# TCAD simulations of a barrier structure designed to improve the performance of very-low bandgap InAs/InAsSb thermophotovoltaic cells

Basile Roux, Jean-Philippe Perez, Frédéric Martinez, Stéphanie Parola, Simond Hurand, Rodolphe Vaillon

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Basile Roux, Jean-Philippe Perez, Frédéric Martinez, Stéphanie Parola, Simond Hurand, et al. TCAD simulations of a barrier structure designed to improve the performance of very-low bandgap InAs/InAsSb thermophotovoltaic cells. Optics Express, 2025, 33 (23), pp.48664-48675. 10.1364/oe.574285. hal-05361604

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# TCAD simulations of a barrier structure designed to improve the performance of very-low bandgap InAs/InAsSb thermophotovoltaic cells

BASILE ROUX,<fnref n="1" /> JEAN-PHILIPPE PEREZ,<fnref n="1" /> ID FRÉDÉRIC MARTINEZ,<fnref n="1" /> STÉPHANIE PAROLA,<fnref n="1" /> SIMOND HURAND,<fnref n="2" /> ID AND RODOLPHE VAILLON<fnref n="3" />,*

**Abstract:** Very-low bandgap TPV cells (<0.4 eV) usually require cryogenic cooling (~ 70 K) because of their high intrinsic dark current densities. To mitigate this effect, a barrier structure combined with a gallium-free InAs/InAsSb absorber, inspired by infrared photodetectors, is studied through optoelectronic TCAD simulations. This analysis reveals that the power output of the cell could be increased by 24% at 200 K thanks to this design, when compared to an equivalent PIN structure. The quantitative effects of contact doping, parasitic absorption, and carrier diffusion length are discussed in detail. An optimum design is extracted, predicting a power output of 0.3 W/cm<fnref n="2" /> and pairwise efficiency of 16% at 200 K under the illumination of an 800°C black-body emitter. The physical mechanisms limiting the performance of the cell at higher temperatures are identified, and a guideline for future improvements is proposed.

Published by Optica Publishing Group under the terms of the [Creative Commons Attribution 4.0 License](https://creativecommons.org/licenses/by/4.0/). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

## 1. Introduction

The intermittent nature of the world's electrical energy production and how it relates to the demand raises a well-known issue: energy storage. Several strategies have been used in this regard (pumped-storage hydroelectricity, flywheels, gas compression etc...). One of these is high temperature heat storage (800-2000°C), which appears to be interesting from a cost-efficiency perspective [1-3]. The idea behind this kind of storage is to utilize the high latent/sensible heat of materials like molten silicium or bricks to store energy, which is subsequently used later or converted back into electrical power using a thermophotovoltaic (TPV) cell. Although thermal batteries are beginning to reach industrialization [4], the integration of a TPV cell to a complete system is still a way off.

In recent years, TPV conversion efficiencies of up to 40 % have been achieved thanks to the spectral management of radiation that is not absorbed by the cell (enabled by very efficient back reflectors [5-8]). These results seem to emphasize efficiency over power output with "high" bandgap cells (~ 1 eV) and high emitter temperatures (>2000°C). However, not many materials can withstand or perform well under such extreme conditions. Thereby, looking for colder emitters could be easier to handle for a full TPV system, while lower bandgaps cells would enable to maintain high power densities [9-11].

To maximize power density and convert the thermal radiation of colder emitters, very-low bandgap (<0.4 eV) cells are required to enable the absorption of colder (less energetic) photons. However, the intrinsic carrier density of these materials is significantly higher, which in turn

<footnote n="1">¹IES, Université de Montpellier, CNRS, 34095, Montpellier, France</footnote>

<footnote n="2">²Institut Pprime, Université de Poitiers, CNRS, 86962, Chasseneuil-du-Poitou, France</footnote>

<footnote n="3">³LAAS-CNRS, Université de Toulouse, CNRS, 31400, Toulouse, France</footnote>

