1. Introduction

Environmental problems have attracted considerable attention in the 21st century. Green energy resources such as wind-driven generator, hydroelectric power, tidal stream generator, geothermal energy and solar cells have been developed to substitute fossil fuel. The ideal solar cell should use the entire solar spectrum as far as possible. In general, a single-gap solar cell can only transfer photons with energies close to the gap energy for generating current because photons with energies less than the energy gap will be lost. In order to raise solar cell efficiency, the solar spectrum should be used fully. One method for achieving this is to use photons with low energy. A. Luque [1] proposed an intermediate band solar cell (IBSC) by inserting an extra band inside the gap of the single-gap solar cell. Because of the intermediate band (IB), the gap energy is separated into three energies: valance band to conduction band (VB-CB), valance band to intermediate band (VB-IB), and intermediate band to conduction band (IB-CB). The solar cell uses photons with energies lower than the bandgap through the intermediate band. In this design, the intermediate band is usually assumed to be half occupied to provide electrons for the IB-CB transition. Simultaneously, the half-occupied intermediate band receives electrons from the VB-IB transition. The transfer efficiency rises by absorbing and transferring photons with energy lower than the energy gap through the intermediate band. Thus, the IBSC is considered to be a potential third generation solar cell. With ideal condition and maximum light concentration, the IBSC exhibits an efficiency of 63.2% [1], which significantly exceeds the efficiencies of ordinary solar cells under the Shockley-Queisser limit of 37% [2].

Quantum dots (QDs) have provoked intense research in recent decades because of their atomic-like density of states and three-dimensional carrier confinement. Effective optoelectronic have been developed using QDs, including semiconductor lasers, infrared detectors, optical amplifiers, and solar cells. Quantum dots are also considered as useful structures for realizing IBSCs. Implementing high density coupled-QDs will benefit in generating IBs [3]. The energy levels belonging to individual QDs can form an energy band owing to the coupling effect arising from closely packed QDs or a QD array. To achieve this, the QD structure is typically designed as a significantly closely packed array [3–8]. Moreover, QD crystal with small QD can separate the IB from the rest of CB [3, 4]. The effect of IB is limited by IB-CB absorption. Because of the weak IB-CB absorption, the IB only exhibits small contribution to the solar photovoltaic conversion efficiency. To strengthen the intraband electron transitions, the geometry of the QD and matrix should be considered [5, 6].

Usually, electrons in IB fall back to VB before they jump to CB because of their short lifetime. If carriers in IB cannot accomplish the IB-CB transition, they will not contribute to the current. To increase the lifetime of electron in IB, a band structure with separations of electron and hole wave functions is necessary. This type of band structure is called a “type-II” band structure, in which a longer carrier lifetime in IB allows an IB-to-CB transition. Meanwhile, strain accumulation is a problem in self-assembled QD growing process. The structure with several QD layers exhibit considerable defects if the speed of strain accumulation is significantly rapid. Recently, InAs QDs that are covered by a thin GaAsSb layer have attracted considerable interests. An InAs/GaAs quantum dot system with GaAsSb as a strain reducing layer can change the band structure to be type-II [7]. These QDs have better quality because of the surfactant effect of Sb [8]. Liu et al. show that GaAsSb strain reducing layer can protect QD structure by inhibiting In-Ga intermixing during the thermal annealing process [9]. The level of the type-II band alignment can be adjusted by designing the geometry of the GaAsSb layer properly [10, 11]. Hospodková et al. report that the size of QDs also effects the band alignment in vertically combined InAs and GaAsSb QDs [12]. Tomić show that the lifetime of the VB-IB transition can be put into the microsecond range with a high Sb concentration GaAsSb buffer layer [13]. Vysločil at al report that the type II band structure introduced by GaAsSb helps in electron-hole separation for increasing the photocurrent in a solar cell [14]. Quantum dot solar cell usually has lower efficiency than bulk material because of severe open voltage reduction. Luque et al. show that type-II quantum dot prevents the reduction voltage in IB solar cells [15].

