Modelling and Simulation of Field-effect Surface Passivation of Crystalline Silicon-based Solar...

Energy Procedia 15 (2012) 155 – 161

1876-6102 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of International Conference on Materials for Advanced Technologies.doi:10.1016/j.egypro.2012.02.018

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Procedia Energy Procedia 00 (2011) 000–000

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International Conference on Materials for Advanced Technologies 2011, Symposium O

Modelling and Simulation of Field-effect Surface Passivation of Crystalline Silicon-based Solar Cells

Fa-Jun Maa,b,*, Bram Hoexa, Ganesh S. Samudraa,b and Armin G. Aberlea,b a Solar Energy Research Institute of Singapore , National University of Singapore, 7 Engineering Drive 1, Building E3A,

Singapore 117574, Singapore b Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Building E4,

Singapore 117576, Singapore

Abstract

An effective surface passivation plays a vital role in the performance of crystalline silicon (c-Si) solar cells. Experimental research shows that fixed charge-induced field-effect passivates the c-Si efficiently. In this work, n-type and p-type c-Si wafers symmetrically passivated by the negative-charge dielectric Al2O3 were numerically modelled with SENTAURUS TCAD. Surface recombination is traditionally modelled by employing the extended Shockley-Read-Hall (SRH) model with single energy level of interface traps. However, experiments show interface traps distribute across the silicon bandgap. Thus, we implemented the extended SRH model with the ability to describe arbitrary energy distribution of interface traps within the bandgap. The extended SRH model predicts a constant effective surface recombination velocity at low injection levels for lightly doped n-type and p-type c-Si passivated by dielectrics with either a high negative or positive charge density. However, this prediction contradicts experimental results which show a significant reduction of the effective lifetime at low injection levels if the polarity of the fixed charge is attracting the minority bulk charge carriers. One explanation is assuming the presence of a thin defect-rich layer close to the c-Si surface in which the lifetimes are degraded. However, the choice of the lifetime and depth of such damaged surface region seem rather arbitrary and its physical origin is still unclear. We show that unequal electron and hole bulk lifetime parameters can also account for the phenomenon. This proposition is physically plausible and the simulation results also show a good agreement with the experimental data from both n-type and p-type c-Si wafers passivated by Al2O3. Our modelling results predict a simple but unambiguous experiment to distinguish between these two explanations. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Solar Energy Research Institute of Singapore (SERIS) – National University of Singapore (NUS). Keywords: Solar cell; surface passivation; field effect

* Corresponding author. Tel.: +65 6601 1032; fax: +65 6775 1943 E-mail address: Fajun.Ma@nus.edu.sg

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the organizing committee of International Conference on Materials for Advanced Technologies.

156 Fa-Jun Ma et al. / Energy Procedia 15 (2012) 155 – 1612 F.-J. MA et al. / Energy Procedia 00 (2011) 000–000

1. Introduction

An excellent surface passivation is of key importance to the performance of crystalline silicon (c-Si) wafer solar cells. As a result of the continuous drive to cost reduction, c-Si wafer solar cells move toward lower substrate thicknesses. Consequently, the surface to volume ratio is increasing which makes the role of surface passivation more important in determining the solar cell efficiency. The solar cell efficiency as a function of the silicon wafer solar cell thickness (Fig. 1) has been simulated with PC1D [1]. By effectively suppressing surface recombination losses, which can be optimised with effective surface passivation, thinner solar cells can even outperform their thicker counterparts. Recently, Al2O3 thin films synthesised by atomic layer deposition have received a lot of interest as they provide an unravelled level of surface passivation, especially on p-type c-Si [2]. It was shown that fixed charge induced field-effect passivation plays a key role in the c-Si surface passivation mechanism of Al2O3 [3].

Fig. 1. PC1D [1] simulation of the dependence of the efficiency of a p-type c-Si solar cell on the wafer thickness. Shown are the results for two different rear effective surface recombination velocities (Seff).

In this work, n-type and p-type c-Si wafers symmetrically passivated by the negative-charge dielectric Al2O3 were numerically modelled with SENTAURUS TCAD [4]. Complete study of key parameters in the model helps us to reproduce experimental results obtained on c-Si wafer passivated by the negative-charge dielectric Al2O3. Surface recombination is traditionally modelled by employing the extended Shockley-Read-Hall (SRH) model [5] with single energy level of interface traps. However, experiments show interface traps distribute across the silicon bandgap [6]. Thus, we implemented the extended SRH model with the ability to describe arbitrary energy distribution of interface traps.