<footnote>*rodolphe.vaillon@cnrs.fr</footnote>
results in strong dark current densities, short carriers lifetimes and short carriers diffusion lengths [12]. This is why such devices are usually refrigerated at cryogenic temperatures to mitigate this effect [13–15], which is unfortunately energy-consuming. In order to address this issue, it can be interesting to look at the closely related field of infrared (IR) photodetection, where a "barrier structure" (alternative to PN or PIN junctions) was developed to reduce the dark current of the photodetectors and elevate their operating temperature. In addition, the gallium-free InAs/InAsSb type 2 superlattice (T2SL) used in some of these photodetectors demonstrates longer lifetimes than similar devices based on InAs/GaSb [16], a limitation which was already reported in previous analyses [12,17]. Thus, in this work, we propose to continue exploring new TPV cell designs and determine through optoelectronic simulations if the barrier structure based on the InAs/InAsSb T2SL IR photodetectors would be worth adapting for TPV conversion.

In the first section of this paper, the barrier structure and its benefits are presented in greater detail, along with the issues that very-low bandgap optoelectronic devices have to face. In the second section, the numerical simulations methods and the input data pertaining to the materials are presented. In the third section, the results of the simulations are discussed in different aspects, including cell temperature, parasitic absorption, emitter temperature, doping levels, and carrier diffusion length. Finally, the last section provides a synthesis and concluding remarks.

## 2. Barrier structure

As indicated in the introduction, very-low bandgap cells exhibit high dark current densities. This current, which opposes the photogenerated one, arises from the generation and recombination of carriers within the device. In the depletion region, where the carrier density is near zero, the dark current is typically governed by the Shockley-Read-Hall (SRH) recombination mechanism and referred to as the generation-recombination dark current ($J_{GR}$) [18]. Outside the depletion region however, the carrier density is non-zero and the dark current originates from their diffusion and recombination, and is consequently referred to as the diffusion dark current ($J_{diff}$) [18]. As $J_{GR} \propto n_i(T)$ and $J_{diff} \propto n_i^2(T)$, these two components strongly depend on the intrinsic carrier density $n_i(T) = \sqrt{N_C N_V} \times \exp\left(-\frac{E_g}{2k_b T}\right)$ (where $N_C$ and $N_V$ are the effective densities of states in the valence and conduction band and $k_b$ the Boltzmann constant). Thus, they may become significant and problematic when the bandgap energy ($E_g$) is too small and/or the temperature ($T$) too high.

In response to this issue, the infrared community has devised an original design known as a "barrier structure" [19,20]. The concept was to suppress the generation-recombination current by inserting a high bandgap layer between the top contact and the absorbing layers, which is where the depletion region is located (cf. Figure 1). Additionally, the band offset of this barrier should allow to block only one type of carrier, thereby enhancing the contact selectivity of the device. With these features, the barrier structure is intended to outperform a basic PIN one and/or raise the device’s operating temperature.

In the next sections, a barrier structure made of an AlAsSb electron barrier and an InAs/InAsSb T2SL absorber (based on the Refs. [21–23]) is compared to its PIN equivalent using optoelectronic simulations. A "double-barrier" structure with an additional hole barrier at the bottom contact is also studied. The hole barrier considered is purely theoretical and does not represent an existing material. The objective with this imaginary "double barrier" structure is to highlight the limitations of the single barrier structure and reveal the potential of an improved barrier design. For simplicity, we will keep referring to the single barrier structure when mentioning "the barrier structure", and not the double-barrier one.

