Optimising Layer Thickness of Multi-Junction Silicon Devices for Energy Production in a Maritime Climate

Optimising Layer Thickness of Multi-Junction Silicon Devices for Energy Production in a Maritime Climate S. Andre, T.R. Betts, R. Gottschalg *, D.G. Infield Centre for Renewable Energy Systems Technology, Department of Electronic and Electrical Engineering, Loughborough University, Loughborough, Leicestershire, LE 3TU, UK Abstract: Solar cells are predominantly optimised for laboratory efficiency which is likely to be at the expense of energy production. This paper demonstrates that optimising for energy production has the potential to decrease energy costs by 5-0%. This is achieved by building an equivalent circuit model to simulate the device performance under varying spectra. Combining this simplified model with real measurements of the operating environment, including incident spectra, allows an estimation of the optimisation potential. Introduction Today s generation of solar cells is predominantly sold based on performance under STC conditions. This fixation on rather artificial operating environments results in an optimisation of devices to these conditions, which can actually be at the expense of energy production and thus might result in an increase of energy generation cost. The impact of environmental conditions can only be minimised in some cases, e.g. the effect of low irradiance by ensuring a high shunt resistance, and thus this artificial characterisation of device performance is no problem. There is, however, one effect which potentially could affect the performance of devices quite significantly if not considered in the design state of advanced multi-junction devices. This effect is the spectrum, which can vary significantly from the design conditions and can have an observable effect on device performance []. Multi junctions are particularly vulnerable to changes in the spectrum, because the top cell effectively acts as a filter for the lower cell. A change in the spectrum will change the weighting of the photon absorption among the sub cells and the devices may no longer be perfectly matched. The separate junctions should, ideally, be perfectly matched because in any mismatched connection of devices, the worst cell will determine the performance of the series connection, as described e.g. for macroscopic interconnections by Bishop [2]. Thus a severely mismatched cell will cause a significant loss of energy production although this might not show up at the conditions considered for design purposes. Repmann et al. [3] showed that e.g. changes in solar altitude which changes the incident spectrum can result in the top limitation of a cell being switched to a bottom cell limitation. The spectrum is quite different in different locations. It is also rather cumbersome to use the entire spectrum for the description of solar cell performance, thus it is convenient to * corresponding author: Tel.: 0509-22848, Fax: 0509-6003, email: R.Gottschalg@lboro.ac.uk

reduce the spectrum to a single number descriptor. In this paper, the average photon energy APE of a spectrum is chosen as an indicator of the spectral hew which is measured for sake of comparison the band gap in electron Volts. This was demonstrated a good description []. The APE of a standard AM.5 spectrum is around.6 ev (calculated in the 300-700 nm region). In cloudy environments, such as the UK, the energy distribution can be shifted to higher energies, as shown in Figure for Loughborough, UK. 0 8 Frequency Count (%) kwh (%) kwh Cumulative (%) 00 80 6 60 4 40 2 20 0 0.2.3.4.5.6.7.8.9 2 2. 2.2 Average Photon Energy Bin [ev] Figure : Energy Distribution and Frequency of APE in Loughborough It is clear from Figure, that optimisation of the layers to AM.5 conditions might result in losses for some locations. The aim of this paper is to investigate the magnitude of these mismatch errors for current device technologies and see how much energy could be gained by optimising to the maritime climate experienced in Loughborough. This is done by developing a model to predict the influence of spectral variations on the annual performance of devices and in a second step by optimising the device structure to best suit the non-standard spectral conditions measured in Loughborough. 2 Model Development In order to describe the effects of mismatch on interconnected circuits, the individual cell operating currents and voltages must be determined. This is accomplished by determining the I-V characteristic of each individual sub cell based on the irradiance incident on each of them. The mismatched operating point is then established from the combination of the individual sub cell characteristics. The procedure followed in the model is summarised in the Figure 2.

