optimal thickness for crystalline silicon solar...

PROPRIETARY AND CONFIDENTIAL 1

OPTIMAL THICKNESS FOR CRYSTALLINE SILICON SOLAR CELLS Christopher Petti, Bonna Newman, Robert Brainard, Jian Li

Twin Creeks Technologies, Inc.

Abstract

A simple model is described wherein optimal thicknesses for crystalline silicon solar cells are calculated. It is found that, for cells with excellent surface passivation (<=8 cm/sec), Auger‐limited bulk recombination, and good optical confinement, optimal thickness can be 30‐60 µm. Such cells can be realized using amorphous silicon heterojunction passivation and dense, low‐relief texturing.

Introduction

For photovoltaics, the reduction of the active cell thickness – sometimes referred to the “Moore’s law” of solar cells [1] – has been one of the most active areas of research and development. Although this work is driven primarily by the desire to reduce silicon usage and thereby materials costs, there can be performance advantages in reducing the volume of silicon in which carriers can recombine. This is especially true for cells whose dominant recombination mechanism is bulk recombination rather than surface recombination.

The relationship of cell performance to bulk and surface recombination effects can be described by the effective lifetime τeff, defined by

€

1τ eff

=1

τ bulk+2Seffd

, (1)

where τbulk is the bulk lifetime, Seff is the effective recombination velocities at the cell surfaces, and d is the cell thickness. It is clear from equation (1) that, as cell thickness is decreased, surface recombination tends to dominate over bulk recombination in determining the effective lifetime. Thus, if surface recombination is high, the performance benefits of reducing cell thickness will not be realized.

One way to suppress the surface recombination is to use heterojunction passivation, wherein an amorphous silicon emitter is formed on a crystalline silicon base. First proposed in 1974 [2], this structure is formed by depositing a thin hydrogenated aSi (aSi:H) layer on a cSi wafer at low temperatures, typically less than 200C. Values of Seff can be reduced from typical values of 50‐200 cm/sec for nitride‐passivated surfaces [3,4] to 8‐15 cm/sec [5‐7] by using this scheme. Although other methods of surface passivation, including thermally grown and atmospheric pressure CVD SiO2 [8,9], have been applied to c‐Si solar cells, the only alternative to silicon nitride passivation used to produce c‐Si solar cells in high volumes is heterojunction passivation. With such effective surface passivation, development effort in


heterojunction cells has shifted towards thinning down the c‐Si wafer to thicknesses of less than 150‐100 µm [10].

Given well‐passivated surfaces, the main disadvantage of thin c‐Si solar cells is their poor absorption performance in the red and NIR part of the solar spectrum, which leads to lower short‐circuit currents. Thus, excellent light trapping is a requirement for such cells [3,11].

When both of these requirements are met – optimal light trapping and suppressed surface recombination – solar cell efficiency can be higher for thinner active layers than for standard thicknesses. Brendel [3] and Green [11] calculate an optimal thickness of 64 µm and 80 µm, respectively, for Lambertian light trapping, and Brendel further calculates an optimal thickness of 36 µm for “optimal”, or “better‐than‐Lambertian” light trapping. Both of these analyses assume no surface recombination. When surface recombination velocities typical of conventional solar cells are added to the models, both authors find there is no optimal active cell thickness – the conversion efficiency monotonically increases with increasing cell thickness. Thus, it is useful to determine what the optimal solar cell thickness would be if a lower, non‐zero value of SRV, representative of heterojunction passivation, is used in the calculations.

In this work, then, we explore the effect of applying the excellent passivation properties of a‐Si/c‐Si structures to thin films of crystalline silicon [12] with well‐designed light‐trapping schemes. We first describe the modeling methods and results using realistic values for recombination and light trapping parameters. We show that, for these high‐performance technologies, thinner cells offer a distinct efficiency advantage over thicker cells. We then discuss the practical concerns with fabricating these structures: passivation results and light trapping structures and processes. We conclude with a short discussion of non‐random light trapping structures that can approach theoretical limits.

Model Description

A simple model was used to explore the effects of surface passivation, light trapping, and other cell parameters on the optimal cell thickness. The model details for light trapping and bulk and surface recombination are described in this section.

Light trapping The degree of light trapping is modeled by decomposing the incoming light into a completely non‐scattered portion and a portion that is ideally scattered, either in a Lambertian, or “optimal”, method. The ratio of scattered to total light, roughly equivalent to the transmitted haze [13], was used as a modeling parameter.

