Efficiency of GaInAs thermophotovoltaic cells: the effects of incident radiation, light trapping and recombinations

Pamela Jurczak; Arthur Onno; Kimberly Sablon; Huiyun Liu

doi:10.1364/OE.23.0A1208

1. Introduction

The principle of operation of a thermophotovoltaic (TPV) cell is the same as the one of standard photovoltaic (PV) devices. Photons are absorbed within the semiconductor and charge is generated. The excess positive and negative charges are separated at the p-n junction and then extracted from the cell as electric current. The main difference lies in the irradiance spectra used for the operation of TPV and PV devices. The solar cells receive radiation from the sun at 5778 K from a distance of 150 × 10⁹ m resulting in an incident power density of 1 kW.m⁻² [1]. The TPVs operate with thermal emitters at temperatures ranging from 1000 to 1800 K placed as close as a few centimetres away from the device, resulting in a power density of 50 to 600 kW.m⁻². Hence the power output of TPV devices is significantly higher compared to conventional PV solar cells under direct solar radiation [2]. As TPVs operate in the infrared region of the spectrum, materials with low bandgaps, typically from 0.35 to 0.75 eV, need to be used. Ga_xIn_1-xAs is an attractive choice for this application as its bandgap can be engineered to match the optimal range for TPV operation by adjusting the indium to gallium composition ratio.

The use of Ga_xIn_1-xAs for thermophotovoltaic applications has been previously explored by Wilt et al. [3], Wanlass et al. [4] and Coutts [1]. Devices with a 0.74 eV bandgap lattice-matched to an InP substrate have been grown by MOCVD [3,5] and MBE [6] techniques. Introduction of step-graded [7] and metamorphic [8] buffers allowed for growth of lattice-mismatched Ga_xIn_1-xAs structures with bandgaps of 0.55 eV [5] and 0.6 eV [9–12], resulting in higher efficiency cells. Recently, a study of bandgap-dependent TPVs under low temperature black body radiation has been performed by Tulley and Nicholas [2]. In this paper, we present a detailed analysis of the theoretical performance of Ga_xIn_1-xAs thermophotovoltaic devices under different illumination conditions. Focusing mainly on the temperature of the source and the incident power density, the efficiencies of cells within a wide range of bandgaps have been calculated. Other parameters like Auger recombinations, threading-dislocation-related Shockley-Read-Hall recombinations and thickness of the cell have also been considered in the model.

2. Method

The main challenge in modelling III-V semiconductors with variable composition is the lack of accurate data regarding their electronic parameters. In order to minimise the impact of this limitation, our calculations of radiative recombination rates are based on a thermodynamic approach using solely the absorption spectrum of the material. This way the number of electronic parameters used in the model is reduced to a minimum. The bandgap of the material E_g(Ga_xIn_1-xAs) and the corresponding absorption spectrum are the main parameters needed to determine the maximum theoretical efficiency of a perfect crystal.

The model has been developed using MATLAB^®2014b and all the calculations are wavelength-dependent. The simulations have been run with rectangular integration on the wavelength from 200 to 10000 nm with a 1 nm step. The percentage of gallium x vary from x = 0 to 0.5, representing the bandgap range between 0.36 eV and 0.78 eV, which is relevant to the TPV operation. The efficiencies have been calculated using the black body spectrum at different temperatures, obtained from Planck’s radiation formula.

2.1. Architecture of the cell

The architecture of the modelled cell, a p⁺/n Ga_xIn_1-xAs cell with a variable thickness from 500 nm to 5 μm, is presented in Fig. 1. The gallium content varies from x = 0 to 0.5 simultaneously in both the emitter and the base of the cell. The p⁺-emitter has a fixed thickness of 0.1 μm and doping of N_a = 10¹⁸ cm⁻³. The n-base thickness is variable and doping is held constant at N_d = 10¹⁷ cm⁻³.

Fig. 1 Details of the architecture with (a) and without (b) light trapping of the Ga_xIn_1-xAs thermophotovoltaic cell investigated.

