Category Thin-Film Crystalline Silicon Solar Cells

Effective grain size for log-normal grain size distribution

Polycrystalline cells consist of grains with different sizes. Figure 2.31 on p. 49 shows the measured log-normal grain size distribution that is well described by the function [200,201]

( Ґ — 2^

Подпись: m=Подпись: (C.38)1 1 [ ln(G/ G) cr’

(^exphl—-% which that describes a Gaussian distribution of the logarithm of the grain size G. The average grain size is G, and cr is the width parameter of this distribution. For simulations we would not want to simulate many grains with various grain sizes. The question we address here is: what is an appropriate choice for an effective grain size Geff that we choose to represent an ensemble of grains with a log-normal size distribution? To answer this question we proceed in two steps...

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Laplace transform of quantum efficiency spectra

The local carrier collection probability rfc(Z) is defined as the probability that a carrier generated at the depth Z is collected at the junction of a short-circuited cell. In this sec­tion, we assume a planar cell of thickness ^ with one-dimensional transport and the cell surface located at Z = 0. In contrast to the previous section, the thickness of the emitter We and the space charge region Wscr are not neglected and Wf=We + Wscr + Wbas – For a zero back surface reflectance of a cell with thickness Wf, the internal quantum efficiency


IQE = J r]c(z) as exp(-as Z)dZ =as L{j7c(z)} (C.30)


image558 Подпись: (C.31)

is the Laplace transform l{t]c(z) } of the local carrier collection efficiency rjc(Z) [209]. Sinkkonen et al. suggested that the local carrier collection efficiency

could be determined f...

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Polycrystalline semiconductors

Minority carrier recombination in polycrystalline semiconductor materials occurs in the volume of the grains, at the grain boundaries and at the surface of the cell. The quantum efficiency model has therefore to account for all three locations of recombina­tion. Three-dimensional modeling is necessary.

Referring to the cell geometry shown in Figure 2.28 on p. 46, we calculate the quan­tum efficiency under monochromatic illumination with light that has the absorption coefficient as. The spatial carrier generation rate

g(x, y,z) = asexp(-asz) (C. 13)

decays exponentially into the depth Z. The reduced absorption coefficient as is measured in units of inverse grain size G~l here. The position z = Z/G, and similarly x and y, are also scaled by the grain size...

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Monocrystalline semiconductors

Quantum efficiency diffusion length Lq

Подпись: JQ,mono Подпись: L ShLsmh(WhJL)+Dn cosh{WbJL) SbLcosb{WbJL)+Dnsmh(WbJL) Подпись: (C.10)

For planar monocrystalline sheets of Si material, the effective quantum efficiency diffusion length

depends on the diffusion length L of the semiconductor, the back surface recombination velocity Sb, the base thickness Wbas, and the minority carrier diffusion coefficient Dn [24]. The value of LQmono equals the effective current-voltage diffusion length LJ>mono, which determines the dark saturation current density

image529(C. ll)

of a single-sided p-n junction (Eqs. (8) and (9) of Ref. [24]). The symbol q denotes the elementary charge and nQ is the equilibrium minority carrier concentration. The quantum efficiency can therefore be used to evaluate the amount of recombination in the base of a single-crystalline solar cell [24, 177, 411].

Подпись: JC,mono Подпись: L SbL{cosh{WbJL)-)+Dn sinh{WJL) SbL sinh(fFte /L)+Dn cosh(fFte /L) Подпись: (C.12)
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Effective diffusion lengths (formulas)

As sketched in Figure 3.2 on p. 56, a quantum efficiency spectrum of a crystalline thin-film cell shows, in general, two linear regions if plotted as IQE~La ). Both regions define an effective diffusion length:

• The length Lq that we call the quantum efficiency diffusion length and that we derive from the IQE spectrum measured with strongly absorbed light {La « Wbas). The defi­nition of Lq is given on p. 55.

• The length Lc that we call the collection diffusion length and that we derive from the IQE spectrum measured with weakly absorbed light (La » Wbas). The definition of Lc is given on p. 56.

We give the formulas for both effective diffusion lengths Lq and Lc in monocrystalline and polycrystalline material.

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Rear illumination

Illuminating the cell through the back achieves a higher sensitivity to the back surface recombination than illumination through the front surface. Obviously, the cell has to be bifacially sensitive to permit rear illumination. The quantum efficiency for back illumi­nation is [409, 410]

IQE =———————- A——————– (C.9)

cosh(^/I) + -^-sinh(^os/I)

Here, plotting IQE versus La yields a linear relation. The slope and intercept provide information on Sb and L. Equation (C.9) predicts that the ratio of the slope to the inter­cept is Sb/Dn; here Dn is the diffusion coefficient of the minority carriers (electrons).

Подпись: Figure C.5. The inverse internal quantum efficiency is linear in the optical absorption length. For absorption lengths greater than the cell thickness the linear relation does not hold.

C.3 Effective diffusion lengths (formulas)

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Standard analysis

C. 2.1 Front illumination

The standard technique for the evaluation of internal quantum efficiency spectra [36] assumes a cell that is thick, compared to the optical absorption length La = l/as, and has a spatially homogeneous minority carrier diffusion length. Here, as denotes the absorp­tion coefficient of crystalline Si. The profile of the minority carrier generation rate g(Z) decays exponentially with the distance from the cell surface. When the optical absorp­tion in the emitter of the solar cell is neglected, the inverse internal quantum efficiency

IQE’= + LJLq (C.8)

depends linearly on the optical absorption length...

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Measurement example

Figure C.3 shows the quantum efficiency of a high-efficiency thin-film Si solar cell with a thickness of 46.5 pm (see description of Cell A on p. 83 for more details) under illumination with light of wavelengths 500 and 800 nm. For both wavelengths the IQE data depend on the forward bias voltage Ub. At bias voltages up to 500 mV the value of IQE{500 nm) is constant, while IQE($00 nm) starts to increases at 350 mV. For voltages Ub >550 mV IQE(500 nm) and IQE(500 nm) both decrease.

Interpretation of the measurement

Light of wavelength 500 nm penetrates a distance of 0.9 jam into the cell. Hence, the light is mainly absorbed in the emitter and the quantum efficiency therefore reflects the recombination in the emitter that is known to be, in general, independent of the injection level.

In cont...

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