Three-Terminal Heterojunction Bipolar Transistor Solar Cells with Non-Ideal Effects Efficiency Limit and Parametric Optimum

Energy Conversion and Management 188 (2019) 112–119

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Energy Conversion and Management

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Three-terminal heterojunction bipolar transistor solar cells with non-ideal effects: Efficiency limit and parametric optimum selection T ⁎ ⁎ Xin Zhanga,b, Yee Sin Angb, Zhuolin Yea, Shanhe Sua, Jincan Chena, , Lay Kee Angb, a Engineering Research Center of Micro-nano Optoelectronic Materials and Devices, Ministry of Education, Fujian Key Laboratory of Semiconductors and Applications, Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, and Department of Physics, Xiamen University, Xiamen 361005, People’s Republic of China b Singapore University of Technology and Design-Massachusetts Institute of Technology International Design Center & Science and Math Cluster, Singapore University of Technology and Design, 8 Somapah Road, Singapore 487372, Singapore

ARTICLE INFO ABSTRACT

Keywords: Without fabricating intermediate tunnel junctions or wafer bonding schemes for interconnecting the subcells, Three-terminal solar cell heterojunction bipolar transistor solar cells offer a promising new route in solar energy conversion. In this work, Heterojunction bipolar transistor an improved theory for the three-terminal heterojunction bipolar transistor solar cell is presented with inclusion Irreversible loss of non-ideal effects missing from the previous treatment, namely the non-radiative recombination and the Performance evaluation thermal conduction losses that are inevitably present in realistic devices. Following detailed balance theory, the Parametric optimization revised analytical formula for the cell conversion efficiency is derived, and the maximum efficiencies under different conditions are further calculated. Under the condition of 100 sun irradiance and 50% injection efficiency, a Gallium arsenide/Gallium antimonide-based solar cell operating at 465 K yields a maximum efficiency of 46.4%. Moreover, the effects of solar concentration, injection efficiency, and other key parameters on the cell performance are analyzed, and, consequently, optimal operating conditions and limiting factors on the conversion efficiency are determined. Simulation results show that such a solar cell operating with low injection efficiency under moderate concentration factor and low cell temperature can significantly boost its conversion performance. This work provides new physical insights for optimal designs, thus paving a route towards the development of low-cost high-performance solar cells.

1. Introduction Shockley-Queisser efficiency limit of 32.2% for silicon-based PV cells operated at room temperature under unconcentrated solar illumination Solar energy, a promising renewable energy source, has attracted [7]. widespread interests due to its abundant reserves and environmental For the purpose of improving light utilization and minimizing the friendliness [1]. It plays a significant role in reducing global climate thermalization losses, numerous methods, including multi junction [8], change and the next-generation energy resources [2]. The most heavily spectrum splitting [9], hot carrier collection [10], and intermediate- deployed technology for solar power conversion is single junction si- band [11] photovoltaics have been developed to minimize the ther- licon-based photovoltaics (PV) with a record efficiency of 28.3% [3]. modynamic losses by expanding the device wavelength responses to the Despite worldwide cumulative photovoltaic installed capacity exceeded ultraviolet and infrared regions. In 1958, Jackson first presented the 401 GW by 2018, the conversion efficiencies for most of this manu- model of multi-junction cells with different bandgap semiconductors in factured output still remain in the range of 10–18% [4]. In such PV a series connected architecture, in which each subcell acts as a filter cells, photons with energy larger than semiconductor bandgap excite absorbing the spectral range corresponding to the bandgap of each electrons into the conduction band, which diffuses to the electrodes to semiconductor layer, thus allowing the solar spectrum to be more ef- form an electrical current [5]. However, photons with energy lower fectively utilized [12]. One disadvantage of this design is reflected in than the bandgap cannot be utilized, while photons with energy above the epitaxial growth of the single-crystalline semiconductor layers and the bandgap will lose excess energy due to thermalization [6]. Together the intermediate tunnel barrier buffer layers, which requires complex with radiative recombination losses, these spectral losses result in the and expensive ultrahigh-vacuum crystal-growth techniques [13].

