Numerical Simulation and Modeling of Resistive and Recombination ...

IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 4, OCTOBER 2013

1215

Numerical Simulation and Modeling of Resistive and Recombination Losses in MWT Solar Cells Paolo Magnone, Diego Tonini, Raffaele De Rose, Michel Frei, Felice Crupi, Enrico Sangiorgi, and Claudio Fiegna

Abstract—This study analyzes the impact of resistive and recombination losses in metal wrap through (MWT) solar cells through technology computer aided design (TCAD) numerical simulations. Two types of MWT architectures are considered in this study: “point busbar,” featuring one circular tabbing contact for each via at the back side, and “continuous busbar,” in which the rear busbar connects all the vias along a line. A comparison with conventional, H-pattern, front contact (FC) solar cells is performed by adopting the surface recombination velocity at the rear-contact isolation region as a parameter representative of possible passivation options. The differences under dark and light conditions are highlighted. Moreover, the following resistive losses in MWT cells are investigated: via resistance, shunting effect, and lateral conduction of charge carriers above rear busbar. An analytical model to account for the lateral conduction of charge carriers is proposed and validated by means of numerical simulations. While the advantage of MWT over FC cells is confirmed by simulation, we quantitatively show how the resistive and recombination losses limit the efficiency of MWT cells. Index Terms—Back-contact, metal wrap through (MWT), numerical simulation, photovoltaics, solar cell, via.

I. INTRODUCTION ACK-contact architectures represent a valuable solution for the development of more efficient solar cells by reducing the shadowing of the front metal grid and the losses in terms of Fill Factor (FF) and short-circuit current (Jsc ) at the module level [1]. Among the different solutions, metal wrap through (MWT) solar cells [2] allow to benefit from the advantage of the back-contact scheme by requiring only a few additional processing steps, such as laser drilling of holes [3], [4] and, eventually, rear-contact isolation (RCI) [5]. The presence of metal-filled

B

Manuscript received April 11, 2013; revised June 13, 2013; accepted June 18, 2013. Date of publication July 11, 2013; date of current version September 18, 2013. This work was supported in part by the Energy for a green society (ERG) Project funded by the European Nanoelectronics Initiative Advisory Council Joint Undertaking under Grant 2010/270722–2. P. Magnone, R. De Rose, E. Sangiorgi, and C. Fiegna are with the Advanced Research Center on Electronic Systems, the Department of Electrical, Electronic, and Information Engineering, University of Bologna and Italian University Nano Electronics Team (IUNET), Cesena (FC) 47521, Italy (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). D. Tonini is with Applied Materials Italia s.r.l., Olmi di S. Biagio di Callalta 31048, Italy (e-mail: [email protected]). M. Frei is with Applied Materials, Inc., Santa Clara, CA 95054–3299 USA (e-mail: [email protected]). F. Crupi is with the Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Universit`a della Calabria and IUNET, 87036 Rende, Italy (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JPHOTOV.2013.2270352

holes (vias) allows carrying the current collected by the front fingers toward the rear busbars. The removal of the front busbars, which is required in order to increase the photogenerated current, calls for the implementation of nonconventional front metal grid layouts [1], [6] in order to have effective photogenerated current collection and transport to the vias. A different approach is to maintain an H-pattern-like structure for the front side, with parallel fingers intersecting thin busbars at the vias position. This way, a simple, easy to screen print layout is used, and the shadowing is reduced because the front busbars are thinner than in front contact (FC) cells, but a larger number of vias is required [7]–[9]. Moreover, n- and p-type back contacts are isolated by a separation region in which RCI is created by means of laser processing [5], [7]–[9]. MWT structures without emitter at the rear interface [3] are not considered in this study. Several works have focused on the modeling of MWT solar cells using TCAD numerical simulators, in order to study the influence of geometrical and technological parameters [7], [10]. In order to minimize the computational effort, simplified 2D approximations are typically adopted. However, due to the cylindrical shape of the via and to the ring shape of the separation region, the structure is intrinsically 3-D. In this study, we analyze two types of MWT structures. For the first one, we adopt a simulation setup similar to that in [7] and [10]. In the second case, a quasi-3-D analysis is performed as we exploit the axial symmetry of the structure by solving the semiconductor equations recast in cylindrical coordinates, over a 2-D section of the device. This allows to extend the simulation to a 3-D domain with acceptable computational effort [11]. The goal of this study is to analyze and to model the resistive losses introduced by the MWT architecture, such as the via resistance, the shunting resistance and the lateral conduction of charge carriers above the rear busbar. Moreover, we analyze the impact of the separation region and of the RCI region on the recombination losses. The remainder of the work is organized as follows: in Section II, we describe the adopted simulation methodology; in Section III, we compare the performance of MWT cells with conventional FC cells; in Section IV, the impact of the resistive losses is evaluated for the two considered topologies of MWT cells; in Section V, the main results of the study are summarized. II. SIMULATION METHODOLOGY Fig. 1 reports a schematic representation of the MWT architectures considered in this study. Fig. 1(a) shows a structure with a back point busbar (PB) featuring a ring-shaped separation region between the p- and n-contact. Fig. 1(b) depicts a structure with a continuous busbar (CB) at the back side, extending from one side of the cell to the other. In the case of nonconventional