The barrier structure's behavior and optimal design for TPV conversion was expected to differ from that of photodetection, as in TPV conditions the radiative power incident on the cell is significantly larger, and the operating voltage positive rather than negative.
<figure><img src="image_3.png" /><figcaption>Fig. 1. Schematic illustration of the dark current contributions in a PIN and a barrier structure under positive bias voltage.</figcaption></figure>

## 3. Methods

### 3.1. Metrics used to evaluate the performances of the TPV device

The metrics used to assess the performances of a TPV system differ slightly from those used in conventional solar photovoltaic conversion. The main difference comes from the fact that the emitter is part of the system, and not outside. This means that any radiation that is not absorbed by the cell can be sent back to the emitter and does not count as a loss. The efficiency of the cell $\eta_{pair}$, called in this case "pairwise efficiency", is defined as the ratio of the electrical power output $P_{out}$ to the net radiative power absorbed by the cell $P_{abs}$ [9,24]:

$$ \eta_{pair} = \frac{P_{out}}{P_{abs}} \qquad (1) $$

It is important to note that the conditions maximizing the pairwise efficiency are usually different from those maximizing the power output of the cell [9,10].

### 3.2. Modeling and simulation code

The simulations in this work are one-dimensional and were run with a Matlab code developed within our research team [25]. It is composed of two solvers: optical and electrical.

The optical solver uses the transfer-matrix method (TMM) to compute the local spectral photon flux ($\Phi_v(z, \lambda)$), with $z$ the depth in the cell and $\lambda$ the radiation wavelength). Thus, the optical generation rate of electron-hole pairs ($G(z, \lambda)$) is obtained by taking the divergence of the photon flux:

$$ G(z, \lambda) = \frac{d}{dz} \Phi_v(z, \lambda) \qquad (2) $$

The generation rate of carriers is then used by the electrical solver to compute and solve the following set of equations (drift-diffusion, Poisson and carriers continuity):

$$ \vec{\nabla} \cdot \epsilon_r \epsilon_0 \vec{\nabla} U(z) = -q(p - n + N_D - N_A) \qquad (3) $$

$$ \frac{\partial n}{\partial t} = \frac{1}{q} \vec{\nabla} \cdot \vec{J}_n - R + G \qquad (4) $$

$$ \frac{\partial p}{\partial t} = -\frac{1}{q} \vec{\nabla} \cdot \vec{J}_p - R + G \qquad (5) $$

where $\epsilon_r$ is the material low frequency permittivity, $\epsilon_0$ the absolute permittivity in vacuum, $U(z)$ the electrical potential, $q$ the elementary charge (absolute value), $n$ and $p$ the carrier densities, $N_D$
and $N_A$ the electron and hole ionized dopants densities, $G = \int_0^{+\infty} G(z, \lambda)d\lambda$ and $R$ the generation and recombination rates of carriers, $J_n$ and $J_p$ the electron and hole current densities.

$\vec{J}_n$ and $\vec{J}_p$ are defined as:

$$ \vec{J}_n = n\mu_n\vec{\nabla}E_{Fn} \qquad (6) $$

$$ \vec{J}_p = p\mu_p\vec{\nabla}E_{Fp} \qquad (7) $$

with $\mu_n$ and $\mu_p$ the mobilities of the carriers, and $E_{Fn}$ and $E_{Fp}$ the quasi-Fermi levels.

The recombination rate $R$ is the sum of the different recombination contributions: $R_{SRH}$ (Shockley-Read-Hall), $R_{Auger}$ (Auger), and $R_{rad}$ (radiative). Their expressions (conventional) are given below:

$$ R_{SRH} = \frac{np - n_i^2}{\tau_{SRH,n}(p + p_t) + \tau_{SRH,p}(n + n_t)} \qquad (8) $$

$$ R_{Auger} = (C_n n + C_p p)(np - n_i^2) \qquad (9) $$

$$ R_{rad} = B_{rad}(np - n_i^2) \qquad (10) $$

where $n_i$ is the intrinsic carrier density, $\tau_{SRH,n}$ and $\tau_{SRH,p}$ the electron and hole Shockley-Read-Hall (SRH) lifetimes, $C_{Auger}$ the Auger recombination coefficient, $B_{rad}$ the radiative recombination coefficient, $n_t = N_c \times \exp((E_t - E_c)/kb/T)$ and $p_t = N_V \times \exp((E_V - E_t)/kb/T)$, $E_t = E_g/2$ the trapping energy level (arbitrary value).