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Two architectures have been investigated: one with a textured front surface, perfectly randomising the photon flux in order to obtain a Lambertian distribution of the scattered light, and one with a flat top surface. The cell with the patterned front also has a perfectly reflecting mirror at the back, which allow optimal light trapping and eliminates dark-current radiative reemissions from the bottom side of the cell. This architecture is used to evaluate the maximum theoretical efficiency of the cell.

The structure with a flat top has no back mirror. Consequently, radiative reemissions also occur from the back surface. This gives a better approximation of the performances of early-stage TPV devices grown and processed in laboratory. In both cases it has been assumed that there is no shadowing from the front contact and there is no reflection from the top surface.

2.2. Absorptivity models for the two architectures

The absorptivity of the cell depends on its architecture, as shown in Fig. 2. In the model we use two surface geometries, a textured one perfectly randomising the photon flux, creating a Lambertian distribution of the photons entering the cell, and a planar one. The textured surface has also been combined with a perfectly reflecting back mirror in order to create light trapping. In this case the absorptivity from the back of the cell a_back = 0 so that total absorptivity equals absorptivity from the front of the cell a(λ) = a_front(λ). However, in the cell without light trapping, the total absorptivity is the sum of back and front absorptivities a_back(λ) and a_front(λ).

Fig. 2 Details of the different absorptivity models used: flat surface with front surface (red arrows) and back surface absorption (green arrows) (a) and ideally textured surface with back mirror creating light trapping (orange arrows) (b).

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For the cell with textured front surface and back mirror we consider light trapping to be ideal [18], therefore the absorptivity of the cell can be expressed as:

a (λ) = \frac{4 n_{r}^{2} α_{G a I n A s} (λ)}{1 + 4 n_{r}^{2} α_{G a I n A s} (λ)}

where α_GaInAs(λ) is the wavelength-dependent absorptivity coefficient of Ga_xIn_1-xAs, n_r is the refractive index and L is the cell thickness.

The absorption spectra of Ga_xIn_1-xAs for different percentages of gallium x have been calculated based on the absorption model for semiconductors [14]:

α (E) = {\begin{cases} α_{0} \exp (\frac{E - E_{g}}{E_{0}}), E \leq E_{g} \\ α_{0} (1 + \frac{E - E_{g}}{E'}), E^{} > E_{g} \end{cases}

where α₀ is the absorption coefficient near the band edge, E_g is the bandgap energy and E₀ is the Urbach energy (for GaAs α₀ = 8000 cm⁻¹ and E₀ = 6.7 meV [14], for InAs α₀ = 2500 cm⁻¹ and E₀ = 6.9 meV [15], E’ = 140 meV [14], the bandgap energies range from 0.36 to 0.78 eV). The values for E₀ and α₀ for different compositions of Ga_xIn_1-xAs have been linearly interpolated from those of GaAs and InAs.

When planar front surface is considered, the incident light is refracted at the front surface of the cell with an angle very close to perpendicular due to the large refractive index of Ga_xIn_1-xAs. The front surface absorptivity is then:

a_{f r o n t} (λ) = 1 - e^{- α_{G a I n A s} (λ) L} .

Due to the lack of a back mirror in this architecture, absorptivity from the back of the cell has to be included as well in the calculation of the radiative recombination rate. It has to take into account the increase due to total internal reflection on the front side of the cell for photons with a high angle of incidence, as shown by Miller et.al [14]:

a_{b a c k} (λ) = 2 n_{r}^{2} (\begin{array}{l} \int_{0}^{θ_{e s c}} (1 - e^{- α_{G a I n A s} (λ) \frac{L}{\cos θ}}) \cos θ \sin θ d θ \\ + \int_{θ_{e s c}}^{\frac{π}{2}} (1 - e^{- 2 α_{G a I n A s} (λ) \frac{L}{\cos θ}}) \cos θ \sin θ d θ \end{array})

where θ is the polar angle at which light is reflected and θ_esc = arcsin(1/n_r) is the critical escape angle.

