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p-a-Si:H interface in an a-Si:H solar cell
Solar Energy Materials a Solar Cells 71 (2002) 131–140
Effect of interface states at the SnO2=p-a-Si:H interface in an a-Si:H solar cell J.S.C. Prentice* Department of Applied Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006, South Africa Received 9 November 2000
Abstract Computational investigations of an a-Si:H solar cell have indicated that interface states at the SnO2 =p-a-Si:H interface enhance device performance by about 5%. A detailed analysis has revealed that the interface states enhance the drift field by capturing electrons from the valence band. This enhances the effective electric field acting on the electrons, resulting in electrons being swept out of the p-layer. This, in turn, decreases the electron concentration in the player, relative to the case where interface states are absent. It was found that dangling-bond states are the dominant recombination mechanism in the p-layer, and that their location very near to midgap ensures that Shockley–Read–Hall recombination through them is proportional to the electron concentration only. Since the introduction of interface states reduces the electron concentration, dangling-bond recombination in the p-layer is reduced, resulting in an increase in the short-circuit current and maximum power output, relative to the cell in which interface states are absent. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Interface states; Solar cell; Amorphous silicon; Recombination
1. Introduction Simulations of the interface between SnO2 and p-type a-Si:H have indicated that the contact potential at that interface is dependent on the parameters of a distribution of acceptor-like states in the p-layer in the immediate vicinity of the interface [1,2]. In the absence of these interface states, the contact potential is about @0:47 eV (the minus sign indicates band bending towards the valence band). *Tel.: +27-11-4893145; fax: +27-11-4892616. E-mail addresses: [email protected] (J.S.C. Prentice). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 0 4 9 - 6
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However, simulations of a glass=SnO2 =a-Si:H p–i–n=Al=glass solar cell suggest that in order to achieve agreement between experimental and simulated open-circuit voltage VOC , a contact potential of @0:14 eV is required at this interface [3]. The very nature of photovoltaic device simulations allows such a contact potential to be implemented without actually including the interface states, and the results for the short-circuit current and maximum power output were JSC ¼ @13:43 mA cm@2 and PM ¼ 4:42 mW cm@2 . However, when the interface states were included (in the form of a Gaussian distribution located in the lower part of the gap) we found JSC ¼ @13:99 mA cm@2 and PM ¼ 4:64 mW cm@2 . There is thus an improvement in the cell performance of about 5%. Intuitively, we might have expected the inclusion of a large concentration of states in the p-layer to boost Shockley–Read– Hall (SRH) recombination, and so degrade device performance. It is the objective of this paper to describe the reasons for the observed improvement in the performance of the cell.
2. Simulation and device parameters The cell studied here has been described previously [3]. Indeed, in that paper, the improvement in cell performance due to the interface states was mentioned, but not investigated. The simulation used is RAUPV2 which solves the semiconductor equations in thermodynamic and steady-state equilibrium using a generalised Newton’s method. We will not repeat the device parameters here, except to say that the interface states are Gaussian distributed with width s ¼ 0:15 eV. The position of the distribution peak is 0:4 eV above the valence band edge EV , the total concentration in the distribution is 3:2 1019 cm@3 (corresponding to 1 1013 cm@2 ) and these states extend 7:5 nm into the p-layer, which has a thickness of 15 nm. We also mention that dangling bonds in the p-layer are represented by a donor-like Gaussian of width 0:15 eV peaking 1 eV above EV , and having a total concentration of 3:6 1018 cm@3 : Valence and conduction band tail states are also modelled. In this paper we will refer to the simulated cell without interface states as the O-cell, and the simulated cell including interface states as the I-cell. Their J–V curve parameters were mentioned in the previous section; for both of these cells the fill factor and open-circuit voltage are FF ¼ 51% and VOC ¼ 0:65 V.