The equations are solved using the finite volume method with double points interfaces. At the domain boundaries, the conditions are defined by the applied voltage $V$ and the assumption of an infinite carrier recombination velocity ($E_{Fn} = E_{Fp} = qV$).

The different layers and the band diagrams of the simulated structures are shown in Fig. 2. The electron barrier of the cell is made of the ternary alloy AlAs$_{0.09}$Sb$_{0.91}$, while the top, bottom, and absorbing layers are composed of the type 2 InAs/InAs$_{0.65}$Sb$_{0.35}$ superlattice (which has a bandgap of 0.23 eV at 200 K). The barrier and absorbing layer are both not intentionally doped (nid), with a P-type residual doping for the barrier layer (~ $10^{15}$ cm$^{-3}$) and N-type for the absorbing layer (~ $10^{15}$ cm$^{-3}$). Concerning the imaginary hole barrier for the "double-barrier" structure, the parameters for the material in the simulations were chosen identical to the AlAs$_{0.09}$Sb$_{0.91}$, except for the electronic affinity ($X = 4.7$, same as the T2SL for conduction band alignment), and the doping (N-type, $10^{18}$ cm$^{-3}$).

The input data for the materials used in the simulations and the different layers in each structures are summarized in Table 2, Table 1 and Fig. 3.

The refractive indices for the InAs/InAsSb T2SL and AlAsSb barrier layers were measured experimentally by spectroscopic ellipsometry (cf. Figure 3). For these measurements, a 1 µm-thick film of T2SL and barrier layer material were prepared by molecular beam epitaxy on a GaSb substrate and buffer layer, for which the optical indices had already been measured. In the case of the AlAs$_{0.09}$Sb$_{0.91}$ barrier, a 10 nm GaSb capping layer (same indices as the buffer layer) was grown on top of the sample to prevent oxydation. The backside of these samples was roughened to remove backside reflection. The spectroscopic ellipsometry measurements were performed at room temperature on a broad spectral range from 211 nm to 20 µm using two ellipsometers from J.A. Woollam: a M2000X for the UV-visible-NIR range (211 nm - 1.7 µm) and a IR-VASE Mark II for the IR range (1.7 µm - 20 µm). The optical indices of the T2SL layer are shown in Fig. 3(b). In the infrared range, measurements were also performed at 77 K, 200 K and 300 K inside a cryostat under secondary vacuum (< $10^{-7}$ mbar), evidencing the increase in the energy gap with decreasing temperature, as shown in Fig. 3(c).

Unless otherwise stated, the simulations were performed under the illumination of a 800°C blackbody emitter, with a view factor of 0.5 (fraction of the power emitted by the emitter's surface received by the cell).
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Description of each layer for both the PIN and barrier structures with their respective simulated band diagrams (0 V).</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Real (n) and imaginary (k) refractive indices for (a) the AlAs<sub>0.09</sub>Sb<sub>0.91</sub> alloy, and (b) the InAs/InAsSb T2SL. The temperature dependence near the bandgap for the T2SL is displayed in (c). The measurements were performed by spectroscopic ellipsometry.</figcaption></figure>
<table><caption>Table 1. Thickness, doping and radiative power absorbed (at 200 K) in each layer and each cell structure simulated</caption><thead><tr><th>Structure</th><th>Layer</th><th>Thickness (μm)</th><th>Doping (cm<sup>-3</sup>)</th><th>Absorbed power density (W/cm<sup>2</sup>)</th></tr></thead><tbody><tr><td rowspan="3">PIN</td><td>Top contact</td><td>0.3</td><td>5 × 10<sup>17</sup> (P)</td><td>0.348</td></tr><tr><td>Absorber</td><td>3</td><td>10<sup>15</sup> (N)</td><td>1.125</td></tr><tr><td>Bottom contact</td><td>0.5</td><td>10<sup>17</sup> (N)</td><td>0.060</td></tr><tr><td rowspan="4">Single barrier</td><td>Top contact</td><td>0.3</td><td>5 × 10<sup>17</sup> (P)</td><td>0.351</td></tr><tr><td>e-barrier</td><td>0.2</td><td>10<sup>15</sup> (P)</td><td>~0</td></tr><tr><td>Absorber</td><td>3</td><td>10<sup>15</sup> (N)</td><td>1.09</td></tr><tr><td>Bottom contact</td><td>0.5</td><td>10<sup>17</sup> (N)</td><td>0.056</td></tr><tr><td rowspan="6">Double barrier</td><td>Top contact</td><td>0.3</td><td>5 × 10<sup>17</sup> (P)</td><td>0.351</td></tr><tr><td>e-barrier</td><td>0.2</td><td>10<sup>15</sup> (P)</td><td>~0</td></tr><tr><td>Absorber</td><td>3</td><td>10<sup>15</sup> (N)</td><td>1.09</td></tr><tr><td>h-barrier</td><td>0.2</td><td>10<sup>18</sup> (P)</td><td>~0</td></tr><tr><td>Bottom contact</td><td>0.5</td><td>10<sup>17</sup> (N)</td><td>0.056</td></tr></tbody></table>

