . The dierence in contact potentials is apparent.
3. Discussion It is clear that the parameters for the surface states determined in the manner described above are dependent on the choice of ESS ÿ EV 0:4 eV. What would happen if ESS ÿ EV 0:1 eV, or if ESS ÿ EV 0:6 eV? In the case of the former, we ®nd that r 0:1395 eV, dS extends 5:84 nm into the p-layer and NSS 5:59 1012 cmÿ2 . These parameters yield a contact potential of ÿ0:194 eV. In the latter case, we ®nd that r 0:1483 eV, dS extends 3:95 nm into the p-layer and NSS 2:35 1013 cmÿ2 . These parameters yield a contact potential of ÿ0:185 eV. The parameter values for ESS ÿ EV 0:1 eV are in closer agreement with those for ESS ÿ EV 0:4 eV, than are those for ESS ÿ EV 0:6 eV. This is ostensibly due to the T at ESS ÿ EV 0:6 eV, signi®cant variation in NSS for various r (Fig. 4). The fact that the contact potentials are dierent (albeit only slightly) from the target value of ÿ0:19 eV suggests that we
should be reasonably con®dent in our choice of ESS ÿ EV 0:4 eV. Of course, if one or more of T ; dS and r were known with cerESS ÿ EV ; NSS tainty, then we would be able to determine the others with greater accuracy. It is instructive to compare these results with those presented by Smole et al. [2]. Before doing so however, we should describe the dierences between the two works. Firstly, Smole et al. have considered a-Si:C:H, whereas we have considered a-Si:H. However, the parameters for these two materials are almost identical, so that we would not expect any dierences in the results to be due primarily to material dierences. Secondly, Smole et al. have assumed a uniform distribution of interface states in the gap, whereas our distribution has been Gaussian. Thirdly, their target contact potential was ÿ0:14 eV, as opposed to our ÿ0:19 eV, although Fig. 3 will enable us to make statements regarding a contact potential of ÿ0:14 eV (for the bene®t of readers who wish to consult Smole et al., we should point out that they have used the term `interface state', while we have used the term `surface state'). Despite these dierences, there is an important similarity in the results of the two works: both ®nd the contact potential to become less negative as the surface state concentration is increased. Moreover, they ®nd that to achieve a contact potential of ÿ0:14 eV, an interface state concentration of 2 1013 cmÿ2 is needed. If we had been seeking such a contact potential then, as can be inferred from Fig. 3, we would have required NSS 7 1012 cmÿ2 (for ESS ÿ EV 0:2 eV), NSS 1 1013 cmÿ2 (for ESS ÿ EV 0:4 eV), or NSS 3:5 1013 cmÿ2 (for ESS ÿ EV 0:6 eV). These values of NSS are similar to that obtained by Smole et al., despite the fact that their distribution was uniform, and ours is a fairly narrow Gaussian. 4. Conclusions The essence of this paper is the fact that the contact potential and the nature of the surface state concentration at the SnO2 =p-a-Si:H interface are intimately related. Indeed, if the contact potential is known, then a reasonable attempt at determining the surface state concentration at the
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SnO2 =p interface can be made. On the other hand, if the surface state parameters are known, then the contact potential can be calculated by simulating the SnO2 =p interface. Of course, other TCOs can also be used in these calculations (such as ZnO) provided their input parameters are known. It must be acknowledged that, due to the general lack of knowledge regarding surface states at the SnO2 =p interface, the calculations performed in this paper are somewhat speculative. Nevertheless, we state the following result: if the contact potential at the SnO2 =p interface is ÿ0:19 eV and if the surface states are acceptor-like and may be assumed to have a Gaussian distribution, then the parameter values r 0:1435 eV, dS 5:8 nm, NSS 8:28 1012 cmÿ2 and ESS ÿ EV 0:4 eV could very well be considered for use in a simulation of such an interface.
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Acknowledgements The Foundation for Research Development is thanked for ®nancial support. References [1] J.S.C. Prentice, PhD thesis, Department of Physics, Rand Afrikaans University, 1999. [2] F. Smole, M. Topic, J. Furlan, J. Non-Cryst. Solids 194 (1996) 312. [3] F. S anchez Sinencio, R. Williams, J. Appl. Phys. 54 (1983) 2757. [4] Z. Crnjak Orel, B. Orel, M. Klanjsek Gunde, Solar Energy Mater. Solar Cells 26 (1992) 105. [5] A. Antonaia, P. Menna, M.L. Addonizio, M. Crocchiolo, Solar Energy Mater. Solar Cells 28 (1992) 167. [6] I. Balberg, Y. Goldstein, A. Many, Solid State Phenomena 44±46 (1995) 791 and references therein.