3. Analysis The analysis that follows is for the case of short circuit. We begin by looking at the recombination in both cells. To this end we define the integrated recombination IR by Z IR ¼ q RðxÞ dx; ð3:1Þ
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where RðxÞ is the recombination rate at position x in the cell and q is the elementary charge. We incorporate q so that the units of IR are the physically intuitive ones of mA cm@2 (these will be the units of IR throughout the remainder of this paper). The IR in the p-, i- or n-layer is then simply the above integral evaluated between the limits that are appropriate to the boundaries of the desired layer. Now, for the O-cell the IR in the p-, i- and n-layer is 3:23; 2:46 and 0.15, respectively. For the I-cell the IR in the p-, i- and n-layer is 2:61; 2:57 and 0.15, respectively. The IR in the n-layer exhibits no change, and in the i-layer a slight increase is apparent. In the p-layer, however, the IR decreases considerably. The difference in JSC for the two cells is 0:57 mA cm@2 , and the decrease in IR in the p-layer is 0:62 mA cm@2 . Clearly, we must study the p-layer to understand the improvement in cell performance. There are five types of gap states that are modelled in the p-layer. These are acceptor dopants (boron), acceptor-like conduction band tail states, donor-like valence band tail states, donor-like dangling-bond states and the acceptor-like interface states (which are absent in the O-cell). It is possible to determine IR in the p-layer for each of these types of gap states, for both cells. The results are shown in Table 1. We see that IR increases for all the state types, when interface states are added, except for the dangling-bond states. In fact, the decrease in IR for the dangling-bond states is greater than the combined increase in IR for all the other states. It is thus necessary to offer some explanation of why the recombination through the dangling bonds decreases, while recombination through all other mechanisms increases. Consider the expression for the recombination rate R through a concentration of defects Nd located at an energy E above EV , as given in the SRH model [4–6]: Nd sn sp np RðEÞ ¼ : ð3:2Þ sn ðn þ n1 Þ þ sp ðp þ p1 Þ Here, sn and sp denote the electron and hole capture cross-sections for the defects, n and p are the free electron and hole concentrations, and n1 and p1 are given by E@Eg n1 ðEÞ ¼ NC exp ; ð3:3Þ kT @E p1 ðEÞ ¼ NV exp ; ð3:4Þ kT
Table 1 Integrated recombination IR for various types of gap states in the p-layera
O-cell I-cell a
B dopants
C tails
V tails
DBs
IS
3:8 10@6 2:8 10@5
0:0020 0:0048
0:1064 0:1798
3:1698 1:9939
0 0:4283
B dopants are boron acceptors, C and V tails are conduction and valence band tail states, respectively. DBs are donor-like dangling bonds, and IS are acceptor-like interface states. Units are mA cm@2 .
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where NC and NV are the accessible states concentrations in the conduction and valence bands (B1020 cm@3 Þ; Eg is the band gap ð1:87 eVÞ; k is Boltzmann’s constant and T is the absolute temperature (300 K). In the p-layer, under illumination, nB1011 cm@3 and pB1016 cm@3 , so that the term in n can be neglected from the denominator in Eq. (3.2). For states very near to the valence band, such as the valence tail states and the boron acceptors, n1 B10@11 cm@3 and p1 B1019 cm@3 , so that all terms in the denominator of (3.2) are negligible compared to the term in p1 . For such states, the recombination rate becomes Nd sn sp np Nd s n ¼ RðEÞE np ð3:5Þ sp p1 p1 which is proportional to the product np. For states close to the conduction band a similar argument can be made, except that we have p1 B10@11 cm@3 and n1 B1019 cm@3 , which gives Nd sp RðEÞE np: ð3:6Þ n1 However, for states near midgap (such as the dangling bonds) we have n1 ; p1 B105 cm@3 , so that all terms in the denominator of Eq. (3.2) are negligible compared to the term in p. For such states, the recombination rate becomes RðEÞE
Nd sn sp np ¼ Nd sn n sp p
ð3:7Þ
which is proportional to n. In other words, recombination through states near midgap is sensitive only to variations in n, and not to variations in the product np. Fig. 1 shows the product np in the p-layer for both cells. It is seen to be enhanced throughout the p-layer for the I-cell, and this explains the increase in IR for the tail states and the boron dopants. Although not shown, np was seen to be enhanced throughout the cell, although the enhancement near and in the n-layer was negligible. Fig. 2 shows p in the p-layer for both cells. For the I-cell p is enhanced throughout the p-layer. This is due simply to the acceptor action of the interface states. They are located in the lower part of the gap and so interact strongly with the valence band electrons, which they capture with about 1% efficiency. Since there are about 1019 cm@3 interface states, the number of captured electrons is about 1017 cm@3 . This is the extent to which p is increased, as can be seen in the figure. These holes are able to diffuse into the i-layer, resulting in an increase in p in the i-layer as well. Fig. 3 shows n in the p-layer and the front part of the i-layer. We see that in the I-cell n decreases up to about 300 nm whereafter it increases. The decrease in n in the p-layer explains the decrease in IR for the dangling bonds in that layer, in accordance with Eq. (3.7). We may be tempted to associate the decrease in n in the p-layer as being due to the interaction of the interface states with the conduction band, but this is not so. Firstly, the interface states are simply too far from EC to be able to capture a sufficient amount of electrons to account for the decrease in n.