2.3. Blackbody theory and flow equilibrium

The blackbody theory and the flow equilibrium in the cell, in the dark and under illumination, have been used in order to calculate the radiative recombination under ideal conditions (no other sources of recombinations). In our model thereby we use the radiative limit as the theoretical maximum efficiency achievable by the devices investigated. This limit arises from the flow equilibrium within the diode, part of the absorbed photons being reemitted and escaping through the surfaces of the cell. These radiative reemissions are a fundamental loss mechanism intrinsic to the physics of semiconductors and cannot be avoided. Under the Bose-Einstein approximation (E >> k_BT), Würfel’s blackbody theory extended to semiconductors gives the emission rate of each cell under ideal conditions and in the dark [16]:

R_{r, r a d} (V) = e^{\frac{q V}{k_{B} T}} \int_{0}^{+ \infty} \frac{2 π c a (λ)}{λ^{4}} e^{- \frac{h c}{λ k_{B} T}} d λ = R_{r, r a d, s c} e^{\frac{q V}{k_{B} T}}

where q is the elementary charge, V the voltage of the cell, k_B the Boltzmann constant, T temperature (set at 300 K), c the speed of light, a(λ) is the wavelength-dependent absorptivity of the cell, λ is the wavelength of photons and h the Planck constant.

The voltage-independent part of the equation represents the short-circuit recombination rate and can be renamed R_r,rad,sc in order to simplify further derivations. Its value directly derives from the thermal equilibrium in the dark: R_r,rad,sc = R_r,rad(V = 0) and represents the amount of photons reemitted from the cell in the dark to balance the flow received from the surrounding blackbody environment at 300 K.

Considering the flow equilibrium in the cell under illumination and with non-radiative recombinations taken into account, the current density can be expressed using Shockley diode equation under illumination [17]:

J (V) = J_{p h} + q R_{r, r a d, s c} (1 - e^{\frac{q V}{k_{B} T}}) + q \sum_{m} R_{r, m} (1 - e^{\frac{q V}{n_{m} k_{B} T}})

where J_ph is the photo-generated current, R_r,m the short-circuit non-radiative recombination rates and n_m the associated ideality factor for each non-radiative recombination mechanism m (m ∈ {SRH, Auger,…}). Under TPV operations, J_ph is several orders of magnitude higher than q R_r,rad,sc and q R_r,m so we can approximate under illumination:

J (V) = J_{p h} - q R_{r, r a d, s c} e^{\frac{q V}{k_{B} T}} - q \sum_{m} R_{r, m} e^{\frac{q V}{n_{m} k_{B} T}} .

The photo-generated current J_ph can be calculated by counting the number of absorbed photons, assuming perfect external quantum efficiency:

J_{p h} = q \int_{0}^{+ \infty} (\frac{λ}{h c}) I (T_{s o u r c e}, λ) a_{f r o n t} (λ) d λ = q R_{g}

where I(T_source,λ) is the temperature and wavelength dependent blackbody irradiance, a_front(λ) is the absorptivity from the front of the cell and R_g is the photo-generation rate.

The Auger recombinations and Shockley-Read-Hall recombinations have been included in the model while other recombination processes such as surface recombinations have been neglected so that:

J (V) = q (R_{g} - R_{r, r a d, s c} e^{\frac{q V}{k_{B} T}} - R_{r, S R H} (V) - R_{r, A u g e r} (V))

where R_r,SRH(V) is the voltage-dependent Shockley-Read-Hall recombination rate and R_r,Auger(V) is the voltage-dependent Auger recombination rate.

2.4. Bulk non-radiative recombinations

In our model we have assumed that SRH recombinations are only due to threading dislocations – arising from a lattice mismatch between the Ga_xIn_1-xAs cell and the substrate – and the impact of all other crystal defects has been neglected. We have therefore used the model developed by Yamaguchi et al. [19] to determine the Shockley-Read-Hall recombination rate. From [19], the minority-carrier diffusion length associated with threading dislocations of density N_TD, for both types of carriers, can be expressed as:

L_{T D} = \sqrt{\frac{4}{π^{3} N_{T D}}} .