2156-3381 © 2013 IEEE

1216

Fig. 1. MWT architectures under test. (a) Point busbar (PB); (b) continuous busbar (CB); (c) cross section of both structures.

front grid layout, such as in [1] and [6], front fingers are no longer parallel lines, which allow to remove the front busbars. In this case, a limited number of vias is implemented (typically 16), which are far between, and the back configuration is well represented by the PB [see Fig. 1(a)]. When considering an Hpattern-like front layout, in order to reduce the width of the front busbar, a larger number of vias is required and the rear busbar typically groups two or more vias. We describe this case with the CB structure in which the same busbar groups all the vias on a line. This represents a limit condition highlighting the influence of the separation region at the back side and allowing a simplification of the simulation domain, as already reported in [7]. The cross section (which is the same for both structures) is reported in Fig. 1(c). In order to simulate the CB structure, we perform a 2-D simulation of the cross section, hence, adopting Cartesian coordinates. It is worth pointing out that this 2-D modeling approach does not allow to represent the cylindrical shape of the via. On the contrary, in the PB case, the axial symmetry is exploited, limiting the numerical calculations to the cross section of Fig. 1(c) and by recognizing the via axis as the rotation axis for such symmetry, thus accounting for a 3-D geometry. In both cases of Cartesian and cylindrical coordinates, the front surface of the simulation domain is treated as a homogenous metalized region equivalent to the physical grid. This approach eliminates the details of the front layout so that any observed difference between the structures is only due to the differences in rear-side geometry. For this reason, the front metallization is assumed to be transparent to the incident radiation and the optical generation rate is weighted according to the front metallization fraction (3.75%). The surface recombination velocity (SRV) at the front interface is a weighted average between the surface recombination velocities at the passivated and metalized front regions. We also consider a front-side series resistance of 0.43 Ω·cm2 in order to account for finger, contact, and emitter resistance (representative of a three-busbar H-pattern front

IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 4, OCTOBER 2013

metal grid with a finger pitch of 2 mm, a finger sheet resistance of 2 mΩ/sq, and a contact resistivity of 2 mΩ·cm2 ). In the case of PB, we assumed a structure featuring 4 × 4 vias; hence, the element of symmetry features an area of 3.9 cm × 3.9 cm. Because of the adoption of cylindrical coordinates, the simulation domain has a circular shape, while the real domain features a square shape. Therefore, the radius of the circular domain is chosen in order to obtain the same area as the actual square. Numerical simulations are performed by using a state-ofthe-art TCAD device simulator with parameters of physical models tuned for typical silicon PV technologies [12]–[15]. The c-Si solar cell is 180-μm-thick and 15.6 cm × 15.6 cm wide. The fine-tuned models include the band-gap narrowing model by Schenk to account for the effective intrinsic carrier density [16], the Auger recombination model with the parameterization adopted by Altermatt in [17], the mobility model proposed by Klaassen [18], [19], the bulk Shockley–Read–Hall (SRH) lifetime model in nondegraded boron-doped Cz-Si according to Glunz’s parameterization [20], and in Al-p+ Cz-Si according to Altermatt’s parameterization [21]. We accounted for Fermi–Dirac statistics in order to properly model highly doped regions. We adopted the parameterization proposed by Kimmerle et al. in [22] for the SRV at SiNx -passivated front surface, assuming an Auger-limited lifetime in the emitter bulk and chemical phosphorus surface concentration dependence for the SRV. Because of the laser processing, the surface in the RCI region is assumed to be highly defective and a large value of the SRV is adopted [7]. However, the effect of laser could be also extended in the bulk region leading to a local degradation of lifetime. This effect is not accounted for in our simulation setup, possibly leading to an underestimation of recombination currents. Optical generation rate profiles are calculated by assuming the standard AM1.5G spectrum and accounting for random pyramids textured SiNx front surfaces. Relevant parameters of the simulated cells are reported in Table I. III. COMPARISON BETWEEN METAL WRAP THROUGH AND FRONT CONTACT SOLAR CELLS In order to compare PB MWT solar cells with conventional FC counterparts, we consider the same doping profiles and physical models for emitter, bulk, and BSF regions, the same SRV at metalized regions, and the same contact and finger resistance. In the case of FC, we assume a finger and busbar metallization fractions of 3.75% and 2.88% (resulting from the adoption of three, 1.5 mm wide, front busbars), respectively. Since the performance of the MWT cell is significantly influenced by the RCI region, the comparison with FC solar cells is performed by considering different values for the SRV in this region. In Fig. 2, the dark I–V curves are reported for PB MWT as a function of the SRV in the RCI region and fitted with a two-diodes model [23]. As shown in Table II, the J01 component is not significantly affected by the SRV value, while an increase of J02 component is observed as this parameter is increased. For the FC solar cell, we simulated both 1-D and 2-D domains, assuming, in the first case, a fully metalized front surface with equivalent spatial weighted average SRV and optical generation

MAGNONE et al.: NUMERICAL SIMULATION AND MODELING OF RESISTIVE AND RECOMBINATION LOSSES IN MWT SOLAR CELLS

1217

TABLE I PARAMETERS OF THE SIMULATED STRUCTURES

TABLE II DARK AND LIGHT ANALYSIS OF PB MWT (WITH 16 VIAS) AND FC CELLS

Fig. 2. Dark current analysis of PB MWT solar cells as a function of the SRV at the RCI region. The separation region is 1-mm wide. The curves are fitted with a two-diodes model.

rate. Moreover, in case of 1-D domain, the voltage drop due to the emitter is accounted for in the postprocessing analysis by considering the distributed emitter resistance and the external metal resistance. The comparison between 1-D and 2-D simulations allows us to validate the adoption of equivalent uniform spatial weighted average SRV and optical generation rate at the front surface of MWT cells. In fact, as observed in Table II, the recombination currents are very similar in the case of 1-D and 2-D structures. Small changes can be attributed to the nonuniform potential distribution in the case of the 2-D structure. By comparing MWT and FC cells, we observe that the J01 recombination currents in the emitter, bulk, and BSF are comparable in magnitude. Hence, the contributions due to the via contact, busbar contact, and unpassivated rear emitter are negligible. As a matter of fact, the same open-circuit voltage Vo c is found for both architectures. On the other hand, there is a significant reduction of FF in the case of the MWT architecture. This is due to the higher J02 component (related to the RCI region) and to the resistive losses, which will be discussed in the next section. This effect partially jeopardizes the performance gain associated with the increase of Jsc , leading to an increase of cell efficiency to 0.5%abs compared with the FC cell. However,

the advantage of MWT can be even larger if we consider the losses at module level and the recombination current at the front busbar interface in the case of the conventional FC, which is not accounted for in our simulation setup. IV. MODELING OF RESISTIVE LOSSES IN METAL WRAP THROUGH SOLAR CELLS A. Via Resistance As discussed in [7], in the case of CB structure, featuring a large number of vias, the via resistance does not significantly

1218

Fig. 3. Efficiency and FF versus via resistance as a function of the number of vias, in PB MWT cells. By increasing the number of vias, the figures of merit are less sensitive to the via resistance, but the recombination current (due to the RCI region) increases.