⁎ Corresponding authors. E-mail addresses: [email protected] (J. Chen), [email protected] (L.K. Ang). https://doi.org/10.1016/j.enconman.2019.03.034 Received 16 January 2019; Accepted 12 March 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved. X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119

−2 Nomenclature Psun incident solar energy (W cm ) q Elementary charge (C)

C solar concentration TS sun temperature (K) Cm maximum theoretical solar concentration TC cell temperature (K) −1 c speed of light (cm s ) TA ambient temperature (K) −1 −2 Efe electrons quasi-Fermi level (eV) U heat leak coefficient (W K cm ) Efh holes quasi-Fermi level (eV) VE Voltage output of the emitter terminal (V) ET top bandgap (eV) VC Voltage output of the collector terminal (V) EB Bottom bandgap (eV) F solar concentration factor Greek symbols − h the Planck constant (eV s 1) e −2 ffi JBC current density crossing BC junction (A m ) γ Injection e ciency h −2 JB current density in the Base region (A m ) λ sensitivity for the non-radiative process e −2 ffi JEB current density crossing EB junction (A m ) η e ciency −2 JC (A m ) −2 JE (A m ) Abbreviations − k Boltzmann constant (eV K 1) n refraction index BC base–collector − P power output density (W cm 2) EB emitter–base −2 Pleak heat flux due to heat conduction (W cm ) HBTSC heterojunction bipolar transistor solar cell −2 Prad radiative flux from the HBTSC (W cm )

Additionally, due to the current-matching, the lowest current generated without the need of an intermediate tunnel junctions or wafer bonding by the subcell will ultimately limit the overall cell current. An alter- schemes for cell interconnection [26], HBTSC shares the same limiting native approach is the use of spectrum-splitting technology to overcome efficiency as the dual-junction solar cell and is free from the current the limitations of current matching and material choice for the different mismatch problem [27]. Nowadays, several theoretical investigations subcells, by splitting the solar spectrum into two bands of photons with regarding the HBTSC have been reported. The pioneering work by different-wavelength [14]. Here, photons with energy greater than the Luque and Martí put forward a concrete theoretical framework that bandgap are directed to the PV cell, while those with energy less than underlies the novel concept and calculated the efficiency limits of n/p/ the bandgap are absorbed by thermal receiver [15]. Ross and Nozik first n-type ideal HBTSCs [22]. The simulation results predicted that the reported that the conversion efficiency of the hot carrier solar cell HBTSC obtains a detailed-balance limit of 54.7% under the maximum under AM1.5 can reach a theoretical limit of 66%, which is 52% higher concentration, which is the same as that of a dual-junction solar cell. than that of traditional Si PV cell systems [16]. König et al. further Martí et al. further discussed the working principle of the HBTSC based proposed the principle, materials and design of hot carrier solar cells on a circuit model, revealing the transistor effect should be avoided with energy selective contacts [17]. The main challenges of this tech- [28]. Linares et al. presented three-terminal solar cells resembled by a nology are the lack of suitable materials with drastically reduced carrier heterojunction BJT, and then explored Si, a-Si: H, III-Vs, nanomaterials cooling rates and the fabrication of selective energy contacts to extract and perovskites for practical implementation [23]. the photogenerated carriers, which severely impedes its progress to- For practical HBTSCs, the cell temperature always increases dyna- wards commercial applications [18]. Luque and Martí theoretically mically above the ambient when exposed to concentrated sunlight. analyzed the efficiency improvement of ideal solar cells by introducing Moreover, there exist several irreversible losses in the HBTSC, which an intermediate band between the conduction and valence bands to may cause additional performance degradation. Such effects are, absorb low-energy photons [19]. Based on this concept, Wang et al. however, not considered in the proof-of-concept calculation presented fabricated bulk intermediate band solar cell using Zinc telluride doped in Ref. [22]. Importantly, for the realistic simulation of HBTSCs, it is with oxygen impurities to form the intermediate band [20]. The prac- necessary to include these effects, so to obtain a reliable theoretical tical implementation of this approach remains challenging due to the efficiency limit and the optimum design of HBTSC. expensive cost of nanostructured intermediate-band materials and the In this paper, an updated model of a HBTSC are proposed with in- fabrication complexity in achieving energy-level alignment [11]. The clusions of: (i) variable temperatures of HBTSC due to sunlight illumi- approaches mentioned above pave the way towards the development of nation, where the cell temperature is determined by the energy balance; novel solar harvesting technology light management through mini- and (ii) the recombination loss in the cell. Using the improved model, mizing thermodynamic losses. Due to the practical importance of solar the conversion efficiency of three-terminal HBTSCs with an n-p-n type energy harvesting, the search for new types of photovoltaics with ease- configuration is re-examined. The conversion efficiency formula of the of-fabrication, low operating cost, and high energy output remains n-ideal HBTSC is analytically derived under the framework of detailed ongoing quests in current energy research. balance theory. Additionally, the performance characteristics and op- Benefiting from the unique structure and working principle of bi- timum design strategy of the HBTSC are analyzed under 100 sun irra- polar junction transistors (BJTs) [21], the three-terminal heterojunction diance and 50% injection efficiency. The obtained results show that a bipolar transistor solar cell (HBTSC) hosts multiple bandgaps to divide Gallium arsenide (GaAs)/Gallium antimonide (GaSb)-based HBTSC the broad solar spectrum into smaller sections [22]. Here, each in- yields a maximum conversion efficiency of 46.4% operated at 465 K. dividual layer more efficiently converts photon energy into electricity, The findings provide new physical insights for achieving the maximum thus allowing the performance to go beyond the Shockley-Queisser conversion efficiency of HBTSC with non-ideal effects under different theoretical limit of a single junction PV cell without concentrated conditions, such as the concentration factor, injection efficiency, and sunlight [23]. Three-terminal structure can substantially deliver com- working temperature. The improved HBTSC model proposed here parable power output than the two-terminal or four-terminal solar cells opens up a new avenue towards the design and optimization of low-cost [24], while also enables power injection and extraction between the and high-efficiency solar cells. two sub-circuits under a variety of spectral conditions [25]. Strikingly,