The portion of light not scattered by the front surface, and not absorbed in the bulk of the cell, has another chance to scatter at the rear surface. To model this, a similar reflected haze parameter for the rear surface is introduced.


The fraction of light absorbed A, for non‐scattered light, is calculated from the Beer‐Lambert law:

€

A =1− exp(−α sd) , (2)

where αs is the silicon absorption coefficient and d is the cell thickness. For the portion of light that is scattered in a Lambertian angular distribution, the absorption fraction is given by [3]

€

A =(1−Tr )(1+ RbTr)ns

2(1− Rf )ns2 − Rb (ns

2 −1+ Rf )Tr2 , (3)

where ns is the silicon index of refraction, Rf and Rb are the angle‐averaged front and rear cell reflectances, respectively, and Tr is the transmittance of the fully randomized light through a planar film of thickness d. This transmittance can be expressed as [14]

€

Tr = exp(−α sd)(1−α sd) + (α sd)2E1(α sd) , (4)

where

€

E1(z) =exp(−t)

tz

∞

∫ dt , (5)

which can be calculated numerically. This method of modeling the absorption of light in a slab of silicon with fully or partially scattering surfaces is shown in Figure 1.

Equations 3‐5 are used to model Lambertian scattering; however, it is possible, using regular and semi‐regular scattering geometries, to exceed Lambertian scattering [15]. To model the physical limits of light trapping, equations 3‐5 were replaced in some scenarios with an expression for the maximum absorption possible with perfect geometric light trapping [16]:

€

A =1− exp(−α s4ns2d) . (6)


Equation (6) does not represent any physical system currently in existence; rather it represents the theoretical limit of light capture for a given semiconductor thickness.

Recombination Bulk lifetime, dependent on dopant and excess carrier concentrations, was modeled by modifying the semi‐empirical expression developed by Kerr [17]:

€

1τ b

=1τ b0

+ ND 1.8 ×10−24ND

0.65 + 6 ×10−25 ni2

ND

0.65

+ 3×10−27Δn0.8

(7)

In this equation, shown for N‐type material, ND is the base doping, ni is the intrinsic carrier concentration, and Δn is the excess carrier concentration. This equation takes into account Auger recombination, which tends to dominate over SRH and radiative recombination at the dopant and excess carrier concentrations that are of interest for solar cells. We have added the low‐carrier bulk lifetime term τb0 to take into account recombination at bulk defects and other impurities. The excess (or injected) carrier concentration was calculated using the method described in [18]:

€

Δn =ND

2

2

+ ni2 exp qVOC

kT

−

ND

2, (8)

where Voc is the cell’s open circuit voltage.

This lifetime was combined with a base surface recombination velocity Sb into an effective diffusion length for the base [19,20]:

!"#$%&'()(*%+$*(,&&

!"#$%&-"+$./01(2&3+4(&

'(+"&"()(*%+$*(,&

'(+"&"()(*%(2&3+4(&

Figure 1: Modeling scheme for partially or fully scattering surfaces. The red arrows represent the nonscattered portion of the light (equation 2); the black arrows represent the scattered portion (equations 35).


€

L j0 = LSbLsinh d /L( ) + Dp cosh d /L( )SbLcosh d /L( ) + Dp sinh d /L( )

, (9)

where Dp is the hole diffusivity and

€

L ≡ Dpτ b (10)

is the bulk diffusion length. The effective diffusion length of equation (9) is then used to determine the dark current saturation density j0:

€

j0 =qni

2Dp

NDL j 0

(11)

which directly determines Voc:

€

VOC ≈kTqln Jsc

j0

, (12)

where Jsc is the short‐circuit current. Note that the open‐circuit voltage Voc is used to estimate the injected carrier concentration in equation (8); thus, an iterative calculation is performed until the bulk lifetime τbb converges.

The dependence of VOC on a number of parameters can be estimated by combining equations 9‐12 [21], and assuming the cell width d is less than both the bulk diffusion length L and hole diffusivity‐SRV ratio Dp/Sb:

€

VOC ≈kTqln

JSCNDτ effqni

2d

, (13)

where τeff is defined in equation (1).

Recombination losses also affect the short‐circuit current JSC if the bulk diffusion length L (equation 10) is less than the cell width d. This effect was taken into account using the solutions to the standard semiconductor differential equations given in [19].