The voltage-dependent threading-dislocations-related recombination rate is given by [19]:

R_{r, S R H} = \frac{n_{i} W_{D}}{2} \frac{D_{p}}{L_{T D}^{2}} e^{(\frac{q V}{2 k_{B} T})} = R_{r, S R H, s c} e^{(\frac{q V}{2 k_{B} T})}

where n_i is the intrinsic carrier concentration given by the classic relation:

n_{i, G a I n A s} = \sqrt{N_{c} N_{v}} e^{\frac{- E_{g}}{2 k_{B} T}},

D_p is the minority-carrier diffusion coefficient of holes and W_D is the depletion width of the cell calculated using:

W_{D} = \sqrt{\frac{2 ε_{0} ε_{r}}{q} \frac{k_{B} T}{q} \ln (\frac{N_{a} N_{d}}{n_{i, G a I n A s}^{2}}) (\frac{1}{N_{a}} + \frac{1}{N_{d}})} .

Therefore the only parameters necessary for the evaluation of the impact of the threading dislocation density (TDD) on the performances of the cell are the diffusion coefficients of electrons and holes, D_n(Ga_xIn_1-xAs) and D_p(Ga_xIn_1-xAs), the densities of states in the conduction and valence bands, N_c(Ga_xIn_1-xAs) and N_v(Ga_xIn_1-xAs), and the relative permittivity ε_r(Ga_xIn_1-xAs). The formulas used to calculate all of the electrical parameters of the modelled Ga_xIn_1-xAs cells can be found in Table 1.

Table 1. Formulas used for Ga_xIn_1-xAs electronic parameters and their respective sources.

View Table

The effects of the Auger recombinations have been incorporated into the model as well since they become a significant loss factor for low bandgap semiconductors. In order to simplify the calculations, low doping density has been assumed within the cell, although this hypothesis is not strictly correct for real devices. The voltage-dependent Auger recombination rate is given by [24]:

R_{r, A u g e r} = C_{A u g e r} L n_{i, G a I n A s}^{3} e^{(\frac{3 q V}{2 k_{B} T})} = R_{r, A u g e r, s c} e^{(\frac{3 q V}{2 k_{B} T})}

where L is the thickness of the cell and the ambipolar Auger coefficient C_Auger = 3.2 × 10⁻²⁸ cm⁶.s⁻¹ has been used [25]. We assume the cell to be cooled down to 300 K as preliminary simulations showed that increasing the cell temperature has deleterious effects on its performances. Figure 3 in the section 3.1 gives more details on how the efficiency of the cell is impacted with increasing its temperature.

Fig. 3 Maximal theoretical efficiency η (black, left scale) and optimal Ga composition (red, right scale) of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the temperature of the cell T.

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The full current-voltage characteristic of the modelled cell is given by:

\begin{array}{l} J (V) = q (R_{g} - R_{r, r a d, s c} (V) - R_{r, S R H} (V) - R_{r, A u g e r} (V)) \\ \overset{}{}_{}^{} \overset{}{} = q (R_{g} - R_{r, r a d, s c} e^{(\frac{q V}{k_{B} T})} - R_{r, S R H} e^{(\frac{q V}{2 k_{B} T})} - R_{r, A u g e r} e^{(\frac{3 q V}{2 k_{B} T})}) . \end{array}

The maximum power point voltage and current density are calculated by maximising the product J × V using the formulae from Eq. (15). The efficiency η of the cell can then be expressed as:

η = \frac{J_{m p p} \times V_{m p p}}{P_{i n}}

where J_mpp is the current density at maximum power point, V_mpp is the voltage at maximum power point and P_in is the power delivered to the front surface of cell from the thermal emitter.

3. Results and discussion

3.1. Impact of the temperature of the cell

Figure 3 shows the impact of the increase of the cell temperature on the performance of a 5-µm-thick Ga_xIn_1-xAs TPV with perfect light trapping. The temperature of the source has been set to 1300 K and the power density delivered to the cell to 100 kW.m⁻². Auger recombinations have been taken into account and SRH recombinations are assumed to be low enough not to impact the operation of the cell. Since the temperature of the material has a large impact on its bandgap, the optimal composition rather than optimal bandgap has been plotted.

From the plot it can be observed that increasing the temperature of the cell to 400 K causes the efficiency to drop from over 21% to only 12%. Further increase in the cell temperature results in even larger decrease in efficiency, reaching merely 2% at 600 K. The main reason for such behaviour is the decrease in bandgap caused by increase in temperature, which in turn leads to immense levels of Auger recombinations. These results confirm that the cell cooling is essential for efficient operation and hence the temperature of the cell has been set to 300 K in all the other simulations in this paper. The optimal Ga composition increases almost linearly with the increase in the cell temperature. Such a result is to be expected because increasing the Ga content increases the bandgap of the material and hence reduces the impact of Auger recombinations improving the efficiency.