Figure 2: Flowchart showing the procedures used to model cell performance 2. Sub-Cell Characterisation The short circuit current I sc determines the I-V behaviour of each sub-cell and needs to be calculated first. It is given as the integral of the wavelength-dependent spectral response SR(λ) and the spectral irradiance G(λ) multiplied by the area of the device: 2 I = A SR( λ) G( λ) dλ () sc λ λ Once I sc has been determined the cell can be characterised by solving the diode equation. The diode model used for this work is the common one diode equation with a reverse bias model suggested by Bishop [2] and a broad-band voltage dependence of the photocurrent as given by Merten et al. [4]. The diode equation is given as: qv ( + IRs ) I = I I exp I nkt ph o shunt where I is the output current (A), V is the terminal voltage (V), I ph is the photocurrent (A), I0 is the saturation current (A), I shunt is the leakage current (A), Rs is the series resistance (Ω) and n the diode ideality factor. The reverse bias characterisation is important to this model, as it is a crucial contributor to the mismatch operation of series connected devices. I shunt is the component of (2) that characterises the cells reverse bias based on avalanche breakdown and is given by [2] as: (2)

I shunts ( V + IR ) s ( V + IRs) = + a Rsh V br Where R sh is the cell shunt resistance (Ω), V br is the junction breakdown voltage (V), a is the fraction of ohmic current involved in avalanche breakdown and m is the avalanche breakdown exponent. An additional term is used in this model in order to adjust the photocurrent to account for the additional losses associated with amorphous silicon cells p-i-n cell structure. This additional term is given by [4] as: I ph = I ph μτ 2 ( Vfb Vj ) d i Where μ is the mobility of the charge carrier, τ is the lifetime of a charge carrier, d i is the thickness of the intrinsic layer, V fb is the flatband voltage of the device and Vj is the voltage at the junction of the cell. This broad-band approximation is a significant simplification as it has been shown by e.g. Bruns et al. [5] that the voltage dependence of current also depends on the spectrum. This paper is, however, concerned with developing a first order approximation of the magnitude of spectral effects and thus this approximation is sufficient. Equations (2)-(4) allow the individual sub cells to be characterized. Iterative procedures using the VanWijngaarden-Dekker-Brent and the Golden Section Search methods given by [6] are used to numerically solve these equation for V oc and the maximum power point respectively. 2.2 Incident Irradiance on the Bottom Sub Cell The bottom sub cell is effectively shaded by the sub cells above it and is therefore only exposed to the spectrum that is transmitted through these sub cells. In order to approximate this effect the assumption used by Schade in [7] is made that the Quantum Efficiency of a cell is equal to the fraction of photons absorbed by the cell, which is appropriate for relatively thin cells (thicker cells will suffer from recombination). This simplification allows the quantum efficiency of a cell to be estimated in dependence of the thickness of the cell: QE( λ) m (3) (4) ( ) d = e α λ (5) Where α(λ) is the absorption coefficient and d is the thickness of the sub cell. The radiation transmitted through a material is given by: ( ) α( λ) G = G 0 λ exp d (6) 0 Therefore using (5) and (6) the quantum efficiency can be defined in terms of absorbed and unabsorbed radiation as follows: G( λ) QE( λ) = (7) G ( λ) 0 Using this relationship the irradiance incident on the bottom cell can be calculated using the quantum efficiency of the device.