113 X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119

2. The model description and working principle characteristics that decreases the base layer width so to accomplish the complete solar spectrum absorption. Three-terminal heterojunction bipolar transistor solar cells Fig. 1(c) depicts a schematic of the carrier flow diagram. When the (HBTSCs) are one class of optoelectronic devices that convert sunlight HBTSC is illuminated by the sun, the p-n junction is driven out of into electricity. Fig. 1(a) shows the working principle of a HBTSC at a equilibrium state resulting from the generation of excess electrons and steady-state temperature TC, which receives the concentrated radiative holes. Under the condition of the open-circuit, the excess electrons raise flux Psun from the sun via the concentrator. For simplicity, TS = 6000 K the electrons quasi-Fermi level Efe in the N-side, while the holes lower corresponding approximately to the temperature of the sun and an (raise) the holes quasi-Fermi level Efh in the P-side of the emitter ambient temperature of TA = 300 K are assumed. Under a concentrated (collector) region. The carrier mobility across the emitter and collector sunlight, the HBTSC operates well above the ambient. In this case, the is sufficiently large such that the splits of quasi-Fermi levels for elec- heat flux due to Newton heat-transfer between the cell and ambient, trons and holes are equal, respectively, to the chemical potentials, qVE Pleak, should be considered. Here, Prad represents the radiative flux from and qVB, that drive the excitation. This corresponds to the positive open the HBTSC, originating from radiative recombination, and P denotes circuit voltages applied to the EB and BC junctions, thus resulting in an the power output density. electric current in the corresponding load resistances, i.e., RE and RC for In Fig. 1(b), a p/n/p-type HBTSC contains three differently doped power generation. semiconductor regions, i.e., the emitter, base, and collector regions. The top cell contains the emitter and base regions, which are made of wide 3. Energy conversion efficiency of a HBTSC including non-ideal bandgap semiconductors. The bottom cell includes the base and col- factors lector regions, while the collector is made of low-bandgap material. The fi sunlight rst passes through the front emitter region, and the emitter Similar to the Shockley-Queisser detailed balance theory [7], the terminal collects the current JE generated by the top cell. Then the main simplifications and assumptions for calculating the theoretical collector terminal collects the current JC produced in the bottom cell. efficiency limit of the HBTSC are summarized as follows: (1) Each ab- Both electric currents add up at the base terminal, and subsequently sorbed photon generates only one electron-hole pair and vice versa; (2) reenter the cell to complete the electrical circuit. One of the key ad- Ohmic losses are negligible because there are almost no holes flowing ff ff vantages of this structure is that the e ective di usion length of the through the base region. Besides, the quasi-Fermi level splitting be- carrier is reduced [28]. The electrons generated adjacent to the emit- tween the electrons and holes remains constant in the emitter and – ff ter base (EB) junction, for example, can easily di use to the proximate collector region, and is equal to the external applied voltage; (3) The ff – EB junction and are unnecessary to di use towards the base collector front of the HBTSC is surrounded by air whose refraction index is as- (BC) junction, which reduces the probability of recombination during sumed to be unity, while all the semiconductor regions possess a re- ff the di usion process. Thus, such structure possesses favorable fraction index of n; (4) To avoid stimulated emission in the collector