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135
Fig. 1. Product of the free carrier concentrations np in the p-layer, for the O-cell and the I-cell.
Fig. 2. Free hole concentration p in the p-layer (left) and in the first 400 nm of the cell (right).
Secondly, and more damning, is the fact that n decreases well beyond the 7:5 nm over which the interface states exist. The fact that n decreases up to 300 nm and then increases thereafter suggests that a drift mechanism is responsible for sweeping electrons from the front part of the cell towards the back part.
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Fig. 3. Free electron concentration n in the p-layer (left) and in the first 400 nm of the cell (right). Note that n for the O-cell is less than n for the I-cell from about 50 nm onwards.
Poisson’s equation can be written as dED rðxÞ ; ¼ e dx
ð3:8Þ
where ED is the drift field, r is the net charge concentration and e is the dielectric permittivity. This implies Z 1 x ED ðxÞ ¼ rðxÞ dx þ ED ð0Þ: ð3:9Þ e 0 Consider the first 7:5 nm of the cell (so x ¼ 7:5 nm in the above equation). For the O-cell the acceptor dopants are negatively charged. Diffusion of the resulting holes out of the p-layer ensures that these negative charges are not completely compensated (the acceptor- and donor-like tail states would tend to compensate each other). Hence, ED ð7:5 nmÞ is negative. In the I-cell, an additional concentration of acceptor-like states exists. A portion of these are negatively ionised and hole diffusion again ensures that these negative charges are not completely compensated. We thus expect that r is more negative than in the O-cell, and so we expect that ED ð7:5 nmÞ in the I-cell will be more negative than in the O-cell. This is clear from Fig. 4. It is the enhanced drift field that would sweep electrons out of the p-layer, and so reduce n. However, such drift would alter the electron distribution which would alter the electron diffusion field. This, in turn, would
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Fig. 4. Drift field ED in the p-layer, for the O-cell and the I-cell.
affect the net force acting on the electrons. It is therefore inappropriate to consider the drift field only. Rather, we should consider the effective electric field acting on the electrons, denoted En and shown in Fig. 5. We see that En is enhanced throughout the p-layer. We also see that En is enhanced in the front part of the i-layer, consistent with the decrease in n in this part of the I-cell. Although not shown, En is reduced (but still negative) beyond 300 nm, consistent with the increase in n in this region of the I-cell. It is the nature of En in the I-cell, relative to that in the O-cell, that explains the decrease in n in the p-layer when interface states are introduced. Fig. 6 shows the total recombination profiles for both cells. Recombination in the i-layer is greater in the I-cell than in the O-cell, particularly up to about 300 nm. This may be correlated with the behaviour of np which is enhanced throughout the I-cell. In the i-layer gap states are not sufficiently close to midgap for Eq. (3.7) to be valid, so that SRH recombination is determined by the product np. Fig. 7 shows total recombination and recombination through the dangling bonds in the p-layer, for both cells. Also shown is recombination through the interface states in the I-cell. This figure shows that the total recombination in the p-layer is due essentially to the dangling bonds. Despite the fairly high interface state recombination, the total recombination decreases in the I-cell, following the behaviour of the dangling bonds. Comparing with Fig. 3 we see also that recombination through the dangling bonds in the p-layer shows almost identical variation with position as the free electron concentration, for both cells. Of course, this is expected by virtue of Eq. (3.7).
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Fig. 5. Effective electric field acting on the free electrons En in the p-layer (left) and in the first 100 nm of the cell. Scale on the vertical axis is the same for both graphs.
Fig. 6. Total recombination rate throughout the cell. Recombination for the O-cell is higher in the p-layer, but lower in the first B350 nm of the i-layer.