<table><caption>Table 2. Parameters of the materials used in the simulations<sup>a</sup></caption><thead><tr><th>Material</th><th>Symbol</th><th>Value</th><th>Reference</th></tr></thead><tbody><tr><td rowspan="10">T2SL InAs/InAs<sub>0.65</sub>Sb<sub>0.35</sub></td><td>X (eV)</td><td>4.7</td><td>[26]</td></tr><tr><td>E<sub>g</sub> (eV)</td><td>0.258 – 2.013 × 10<sup>-4</sup> <sup>T<sup>2</sup></sup>&frasl;<sub>(117.6+T)</sub></td><td>[26]</td></tr><tr><td>ε<sub>r</sub></td><td>14.55</td><td>[27]</td></tr><tr><td>τ<sub>SRH.n</sub> (s)</td><td>10<sup>-5</sup></td><td>[28]</td></tr><tr><td>τ<sub>SRH.p</sub> (s)</td><td>8.3 × 10<sup>-6</sup></td><td>[28]</td></tr><tr><td>C<sub>Auger</sub> (cm<sup>6</sup>s<sup>-1</sup>)</td><td>3.19 × 10<sup>-26</sup></td><td>[29]</td></tr><tr><td>B<sub>rad</sub> (cm<sup>3</sup>s<sup>-1</sup>)</td><td>1.96 × 10<sup>-12</sup></td><td>[29]</td></tr><tr><td>μ<sub>n</sub> (cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>)</td><td>114</td><td>[30]</td></tr><tr><td>μ<sub>p</sub> (cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>)</td><td>204</td><td>[30]</td></tr><tr><td>N<sub>C</sub> (cm<sup>-3</sup>)</td><td>1.46 × 10<sup>13</sup> × T<sup>1.5</sup></td><td>[27]</td></tr><tr><td>N<sub>V</sub> (cm<sup>-3</sup>)</td><td>1.13 × 10<sup>15</sup> × T<sup>1.5</sup></td><td>[27]</td></tr><tr><td rowspan="10">AlAs<sub>0.09</sub>Sb<sub>0.91</sub></td><td>X (eV)</td><td>3.3</td><td>[27]</td></tr><tr><td>E<sub>g</sub> (eV)</td><td>1.73</td><td>[27]</td></tr><tr><td>ε<sub>r</sub></td><td>11.1</td><td>[27]</td></tr><tr><td>τ<sub>SRH.n</sub> (s)</td><td>3.2 × 10<sup>-5</sup></td><td>[26]</td></tr><tr><td>τ<sub>SRH.p</sub> (s)</td><td>8.1 × 10<sup>-5</sup></td><td>[26]</td></tr><tr><td>C<sub>Auger</sub> (cm<sup>6</sup>s<sup>-1</sup>)</td><td>10<sup>-36</sup></td><td>[26]</td></tr><tr><td>B<sub>rad</sub> (cm<sup>3</sup>s<sup>-1</sup>)</td><td>1.8 × 10<sup>-10</sup></td><td>[27]</td></tr><tr><td>μ<sub>n</sub> (cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>)</td><td>208</td><td>[27]</td></tr><tr><td>μ<sub>p</sub> (cm<sup>2</sup>V<sup>-1</sup>s<sup>-1</sup>)</td><td>220</td><td>[27]</td></tr><tr><td>N<sub>C</sub> (cm<sup>-3</sup>)</td><td>3.64 × 10<sup>15</sup> × T<sup>1.5</sup></td><td>[27]</td></tr><tr><td>N<sub>V</sub> (cm<sup>-3</sup>)</td><td>4.30 × 10<sup>15</sup> × T<sup>1.5</sup></td><td>[27]</td></tr></tbody></table>