The extended SRH model predicts a constant effective surface recombination velocity (Seff) at low

injection levels for lightly doped n-type and p-type c-Si passivated by dielectrics with either a high negative or positive charge density. However, this prediction contradicts experimental results which show a significant reduction of the effective lifetime at low injection levels if the polarity of the fixed charge is attracting the minority bulk charge carriers. One explanation is the assumption of damaged region near the surface with degraded carrier lifetime [7, 8]. We show that unequal electron and hole bulk lifetime parameters can also account for the phenomenon. From our modelling results, a simple but unambiguous experiment is proposed to distinguish between these two explanations.

0 50 100 150 200 250 30017.0

17.5

18.0

18.5

19.0

19.5

Effi

cien

cy [%

]

c-Si wafer thickness [m]

Seff = 1e2 cm/s Seff = 1e5 cm/s

Resistivity = 1.5 cmBulk lifetime = 20 s

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2. Simulation setup

Carrier recombination in a silicon wafer occurs in the bulk and at both its surfaces. Recombination in the bulk occurs via three processes, namely Auger, radiative and Shockley-Read-Hall (SRH) recombination. The SRH recombination rate in the bulk is trap-assisted recombination and its rate RSRH in c-Si is modelled to depend on electron and hole bulk lifetime parameters [9]:

( ) ( ) , (1)

where τn0 and τp0 are bulk electron and hole lifetime parameters, respectively. n1 and p1 are defined by the trap energy Etrap.

(

) , (

) The surface recombination rate Rs is typically modelled by extended SRH with single energy level of

interface traps,

( )

( )

(2)

where ns and ps are interface electron and hole density respectively, Sn0 and Sp0 are the electron and hole surface recombination velocities, respectively. As interface traps distribute across the silicon bandgap, integration over all interface traps within the silicon bandgap yields the following expression:

( ) ∫ ( )

( ) ( ) (3)

where vth is the carrier mean thermal velocity, Dit (E) is the energy dependent interface trap density, and σn and σp are the electron and hole capture cross section, respectively. In the presence of a surface charge region, the Seff at the edge of the surface space charge region is defined as

( ) , (4)

where Δn(edge) is the excess minority carrier density at the edge of the surface space charge region. An analytical method for calculating Seff when a surface space charge region exists has been proposed by Girisch et al. [10]. Alternatively, Seff can be calculated with a numerical device simulator.

3. Results and discussions

From Eq. (3) it can be deduced that the surface recombination rate scales with the interface trap density. In the case of a surface passivation layer consisting of a high temperature thermal oxide on c-Si, the interface trap density is reported to be in the range of ~109 cm-2 eV-1 [11]. Many experiments indicate that the interface trap energy distribution is typically U-shaped [6]. However, surface recombination is mainly

158 Fa-Jun Ma et al. / Energy Procedia 15 (2012) 155 – 1614 F.-J. MA et al. / Energy Procedia 00 (2011) 000–000

through deep level traps and has a maximum value if ns/σp ps/σn. For simplicity, a uniform distribution of interface traps across the bandgap was assumed in the simulations performed in this work.

The surface recombination can also be minimised by increasing the difference between surface

electron and hole density so that ns/σp is either way larger or smaller than ps/σn. In the case of c-Si solar cells this can be realised by either optimised surface doping profiles or by the introduction of fixed charges at the c-Si surface (e.g., in a dielectric thin film). Experimentally, effective lifetime with Al2O3 passivation is measured from lifetime samples: a c-Si wafer symmetrically coated with Al2O3 film [12]. The same test structure is also modelled in this study as shown in Fig. 2.