J.S.C. Prentice / Solar Energy Materials & Solar Cells 71 (2002) 131–140
139
Fig. 7. Total recombination rate in the p-layer (left) and recombination rate through dangling bonds and interface states only in the p-layer (right). Scale on the vertical axis is the same for both graphs.
We have thus shown the manner in which JSC is enhanced in the I-cell. Since VOC and FF are identical for both cells, it is appropriate to correlate the increase in PM for the I-cell with the enhancement of JSC , since PM ¼ JSC VOC FF.
4. Conclusions A computational investigation of the effect of acceptor-like interface states at the SnO2 =p-a-Si:H interface in an a-Si:H p–i–n solar cell has been performed. We find that the presence of the interface states causes a slight ðB5%Þ improvement in cell performance. This was explained in the following manner: the interface states capture electrons from the valence band which increases the hole concentration in the p-layer. Some of these holes diffuse into the i-layer, leaving uncompensated negatively ionised interface states. This leads to an enhancement of the drift field strength in the p-layer, and hence an enhancement of the effective electric field acting on the electrons in the p-layer. This causes electrons to be more effectively swept out of the p-layer, resulting in a reduction in the electron concentration in the p-layer. Recombination in the p-layer is dominated by the dangling bonds located near midgap. By virtue of their location in the gap, Shockley–Read–Hall recombination through these dangling bond states is proportional to the free electron concentration. Since the electron concentration has been reduced, recombination through the dangling bonds is reduced. This reduction in p-layer recombination is the cause
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of the increase in the short-circuit current, and hence the maximum power output of the cell.
References [1] [2] [3] [4] [5] [6]
F. Smole, M. Topi$c, J. Furlan, J. Non-Cryst. Solids 194 (1996) 312. J.S.C. Prentice, J. Non-Cryst. Solids 262 (2000) 99. J.S.C. Prentice, Solar Energy Mater. Solar Cells 61 (2000) 287, and references therein. W. Shockley, T. Read Jr., Phys. Rev. 87 (1952) 835–842. R.N. Hall, Phys. Rev. 83 (1951) 228. R.N. Hall, Phys. Rev. 87 (1952) 387.
Effect of interface states at the SnO2=p-a-Si:H interface in an a-Si:H solar cell J.S.C. Prentice* Department of Applied Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006, South Africa Received 9 November 2000
Abstract Computational investigations of an a-Si:H solar cell have indicated that interface states at the SnO2 =p-a-Si:H interface enhance device performance by about 5%. A detailed analysis has revealed that the interface states enhance the drift field by capturing electrons from the valence band. This enhances the effective electric field acting on the electrons, resulting in electrons being swept out of the p-layer. This, in turn, decreases the electron concentration in the player, relative to the case where interface states are absent. It was found that dangling-bond states are the dominant recombination mechanism in the p-layer, and that their location very near to midgap ensures that Shockley–Read–Hall recombination through them is proportional to the electron concentration only. Since the introduction of interface states reduces the electron concentration, dangling-bond recombination in the p-layer is reduced, resulting in an increase in the short-circuit current and maximum power output, relative to the cell in which interface states are absent. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Interface states; Solar cell; Amorphous silicon; Recombination
1. Introduction Simulations of the interface between SnO2 and p-type a-Si:H have indicated that the contact potential at that interface is dependent on the parameters of a distribution of acceptor-like states in the p-layer in the immediate vicinity of the interface [1,2]. In the absence of these interface states, the contact potential is about @0:47 eV (the minus sign indicates band bending towards the valence band). *Tel.: +27-11-4893145; fax: +27-11-4892616. E-mail addresses: [email protected] (J.S.C. Prentice). 0927-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 4 8 ( 0 1 ) 0 0 0 4 9 - 6
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However, simulations of a glass=SnO2 =a-Si:H p–i–n=Al=glass solar cell suggest that in order to achieve agreement between experimental and simulated open-circuit voltage VOC , a contact potential of @0:14 eV is required at this interface [3]. The very nature of photovoltaic device simulations allows such a contact potential to be implemented without actually including the interface states, and the results for the short-circuit current and maximum power output were JSC ¼ @13:43 mA cm@2 and PM ¼ 4:42 mW cm@2 . However, when the interface states were included (in the form of a Gaussian distribution located in the lower part of the gap) we found JSC ¼ @13:99 mA cm@2 and PM ¼ 4:64 mW cm@2 . There is thus an improvement in the cell performance of about 5%. Intuitively, we might have expected the inclusion of a large concentration of states in the p-layer to boost Shockley–Read– Hall (SRH) recombination, and so degrade device performance. It is the objective of this paper to describe the reasons for the observed improvement in the performance of the cell.