2.3 Mismatch Operation As the sub cells are connected in series Kirchhoff s current law determines the current and voltage of the total cell. If each sub cell produces a current I i (V) and Voltage V i (I) then the total cell current I cell (V) and voltage V cell (I) is given by: n I ( V) = I ( V) and V ( I) = V( I) (8) cell i cell i i= As with the individual sub cell characterization, numerical methods are used to solve these equations for the mismatch I sc, V and the maximum power point. oc 2.4 Cell Thickness and Spectral Response In order to examine the effect of varying spectral response on the overall device performance, the sub cell thickness is varied. The effect of this on the quantum efficiency can be estimated using equation (5) above. This approximation consists of the assumption that the quantum efficiency of an amorphous silicon cell is approximately equal to the fraction of photons absorbed by the i-layer of the cell and that, to a first approximation, the i-layer is equal to the total cell thickness. By using this approximation, the model uses the cell quantum efficiency data to calculate the absorption coefficient of the cell. The absorption coefficient can then be used to calculate the quantum efficiency of the cell for any given change in thickness. 3 Effect of Spectrum On Device Parameters The spectrum first and foremost will affect the short circuit current of any device. Plotting the current in each sub-cell against the blueness of the spectrum (APE) gives a first order approximation of the effects to be expected [8]. This filters through into the efficiency, with relatively minor effects in the given model. This entirely neglects the effects of temperature on the life-time and mobility and thus on fill factor and current collection in each device. However, for the purpose of an approximation of the magnitude of effects this is sufficient. The results of the simulation of the efficiency of the sub-cells and the total stack of a triple junction device are shown in Figure 3. The spectra used as input into the model were extracted from the continuous measurement programme at CREST and filtered for stability during the 90 seconds the monochromator needs to measure the spectrum in the range from 300 to 700 nm. Triple Junction 2. Top SubCell Middle SubCell 2. Total Cell.7 Bottom SubCell.7.3.3 0.5.4.5.6.7.8.9 2 2. APE 300-700nm (ev) 0.5.4.5.6.7.8.9 2 2. APE 300-700nm (ev) Figure 3: Effect of Spectrum on the Efficiency of a Triple Junction Device (normalised to efficiency of the stack at AM.5)

In this simulation, the middle junction limits the performance for the majority of the spectra. The bottom junction dominates for operation in the very blue region (APE >.9 ev). This optimisation results in a relatively flat curve of efficiency of the overall device against blueness of the incident light. However, a significant amount of light appears to be lost in the top cell of the multi-junction, as the current generated in that junction is much higher than that in the other junctions for light bluer that AM.5. This indicates an optimisation potential by varying top and middle cell thickness. An interesting effect can be seen when investigating the fill factor (FF) of a device. The results of such simulations are shown in Figure 4. For single junction amorphous silicon devices, an increase of FF with blueness is expected [9]. Multi-junctions exhibit a different behaviour, as demonstrated in Figure 4...05 5 0.85 0.8 0.75 0.7 Double Junction.4.5.6.7.8.9 2 2. APE 300-700nm (ev).08.06.04.02 8 6 4 2 Triple Junction.4.5.6.7.8.9 2 2. APE 300-700nm (ev) Figure 4: Effect of Varying Spectrum on the Fill Factor of a Double and a Triple Junction (normalised to STC conditions) The behaviour of the double junction is relatively straightforward: with increasing blueness, the FF increases. There is a minimum in this for a blueness slightly below AM.5 conditions and for very red conditions the FF will increase again. The slight knee for higher APEs is due to changes in the spectrum and partially due to lower signals measured with the spectroradiometer, which might result in higher scatter (as the measurement accuracy is slightly lower). The triple junction is similarly affected, but there is a second minimum. These minima are points when different junctions start dominating the performance of the device. The open circuit voltage (not shown) of the devices follows in all simulations very closely the current of the lowest cell, as could be expected, because this cell determines the short circuit current of the entire stack and the V OC broadly shows the logarithmic relationship on this. 4 Layer Optimisation This model now gives the tools for the estimation of potential for the increase in energy production by optimising cell structures for local operating spectra. The two samples investigated here are the double and triple junction simulated above. These simulations were carried out by using a whole year of spectral measurements together with the other operating conditions (irradiance, module temperature). Using the model described above, the thicknesses of two junctions were varied and the energy generated in the course of the year was calculated. Results are normalised with respect to the spectral response of the real devices.