Fig. 1. (a) The schematic diagram, (b) the structure diagram, (c) the band diagram, and (d) the circuit model without transistor eﬀect of a three terminal HBTSC, e e – – h h where JEB(JBC) represents the electron current density crossing the emitter base (base collector) junction, JEB (JBC) denotes the hole current density crossing the emitter–base (base–collector) junction, ET and EB represent the top and bottom band gaps.

114 X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119

[29], the hole mobility at the base region is assumed to be non-infinite. for the electroluminescent photon fluxes emitted by the emitter through That leads to the bending of the hole quasi-Fermi level in the base re- the front surface. The rate of electroluminescent photon flux emitted by gion. the emitter crossing the back surface is given by 2 According to the detailed balance formalism, the number of the Rc =∞nṄ(, ETCE , T , qV ). electrons delivered from the external circuit to the conduction band of Following the assumption of Ref. [22], the base region is short en- the p-sides of the HBTSC is equal to the net number of the absorbed ough such that the generation and recombination of carriers are ig- photons. Under steady state conditions, the net electron current density nored. To avoid the stimulated emission in the base region, the wider crossing the EB junction is the difference between the total generation bandgap of the base than that of the collector is necessary. The reason and recombination may be explained as follows. Due to the electron injection in the EB

e junction, the carrier concentrations of EC in the base are higher than JEB =−qG() R, (1) those of EV and the base would be under the condition of inverted where q is the elementary charge. The top cell is illuminated by the sun population. However, the lower excess photon energy after the ab- and the light emitted by the bottom cell. Hence, the photogeneration sorption of the emitter is unable to provoke the stimulated emission in rate G according to the number of incident photons with energy hν≥ ET the base region. For a short base region, the minority carriers in the base can be calculated by a linear function under the low injection G =∞+∞FNETnNETqV̇(, ,,0) 2 ̇(, , , ), TS TCC (2) condition as 22 where F = C/Cm, Cθθ= sin /sin S represents the solar concentration, θ h 2 qVEC// kT qV CC kT denotes the semi-angle of the solar disc seen from the earth through the JB =−qniB DB (e e )/NBB d , (4) concentrator, θ ≈°0.267 denotes the same angle when no concentrator S 2 is used and C = 46050 is the maximum theoretical solar concentration where niB is the intrinsic concentration of the base semiconductor, NB m ff when the media surrounding the cell is air and is obtained for θπ= /2 denotes the base doping, DB represents the di usion constant of the holes, and d stands for the width of the base. The EB junction injection [30]. The term Ṅ(,ETTS∞ ,,0)represents the photon flux absorbed B efficiency is defined as from the sun, and Ṅ(,ETqVTCC∞ , , )denotes the photon flux absorbing from the collector due to the electroluminescent emission. The photon 2 fl qn DBBB/ N d ux γ = iB . 2 2 qn DBBB/(1) N d++ q n Ṅ(, ETC ∞ , T ,0) (5) 2 iB 2()()π hω2 hω d hω Ṅ(,hω hω ,,) T μ = , 12 32∫ hc hω1 exp[(hω−− μ )/ kT ] 1 (3) The total current density through the emitter terminal can be expressed as J =−JJe h . where h is the Planck constant, k is the Boltzmann constant, and c is the E EB EB Similarly, the electric current density crossing the BC junction is speed of light. The total recombination rate R per unit volume includes written as according to the number of incident photons with energy two part: Re and Rc, where ReTCE=∞λṄ(, E , T , qV )represents the ra- E ≤

Fig. 2. Contour plots showing the (a) conversion efficiency η, (b) cell temperature TC, (c) current density of top cell JE, and (d) current density of bottom cell JC as functions of the top bandgap ET and the bottom bandgap EB, where the voltage outputs of the top and bottom cell have been optimized for maximum efficiency. Stars denote maximum efficiency of 46.1%, which mark optimum values in terms of system properties.