2. Simulation and device parameters The cell studied here has been described previously [3]. Indeed, in that paper, the improvement in cell performance due to the interface states was mentioned, but not investigated. The simulation used is RAUPV2 which solves the semiconductor equations in thermodynamic and steady-state equilibrium using a generalised Newton’s method. We will not repeat the device parameters here, except to say that the interface states are Gaussian distributed with width s ¼ 0:15 eV. The position of the distribution peak is 0:4 eV above the valence band edge EV , the total concentration in the distribution is 3:2 1019 cm@3 (corresponding to 1 1013 cm@2 ) and these states extend 7:5 nm into the p-layer, which has a thickness of 15 nm. We also mention that dangling bonds in the p-layer are represented by a donor-like Gaussian of width 0:15 eV peaking 1 eV above EV , and having a total concentration of 3:6 1018 cm@3 : Valence and conduction band tail states are also modelled. In this paper we will refer to the simulated cell without interface states as the O-cell, and the simulated cell including interface states as the I-cell. Their J–V curve parameters were mentioned in the previous section; for both of these cells the fill factor and open-circuit voltage are FF ¼ 51% and VOC ¼ 0:65 V.
3. Analysis The analysis that follows is for the case of short circuit. We begin by looking at the recombination in both cells. To this end we define the integrated recombination IR by Z IR ¼ q RðxÞ dx; ð3:1Þ
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where RðxÞ is the recombination rate at position x in the cell and q is the elementary charge. We incorporate q so that the units of IR are the physically intuitive ones of mA cm@2 (these will be the units of IR throughout the remainder of this paper). The IR in the p-, i- or n-layer is then simply the above integral evaluated between the limits that are appropriate to the boundaries of the desired layer. Now, for the O-cell the IR in the p-, i- and n-layer is 3:23; 2:46 and 0.15, respectively. For the I-cell the IR in the p-, i- and n-layer is 2:61; 2:57 and 0.15, respectively. The IR in the n-layer exhibits no change, and in the i-layer a slight increase is apparent. In the p-layer, however, the IR decreases considerably. The difference in JSC for the two cells is 0:57 mA cm@2 , and the decrease in IR in the p-layer is 0:62 mA cm@2 . Clearly, we must study the p-layer to understand the improvement in cell performance. There are five types of gap states that are modelled in the p-layer. These are acceptor dopants (boron), acceptor-like conduction band tail states, donor-like valence band tail states, donor-like dangling-bond states and the acceptor-like interface states (which are absent in the O-cell). It is possible to determine IR in the p-layer for each of these types of gap states, for both cells. The results are shown in Table 1. We see that IR increases for all the state types, when interface states are added, except for the dangling-bond states. In fact, the decrease in IR for the dangling-bond states is greater than the combined increase in IR for all the other states. It is thus necessary to offer some explanation of why the recombination through the dangling bonds decreases, while recombination through all other mechanisms increases. Consider the expression for the recombination rate R through a concentration of defects Nd located at an energy E above EV , as given in the SRH model [4–6]: Nd sn sp np RðEÞ ¼ : ð3:2Þ sn ðn þ n1 Þ þ sp ðp þ p1 Þ Here, sn and sp denote the electron and hole capture cross-sections for the defects, n and p are the free electron and hole concentrations, and n1 and p1 are given by E@Eg n1 ðEÞ ¼ NC exp ; ð3:3Þ kT @E p1 ðEÞ ¼ NV exp ; ð3:4Þ kT
Table 1 Integrated recombination IR for various types of gap states in the p-layera
O-cell I-cell a
B dopants
C tails
V tails
DBs
IS
3:8 10@6 2:8 10@5
0:0020 0:0048
0:1064 0:1798
3:1698 1:9939
0 0:4283
B dopants are boron acceptors, C and V tails are conduction and valence band tail states, respectively. DBs are donor-like dangling bonds, and IS are acceptor-like interface states. Units are mA cm@2 .