The results of the double junction, which are shown in Figure 5, indicate that thickening of both sub-cells would have a beneficial effect. However, varying the thickness too much will make the approximation of unchanging recombination invalid and thus the absolute number is a significant overestimation of the effect. The increase of performance indicated in Figure 5 is another way of saying that not all photons are absorbed. However, the trend is that the top cell is dominating device performance and an increase in thickness of the top cell would result in an increased energy production. The absolute magnitude of the possible increase would depend on material quality but a 0% increase would appear feasible. Double Junction.5.4 0.75.0.05.00 5 0 0.85 0.80.5.20.25.3.2. 0.8 Top 0.7 0.6 0.6 0.7 0.8..2.3.4.5 Bottom Figure 5: Normalised Annual Energy Yield as a Function of Sub Cell Thickness CREST DATA.5.4.3.00.05.2. Top 0.85 0 5 0.6 0.6 0.7 0.8 0.9..2.3.4.5 Middle Figure 6: Normalized Annual Energy yield as a function of sub cell thickness for Triple Junction amorphous silicon cells 0.8 0.7 The simulations of the triple junction were carried out between the top and middle junction, as shown in Figure 6. The effect overall is significantly smaller than that for the double junction which is explained by the relative closeness of the effect of middle and bottom cell shown in Figure 3. Thickening the middle junction will result in a reduction of irradiance

available to the bottom junction and thus cause this junction to dominate. The potential appears to be in the range of 5% when only optimising the top two junctions. A more detailed simulation would have to be carried out to completely optimise the performance of the triple junction, to include thermal effects which could be very significant due to the different band-gaps involved in these materials and the documented interaction between temperature and spectrum [0]. 5 Conclusion The model shown in this paper has demonstrated a potential for improving the annual energy yield of devices, which is likely to be at the expense of absolute laboratory efficiency. The potential could be estimated in the range of 5-0% for amorphous silicon devices over their current configuration, which links directly to the energy generation cost of these devices. The model presented here has some limitations which result in estimations of higher optimisation potential but a more detailed study will have to demonstrate this more robustly. 6 Acknowledgements R. Gottschalg is funded through an EPSRC Advanced Research Fellowship (EPSRC GR/T03307/0). 7 References [] T.R. Betts, C. Jardine, R. Gottschalg, D.G. Infield, K. Lane, Spectral Dependence of Amorphous Silicon Photovoltaic Device Performance. Journal of Ambient Energy, 25 (2004) 26-32. [2] J.W. Bishop, Computer Simulation of the Effects of Electrical Mismatches in Photovoltaic Cell Interconnection Circuits. Solar Cells. 25988) 73-89. [3] T. Repmann, J. Kirchhoff, W. Reetz, F. Birmans, J. Müller, B. Rech, Investigations on the Current Matching of Highly Efficient Tandem Solar Cells Based on Amorphous and Microcrystalline Silicon, in: Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, Osaka 2003) 843-846. [4] J. Merten, J.M. Asensi, C. Voz, A.V. Shah, R. Platz, J. Andreu, Improved Equivalent Circuit and Analytical Model for Amorphous Silicon Solar Cells and Modules. IEEE Transactions on Electron Devices, ED-45 (998) 423-429. [5] J. Bruns, S. Gall, H.G. Wagemann, On the Bias Dependent Spectral Characteristics of a-si:h Solar Cells. Journal of Non-Crystalline Solids, 37/38 (99) 93-96. [6] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in Pascal - The Art of Scientific Computing. Cambridge, (Cambridge: Cambridge, 989). [7] H. Schade, Z.E. Smith, Optical Properties and Quantum Efficiency of a-sixcx-/a-si:h Solar Cells. Journal of Applied Physics, 57 (985) 568-574. [8] H. Al-Buflasa, T.R. Betts, R. Gottschalg, D.G. Infield, Modelling the Effect of Spectral Variations on the Performance of Amorphous Silicon Solar Cells, in: Proceedings of the 9th Photovoltaic Solar Energy Conference, Paris 2004) to be published. [9] R. Rüther, G. Kleiss, K. Reiche, Spectral Effects on Amorphous Silicon Solar Module Fill Factors. Solar Energy Materials and Solar Cells, 7 (2002) 375-385. [0] R. Gottschalg, T.R. Betts, D.G. Infield, M.J. Kearney, On the Importance of Considering the Incident Spectrum When Measuring the Outdoor Performance of Amorphous Silicon Photovoltaic Devices. Measurement Science and Technology, 5 (2004) 460-466.