The width of the IB depends on the strength of the coupling effect between the QDs. A coupled-QD structure exhibits stronger coupling effect. In this study, a coupled-QD structure with a GaAsSb interlayer is investigated. The Sb concentration for the structure exhibiting the advantages of both type-I and type-II band alignments was observed. The properties of the formed IB were also analyzed. Then, we determined the optimal geometry parameters of the designed structure.

2. Structure design

In this study, the structure of coupling QDs with GaAsSb as the interlayer is modeled (hereafter referred to as the “designed structure”). The entire structure was designed on a GaAs substrate and finally capped with GaAs. The QD material was made of InAs, having a base b and height h. To increase the band separation for the VB-IB, IB-CB, and VB-CB transitions, AlAs layers were inserted below and above the coupled-QD structure [16]. The thicknesses of GaAs_1-xSb_x and AlAs were d₁ and d, respectively. The GaAs substrate exhibited a thickness of d₂ with h + d₂ thick GaAs cap layer. The width of the matrix (W) was set at 2.5b. A schematic diagram of the designed structure is shown in Fig. 1. The entire structure was considered as a unit cell for analyzing the optical properties of the QD crystal and the IB. The energy gap between the IBs and CBs is also important for ensuring the existence of the IB. If this gap is not sufficiently large, electrons will transit to CB because of thermal energy rather than by photon absorbing. The lateral-coupling effect is also important for the formation of IB. If the QD density is significantly low, no IB will be formed. To achieve a high QD density, a small-sized QD with 6 nm base and 2 nm height was selected. The designed structure with these QDs shows no IB if W is larger than 30 nm. Therefore, W is selected as15 nm, with an areal density of 4.44 × 10¹¹ cm⁻².

 

Fig. 1 The designed structure of coupling quantum dot with GaAsSb as inter layer and AlAs layers. The width of QD is b and the height is h. The thicknesses of AlAs layer, GaAsSb layer and GaAs bottom layer are d, d₁ and d₂, respectively. (a) for 3D structure and (b) for 2D slice.

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3. Theory

In order to estimate the performance of a QD solar cell with the IB, the electron states must be calculated in the designed structure. The electron energy states in the CB were calculated using the effective-mass method, and the hole states in the VB were calculated using the 6 × 6 k$\cdot$p method [17, 18]. The k$\cdot$p model was solved by using commercial finite-element software package, COMSOL Multiphysics Modeling Softwave [19] under 3D simulation. In the structural design, the strain profile is important; thus, the strain field was calculated using the elasticity. The piezoelectric effect of the QD material was also considered. The strain and piezoelectric potential were also solved by using COMSOL Multiphysics Modeling Softwave under 3D simulation. The designed structure was treated as a unit cell for considering the formation of the IB. Thus, periodic boundary conditions were introduced in our simulation. From the calculated electron and hole states, we obtain the optical matrix element, ${\left|e\cdot p_{ba}\right|}^2$, and the absorption spectrum, $\alpha \left(\hslash \omega \right)$, can be calculated from the following equation:

To analyze the optical properties of the band-to-band transitions for the QD array, the absorption coefficients at different points in reciprocal space (k space) should be known. Generally, the momentum matrix should be calculated at every k points along the band direction. However, as reported by Tomić et al., the band absorption coefficient is approximated by using sampling points [22]. The absorption coefficient for continuous valence band to continuous conduction band was calculated as a bulk material. Related parameters for different structures were calculated by linear interpolation of GaAs and GaSb from the effective bandgap of the design structure.

4. Numerical results

In this section, the optimal parameters for the QDs to possess a quasi-type-II band structure are discussed. Then, the properties of the IB are analyzed. Finally, the potential of the designed structure to form an IBSC is investigated.