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where NC and NV are the accessible states concentrations in the conduction and valence bands (B1020 cm@3 Þ; Eg is the band gap ð1:87 eVÞ; k is Boltzmann’s constant and T is the absolute temperature (300 K). In the p-layer, under illumination, nB1011 cm@3 and pB1016 cm@3 , so that the term in n can be neglected from the denominator in Eq. (3.2). For states very near to the valence band, such as the valence tail states and the boron acceptors, n1 B10@11 cm@3 and p1 B1019 cm@3 , so that all terms in the denominator of (3.2) are negligible compared to the term in p1 . For such states, the recombination rate becomes Nd sn sp np Nd s n ¼ RðEÞE np ð3:5Þ sp p1 p1 which is proportional to the product np. For states close to the conduction band a similar argument can be made, except that we have p1 B10@11 cm@3 and n1 B1019 cm@3 , which gives Nd sp RðEÞE np: ð3:6Þ n1 However, for states near midgap (such as the dangling bonds) we have n1 ; p1 B105 cm@3 , so that all terms in the denominator of Eq. (3.2) are negligible compared to the term in p. For such states, the recombination rate becomes RðEÞE
Nd sn sp np ¼ Nd sn n sp p
ð3:7Þ
which is proportional to n. In other words, recombination through states near midgap is sensitive only to variations in n, and not to variations in the product np. Fig. 1 shows the product np in the p-layer for both cells. It is seen to be enhanced throughout the p-layer for the I-cell, and this explains the increase in IR for the tail states and the boron dopants. Although not shown, np was seen to be enhanced throughout the cell, although the enhancement near and in the n-layer was negligible. Fig. 2 shows p in the p-layer for both cells. For the I-cell p is enhanced throughout the p-layer. This is due simply to the acceptor action of the interface states. They are located in the lower part of the gap and so interact strongly with the valence band electrons, which they capture with about 1% efficiency. Since there are about 1019 cm@3 interface states, the number of captured electrons is about 1017 cm@3 . This is the extent to which p is increased, as can be seen in the figure. These holes are able to diffuse into the i-layer, resulting in an increase in p in the i-layer as well. Fig. 3 shows n in the p-layer and the front part of the i-layer. We see that in the I-cell n decreases up to about 300 nm whereafter it increases. The decrease in n in the p-layer explains the decrease in IR for the dangling bonds in that layer, in accordance with Eq. (3.7). We may be tempted to associate the decrease in n in the p-layer as being due to the interaction of the interface states with the conduction band, but this is not so. Firstly, the interface states are simply too far from EC to be able to capture a sufficient amount of electrons to account for the decrease in n.
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135
Fig. 1. Product of the free carrier concentrations np in the p-layer, for the O-cell and the I-cell.
Fig. 2. Free hole concentration p in the p-layer (left) and in the first 400 nm of the cell (right).
Secondly, and more damning, is the fact that n decreases well beyond the 7:5 nm over which the interface states exist. The fact that n decreases up to 300 nm and then increases thereafter suggests that a drift mechanism is responsible for sweeping electrons from the front part of the cell towards the back part.
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Fig. 3. Free electron concentration n in the p-layer (left) and in the first 400 nm of the cell (right). Note that n for the O-cell is less than n for the I-cell from about 50 nm onwards.
Poisson’s equation can be written as dED rðxÞ ; ¼ e dx
ð3:8Þ
where ED is the drift field, r is the net charge concentration and e is the dielectric permittivity. This implies Z 1 x ED ðxÞ ¼ rðxÞ dx þ ED ð0Þ: ð3:9Þ e 0 Consider the first 7:5 nm of the cell (so x ¼ 7:5 nm in the above equation). For the O-cell the acceptor dopants are negatively charged. Diffusion of the resulting holes out of the p-layer ensures that these negative charges are not completely compensated (the acceptor- and donor-like tail states would tend to compensate each other). Hence, ED ð7:5 nmÞ is negative. In the I-cell, an additional concentration of acceptor-like states exists. A portion of these are negatively ionised and hole diffusion again ensures that these negative charges are not completely compensated. We thus expect that r is more negative than in the O-cell, and so we expect that ED ð7:5 nmÞ in the I-cell will be more negative than in the O-cell. This is clear from Fig. 4. It is the enhanced drift field that would sweep electrons out of the p-layer, and so reduce n. However, such drift would alter the electron distribution which would alter the electron diffusion field. This, in turn, would
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Fig. 4. Drift field ED in the p-layer, for the O-cell and the I-cell.