Other loss mechanisms Resistive losses were also included in this model. The resistance of the metal grid lines and transparent conductive oxides was modeled as a lumped element with a value of 1.1 Ωcm2. A realistic value for the shading of the metal grid lines – 5.5% ‐‐ was also used. Lastly, some loss due to absorption in the (non‐collecting) front a‐Si and TCO layers is also taken into account.


Model results

Figure 2 shows the modeled efficiency vs. cell thickness for different light trapping schemes: no light trapping, Lambertian light trapping (equations 2‐5), and optimal light trapping (equation 6). For these calculations, the base doping was optimized (between 1016 and 4x1017 cm‐3) for each thickness. The Lambertian curve is calculated with 95% back reflectance and a front transmitted haze factor of 0.9; the “no light trapping” case assumes 5% back reflectance and front transmitted haze of 0.1.

Figure 2: Modeled efficiency vs. cell thickness for various light trapping schemes, for conventional surface passivtion (a) and heterojunction surface passivation (b,c), with (c) showing a subset of the results shown in (b) but on a linear thickness scale.

With a surface recombination velocity that represents a typical conventional, diffused‐emitter solar cell (Fig. 2a), there is no efficiency advantage in going to a thinner cell, except for the purely theoretical “optimized” light‐trapping scheme. However, when realistic values for the SRV of a heterojunction cell are used (Fig. 2b), using a thinner cell offers a clear efficiency advantage for a practical Lambertian light‐trapping scheme. The optimal thicknesses for this case, ~60 µm and ~30 µm for the Lambertian and optimized light‐trapping schemes, respectively, closely match those obtained earlier [3] using no surface recombination. It is clear, then,


that with heterojunction passivation and very good light trapping, thinner cells can offer a real performance advantage.

Note also that, with Lambertian or optimal light trapping, the efficiency does not depend on thickness to a large degree for thicknesses >10 µm. This can be seen in the Figure 2c, where the results are plotted on a linear scale between thicknesses of 10 and 110 µm. In fact, decreasing the thickness from 57 µm to 20 µm decreases the efficiency by only 1% relative, or 0.4% absolute. Such a decrease in cell thickness would reduce the amount of silicon that produces one Watt of power by 65% over a 57µm cell, and 87% over a conventional (160 µm thick) cell.

The reason for the maximum in the efficiency curves of Figure 2 can be seen by examining short‐circuit current and open‐circuit voltage (Figure 3). Light trapping reduces the dependence of JSC on cell thickness, while VOC increases as thickness decreases regardless of the optical parameters, as shown in equation (13). These two competing effects result in an optimal thickness for cells with good light trapping and good surface passivation. Note that the VOC simulated for thicker wafers is slightly lower than the results shown in [10]; this could imply that practical SRV’s less than 8 cm/sec are achievable in a production process.

Figure 3: Opencircuit voltage (a) and shortcircuit current (b) vs. thickness for the Sb = 8 cm/sec case.

The relative importance of the two major optical parameters – back reflectance Rb and front scattering, or transmitted haze hf – is shown in Figure 4. From this figure, it is clear that back reflectance is important for a wide range of thicknesses. Furthermore, front‐side light scattering does little unless the rear surface is quite reflective. Thus, a good back surface reflector is a critical part of an effective light trapping scheme.


Practical concerns

SRV and bulk lifetime The model results shown above assume a high value for the intrinsic bulk lifetime τb0 (equation 7); that is, bulk recombination is dominated by Auger recombination. However, we have found that, in practice, many factors can reduce the lifetime in thin crystalline silicon films. Furthermore, thinner materials present certain challenges in forming well‐passivated a‐Si heterojunctions compared to thick silicon processes, particularly in the surface preparation steps [22‐24]. Thus, achieving low recombination – both surface and bulk – in thin crystalline silicon films presents a challenge.