4.1 Sb concentration of GaAsSb

Using a GaAsSb layer, the band structure can be transformed to type-II alignment by adjusting the concentration of Sb. It is reported that a single QD array exhibits type-II band alignment if the Sb concentration is larger than 12% [5, 6]. However, the analyzed structure is a coupled-QD array; thus, the concentration for the band structure transition from type-I to type-II could be different. To investigate this transition concentration, the thickness of the GaAsSb layer (d₁) was set at 2.5 nm for analyzing the band-diagram as a function of Sb concentration (x). The analyzed concentrations of GaAsSb were from 0% to 24%. In this part, the thicknesses of the GaAs layer (d₂) and AlAs layer (d) were 1 nm. As shown in Fig. 2, the barrier between the QDs for hole was higher when the Sb concentration of the GaAsSb spacer was low; therefore, the hole wave function was confined inside the quantum dot. The barrier decreases with increasing in the Sb concentration. Then, the hole wave function started to leak into the GaAsSb spacer region. However, the conduction band remained almost the same with variation in the Sb concentration. The major part of the electron wave function remained inside the QD. However, as the effective mass of the electron is small, a part of the wave function leaves QD because of the coupling effect. The band structure with electron and hole wave functions in the same region is called “type-I” band structure, while the band structure with electron and hole wave functions in different regions is called “type-II” band structure. In general, type-I band structure exhibits stronger absorption strength but smaller carrier lifetime; while one with type-II exhibits longer carrier lifetime but weaker absorption. From the examination, the band diagram of the designed structure with 2.5 nm GaAsSb spacer will become as type-II when Sb concentration is higher than 24%. In this research, we need longer IB lifetime with sufficient strength for VB-IB transition. That is, the desired band structure exhibits the advantages of both type-I and type-II. As a result, a little part of the hole wave function that leaks into the GaAsSb layer is required. We treated the band structure with the GaAsSb spacer of Sb concentration between 0% and 24% with lower hole energy barrier to let a small part of the hole wavefunction leak into the GaAsSb region as “quasi-type-II.”

 

Fig. 2 Band-diagram for different Sb concentration (x) with thickness of GaAsSb layer is equal to 2.5 nm.

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4.2 Bandwidth of the intermediate band

In this section, the effect of the coupling QD structure in the formation the intermediate band (IB) is analyzed. First, the existence of the IB should be confirmed. Generally, the ground electron state is treated as the intermediate level. If the bandgap between the bands formed by electron levels is smaller than 25.85 meV, the thermal voltage at room temperature (300 K), the electron in the lower band will “jump” to a higher band by thermal vibration under the room temperature condition rather than by light absorption. Thus, these two bands are merged together to form a continuous band. If all bands connect to each other, then there is only CB in the band structure without IB. Therefore, an individual band below the continuous conduction band is observed as the IB. The bandwidth for the IB (ΔE_IB) is determined by calculating the crystal band structure with the designed structure as a unit cell in this research. In this part, the QD size was set to be 6 nm at the base with a 2 nm height. The thicknesses of GaAs layer (d₂) and AlAs layer (d) were 1 nm. Then, the properties of the IBs formed with different GaAsSb spacer thicknesses and different Sb concentrations of spacer were analyzed. Figure 3(a) shows the variation of the bandwidth of the IB (ΔE_IB) and the bandgap between the IB and the CB (E_gIC) for the designed coupled-QDs structure with different thicknesses of the GaAsSb_0.1 spacer (d₁). In the simulation, the height of the QD was 2 nm. Therefore, as shown in Fig. 3(a), the IB bandwidth and the bandgap between the IB and the CB shown for the GaAsSb thickness are larger than 2.5 nm. The analyzed GaAsSb spacer thicknesses were from 2.5 nm to 9.5 nm. It shows that the designed structure with 2.5 nm GaAsSb spacer exhibited the maximum IB bandwidth. It is due to the smaller spacer benefit that enhances the coupling effect between the QDs. Therefore, the individual ground state of QDs can couple to each other easily through thin GaAsSb spacer. The coupling effect decreased with increase in the spacer thickness. Consequently, the IB bandwidth decreased with increase in the thickness of the GaAsSb_0.1 spacer. In general, the intense coupling effect also generate large energy separation between the ground state and the first excited state for producing large E_gIC. As shown in Fig. 3(a), the designed structure with 2.5 nm spacer, the smallest GaAsSb_0.1 spacer thickness, produces the maximum E_gIC. Adjacent bands of electron connect to each other to form a broader band if the bandgap is smaller than the thermal disturbance energy under the room temperature. If all bands above the IB are connected to each other, the continuous band formed by these bands is treated as CB. Therefore, the first state starts to become as the CB probably not the first excited state. Figure 3(b) shows the schematic band diagram of the IB and CB for the designed coupled QDs structure with different GaAsSb_0.1 spacer thicknesses. It showed that there were extra states between IB and CB for d₁ = 2.5, 3.5, 4.5, 9.5 nm. These structure exhibit larger E_gIC than those without extra states. Consequently, there is some discontinuity in Fig. 3(a) for the variation of E_gIC. These extra states were caused by strong coupling effect with thin GaAsSb_0.1 spacer. With the thickness increasing in spacer, the coupling effect became weaker to reduce energy separation. This phenomenon will let the CB band edge “fall” to the first excited state. The coupling effect will become so weak with too thick GaAsSb_0.1 spacer that the bandwidth of the excited states become narrow. These narrow excited band will enhance the energy of CB band edge because the excited band only can form a continuous band in high energy state. This effect produced extra states between IB and CB. The bandgap between these extra states and their adjacent states were sufficient to be treated as individual states. However, as Yoshida [23] reported, the carrier in IB should meet the carrier balance condition; that is, the net carrier generation rate (G) via IB should be the same, G_VI = G_IC. IBSC, with this IB carrier balance condition, ensures that the IB works continuously. In this simulation, a pre-filling IB was used for achieving this transition balance condition. These extra bands between the ground state and the CB are also treated as IB, but the extra bands and the ground state band belong to the same structure. In general, it is difficult to fulfill the two balance conditions with one doping concentration. Subsequently, the remaining IBs gradually lose their effect. As the bandwidth of the ground state is broader, it is selected as the IB for absorbing more photons.