3.1. The effect of surface charges

The fixed charges at the c-Si surface interact with the charge carriers in the c-Si bulk and induce a depletion or accumulation layer close to the c-Si surface. If the fixed charge density is sufficiently large, this can even result in an inversion layer at the c-Si surface. A thorough understanding of field-effect passivation is of key importance in understanding the performance of surface passivating films in c-Si test structures such as lifetime samples and in the final c-Si solar cell devices. The effect of the negative fixed charge on Seff is studied in both p-type and n-type c-Si as shown in Fig. 3. In p-type c-Si, negative fixed charges attract majority carriers and consequently decrease the minority carrier concentration at the surface. With the increasing density of negative fixed charges, the Seff decreases monotonically. In n-type c-Si, however, the situation is more complicated. Initially, the Seff increases with the increasing density of negative fixed charges due to decreasing difference between surface electron and hole density. After reaching a maximum value, the Seff decreases monotonically with the increasing density of negative fixed charges due to increasing difference between surface electron and hole density.

Fig. 2. Test structure investigated in this work. The negative charge density at the Al2O3/Si interface is taken to be ~1.3×1013 cm-2. The doping concentration is set to be 2.5×1015 cm-3 (1.9 Ωcm) and 7.2×1015 cm-3 (2.0 Ωcm) for n-type and p-type c-Si, respectively [12].

Fig. 3. Simulated Seff as a function of the density of the negative fixed charges at low injection level (1×1014 cm-3) for p-type and n-type c-Si. A high density of negative fixed charges effectively reduces Seff. Dit = 1×1010 cm-2 eV-1, σn = 1×10-14 cm2, σp= 1×10-16 cm2 [6].

108 109 1010 1011 1012 101310-2

10-1

100

101

102

Sef

f [cm

/s]

Negative fixed charge density [cm-2]

p-type n-type

n = p = 1x1014 cm-3

Al2O

3

Al2O

3

c-Si wafer

159Fa-Jun Ma et al. / Energy Procedia 15 (2012) 155 – 161 F.-J. MA et al. / Energy Procedia 00 (2011) 000–000 5

3.2. Proposition of damaged surface region

At low injection levels, Kerr et al. [13] reported the strong reduction in effective lifetime for p-type c-Si test samples passivated by positively charged a-SiNx:H films. A similar reduction was reported for n-type c-Si test samples passivated by the negative-charge containing Al2O3 [12]. Either a-SiNx:H or Al2O3 have a surface charge density more than 1012 cm-2, the corresponding Seff is expected to be very low according to Fig. 3, assuming a sufficiently low interface defect density. Thus the reduction of the effective lifetime at low injection level is not from enhanced surface recombination but most likely due to enhanced bulk SRH recombination rate. For surface passivation by SiO2, Glunz et al. proposed a new model for the surface recombination to include the bulk recombination within the space charge region [14]. Dauwe et al. followed the same model and explain the enhanced Seff at low injection level for surface passivation by a-SiNx:H [15]. Recently, Martin et al. and Steingrube et al. took one step further by not only taking such bulk recombination into account but also assuming high defect density within the space charge region [7, 8]. The simulation results with this proposition are plotted with the experimentally measured effective lifetime results of both p-type and n-type c-Si test samples passivated by the negative-charge Al2O3 as shown in Fig. 4. The assumption of a damaged surface region results in simulated curves that agree well with measurement results.

3.3. Proposition of unequal bulk lifetime parameters for electron and hole

The choice of the lifetime and depth of a damaged surface region mentioned above, however, is rather arbitrary. Moreover, its physical origin is still unclear. In Fig. 5 it is shown that unequal bulk lifetime parameters for electron and hole due to different carrier capture cross sections can also account for the reduction of effective lifetime at low injection levels. This proposition is physically plausible as the electron bulk lifetime parameter is unlikely to be identical to the hole bulk lifetime parameter. With an effective surface passivation, the effective lifetime is dominated by the minority carrier lifetime at low injection levels, by the majority carrier lifetime at middle injection levels, and by Auger recombination at high injection levels. In contrast to the proposition of damage surface region, the effective lifetime reduction at low injection levels is caused by enhanced SRH recombination in the bulk, instead of in the space charge region. The simulation results also have a good agreement with the experimental data from both n-type and p-type c-Si wafer passivated by the negative-charge Al2O3.

Fig. 4. The experimentally measured effective lifetime results (symbols) of both p-type and n-type c-Si test samples passivated by the negative-charge Al2O3 are fitted with the proposition of damaged surface region (curves).

Fig. 5. The experimentally measured effective lifetime results (symbols) of both p-type and n-type c-Si test samples passivated by the negative-charge Al2O3 are fitted with the proposition of unequal electron and hole bulk lifetime parameters (curves).