<footnote><sup>a</sup>T is the temperature in kelvin, X the electronic affinity, E<sub>g</sub> the bandgap, ε<sub>r</sub> the low frequency permittivity, τ<sub>SRH.n</sub> and τ<sub>SRH.p</sub> the electron and hole Shockley-Read-Hall (SRH) lifetimes, C<sub>Auger</sub> the Auger recombination coefficient, B<sub>rad</sub> the radiative recombination coefficient, μ<sub>n</sub> and μ<sub>p</sub> the electron and hole mobilities, N<sub>C</sub> and N<sub>V</sub> the effective densities of states in the conduction and valence bands. The values are given for a temperature of 300 K by default. See the references for more details.</footnote>
# 4. Results and discussion

## 4.1. Cell temperature and PIN-barrier comparison

The Fig. 4 illustrates how the cell’s temperature impacts its performances, depending on the type of structure. As expected, the performance of the cells reaches a maximum at very low temperatures: 0.35 W/cm² at 100 K for the PIN structure and 0.31 W/cm² at 140 K for the barrier structure. The dark current diminishes as the temperature gets lower and the open-circuit voltage gets higher (cf. figure 4(b)). However, below 150 K the power output of the cell stagnates or even regresses in the case of the double-barrier structure. This phenomenon results from the T2SL hole mobility which diminishes when the temperature is reduced (4.4 cm²/V/s at 100 K against 25.5 cm²/V/s at 200 K [30]), hindering the collection rate of the holes. The effect is even stronger for the barrier structure because of the electron barrier, which makes it more reliant on the hole transport properties. The short-circuit current is also affected in the same way (cf. figure 4(a)), while the diminution of the T2SL bandgap only plays a minor role to it.

<figure><img src="image_6.png" /><figcaption>(a) Short-circuit current and fill factor for the PIN, single-barrier and double-barrier structures.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Main cell performance metrics and their temperature dependence.</figcaption></figure>

Between 150 and 250 K, the hole mobility increases (and so does the diffusion length), thereby ceasing to be the primary factor limiting the performances of the cell. The barrier structure (power output of 0.202 W/cm² at 200 K) becomes progressively more attractive than the PIN
one (0.169 W/cm² at 200 K), thanks to its ability to suppress the generation-recombination dark current at the top contact junction. This improvement is very visible through the increased open-circuit voltage in figure 4(b), but gradually disappear above 200 K. In fact, the dark current reduction enabled by the electron barrier is partially canceled out by an intensification of the current leaking through the bottom contact junction. We can see in figures 4(b) and 4(c) that adding a hole barrier (double-barrier) prevent this leakage and drastically increases the cell's performances. At 200 K, the single-barrier structure improves the power density of the cell by 24% compared to its PIN equivalent, a value that could be increased to 32% thanks to a supplementary (hole) barrier. However, even with two barriers, the dark current originating from the absorbing layer (diffusion and recombination of carriers) is still present, and thus becomes the next limiting factor, exacerbated by the T2SL Auger lifetime drop beyond 200 K [28].

