Thermal Optimization of a Solar Cell Carrier for Concentrator Systems

Aaron Muron*a, Simon Chowa, Jeffrey Wheeldona, Karin Hinzera, Henry Schriemera

aCentre for Research in Photonics, 800 King Edward Avenue, Ottawa, ON, Canada K1N 8P5

ABSTRACT

Solar cell efficiency decreases as its temperature increases. Therefore, it is necessary to design a thermally optimal solar cell carrier that will maintain a minimal solar cell temperature. To achieve this optimal solar cell carrier design, a finite-element analysis model of the solar cell on carrier was developed. This numerical model was experimentally calibrated against a known design, in which the average solar cell temperature was determined by examining the shift in the open circuit voltage. This allowed us to explore the relationship between the carrier geometry and the average solar cell temperature. That is, the solar cell carrier is characterized by two independent thermal resistances: the uniform flow thermal resistance, and the thermal spreading resistance. As the copper thickness was increased, the uniform flow resistance acted to raise the cell temperature while the spreading thermal resistance decreased the cell temperature. Therefore, when the carrier geometry minimized the thermal resistances, it was found that the minimum solar cell temperature was achieved at a copper thickness between 1.5 and 3 mm depending on the surface area of the carrier. This optimized carrier design reduced the average solar cell temperature by 16 °C, which corresponds to an increase of 0.8% in cell efficiency at 1666 suns as compared to the original design used to experimentally calibrate the numerical model.

Keywords: multi-junction solar cell, thermal optimization, spreading resistance, photovoltaics, heat spreader, carrier

1. INTRODUCTION In recent years, solar concentrator systems have become increasingly popular in III-V high-efficiency photovoltaic systems. III-V solar cells have attained efficiencies greater than 40% under a concentration of 454 suns1. Therefore, solar concentrators provide the ability to maximize solar cell efficiency while minimizing the need for expensive semiconductor materials2. Of course, minimizing the materials cost is paramount to developing an economically viable option. However, a solar cell efficiency of about 40% implies that approximately 60% of the remaining energy is absorbed as thermal energy. The absorption of such high concentrations of solar energy represents a marked increase in solar cell temperature. Unfortunately, as the solar cell temperature increases its electrical efficiency decreases. In particular, an increase in cell temperature reduces both the open circuit voltage of the cell by 4.3 mV/°C and the solar cell efficiency by 0.05 %/°C3. Therefore, to maintain a high level of solar cell efficiency the solar cell carrier must dissipate heat both quickly and efficiently to keep the solar cell cool.

In order to continuously operate at high efficiencies, the most thermally efficient design of the solar cell carrier must be ascertained. In this context, improving the thermal efficiency of the carrier means designing the carrier to remove heat from the solar cell as quickly as possible. The extent to which the thermal efficiency of the carrier can be improved is dependent on the physical characteristics of the carrier. The geometry of the carrier, the carrier materials, and the quality of the thermal contact between the carrier and heat sink all have a significant impact on the carrier’s ability to transfer heat.

In this paper, the effect of varying the physical dimensions of the carrier is explored to determine the optimal carrier geometry. To this end, a numerical model of the solar cell on carrier is constructed. The simulated solar cell temperature data is then compared with experimental data to calibrate the numerical model and ensure that it is self-consistent. Comparing the calibrated model and experimental data, the convective heat transfer coefficient at the interface between the heat sink and carrier was quantified (h). Moreover, with the calibrated model, the geometrical parameters of the carrier were then varied. With this parameter study, it was determined that an optimal geometry exists and a minimal solar cell temperature can be achieved for a specific carrier geometry.

Photonics North 2011, edited by Raman Kashyap, Michel Têtu, Rafael N. Kleiman, Proc. of SPIE Vol. 8007,800722 · © 2011 SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.905692

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2. NUMERICAL MODEL With COMSOL Multiphysics an archetypical numerical heat transfer model of the solar cell on carrier was developed to examine its heat transfer characteristics. In concentrating photovoltaic systems, the carrier typically consists of a ceramic substrate sandwiched between a top and bottom copper contact. A popular choice for the substrate material is alumina since it is a relatively inexpensive material with sufficient thermal conductivity. The bottom of the carrier is in contact with a heat sink which can employ either active or passive cooling. The solar cell was assumed to be an InGaP/InGaAs/Ge triple junction cell with a surface area of approximately 1 cm2. The solar cell is mounted on the top of the carrier as seen in Figure 1.