3.2. Impact of the thermal emitter temperature and the incident power density

In this section the thickness of the cell is assumed constant at 5 µm. Figure 4(a) shows the impact of the temperature of the illumination source on the maximal theoretical efficiency and the optimal bandgap of a Ga_xIn_1-xAs cell with a textured front surface and a perfectly reflecting back mirror. The cell material is assumed to be dislocation-free (no Shockley-Read-Hall recombinations). Auger recombinations have been taken into account, as they are an intrinsic recombination process and a sizable source of losses for low bandgap materials.

Fig. 4 (a) Maximal theoretical efficiency η (black, left scale) and optimal bandgap E_g (red, right scale) for a dislocation-free Ga_xIn_1-xAs cell with perfect light trapping as a function of the temperature of the thermal emitter T_source. (b) Maximal theoretical efficiency η of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the bandgap of the cell E_g and the temperature of the thermal emitter T_source.

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The optimal bandgap of the cell increases with the temperature of the thermal emitter, as well as the maximal theoretical efficiency. For a low temperature thermal emitter at 1000 K, a maximum of 17.1% can be yielded by a pure InAs cell with a 0.36 eV bandgap, while up to 34% can be achieved for cells with a 1.28 eV bandgap illuminated at 6000 K. The discrepancy between the maximum efficiencies for high temperature sources calculated in this simulation and the theoretical values reported in the literature (33.5% theoretical limit for thin film single-junction 1.42 eV GaAs PV cell [14]) arises from the difference between the incident spectrums (AM1.5 solar spectrum versus blackbody spectrum at 6000 K) and applied powers. The incident power density used here has been set to 100 kW.m⁻², appropriate for TPV operation, as opposed to 1 kW.m⁻² conventionally used for solar cells simulations. From Fig. 4(a) it can also be observed that the optimum bandgap for cells operating between 1000 and 2000 K does not exceed 0.5 eV. Consequently, in all of the further simulations, Ga_xIn_1-xAs compositions from x = 0 to 0.5 have been used instead of the full range.

Figure 4(b) shows the maximal theoretical efficiency of a Ga_xIn_1-xAs cell with perfect light trapping (an ideally textured front surface and a perfectly reflecting back mirror) for a range of operating temperatures relevant to the TPVs as a function of the bandgap of the material. For cells operating at source temperatures of up to 1400 K, the optimal bandgap is 0.36 eV, corresponding to pure InAs. For higher source temperatures, cells with larger bandgaps are favoured due to the higher energy of incoming photons and the reduced impact of Auger recombinations. A maximum theoretical efficiency of 24.2% has been calculated for a cell with a 0.43 eV bandgap illuminated with a source at 1800 K. At a lower thermal emitter temperature of 1300 K, a maximum of 21.1% can be obtained with a pure InAs cell.

The maximal theoretical efficiency of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the bandgap and the incident power density is shown in Fig. 5(a). The impact of Auger recombinations has been taken into account, while the threading dislocation density has been assumed to be low enough to have negligible effect on the operation of the cell. The temperature of the thermal emitter has been set to 1300 K, a typical value for TPVs. The efficiency of the cell improves with the incident power density, especially for cells with lower bandgaps. For a cell with a 0.36 eV bandgap, power density of 100 kW.m⁻² yields the efficiency of 21%, while increasing the power to 500 kW.m⁻² improves the performance by about absolute 3.5% to 24.5%. In practice, power densities above 300 kW.m⁻² for a 1300 K source can only be achieved using a concentrator system. The small difference in the efficiencies for a large increase in the incident power is to be expected because of the logarithmic nature of the evolution of the efficiency as a function of incident power density. This is confirmed by Fig. 5(b), which shows the maximum efficiency and the optimal bandgap of the cell as a function of the incident power density. For values over 100 kW.m⁻², the improvement in the maximum theoretical efficiency is minimal. Therefore, in practice, the distance between the source and the cell can be adjusted so that enough power is delivered. It can also be observed that the optimal bandgap remains constant at 0.36 eV for all power densities above 100 kW.m⁻².