 

Fig. 3 (a) Bandwidth of the intermediate band (ΔE_IB) and bandgap between intermediate band and conduction band (E_gIC) for d₁ with x = 10%, (b) schematic diagram of band structure for IB and CB, orange frame represents IB.

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The IB properties formed by the structure with different Sb concentrations of 2.5 nm GaAsSb layer were also analyzed, as shown in Fig. 4. The analyzed Sb concentrations of the GaAsSb spacer were from 0% to 16%. In the figure, the IB bandwidth increases with increase in the Sb concentration increasing. It reveals that the maximum bandwidth of the IB occurs at x = 16%. However, the difference between the maximum value was less than 3 meV. The coupling effect between the QDs was approximately the same because of the same GaAsSb spacer thickness. Variation in the Sb concentration of the GaAsSb spacer exhibited considerable effect on the valence band, rather than on the conduction band. Consequently, the variation in the Sb concentration only had a little effect on the IB bandwidth. However, with different Sb concentrations, the designed structure exhibits different strain profiles. It changes the conduction band slightly. As a result, the energy of the electron ground state increases with increase in the Sb concentration of the GaAsSb spacer, but the conduction band edge almost remained the same. This phenomenon led to the decrease in the band gap between IB and CB. Meanwhile, the increase in energy stimulated the individual ground states of the QDs to easily couple to each other. Consequently, the coupling effect increased with increase in the Sb concentration. However, as mentioned, the increase in the coupling effect was weak because of the same GaAsSb spacer thickness with slight variation in the conduction band structure. As shown in Fig. 3(b), there were also extra bands between IB and CB for the designed structure with different concentrations of the GaAsSb spacer. Figures 3 and 4 show that the properties of IB depend on the GaAsSb spacer thickness and the Sb concentration only affects the position of the IB slightly.

 

Fig. 4 (a) Bandwidth of the intermediate band (ΔE_IB) and bandgap between intermediate band and conduction band (E_gIC) for d₁ with d₁ = 2.5 nm, (b) schematic diagram of band structure for IB and CB, orange frame represents IB.