115 X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119

e ffi JBC =−qFNE[ ̇(,BTS E , T ,0)(1)+ λNĖ(, BTC E , T , qV C) e ciency η, (b) cell temperature TC, (c) current density of top cell JE, 2 2 and (d) current density of bottom cell JC as functions of the top bandgap −∞nṄ(, ETCC , T , qV ) +∞ nṄ(, ETCE , T , qV )]. (6) ET and the bottom bandgap EB, where the voltage outputs of the top and The total current density through the collector terminal is bottom cell have been optimized for maximum efficiency. Fig. 2(a) e h h h h ffi JC =+JJBC BC, where JBC ==JJEB B . Finally, the power output density shows that the maximum e ciency of 46.4% occurs for top bandgap of of the HBTSC considering non-ideal factors can be expressed as 1.78 eV and bottom bandgap of 0.82 eV, which corresponds to the operating temperature for cell of 465 K. Since the conversion efficiency of P =+=JV JV Je V + Je V − Jh () V − V , (7) EE CC EB E BC C B EC a HBTSC is defined as the ratio of the power output to the solar input h fl where the term JB (VVEC− ) represents the power loss under the energy ow, the maximum power density point coincides with that of ffi condition of VE > VC. Note that when γ equals zero, the HBTSC the maximum e ciency. The optimal values of bandgaps and operating e e transforms into the equivalent circuit represented in Fig. 1(d), JEB (JBC) temperature allow the appropriate materials for constructing the describes the current–voltage characteristic of the top (bottom) cell so HBTSC to be chosen. The existence of optimal bandgaps for maximizing that the HBTSC and dual-junction solar cell share the same limiting efficiency can be understood as follows. The HBTSC conversion effi- efficiency. ciency is dependent on the output power, which is a product of the According to Fig. 1(a) and the first law of thermodynamics, the cell output current and the output voltage. For large-bandgap materials, temperature is determined by the coupled thermal and electricity en- although the output voltage is large due to the strong mismatch of the fi ergy balance, which is given by Psun=++PPP leak rad, where quasi-Fermi level, the large bandgap signi cantly reduces sunlight ab- Psun =∞FĖ(0, , TS , 0) represents the concentrated radiation flux sup- sorption, thus leading to small photocurrent. For small-bandgap mate- plied by the sun. The radiative energy flux rials, although the photocurrent is enhanced, the output voltage re-