Fig. 5 (a) Maximal theoretical efficiency η of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the bandgap of the cell E_g and the incident power density P_in. (b) Maximal theoretical efficiency η (black, left scale) and optimal bandgap E_{g opt} (red, right scale) of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the incident power density P_in.

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The results presented above aim to determine the optimal bandgap for a device operating with an emitter at a certain temperature delivering a set amount of power. The model can also be used to determine the optimal operating conditions for a cell with a specific bandgap. Based on Figs. 4 and 5, the maximum theoretical efficiencies for a range of emitter temperatures and incident power densities can be calculated. These results can be useful in establishing the optimal operating parameters for experimental devices, showing how these two factors can be altered to achieve high efficiencies.

3.3. Impact of the threading dislocation density

Figure 6 shows the impact of TDD on the efficiency of a 5-μm-thick Ga_xIn_1-xAs TPV cell with perfect light trapping. The thermal emitter temperature has been set to 1300 K and the incident power to 100 kW.m⁻² to ensure that the simulations reflect realistic operating conditions of a TPV system. The losses due to Auger recombinations have been taken into account.

Fig. 6 Maximal theoretical efficiency η of a Ga_xIn_1-xAs cell with perfect light trapping as a function of the bandgap of the cell E_g and the threading dislocation density N_TD.

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Figure 6 demonstrates that TDDs up to 10⁴ cm⁻² have a negligible impact on the efficiencies. When the dislocation density is increased to 10⁵ cm⁻², SRH recombinations begin to have a higher impact on the performances of the cell. They cause a reduction in the open-circuit voltage, and hence lower the overall efficiency of the cell. Further increase in the TDD over 10⁶ cm⁻² shortens the diffusion lengths of the minority carriers, which becomes smaller than the thickness of the cell. The photon collection efficiency is then reduced and the short-circuit current begins to drop. This leads to a rapid reduction in the efficiency of the cell, up to only a few per cent for TDDs above 10⁸ cm⁻². The optimal bandgap of 0.36 eV remains unaffected up to TDD values of 10⁷ cm⁻². These results show that for real devices the TDD should not exceed 10⁵cm⁻² in order to achieve practical performances.

The model used for the evaluation of the impact of the reduced diffusion lengths of the minority carriers assumes a uniform generation rate. As this hypothesis is not verified in real devices, results for TDDs over 10⁶ cm⁻² are not strictly accurate. However the overall model gives a good approximation on how threading dislocations affect the performance of the cells.

3.4. Impact of the cell thickness and light trapping

The optimal thicknesses for Ga_xIn_1-xAs TPV cells have been investigated for architectures with a patterned front surface and a perfectly reflecting back mirror and cells with a flat front surface and no back mirror. The results of the source temperature-dependent and the incident power-dependent simulations showed that the effect of the light trapping mechanism is limited to improving the efficiency of the cell by 3-4%, without impacting the general trend. The discrepancies between the behaviours of the two structures are more significant when various cell thicknesses are investigated.

Figure 7(a) shows the impact of the thickness of the cell on the performance of a device with an ideally textured front surface and a back mirror. The thickness of 0.5 μm yields lower efficiencies because the cell is too thin to absorb all of the incoming radiation. Light trapping overcomes this limitation and just a 1-μm thickness is sufficient for close to optimal efficiency of cells with a bandgap of 0.45 eV and higher. Further increase in the cell thickness does not improve the performance. Cells with lower bandgaps between 0.36 and 0.45 eV behave in a similar fashion but additionally experience a boost in efficiency of up to 1.5% for thicknesses between 0.5 μm and 1 μm, compared to 5 μm. The origin of this effect lies in the Auger recombination rate, which becomes very high for cells with low bandgaps, but also depends linearly on the cell thickness (bulk recombinations). Therefore, when the cell thickness is small, losses due to Auger recombinations are reduced. The light trapping mechanism ensures that the optical path is sufficiently long despite the decreased thickness.

Fig. 7 Maximal theoretical efficiency η of a Ga_xIn_1-xAs cell with (a) and without (b) light trapping as a function of the bandgap E_g and the thickness L of the cell.