## 4.2. Parasitic absorption

Figure 4(d) shows that the short-circuit current of the barrier structure is shifted down compared to that of the PIN one. This difference (around 0.6 A/cm²) comes essentially from the absorption that takes place in the top contact layer. In the PIN structure, the electrons generated in the top contact contribute to the photogenerated current by flowing toward the absorber through the space-charged region. In the barrier structure however, they end up blocked by the barrier meaning they can only either recombine or be collected at the same contact. Thus, all the absorption occurring in the top contact layer of the barrier structure is parasitic and reduces the radiative power reaching the absorbing layer. Figure 5 highlights this effect by comparing the performance of a barrier structure with a transparent top contact to that of the actual one. Absorption by the top contact represents 23% (0.351 W/cm²) of the total radiative power absorbed by the cell at 200 K (cf. Table 1). To address this issue, the T2SL top contact could be thinned and/or replaced by GaSb material, which is more transparent in the spectral range of interest.

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Barrier structure performances and comparison between an actual and transparent top contact (i.e. non-modified and zero imaginary optical index $k$).</figcaption></figure>

According to the simulations, if the top contact layer was made transparent, the power output of the barrier structure at 200 K would be increased by 37% (a gain of 0.075 W/cm²). It is surprising that this parasitic absorption was not considered in the original photodetector design, though the reason could arise from the difference in metrics and/or operating conditions.
### 4.3. Contact selectivity and dopant concentration

In a conventional PIN structure, selectivity of the contacts derive from their doping difference. However, in the case of the barrier structure, it is the barrier layer that plays this role, leading the two structures to display different behaviors when the doping concentration of the top contact layer and/or the temperature of the cell are varied. Figure 6 shows that the barrier structure is much less dependent on the concentration of dopants than the PIN structure. The effect becomes even stronger as the cell temperature increases. The disadvantage of the PIN structure pointed out here, comes from the competition between the doping concentration of the top contact ($\approx 10^{17}$ cm$^{-3}$) and the intrinsic carrier concentration ($n_i(T=300 K)\approx 10^{16}$ cm$^{-3}$) which can be pretty close at room temperature. Thus, for the PIN structure, the contact loses its selectivity and the device is no longer efficient in separating carriers. This effect is also visible in figure 4(a), where the short-circuit current of the PIN structure near 300 K is more affected by the cell temperature than that of the single-barrier or double-barrier ones.

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Power output of the cell versus the doping concentration of the top contact layer. The computations were performed for the PIN and barrier structures at 200 K and 300 K, for which the corresponding InAs/InAsSb T2SL intrinsic carrier densities are indicated.</figcaption></figure>

With these observations, it appears to be more advantageous to rely on a barrier layer rather than dopants when working with very-low bandgap materials.

### 4.4. Emitter temperature effect

Depending on the emitter temperature ($T_e$), the power output and pairwise efficiency of the TPV cell are expected to vary. Figure 7 illustrates this effect for the barrier structure. As expected, with regard to the power output of the cell, the hotter the emitter, the more power the cell generates (following the Stephan-Boltzmann law $P_{out} \propto T_e^4$). The improvement is mainly driven by the increase in the short-circuit current, although the open-circuit voltage also improves slightly, while the fill factor remains constant ($\sim 0.59 \pm 0.01$). Concerning pairwise efficiency, the optimal emitter temperature appears to be around 750°C. This optimum also depends on the thickness of the absorbing layer: it shifts toward higher emitter temperatures if the absorber is thinner (around 900 °C for a 1 µm absorbing layer) or toward lower temperatures if it is thicker (around 600 °C for a 9 µm absorbing layer).
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Performance of the barrier structure, depending on the emitter temperature (blackbody).</figcaption></figure>

#### 4.4.1. Carrier diffusion length and thickness of the absorber

Two other important parameters are of interest when studying the temperature dependence of the cell performances: the diffusion length of the carriers ($L_h$ for the holes and $L_n$ for the electrons) and the penetration depth of the light ($\delta_{opt} = \lambda/(4\pi \cdot k(\lambda))$) with $k$ the imaginary refractive index and $\lambda$ the wavelength). They determine (mainly) the optimum thickness of the absorbing layer. To maximize the absorption, the layer must be thick, while for maximizing the internal quantum efficiency, it should rather be thin.