IEEE JOURNAL OF PHOTOVOLTAICS, VOL. 3, NO. 4, OCTOBER 2013

Fig. 4. Efficiency and FF versus RCI distance from the rear busbar in the case of PB and CB MWT cells. Via resistance is assumed to be negligible in both cases. By moving the RCI region closer to the p-contact, the FF monotonically increases in the case of CB, while an optimum position exists in the case of PB.

affect the FF of the MWT cell. On the other hand, in the case of PB, it is important to account for this effect. In Fig. 3, we analyze the FF and the efficiency of a PB MWT cell as a function of the via resistance and of the number of vias. First, the FF (and hence, the efficiency) linearly decreases when increasing the via resistance. Second, by increasing the number of vias, FF and efficiency are less sensitive to the via resistance, but they tend to lower values in the case of via resistance equal to 0. In fact, when increasing the number of vias, the overall series resistance decreases, but at the same time, the J02 current increases due to the larger extension of the RCI region. According to Fig. 3, for a typical via resistance of about 3–4 mΩ, an optimum number of vias exists: close to 16. B. Shunting Resistance In MWT cells, the back emitter is in direct contact with the p-contact, leading to a shunting effect and, hence, to a degradation of the FF. The extension of this short-circuit region depends on the RCI position. As already proved in [7], in the case of CB, by placing the RCI region closer to the p-contact, the FF strongly improves (see Fig. 4). However, in the case of PB, a different behavior is observed: By placing the RCI region closer to the p-contact, on one hand, the FF increases due to lower shunting effect, while on the other hand, the FF decreases due to the larger area of the RCI region, which leads to an increase of J02 . These two competing effects explain the bell-shaped FF dependence reported in Fig. 4. C. Lateral Conduction of Charge Carriers Holes generated above the rear busbar or in the separation regions must drift laterally through the bulk, in order to be collected by the p-contact. Hence, the lateral width of the separation region is an important parameter affecting the resistive losses of the MWT architecture. In Fig. 5, we report the efficiency and FF as a function of the extension of the separation region (WSEP ) for both PB and CB MWT cells. In both cases, the via resistance is assumed to be negligible. The FF strongly reduces by increasing WSEP . Moreover, this effect is more severe in the

(a)

(b)

Fig. 5. (a) Efficiency and (b) FF as a function of separation region extension in PB and CB MWT cells. Both figures of merit degrade by increasing the separation region.

case of CB MWT cell. This degradation is due to the increase of lateral path for holes and to the increase of shunting effect. In fact, since the RCI region is kept in the middle of the separation region, when WSEP increases, the short-circuited emitter region enlarges as well. Moreover, Fig. 6 shows that in the case of PB MWT cells, the increase of WSEP causes the enhancement of the J02 recombination current, due to larger area of the RCI region. This is a further source of degradation for the FF. The lower FF observed in the case of CB MWT cell can be partially explained by the significantly higher J02 component, as observed in [11], due to the larger RCI area. In [7], a model for the series resistance associated with the lateral conduction of holes in CB MWT structure is proposed  2 ρsub rn3  Ωcm2 (1) 3 s L where s is the substrate thickness, L is the width of the element of symmetry (distance between adjacent vias), and rn is the distance between the p-contact and the via. In order to derive a model for the lateral conduction that is valid in the case of the PB MWT cell, let us consider the schematic configuration of Fig. 7. By considering a radial transport from the center to the Rlat,CB =

MAGNONE et al.: NUMERICAL SIMULATION AND MODELING OF RESISTIVE AND RECOMBINATION LOSSES IN MWT SOLAR CELLS

1219

(a)

(b)

Fig. 6. Dark current analysis in PB MWT cells as a function of the separation region. By increasing the separation region, the recombination current in the RCI region is enhanced, leading to a reduction of FF.

Fig. 8. Efficiency and FF as a function of separation region in (a) PB and (b) CB MWT test structures. Numerical simulations are well fitted by the analytical model in the case of PB, while a significant mismatch is observed in the case of CB when considering R la t modeling only. The accuracy of the modeling improves if the spreading resistance R sp r is accounted for.

Fig. 7.

Schematic of radial transport in the case of PB MWT cell.

p-contact, the infinitesimal resistance dR can be expressed as dr . (2) 2πrs The dissipated power on the dR element is calculated by considering the current I(r) generated within the radius r, as given by 2   2 dP = dR · I 2 (r) = dR · Jπ r2 − rvia (3) dR = ρsub

J being the generated current density and rvia the radius of the via. Therefore, the total dissipated power can be calculated integrating (3) in the range rvia − rn .  rn  rn 2 πρsub 2  2 πρsub 4 2 2 J r − rvia r J P= dP (r) = dr ≈ 8s n rv ia r v i a 2rs (4) where we have assumed rvia