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For devices without light trapping, the absorption within the cell is significantly reduced, especially for small thicknesses, resulting in efficiency decrease as can be seen in Fig. 7(b). The adequate thickness for this architecture is about 3 μm and further increase slightly improves the efficiency. The drop in efficiency with reducing cell thickness is more significant for cells with lower bandgaps. On the other hand these low bandgap cells can achieve better efficiencies when the thickness is sufficiently high, compared to higher bandgaps. The optimal bandgap for both architectures is 0.36 eV, so pure InAs, for all the investigated thicknesses.

4. Conclusion

A theoretical model has been developed for Ga_xIn_1-xAs thermophotovoltaic cells. The model is based on the black body theory extended to semiconductors and the flow equilibrium in the cell, taking the radiative limit as the theoretical maximal efficiency. The number of electronic parameters needed for the simulations has been reduced to a minimum to overcome the lack of accurate data for the properties of the investigated materials. The main inputs into the model are the emission spectrum of the black body and the absorption spectra for different compositions of Ga_xIn_1-xAs.

The impact of the incident power density and the incident spectrum has been investigated. It has been shown that increasing the temperature of the thermal emitter from 1300 K to 1800 K improves the efficiency by up to 4%. Increasing the amount of delivered power from 100 kW.m⁻² to 500 kW.m⁻² results in a maximum of 3.5% efficiency boost, which results from the logarithmic nature of the evolution of the efficiency. A maximum theoretical efficiency of 24.2% has been calculated for a cell with a 0.43 eV bandgap illuminated with a source at 1800 K delivering 100 kW.m⁻² of power.

The threading-dislocation-related Shockley-Read-Hall recombinations and Auger recombinations have also been taken into account. It has been demonstrated that the efficiency is not strongly impacted with TDD values of up to 10⁵ cm⁻². Above 10⁵ cm⁻² the efficiency starts do drop at a fast rate and this value should not be exceeded for real devices.

The impacts of the thickness and the architecture of the cell have also been investigated, showing a 3-5% improvement when the light trapping is implemented. The optimal bandgaps for cells operating with sources of a specific power and temperature have been calculated. Moreover, the model shows how these parameters can be adjusted to maximise the performance of the devices. Finally, the model can be easily adapted to simulate cells of different materials and architectures.

Acknowledgments

The authors acknowledge the financial support of US Army International Technology Center-Atlantic. H. Liu would like to thank The Royal Society for funding his University Research Fellowship.

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Electronic parameter	Equation	Source
Bandgap [eV]	E_g(Ga_xIn_1-xAs) = 0.436x² + 0.629x + 0.36	[13]
Diffusion coefficient of electrons [cm²/s]	D_n(Ga_xIn_1-xAs) = (10-20.2x + 12.3x²)·10²	[20]
Diffusion coefficient of holes [cm²/s]	D_p(Ga_xIn_1-xAs) = 16.42x²-19.42x + 13	Extrapolated from [20], [21] and [23]
Density of states in the conduction band [cm⁻³]	N_c(Ga_xIn_1-xAs) = 2.289·10¹⁷ x² + 1.541·10¹⁷ x + 8.7 ·10¹⁶	Extrapolated from [20], [22] and [23]
Density of states in the valence band [cm⁻³]	N_v(Ga_xIn_1-xAs) = 1.124·10¹⁷ x² + 2.288·10¹⁸ x + 6.6 ·10¹⁸	Extrapolated from [20], [22] and [23]
Relative permittivity	ε_r(Ga_xIn_1-xAs) = 0.67x²-2.87x + 15.1	[20]

Efficiency of GaInAs thermophotovoltaic cells: the effects of incident radiation, light trapping and recombinations

Abstract

1. Introduction

2. Method

2.1. Architecture of the cell

2.2. Absorptivity models for the two architectures

2.3. Blackbody theory and flow equilibrium

2.4. Bulk non-radiative recombinations

3. Results and discussion

3.1. Impact of the temperature of the cell

3.2. Impact of the thermal emitter temperature and the incident power density

3.3. Impact of the threading dislocation density

3.4. Impact of the cell thickness and light trapping

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (7)

Tables (1)

Equations (16)

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