affect the net force acting on the electrons. It is therefore inappropriate to consider the drift field only. Rather, we should consider the effective electric field acting on the electrons, denoted En and shown in Fig. 5. We see that En is enhanced throughout the p-layer. We also see that En is enhanced in the front part of the i-layer, consistent with the decrease in n in this part of the I-cell. Although not shown, En is reduced (but still negative) beyond 300 nm, consistent with the increase in n in this region of the I-cell. It is the nature of En in the I-cell, relative to that in the O-cell, that explains the decrease in n in the p-layer when interface states are introduced. Fig. 6 shows the total recombination profiles for both cells. Recombination in the i-layer is greater in the I-cell than in the O-cell, particularly up to about 300 nm. This may be correlated with the behaviour of np which is enhanced throughout the I-cell. In the i-layer gap states are not sufficiently close to midgap for Eq. (3.7) to be valid, so that SRH recombination is determined by the product np. Fig. 7 shows total recombination and recombination through the dangling bonds in the p-layer, for both cells. Also shown is recombination through the interface states in the I-cell. This figure shows that the total recombination in the p-layer is due essentially to the dangling bonds. Despite the fairly high interface state recombination, the total recombination decreases in the I-cell, following the behaviour of the dangling bonds. Comparing with Fig. 3 we see also that recombination through the dangling bonds in the p-layer shows almost identical variation with position as the free electron concentration, for both cells. Of course, this is expected by virtue of Eq. (3.7).
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Fig. 5. Effective electric field acting on the free electrons En in the p-layer (left) and in the first 100 nm of the cell. Scale on the vertical axis is the same for both graphs.
Fig. 6. Total recombination rate throughout the cell. Recombination for the O-cell is higher in the p-layer, but lower in the first B350 nm of the i-layer.
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Fig. 7. Total recombination rate in the p-layer (left) and recombination rate through dangling bonds and interface states only in the p-layer (right). Scale on the vertical axis is the same for both graphs.
We have thus shown the manner in which JSC is enhanced in the I-cell. Since VOC and FF are identical for both cells, it is appropriate to correlate the increase in PM for the I-cell with the enhancement of JSC , since PM ¼ JSC VOC FF.
4. Conclusions A computational investigation of the effect of acceptor-like interface states at the SnO2 =p-a-Si:H interface in an a-Si:H p–i–n solar cell has been performed. We find that the presence of the interface states causes a slight ðB5%Þ improvement in cell performance. This was explained in the following manner: the interface states capture electrons from the valence band which increases the hole concentration in the p-layer. Some of these holes diffuse into the i-layer, leaving uncompensated negatively ionised interface states. This leads to an enhancement of the drift field strength in the p-layer, and hence an enhancement of the effective electric field acting on the electrons in the p-layer. This causes electrons to be more effectively swept out of the p-layer, resulting in a reduction in the electron concentration in the p-layer. Recombination in the p-layer is dominated by the dangling bonds located near midgap. By virtue of their location in the gap, Shockley–Read–Hall recombination through these dangling bond states is proportional to the free electron concentration. Since the electron concentration has been reduced, recombination through the dangling bonds is reduced. This reduction in p-layer recombination is the cause
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of the increase in the short-circuit current, and hence the maximum power output of the cell.
References [1] [2] [3] [4] [5] [6]
F. Smole, M. Topi$c, J. Furlan, J. Non-Cryst. Solids 194 (1996) 312. J.S.C. Prentice, J. Non-Cryst. Solids 262 (2000) 99. J.S.C. Prentice, Solar Energy Mater. Solar Cells 61 (2000) 287, and references therein. W. Shockley, T. Read Jr., Phys. Rev. 87 (1952) 835–842. R.N. Hall, Phys. Rev. 83 (1951) 228. R.N. Hall, Phys. Rev. 87 (1952) 387.