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Si p-i-n heterojunction solar cells for high efficiency
Solar Energy 158 (2017) 654–662
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Simulation of planar Si/Mg2Si/Si p-i-n heterojunction solar cells for high efficiency Quanrong Denga,b,1, Zhuo Wanga,c,1, Shenggao Wangb, Guosheng Shaoa, a b c
MARK
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State Centre for International Cooperation on Designer Low-Carbon & Environmental Materials (CDLCEM), Zhengzhou University, Zhengzhou 450001, China Hubei Key Laboratory of Plasma Chemistry and Advanced Materials, Wuhan Institute of Technology, Wuhan 430073, China School of Physics and Electronic Technology, Hubei University, Wuhan 430062, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Silicide solar cells Mg2Si Theoretical modelling p-i-n heterojunctions
A novel Si(p)/Mg2Si(i)/Si(n) PV cell architecture is proposed on the basis of numerical simulation and ab intio calculation in the framework of the density functional theory (DFT). First-principles calculations on the basis of the relaxed Mg2Si(1 1 0)/Si(1 1 1) heterojunction suggest that the valence band offset is about −0.35 eV with respect to the valence band maximum (VBM) of Si. The effect and corresponding mechanism of band offsets, doping concentration, layer thickness, as well as defect states on the performance of solar cells have been studied and discussed in detail. The optimised ideal Si(p)/Mg2Si(i)/Si(n) heterojunction solar cell with a total thickness of 2.15 μm of active materials is predicted to provide a large open-circuit voltage of 0.654 V and a high conversion efficiency up to 22.254%, which is much higher than single junction cells and rivals the performance of crystalline silicon solar cells over 100 times thicker. This work demonstrates great potential to develop Mg2Si based low-cost and environmentally friendly solar cells on the ground of the well-established silicon technology.
1. Introduction Photovoltaic (PV) devices have been extensively investigated and exploited to address worldwide energy crisis and associated environmental problems due to the dependence on fossil fuel. Current PV market is mainly dominated by silicon solar cells, including bulk crystalline silicon (c-Si) solar cells and thin film amorphous silicon (a-Si) solar cells. However, the low optical absorption coefficient of crystalline silicon makes it necessary for silicon solar cells to be rather thick, generally hundreds of microns and thus relatively costing in materials consumption (Avrutin et al., 2011). Besides, photo-generated carriers have to travel for a long distance to reach the electrodes, so that the material has to be of a very high purity and of high crystalline perfection to avoid carrier recombination and scattering, resulting in high manufacturing cost with extensive energy drainage. Although a-Si offers a much higher optical absorption coefficient that a layer about 1 μm thick can absorb sufficient sunlight to enable efficient solar cell operation, the high defect state density in amorphous phase limits the typical carrier motilities and diffusion lengths, resulting in much lower efficiency (Kosyachenko, 2011). Moreover, a-Si solar cells also suffer from the problem of performance degradation due to poor material stability (Shah et al., 2003, 2004).
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In order to achieve high energy conversion efficiency at low cost, researchers around the world have endeavoured to exploit new semiconducting materials with high optical absorption coefficients, suitable band gap and electrical properties. Semiconducting Mg2Si is recognized as an attractive alternative on account of its reported narrow band gap ranging from 0.66 to 0.80 eV (Scouler, 1969; Au-Yang and Cohen, 1969; Kato et al., 2011; Tamura et al., 2007), high optical absorption coefficient over 105 cm−1 at 500 nm, irrespective of its indirect bandgap, and high carrier mobility (Au-Yang and Cohen, 1969), which makes it suitable for light absorption layer in solar cells. Mg and Si are abundant in natural sources and environmentally friendly. This makes Mg2Si quite promising in enabling thinner solar cells to reduce materials cost, while maintaining the benefit of a-Si solar cells particularly for flexible applications. Considering that the narrow band gap of Mg2Si could result in lowered open circuit voltage (Voc), it is envisaged to be necessary in combining Mg2Si and Si films into p-i-n heterojunctions, in order to improve the Voc while maintaining large short circuit current (Jsc) on the basis of recent theoretical work (Gao et al., 2011; Zhu et al., 2013). In addition, Mg2Si and Si are in thermodynamic equilibrium, so that good and clean interface of the two materials can be readily achieved. This helps to realize novel practical solar cells using sustainable resources (Vantomme et al., 1997, 2000; Wang et al., 2007).