1013 1014 1015 1016 101710-1

100

101

p-type & n-type: Bulk: n0 = p0 = 20 msDam: n0 = p0 = 10 s d = 500 nm

Qf = -1.3x1013 cm-2 p-type exp n-type exp p-type sim n-type sim

Effe

ctiv

e lif

etim

e [m

s]

Excess carrier density [cm-3]

1013 1014 1015 1016 101710-1

100

101

n-type: n0 = 30 msp0 = 1 ms

p-type: n0 = 3 msp0 = 15 ms

Effe

ctiv

e lif

etim

e [m

s]

Excess carrier density [cm-3]

p-type exp n-type exp p-type sim n-type sim

Qf = -1.3x1013 cm-2

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3.4. Verification of both propositions

Under the proposition of damaged surface region, the enhanced SRH recombination at low injection levels takes place in the damaged surface region. Thus the effective lifetime curve is sensitive to the polarity of the net surface fixed charges. Under the proposition of unequal electron and hole bulk lifetime parameters, the enhanced SRH recombination takes place in the bulk. Thus the effective lifetime curve is insensitive to the polarity of the net surface fixed charges. The different response of simulated effective lifetime curves to the polarity of the net surface fixed charges is illustrated in Fig. 6.

As it is convenient to use a corona discharger to change the polarity of the net surface fixed charges, a

simple experiment is designed as follows. The validity of the two propositions can then be checked.

Measure the effective lifetime curve as a function of the injection level for both n-type and p-type c-Si wafer passivated by the negative-charge Al2O3.

Change the polarity of the net surface fixed charges with a corona discharger. Measure the effective lifetime curve as a function of the injection level again. One of the propositions can be experimentally confirmed by checking whether the reduction of

effective lifetime is present or gone.

Fig. 6. In response to the polarity of the net fixed surface charge, the simulated effective lifetime curves are (a) different under the proposition of damaged surface region and (b) similar under the proposition of unequal electron and hole bulk lifetime.

4. Conclusions

In this paper we investigated field-effect surface passivation of c-Si test structure with SENTAURUS TCAD simulator. To accurately model surface passivation, we implemented the extended SRH model with the ability to describe arbitrary energy distribution of interface traps. Experimentally it has been found that the effective lifetime of the generated charge carriers is reduced for low excess carrier densities. This phenomenon is in contradiction to the extended SRH model. It is currently assumed that the reduced lifetime is caused by the damaged surface region. However, the physical details of the damaged surface region are unclear and the choice of simulation parameters is therefore somewhat arbitrary. In our study we found that the reduced lifetime at low excess carrier density can also be

1013 1014 1015 1016 101710-1

100

101

(a) Damaged surface region

effe

ctiv

e lif

etim

e [m

s]

Excess carrier density [cm-3]

Negative Positive

|Qf| = 1.3x1013 cm-2

n-type c-Si Bulk: n0 = p0 = 20 msDam: n0 = p0 = 10 s d = 500 nm

1013 1014 1015 1016 101710-1

100

101

(b) Unequal bulk lifetime parametersE

ffect

ive

lifet

ime

[ms]

Excess carrier density [cm-3]

Negative Positive

IQfI = 1.3x1013 cm-2

n-type c-Si n0 = 30 msp0 = 1 ms

161Fa-Jun Ma et al. / Energy Procedia 15 (2012) 155 – 161 F.-J. MA et al. / Energy Procedia 00 (2011) 000–000 7

explained, if a different lifetime for electrons and holes is assumed. This assumption is justified, because there is no physical reason, why electron and hole lifetime should be equal. With both assumptions good agreement can be achieved between simulation and reported measurement results. We found that the two causes can be distinguished if a simple experiment is performed. In this experiment the polarity of the net surface charge is changed. Measurement of the effective lifetime for the normal and the changed polarity results in different characteristics for a damaged surface and similar characteristics for unequal electron and hole lifetime parameters.

Acknowledgement

The authors gratefully thank Dr Marius Peters at SERIS for thought-invoking discussions. SERIS is sponsored by the National University of Singapore and Singapore’s National Research Foundation through the Singapore Economic Development Board. This work was sponsored by the grant NRF2009EWT-CERP001-056 from the National Research Foundation of Singapore.

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