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4.3 Thickness of AlAs

AlAs layers were inserted above and below the QDs for generating higher energy barrier in this research. With the energy barriers, the quantum effect will become more apparent to create a high energy electron ground state. The QD size was again set to be 6 nm at base with a 2 nm height. The thicknesses of GaAsSb_0.16 spacer and GaAs layers were set as 2.5 nm and 1 nm, respectively. To ensure smaller height of the matrix, the analyzed thicknesses of the AlAs layers were selected as 1 nm, 2 nm and 3 nm. As shown in Fig. 5(a), the major part of the absorption spectrum is in the far infrared region. This is because of the small energy separation between IB and CB. With 1 nm thick AlAs layers, the absorption width exhibits enhancements, particularly in the near infrared range. The energy level of the IB is increased by the AlAs layer, yielding better overlaps with the levels in the CB to achieve better absorption strength. Figure 5(b) shows that the absorption spectrums of valence band to conduction band for the structure with different AlAs layer thicknesses are almost the same because of the similar effective bandgaps. The absorption from transitions of electron between VB and CB is important because of the strong absorption coefficient. If the bandgap becomes significantly large, more photons will be wasted. In addition, the AlAs layer is the barrier between the QDs, the region of IB, and the GaAs, the region of CB. Moreover, if this layer is significantly thick, it will inhibit the IB-CB transition. As shown in Fig. 5(a), when the thicknesses of the AlAs layers increase to 3 nm, the transition peak in the far infrared region and the near infrared region will disappear. The bandwidth loss is 30% compared to the bandwidth of the designed structure with 1 nm AlAs layers. The QD density is a significantly factor affecting the absorption efficiency and the coupling effect. Thus, the thickness of AlAs layer is selected as 1 nm, in order to minimize the thickness of the total cell. For these reasons, the AlAs-layer thickness is set to be 1 nm for an optimized design.

 

Fig. 5 Absorption spectrum for (a) IB-CB transition, (b) VB-CB transition for different for AlAs layer thicknesses.

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4.4 Thickness of GaAs

GaAs is commonly used as substrate and cladding layers of InAs QDs. The QD size was set to be 6 nm at base with a 2 nm height. The thickness of GaAsSb_0.16 spacer and AlAs layers were set as 2.5 nm and 1 nm. In our analysis, GaAs layers were also contained in the unit cell. To maximize the QD density, the GaAs layers thicknesses should be as small as possible. For this reason, the thickness of GaAs layers was considered as 1~3 nm. Meanwhile, GaAs layers are the spacer between the unit cells in this designed structure. As a result, if the GaAs thickness is small, a coupling effect is introduced between the unit cells through the GaAs. Therefore, thin GaAs layers help to broaden the absorption spectrum, as shown in Fig. 6. In Fig. 6(a), the structure with 1 nm GaAs layers absorbs high energy photon through IB to CB transition, in the near infrared range. When the thickness of GaAs layer increases to 3 nm, although the absorption in far infrared region is excited, the entire absorption spectrum exhibits a red shift. Solar spectrum contains most photons in the visible light region with only a little in the far infrared region. To increase the intraband transition (IB-CB transition), we believe that it is essential to force the absorption to the near-infrared range, even in the visible light region. Meanwhile, the bandwidth of structure with 3 nm GaAs layers exhibits 24% shrink compared to the one with 1 nm GaAs layers. Because of these reasons, the effective bandgap for the structure with 1 nm GaAs layers is larger resulting in the weaker VB-CB absorption from Fig. 6(b). The designed structure with 1 nm GaAs layer is considered to exhibit better IB performance.

 

Fig. 6 Absorption spectrum for (a) IB-CB transition, (b) VB-CB transition for different GaAs layer thicknesses.