3 mains small. The interplay between these two aspects leads to an 2()()π hω2 hω d hω Ė(,hν hν ,,) T μ = . optimal bandgap for achieving maximum conversion efficiency. 12 32∫ hc hω1 exp[(hω−− μ )/ kT ] 1 (8) To enhance the conversion efficiency of the HBTSC, the bandgap of the materials should be such that photon absorption maximizes as a Prad=∞EĖ(, T , TqV C , E ) + EEĖ(, B T , TqV C , C) denotes the radiation whole. GaAs and GaSb as promising candidates for the emitter and flux due to radiative recombination.Pleak=−UT() C T A represents heat leak rate between the cell and the environment, where U is the heat collector are selected in the HBTSC. The reasons can be explained as transfer coefficient. follows. The bandgap of GaAs (GaSb) is ∼1.42 (0.72) eV, corre- Based on the above analysis, the conversion efficiency is expressed sponding to a wavelength of ∼800 (1150) nm [32]. These wavelengths as correspond to the high-energy density portion of the solar spectrum. Generally, the electron diffusion length in p-type GaAs (emitter region) P PP+ η ==−1.rad leak reaches up to 70 μm, thus providing a much thicker base for broadband Psun Psun (9) absorption. Furthermore, GaAs is resistant to radiation damage, thus Clearly, the conversion efficiency of such a HBTSC using thermal contributing to the long-term stability of the solar cells. The binary III-V conduction and radiation to reject entropy is bounded by the Carnot compound, GaSb, is capable of generating a higher voltage than Ge (0.72 eV). Furthermore, since GaSb is a direct bandgap material, GaSb- limit ηC =−1TTAS / = 95\% . Particularly, when TC = TS, the power output density P = 0, which is of no practical use. In addition, Eq. (9) based cells will generate higher currents in comparison to the indirect indicates that the radiative recombination and the heat transfer losses bandgap semiconductor Ge. Thus, GaSb is chosen as the collector, ra- ffi will significantly degrade the performance of the cell. ther than Ge, to achieve higher energy conversion e ciency. Moreover, the temperature coefficient of GaAs is zero, which means that GaAs is 4. Performance analysis and parametric optimum design suitable for high-temperature operations. Therefore, the HBTSC with non-ideal effects combining such two materials has the potential to further improve the performance due to the advantages of the broader In the following, several parameters C = 100, γ = 0.5, λ = 10, and − − U = 0.1 W cm 2 K 1 are used for calculation. These parameters are fraction of the solar spectrum and increased voltage available for the kept constant unless mentioned specifically. Using the Eqs. (1)–(9), one wide band gap materials. can plot three-dimensional projective graphs of (a) conversion Additionally, it is observed from Fig. 2(b) that cell temperature

Fig. 3. The current density–voltage characteristics for (a) the top cell (VC = 0), (b) the bottom cell (VE = 0).

116 X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119 increases with top bandgap and is hardly affected by bottom bandgap. kinds of carrier recombination can cause additional loss of open-circuit Because less photons are absorbed by the emitter semiconductor as the voltage. These two parameters result in the decrease of the open-circuit band gap increases, the more sub-band-gap radiation is absorbed as voltage, and thus lead to the performance degradation. On the other heat in the solar cell, and thus, temperature increase. Fig. 2(c) shows hand, the comparison between the scenarios 1 and 4 reveals an incre- that current density in the emitter terminal monotonically decreases ment of the short-circuit current and open-circuit voltage in the top and with top bandgap and is rarely affected by bottom bandgap, which are bottom cell. It indicates that the concentration factor C is conducive in accordant with the Eq. (1). It implies that the smaller the band gap of enhancing the performance of the solar cell. the emitter material, the more photons are absorbed and thus the larger The dependence of performance parameters, viz. Pm and ηm of the current density is achieved. Moreover, current density in the collector solar cell with injection efficiency γ is shown in Fig. 4(a). The maximum ffi terminal is a monotonically increasing function of top bandgap, but is a power density Pm and maximum conversion e ciency ηm decrease with monotonically decreasing function of bottom bandgap, as shown in the increase of injection efficiency γ. To achieve a better performance Fig. 2(d). The reason originates from the fact that current density is of the HBTSC, γ has to approach zero, which is in contrast to the case of determined by the number of incident photons with energy heterojunction bipolar transistors where the γ needs to be maximized. EB ≤

TC as loss factors to be visualized. From Eqs. (1)–(5), open-circuit vol- gion, thus lowing γ by appropriate base doping is a key to the optimized tage in the emitter terminal closely is mainly determined by TC and λ. design of the HBTSC. Additionally, the concentrating factor is also At these elevated temperatures, the bandgap of the cells usually de- important to enhance the conversion efficiency of the HBTSC. As shown creases, implying that longer wavelength photons can now be absorbed. in Fig. 4(b), Pm increases with F, while ηm is not a monotonic function of Also, as temperature increases, the minority carrier lifetime generally F. When the concentration factor F = 0.3 is used, ηm of the HBTSC can increases. Both these factors will slightly increase the light generated reach 54.6%. It indicates that the choice of F is very significant for current and consequently short-circuit current. However, the saturation obtaining the optimum performance of the HBTSC including non-ideal h current JEB generated by the base terminal decreases exponentially with factors. In the region of F < 0.3, larger the concentration factor cor- the increase of temperature [33]. This acts to reduce the open-circuit responds to more input energy and higher efficiency. In the opposite voltage as temperature increases. The decrease in open-circuit voltage region of F > 0.3, the increase rate of the radiation flux supplied by the is more rapid than the increase in short-circuit current, resulting in an sun is larger than that of the power density, thus leading to the decrease overall reduction in the cell efficiency as the temperature increases. of the efficiency. For differently values of F, the optimal values of the Moreover, open-circuit voltage is inversely proportional to λ. Various device parameters required to achieve the maximum efficiency of

Fig. 4. The maximum power generation density and conversion eﬃciency of the HBTSC varying with (a) injection eﬃciency γ (b) concentration factor F, and (c) cell temperature TC.