Figure 1: Illuminated Solar Cell on Carrier model

In order to numerically model the illuminated solar cell on carrier, several assumptions regarding the environment surrounding the carrier and the physical properties of the carrier were made. First, it was assumed that the solar cell was composed mainly of an indium and a germanium layer of overall thickness of ~200 μm. Next, the indium, germanium, copper, and alumina components were assigned appropriate thermal conductivities, k, as given in Table 1. Furthermore, it was assumed that only the top surface of the solar cell was to be uniformly illuminated with concentrated light. Therefore, a constant heat flux, q, was applied to the top surface of the solar cell with a power density proportional to a concentration factor. Herein we assume that one sun equals 1000 W/m2 and the concentration factor is specified in Table 1. Therefore, the heat flux flowing into the solar cell is expressed as,

Concentration 1000 / (1)

This implies that the numerical model only considers the worst case scenario conditions where the solar cell is not electrically connected and all incident photons are absorbed and converted into thermal energy. Since the results are linearly dependent upon the concentration, the average solar cell temperature at maximum efficiency can easily be determined by reading the values at concentrations reduced by the solar cell efficiency. For example in figure 3 at 500 suns concentration, the temperature is 41 °C, but when the solar cell is operating at maximum efficiency the equivalent heat flux is 300 suns and the temperature is 31 °C (assuming the solar cell efficiency is 40%). Next, natural convection was assumed for all surfaces of the solar cell on carrier except the bottom contact. Notwithstanding a rise in air temperature due to natural convection, it was assumed that the ambient air temperature remained constant at ~25 °C. Finally, the bottom surface of the carrier was assumed to be in contact with a water cooled heat sink held at constant temperature of ~18 °C. A convective heat transfer coefficient, hheatsink, which encompasses all of the heat sink’s physical properties including the thermal contact resistance between the carrier and heat sink, was arbitrarily chosen since h was not initially known.

Table 1: Simulation Parameters

Parameter Value

k, Alumina 27 (W/mK)

k, Copper 400 (W/mK)

k, Germanium 60 (W/mK)

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k, Indium 82 (W/mK)

h, all surfaces except bottom 25 (W/m2K)

hheatsink 3000 (W/m2K)

Concentration factor 1000x

q, heat flux (1000 suns) 1 000 000 (W/m2)

The archetypical numerical model was then simulated with the parameters shown in Table 1 with a geometry identical to solar cell on carrier assemblies (test cell assemblies) available for testing and with the parameters shown in Table 1. The dimensions of the archetypical model were 3.3 x 2.5 cm. As seen in Figure 2, the surface temperature distribution of the archetypical model is shown.

Figure 2: Simulated surface temperature of archetypical numerical model under 1000 suns

3. CALIBRATED MODEL Since an effective convective heat transfer coefficient of the heat sink in the numerical model was not known, comparing the simulated and the experimental data was required to determine a calibrated convective heat transfer coefficient. This also allowed us to validate the accuracy of our numerical model.

3.1 Experimental Setup

Using the available test cell assemblies, thermally characterizing the test cell assemblies was done in-house under a Spectrolab XT-30 continuous solar simulator. The XT-30 is a state of the art continuous wave solar simulator that employs a 3kW Xeon arc lamp, parabolic mirrors to concentrate light, and a homogenizer in order to provide light intensities up to 1000 suns4, 5. The test cell assemblies were placed on a liquid cooled stage and were held in place by a vacuum. To ensure the best possible thermal contact between the test cell assembly and the liquid cooled heat sink, thermal paste was applied at the heat sink and carrier interface. The temperature of the liquid cooled heat sink was held constant at ~15.6 °C and the temperature of the stage surface was measured to be 18 °C6. Finally, steady state experimental cell temperature data was measured. This was done by first examining the solar cell’s open circuit voltage (Voc) under continuous illumination. Under the same concentration, the Voc of the cell was then measured under a flash solar simulator where the solar cell temperature remained near ambient6. Knowing that the open circuit voltage changes by -4.3 mV/°C5, we were able to determine the solar cell temperature over a range of concentrations.

3.2 Parameter Study

With the cell temperature of the test cell assembly known over a range of concentrations, the next step was to quantify the heat sink’s convective cooling capability (hheatsink). To accomplish this, scripting COMSOL within MATLAB enabled the concentration factor and convective heat transfer coefficient of the archetypical model to be varied

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sequentially so that a multitude of simulations could execute autonomously. Specifically, the convective heat transfer coefficient was varied from 200 W/m2K to 30000 W/m2K in step sizes of 100 W/m2K while the concentration factor was varied from 100x to 1000x in step sizes of 100x. For each simulation, the simulated average solar cell temperature was calculated and plotted against concentration. This produced a set of curves that were compared with the experimental results. As shown in Figure 3, it was determined that a convective heat transfer coefficient of 14500 W/m2K accurately modeled the overall heat sinking capability of the XT-30’s heat sink when thermal paste was used.