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4.5. Efficiency for IBSC with coupled quantum dots structure

In this section, the photovoltaic efficiencies of IBSC with the designed coupling quantum dot, I region, were analyzed. The simulation method is a self-consistent drift-diffusion method for IBSC as reported by Yoshida. This simulation was done by COMSOL Multiphysics Modeling Softwave under 1D simulation. However, the recombination terms were eliminated for simplicity. The design of the device PIN junction was also similar to that reported by Yoshida; that is, the whole device consists of 0.5 μm P region, 1 μm I region and 2 μm N region, from top to bottom. It was assumed that the I region was filled with the designed structure without defects. To ensure that the intermediate band solar cell functions properly, the IB is pre-filled for achieving carrier balance via the IB. The pre-filled profile of IB was solve by MATLAB with 1D IB design. Because of the large difference between absorption coefficients of VB-IB and IB-CB, the occupation probability of electrons in IB is significantly large from pre-filled IB (above 0.98). Moreover, to maintain the PNN⁺ doping profile, the acceptor concentration was 7.0 × 10¹⁷ cm⁻³ with the donor concentration as 6.0 × 10¹⁷ cm⁻³. To compare the efficiency for different parameters, the doping concentrations of the P and N regions were fixed. In this paper, we analyzed two cases of efficiencies for coupling InAs-QDs structure as I region with different spacers: the coupling InAs-QD structure with a 2.5 nm GaAsSb spacer with different Sb concentrations (0% - 16%) and the structure with different GaAsSb_0.1 spacer thicknesses (2.5 nm - 9.5 nm). Figure 7 shows the efficiency for the coupling QD with 2.5 nm GaAsSb_x for different Sb concentrations as I region with corresponding IB bandwidth and the effective bandgap. The efficiency increases with increasing Sb concentrations and broadening of the IB bandwidth. However, only some cases of the designed structure, with IB, had higher efficiency than GaAs bulk as I region for GaAsSb spacer with different concentrations. Figure 9 shows the efficiency for the coupling QD with 10% Sb concentration for different GaAsSb thicknesses with corresponding IB bandwidth and effective bandgap. It shows an opposite tendency compared to Fig. 7, the efficiencies and the IB bandwidth demonstrate a different variation trend. In Fig. 9, the efficiency for a structure with a 4.5 nm GaAsSb_0.1 spacer is slightly higher than the GaAs, and its effective bandgap is close to that of GaAs. The efficiency enhancement is only 0.01%. The rise in the efficiency is due to the excitence of the IB; however, the absorption strength for the IB-CB is significantly weak and hence the enhancement is not apparent. Subsequently, considerable increase in efficiency results from the decrease of the effective bandgap. With a smaller bandgap, the structure can use more solar spectrum, and the absorption spectrum is similar to that of a bulk material with sufficient strength. If the effective bandgap is greater than that of GaAs, because of the weak intraband transition, the efficient gain from IB cannot compensate for the loss in the VB-CB transition, and resulting in efficiency decrease. As shown in Figs. 7 and 9, the structures show higher efficiencies because of the smaller band gap than GaAs or the similar band gap with GaAs. From the results of Figs. 7 and 9, a designed structure with an 8.5 nm GaAsSb layer with 16% Sb concentration as I region will have the best efficiency for intermediate band solar cell. From Fig. 8(a), the designed structure with a 2.5 nm GaAsSb layer of 16% Sb concentration has a smaller effective bandgap to help produce higher efficiency with a stronger VB-CB absorption spectrum. In addition, Fig. 8(b) shows the weaker VB-IB absorption coefficient of GaAsSb_0.16 spacer, compared with other Sb concentrations spacers, from its quasi-type-II band structure benefit in increasing the lifetime of carriers in the IB. A wider IB-CB absorption spectrum as shown in Fig. 8(c) implies that the IB can absorb more photons. Meanwhile, the spectrum overlap between VB-IB and IB-CB transitions also enhance the carrier balance in IB with a lower doping concentration to have smaller occupation to obtain smaller occupation probability of electrons. Figure 10 shows the band-diagram for different Sb concentrations (x) with an 8.5 nm GaAsSb layer. Figure 11 shows the yz slice through the center of the structure of ground state hole wave function for different Sb concentration (x) with thickness of GaAsSb layer is equal to 8.5 nm. The top energy of the valence bands in the GaAsSb region increases as the GaAsSb concentration increases. As a result, the top of the valance band between the QDs changes its form from concave to convex. From the band-diagram, the coupling QDs with 20% GaAsSb spacer have a flat top of its valence band to let more part of the hole wave function spread into the GaAsSb spacer, whereas the ground state hole wave function for 16% GaAsSb spacer still confines a large part inside the QD. Therefore, it ensures that the coupling QDs with 16% GaAsSb spacer are treated as quasi-type-II band structure more appropriately rather than 20% GaAsSb spacer.