To illustrate these practical considerations, measurements of VOC (from illuminated IV data) on 4.1 µm thick c‐Si solar cells are shown in Figure 5, superimposed on the modeled VOC vs. Sb and τb0 results. The parameters used in generating the model results reflect the process used in making these cells; in particular, the base doping was set to 5 x 1015 cm‐3. The VOC measurements represent continual process improvements; e.g., in surface preparation, a‐Si deposition conditions, and contamination control. The measured data points were plotted at τb0 values that correspond to lifetimes measured (using the Sinton WCT‐120 lifetime tester) on thicker samples that have undergone identical processing; they are thus likely to over‐estimate the lifetime in the thin films. We estimate τb0 of up to ~200 µsec; from Figure 5, this corresponds to Sb ~ 25 cm/sec (equations 1 and 13 could be used to obtain similar results). If our lifetime estimates are high, our SRV must be even lower in order to explain the measured VOC. Our VOC of up to 660 mV is ~45 mV higher than LIV VOC measurements reported on 30 µm samples [22]. The

Figure 4: Effects of back reflectance (Rb) and front side scattering (hf). Surface recombination velocity Sb = 8 cm/sec.


progressive improvement of VOC shown in Figure 5 indicates that the targets of Sb <~ 8 cm/sec and a bulk lifetime dominated by dopant/carrier concentration effects are quite achievable.

Texturing of thin crystalline silicon Another challenge in fabricating highly efficient thin crystalline silicon solar cells is the light‐scattering mechanism. The dimensions of the texture features on industrial thick‐silicon solar cells are typically 10‐20 µm. Using similar manufacturing processes on 10‐20 µm thick cells is not possible. One approach is to form these films conformally on a textured surface with large features [3]; this can lead to complicated processes and structures that are difficult to handle.

Alternatively, the texturing process can be changed to reduce the size of the features. Such structures should be as effective optically as larger scale textures, as long as the dimensions are larger than the wavelength of light in the silicon [25] – about 300 nm [26]. A scanning electron micrograph of a low‐relief process [27] is shown in Figure 6. The texture dimensions in this case are ~500 nm; the key development needed to achieve these dimensions is a high spatial density initiation step [27].

After deposition of a TCO anti‐reflective layer, the reflectance of this structure is shown in Figure 7. The integrated reflectance between 375 and 1010 nm, weighted by the AM1.5 solar spectrum, is 7.3%. Significantly, this reflectance is mostly diffuse, as shown by the haze plotted in fig. 7b. The haze is close to 1 for a wide range of the spectrum; a haze value of 1 indicates totally Lambertian scattering. This shows that a thin crystalline silicon film can be textured to achieve close to Lambertian scattering conditions.


Figure 5: Contour plot of modeled VOC (in V) vs. Sb and τb0 with measured values of VOC superimposed. Drawn arrow is a guide to the eye.

Beyond random light trapping The “optimal” light trapping modeled by equation (6) has not been reduced to practice; however, many workers have envisioned regular or semi‐regular structures to achieve a super‐Lambertian absortion characteristic [14,15,28]. A method well suited to thin semiconductor films is shown in Figure 8 [29]. The cell surface consists of a series of planes inclined at the same, relatively shallow, angle θ1. Normally incident light is refracted slightly upon entering the cell; upon reflection back to the front surface, it impinges on another slightly inclined surface, and is reflected at a greater angle. With each successive reflection, the angle of the light with respect to the cell normal direction increases by 2θ1. In this way, light can be confined in the cell until it is absorbed. The optimal value for the tilt angle θ1 is 10‐15 degrees, regardless of the cell thickness. Such asymmetric texturing could be realized, for example, by micro‐imprinting a pattern into a polymer [30,31] and transferring the pattern, via a wet or dry etch, into the silicon surface.


Figure 6: Scanning Electron Micrograph of lowrelief texture on a 4.1 µm thick crystalline silicon film.

Figure 7: Measured reflectances (a) and calculated reflected haze = diffuse/total reflectance (b) for a sample textured as in Fig. 6, with a deposited ARC layer.


Figure 8: Schematic for a possible "better than Lambertian" scattering structure (after [29]).

Conclusion

The desire to thin the active area of crystalline silicon solar cells is driven mostly by cost considerations. However, for structures that offer excellent surface passivation and light trapping, thinning cells can offer performance advantages. Simple modeling of cells using realistic, achievable values for surface recombination velocity and optical confinement parameters show that cell thicknesses that give optimal conversion efficiencies are between 30 and 70 µm; even 10 µm cells should be capable of >20% efficiencies. We show a path for achieving the surface recombination velocities and light trapping necessary for these high efficiencies: a heterojunction emitter and base contact, and dense, low‐relief texturing. Further optimization of the heterojunction processes to achieve < 5 cm/sec recombination velocities, and novel texturing structures to confine light to a degree beyond what can be obtained with a Lambertian scattering surface, could enable efficiencies seen now on only the highest quality thick cells (>=22%) to be obtained on cells down to 20 µm.

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