Figure 3 indicates that the imaginary part of the T2SL refractive index ($k$) is not very affected by the cell temperature, with only a small increase of the energy bandgap with decreasing temperature. This makes the penetration depth of the light relatively constant throughout the whole temperature range. On the other hand, the minority carrier (hole) diffusion length is very sensitive to it (cf. Figure 8), which makes it the primary factor responsible of the optimal absorber thickness temperature dependence. At low temperature, the hole diffusion length is mainly limited by the mobility. It reaches a maximum of 21.5 µm at 216 K and drops down again above this temperature because of the Auger lifetime degradation. Accordingly, the absorber thicknesses maximizing power output and pairwise efficiency at 220 K are 11.7 µm and 8.7 µm respectively.

Because of the higher electron diffusion length (~100 µm at 200 K), the electrons do not limit the optimal absorber thickness as much as the holes do. Thanks to this, building an absorber thicker than the optimum value does not affect much the cell performances, as most of the holes are already generated close to the contact where they are collected, and since the absorber length is small compared to the electrons diffusion length.

With a cell temperature of 200 K, an emitter at 800°C, a transparent top contact, and a 6 µm absorber (power density optimum), the simulations predict for the barrier structure a power density of 0.3 W/cm² and a pairwise efficiency of 16%.

### 5. Conclusion

This study has presented opto-electronic simulations of very-low bandgap TPV cells. Some design strategies have been explored to propose solutions to the problems that low-bandgap devices have to face when trying to operate at room temperature. The novelty in the approach was to base the design of the cell on a barrier structure inspired from infrared photodetectors, with an absorber made of an InAs/InAsSb gallium-free superlattice.
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Thickness of the barrier structure absorber ($e_{abs}$) computed for maximizing either power output or pairwise efficiency. The T2SL hole diffusion length (calculated using the experimental mobility and lifetime from Refs. [28] and [30]) is shown for comparison.</figcaption></figure>

Two structures have been compared in the simulations: the barrier structure and its PIN counterpart. The simulations have shown that the barrier structure is able to greatly reduce the generation-recombination (dark) current and also make the selectivity of the contact less sensitive to temperature. The barrier structure has displayed a 24% increase in power density at 200 K compared to its PIN equivalent, a value that could be increased to 32% with a second (hole) barrier. The optimal thickness of the absorber in TPV conditions has also been studied. It has been found to be quite different depending on the metric considered (power output or efficiency), with thicker optima for the maximization of power density.

Some default/limitations to the barrier design have been identified, such as the parasitic absorption that occurs in the top contact layer, the lack of a second barrier to completely suppress the generation-recombination (dark) current, or the strong diffusion (dark) current due to degraded Auger lifetime above 200 K. Nevertheless, according to these simulations, if the barrier structure design is wisely adapted (transparent top contact and 6 µm thick absorber), the cell could display a power density of 0.3 W/cm² and a pairwise efficiency of 16% at 200 K, which would be a huge improvement when considering that previous works had to refrigerate similar cells around 77 K [13–15]. To further increase the operational temperature of the cell, two crucial improvements have been identified: finding a second barrier (for holes), and increasing the Auger lifetime of the carriers.

The barrier structure proposed in this work has specifically been studied to address the issues of very-low bandgap TPV cells. However, the same structure may also be interesting to consider for higher bandgaps cells working in high temperature environments, or for thermoradiative conversion, which also requires very-low bandgap materials and has the advantage to be less sensitive to Auger recombinations [31].

**Funding.** Agence Nationale de la Recherche (ANR-21-CE50-0018); Institut des sciences de l'ingénierie et des systèmes (TREE).

**Disclosures.** The authors declare no conflicts of interest.

**Data availability.** Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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