 

Fig. 7 (a) Efficiency fot the coupling QD with 2.5 nm GaAsSb for different Sb concentration. The red line is represents the efficiency for GaAs bulk used in I region. (b) The IB bandwidth and the effective bandgap for the designed structure. The red line represents the bandgap energy of GaAs.

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Fig. 8 Absorption spectrums for coupling QD structure with different Sb concentration of 2.5 nm GaAsSb layer, (a) absorption coefficients for transition from VB-CB. (b) absorption coefficients for transition from VB-IB. (c) absorption coefficients for transition from IB-CB.

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Fig. 9 (a) Efficiency fot the coupling QD with 10% Sb concentration for different GaAsSb thicknesses. The red line is reprents the efficiency for GaAs bulk used in I region. (b) The IB bandwidth and the effective bandgap for the designed structure. The red line represents the bandgap energy of GaAs.

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Fig. 10 Band-diagram for different Sb concentration (x) with thickness of GaAsSb layer is equal to 8.5 nm.

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Fig. 11 yz slice through the center of the structure of ground state hole wave function for different Sb concentration (x) with thickness of GaAsSb layer is equal to 8.5 nm.

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4.6 Maximum shear stress for different layers of the coupling QD

An ideal structure should exhibit no defects in order to achieve better performance. However, the effect of strain accumulation occurs when the structure has multiple layers of QDs. Maximum shear stresses for different regions are shown in Fig. 12. GaAs represents the spacer between the unit cells, and GaAsSb_x represents the spacer between QDs in a unit cell. It shows that the maximum shear stress occurs in the GaAsSb spacer between the QDs. The maximum shear stresses in the InAs QDs decrease with increasing GaAsSb_x spacer concentrations. However, this is not apparent because the sizes of the QDs for different GaAsSb concentrations are fixed in the simulation. Moreover, the size of the unit cell is designed as small as possible to achieve high QD density, and the QD sizes for different GaAsSb_x spacer concentration are fixed to limit the strain release effect.

 

Fig. 12 Max. shear stress in different materials fot the coupling QD with 8.5 nm GaAsSb_x for different Sb concentration. GaAs represent the spacer between unit cells, and GaAsSb_x represebt the spacer between QDs in a unit cell.

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5. Conclusion

We analyzed the properties of IBSC based on the InAs coupled-QD structure with GaAsSb as the spacer. The absorption spectrum and the properties of the IB produced were also simulated. The electron and hole states are based on k$\cdot$p Hamiltonian with the periodic boundary conditions. The absorption spectrum and the energy separation from the effective band structure with IB were used for drift-diffusion model to analyze the efficiency of IBSC. The results revealed that the designed band structure with quasi-type-II alignment will extend the absorption spectrum to infrared range and reduce the absorption strength for transitions between VB-IBs. With the aid from thin AlAs and GaAs layer, some intraband transitions in the near infrared range were triggered. With appropriate design, the coupling QD structure with GaAsSb spacer will exhibit 3.3% enhancement of the same PIN structure with GaAs as the intrinsic region. However, because of the relative weak absorption coefficient for transition from IB to CB, compared with the VI transition, the main part of the efficiency increased from the effective bandgap decrease, rather than the photon absorption via IB. Furthermore, a GaAsSb layer in the InAs coupled-QD structure will help stress release in the QD. As a result, we conclude that the GaAsSb spacer in the InAs coupled-QD will help improve the properties of IB to increase the photoelectric efficiency of the intermediate band solar cell.