Efficiency and power density potential of thermophotovoltaic energy conversion systems using low bandgap photovoltaic cells

Introduction
Technological improvements in the field of low bandgap photovoltaic cells and selectively radiating infrared radiators have evoked a renewed interest in thermophotovoltaic (TPV) generation of electricity [1, 2, 3]. In a TPV system, thermal radiation is converted to electricity by PV cells. In solar TPV [4], the energy source used to heat the radiator is solar radiation, whereas in terrestrial TPV, fossil fuels are generally considered as energy input.

**Figure 1:** The principle of terrestrial thermophotovoltaic conversion: a heated surface emits thermal radiation which is converted into electric energy by means of photovoltaic cells. The radiation spectrum is adapted to the spectral sensitivity of the PV cells. In the example shown spectral shaping is performed utilizing a selectively reflecting filter. Additionally, a selective radiator may be used.
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In this paper, terrestrial TPV is considered (Fig. 1). There are principally two different approaches to realize such systems. The first one uses existing cell technologies, e.g. silicon cells. The second one makes use of newly developed low bandgap cells. These cells are able to convert a larger part of infrared radiation and are therefore susceptible to give higher efficiencies and higher power output densities.

The purpose of the paper is to give a realistic estimation of conversion efficiency and power density of a TPV system. For each of its components, the upper limit of the attainable efficiency is discussed firstly, taking into account only losses due to fundamental thermodynamical principles. This thermodynamical limit efficiency is a measure for the potential of TPV. In the next step, inherent properties of real materials are considered, but an ideal technology is assumed. The efficiency values obtained here may be seen as the asymptote of an optimization effort. Finally, we examine real devices, extrapolating results achieved at Fraunhofer ISE. We consider that the resulting performance values are realistically attainable within the next few years if a sufficient development effort is undertaken.

Thermodynamical limit:

**Figure 2:** *J-V-characteristics, output power density (dashed) and efficiency (dotted) for a PV converter with bandgap 0.72 eV (thermodynamical limit).*
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Figure 2 shows the characteristics of a PV cell in a thermodynamically ideal TPV system. A bandgap of 0.72 eV, corresponding to GaSb, and a blackbody radiator temperature of 1500 K have been assumed.

The maximum PV cell efficiency and the maximum power output as a function of temperature and cell bandgap are shown in Figure 3.

**Figure 3:** Efficiency (left) and output power density (right) of a PV cell (thermodynamical limit) as a function of blackbody radiation temperature, for different bandgaps, corresponding to different cell materials: 0.35 eV (InAs, dotted), 0.55 eV (InGaAs, short dashes), 0.72 eV (GaSb, solid line), 1.12 eV (Si, long dashes), and 1.4 eV (GaAs, medium dashes).
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Ideal and realistic GaSb cells:

In the thermodynamical limit analysis we did not take into account any specific material characteristics of the PV cell. Now, in addition to the fundamental radiation recombination (B_opt), Auger recombination (C_Auger) and bandgap narrowing ( $\rm\Delta E_{gap}$ ) are considered. For the following analysis of GaSb cells, we assume [5]

B_rad=7*10^-11 cm^-3, C_Auger=3*10^-30 cm^-6, $\rm \Delta E_{gap}$ =1*10^-8 eV cm*(N_A)^1/3

For the ideal GaSb cell we assume no traps in the bulk of the material and a perfectly passivated surface.

In a more realistic approach, the model is complemented by recombination from impurities in the semiconductor material and a finite surface recombination velocity. Since GaSb has a high material quality and a self passivating surface, the differences between the ideal and real cell are small. Additional reduction in output power comes from frontside reflection. Furthermore, it is not realistic to operate a TPV cell at 300 K. Thus, the cell is also simulated at a typical operating temperature of 330 K.

Short discussion:

For comparison, we have compiled the cell performance for the different degrees of idealization discussed above under the spectrum of a 1500 K blackbody radiator being shaped by a perfect edge filter, having a cut-off frequency at E_gap/h.

	cell efficiency (%)	output power density (W/cm²)	FF (%)	J_sc(A/cm²⁾	V_oc(V)
thermodyn. limit	60.5	3.00	83.3	5.76	0.625
ideal GaSb cell	44.0	2.27	80.6	5.50	0.511
realistic cell (300 K)	41.3	2.13	80.9	5.06	0.520
realistic cell (330 K)	37.4	1.93	77.9	5.30	0.467

Because of the additional recombination mechanisms, the ideal GaSb cell has a lower V_oc and J_sc than a cell in the thermodynamical limit analysis. Each cell structure was individually optimized to give maximum power output. This results in a larger V_oc for the realistic cell than for an ideal cell. The J_sc for the realistic cell at 330 K is larger than the J_sc at 300 K because the optical absorption edge is shifted towards lower energies. This increase is overcompensated by the decrease of V_oc due to a higher temperature.

The influence of filter and heat source characteristics on system efficiency and power output will be discussed at the conference.

References

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