117 X. Zhang, et al. Energy Conversion and Management 188 (2019) 112–119

Table 1 6. Concluding remarks The optimal values of several key parameters at the maximum efficiency under different concentration factors. In summary, based on a pioneering work by Luque and Martí [22], −2 the theory of a three-terminal heterojunction bipolar transistor solar F ηm P (W cm ) JE,opt JC,opt ET,opt (eV) EB,opt (eV) − − (A cm 2) (A cm 2) cell is developed with inclusion of non-ideal effects: (1) cell temperature elevation due to sunlight illumination and (2) irreversible losses. 0.001 0.446 3.29 0.890 2.417 1.72 0.72 The model derived in this work shall provide important guidelines for 0.1 0.513 377 114 229 1.86 0.85 0.3 0.546 1202 268 769 1.91 0.94 future experimental design of the HBTSC, which is beyond the scope of 0.5 0.542 1966 395 1471 2.06 1.02 this paper. This model suggests that the HBTSC is a feasible and pro- 0.7 0.536 2621 452 1836 2.15 1.06 mising concept towards high-efficiency solar cell with great ease-of- 1 0.528 3870 696 2762 2.02 0.93 fabrication. It shows that such a HBTSC composed of GaAs/GaSb can provide a remarkable maximum efficiency of 46.4% at concentration of 100 suns. An analytical conversion efficiency formula is developed for HBTSCs are summarized in Table 1. These data shall provide insightful the updated HBTSC which allows the device performance under various guidance for the engineering and the optimum design of HBTSCs. Fi- environmental and material conditions to be characterized. By in- nally, Fig. 4(c) shows the cell temperature dependence of the para- vestigating the energy loss mechanisms, more efforts should be focused metric characteristics of a HBTSC. The parameter, P , decreases line- m on enhancing the base doping, improving the surface passivation, and arly with T , which can be attributed to the decreased light absorption C reducing the cell temperature of the HBTSC in order to achieve max- due to a decrease in the band gap of the emitter region. The decrease in imum efficiency. The findings obtained here offer a practical guide for η with temperature is mainly due to the decrease of P with T . Ap- m m C the design of high-performance HBTSC working under non-ideal con- parently, to achieve a better performance, the temperature of the ditions, thus paving the first-step towards the development of the HBTSC has to be as low as possible. The cell has to be efficiently cooled, practical and efficient solar cells. which requires the thermal exchange coefficient to be high.

Declaration of interests 5. Discussion of practical implementation The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influ- The HBTSC can be considered as the building block of more com- ence the work reported in this paper. plex multi-junction solar cells without the requirement of tunneling junction. For example, four junctions HBTSC can be realized through Acknowledgments complementing two HBTSCs. Without tunneling junction and current mismatch, HBTSC emerges as a photoelectric conversion device owing This work was supported by the National Natural Science to the simplified structure that reduces the number of the layers. Foundation of China under Grant 11675132 and Fundamental Research In practical implementation of the HBTSC, the conversion efficiency Fund for the Central Universities under Grant 20720180011, People’s is limited by the solar concentration, injection efficiency, cell tem- Republic of China, and Singapore A*STAR under Grant A1783c0011. perature elevation, and recombination loss as shown in the presented work. Particularly, the recombination loss originates from the radiative, Appendix A. Supplementary data Auger, Shockley-Read-Hall, and surface defects process, contributing to the internal carrier annihilation during the electrical transport process. Supplementary data to this article can be found online at https:// The non-radiative recombination rate is proportional to the thickness, doi.org/10.1016/j.enconman.2019.03.034. thus using a thicker layer is critical for high performance. 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