Figure 3: Comparing simulated and experimental data to determine effective heat transfer coefficient of the heat sink

4. ANALYSIS AND RESULTS. In electronic chip cooling applications, heat spreaders are often used to improve the heat transfer between a high heat-flux density source (solar cell, high power electronic chip, etc) and a heat sink. Heat spreaders are typically metallic plates with a larger contact surface area than the heat source and spread the heat coming from the heat source over the heat spreader’s volume. This acts to decrease the heat flux density, q, entering the heat sink which means that a heat sink with a lower heat transfer coefficient can be used. Air cooled heat sinks or heat sinks made of cheaper materials with lower thermal conductivities can be used to adequately cool the heat source. More than providing a platform for the electrical contacts of the solar cell, the carrier also functions as a heat spreader since it has a larger contact area than the solar cell (heat source) and exchanges heat between the solar cell and heat sink. Hence, the carrier helps to keep the solar cell cool and increase system efficiency. However, we can go one step further and determine the thermally optimal carrier geometry so that the maximal cell efficiency can be reached.

If we consider the simple case where a square heat source is placed on top of a square heat spreader as depicted in Figure 4, and referring to the work by Maranzana et al.8 and Yovanovich et al9, it is seen that the overall thermal resistance of the heat spreader can be modeled by three independent thermal resistances. The three independent thermal resistances are the uniform flow resistance (RD), the heat spreading resistance (RS), and the convective heat transfer resistance (Rf) of the underside of the heat spreader assuming all other surfaces of the heat spreader are adiabatic. The uniform flow resistance (RD) is the thermal resistance derived from Fourier’s law of heat conduction and accounts for the resistance to heat flow only in the direction normal to the bottom surface of the spreader. The thermal spreading resistance (RS) includes the heat’s ability to spread out over the entire volume of the spreader. The convective heat transfer coefficient

0

20

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200 300 400 500 600 700 800

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Concentration (Suns)

Measured (with Thermal Paste)

Simulated (h=14500 W/m)

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(Rf)) considers the heat sinks ability to carry heat away from the spreader. Implicit in the overall thermal resistance of the heat spreader is its dependence on its physical properties and its boundary conditions. That is, the total thermal resistance is dependent on the spreader’s thickness (t), the spreader’s thermal conductivity (k), the spreader’s side length (L), the side length of the heat source’s footprint (l), and the heat sink’s effective heat transfer coefficient (h). That is, the overall thermal resistance of the spreader can be expressed as,

, (2)

where,

(3)

and

1 . (4)

For a detailed mathematical treatment of the thermal spreading resistance, it suggested that the reader refers to Yovanovich9. However, with care the spreading resistance can be considered to be roughly proportional to the heat spreader thickness such that

, , , . (5)

Since the temperature of the heat source is directly proportional to the total thermal resistance of the heat spreader as seen in eqn (6), we aim to find the heat spreader geometry that minimizes the total thermal resistance.

. (6)

We can conclude an optimum heat spreader thickness exists since RD is directly proportional to the thickness whereas the spreading resistance is inversely proportional to the thickness of the heat spreader. Therefore, the thickness at which the sum of RD and RS is a minimum is the optimal heat spreader thickness. However, an optimum heat spreader surface area does not exist since the larger the surface area, the bigger the heat exchange area between the spreader and heat sink. This implies that the as the surface area of the heat spreader is increased the heat source temperature will decrease.

In view of the complex geometry of the carrier, an analytical description of the solar cell on carrier was not sufficient to determine the optimal carrier geometry. Therefore, the archetypical COMSOL model was modified and the effect of varying the carrier geometry was explored. Specifically, the carrier was assumed to be square for convenience and the outermost dimensions of the carrier were varied from 2 cm to 5 cm while the top and bottom copper layer thicknesses were varied from 200 μm to 2cm. The results of the simulation study are shown in figure 5. It is clear that the optimal carrier design region exists for a carrier thickness of 1.5 mm to 3 mm depending on the side length of the square carrier.

Figure 4: Heat source (solar cell) on a typical heat spreader

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t k

L

L

l

l

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5. CONCLUSION The thermal properties of concentrator photovoltaic solar cell on carrier model were explored. To accomplish this, a numerical model was constructed in COMSOL Multiphysics that closely simulated in house test assemblies. The numerical model was then compared with experimental data to determine an effective heat transfer coefficient for the heat sink to be used in the numerical model. This also ensured that the results of the numerical simulations were consistent with experimental results. Finally, scripting COMSOL within MATLAB allowed us to perform a large parameter study in order to explore the effect of carrier geometry on the average cell temperature. It was found that the carrier could be characterized by a thermal spreading resistance and a thermal uniform flow resistance. It was determined that the thermal spreading resistance decreased and the thermal uniform flow resistance increased as the copper contact thickness was increased. This implied that an optimal copper thickness existed and it was found to be between 1.5 mm and 3 mm depending on the carrier side length. Furthermore, it was observed that the average cell temperature decreased as the side length of the carrier was increased except for sufficiently thin layers of copper. Finally, it was found that an increase in cell efficiency of 0.8% can be gained if the carrier design is optimized.

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