Corresponding author. E-mail address: [email protected] (G. Shao). Authors with equivalent contribution.
http://dx.doi.org/10.1016/j.solener.2017.10.028 Received 10 January 2017; Received in revised form 30 September 2017; Accepted 9 October 2017 0038-092X/ © 2017 Elsevier Ltd. All rights reserved.
Solar Energy 158 (2017) 654–662
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This work is dedicated to carry out systematic theoretical simulation and thus optimise the architecture of Mg2Si based solar cells for high energy conversion efficiency. The input materials parameters are largely based on available experimental data. First principle calculation is carried out to assess the electronic structure and band offset at the heterojunction, so as to provide reliable insight essential for improved accuracy of numerical simulation. It will be demonstrated that on the basis of established Si technology in fine-tuning n- and p-type doping levels in Si, thin films Si/Mg2Si/Si p-i-n heterojunction solar cells only 2.15 µm in total thickness could deliver high energy conversion efficiency ravelling that of p-i-n Si solar cells about 100 times thicker.
2. Methods First principles simulation of the heterojunction between Mg2Si and Si is carried out in the framework of the density functional theory (DFT), using the Vienna Ab initio Simulation Package (VASP) with the ionic potentials including the effect of core electrons being described by the projector augmented wave (PAW) method. On the basis of extensive test in recent DFT work (Han and Shao, 2015), the Brillouin zone integration is performed on well-converged Monkhost–Pack k-point grids, using 8 × 1 × 1 K-mesh for the heterojunction. A plane-wave energy cutoff of 500 eV is used in all calculations. All structures are geometrically relaxed until the total force on each ion was reduced to be less than 0.01 eV Å−1. Non-local effect in the exchange-correlation functional is considered for band structure calculations. The AMPS-1D (Analysis of Microelectronic and Photonic Structures,) code, which solves one dimensional dipolar problems according to Poisson’s and continuity equations, is used for numerical modelling under the standard solar spectrum illumination (AM1.5). The proposed device consists of sequentially stacked layers of Si(p)/Mg2Si (i)/Si(n), wherein a middle layer of intrinsic Mg2Si is used as the main optical absorption material, Fig. 1. Both the p- and n-type silicon films, with wider band gap than that for Mg2Si, can act as windows for the solar spectrum to be harvested by the Mg2Si absorber. Herein, silicon layers could be both crystalline (c-Si) and amorphous (a-Si), which can be readily doped to adequate carrier concentrations, using the established Si technology. For simplicity in description, here in this work Si refers to c-Si unless otherwise defined. Initially, such sandwiched architecture is envisaged to be useful not only in avoiding the difficulty in doping Mg2Si to adequate carrier concentration for p-type (Han and Shao, 2015), but also in making use of a p-type material with wider gap to enhance the open-circuit voltage while maintaining large short-circuit current, as was demonstrated by our recent work that the Voc is promoted by using wider gap materials on both sides (Gao et al., 2011; Zhu et al., 2013). Experimentally, such p-i-n heterojunction structures were employed in the well-known a-Si/ c-Si/a-Si (Ok et al., 2009), CIGS (Chaure et al., 2005), and CdTe based solar cells (Oladejia et al., 2000). To clarify the effect of p-i-n heterojunctions, devices made of Si/Mg2Si heterojunction and Mg2Si/Mg2Si homojunction are also studied for comparison.Experimentally measured optical absorption spectra of c-Si, a-Si, and Mg2Si are used as input in this work are shown in Fig. 2 (Kato et al., 2011; Messenger and Ventre, 2004). The spectral response range for the quantification of the external quantum efficiency for device simulation is in line with the range for experimental optical data in Fig. 2, being 380–1600 nm.
Fig. 2. Optical absorption spectra of Mg2Si, c-Si and a-Si used in simulation.
Optical model for the photo-induced free charge populations (electrons and holes) in the Poisson’s equation are inscribed in the continuity equation, and readers are referred to Section 2.2 of the AMPS-1D User Manual for details (http://www.ampsmodeling.org/). In addition, the following assumptions are made between the valence band top Ev, the conduction band bottom Ec and the Fermi energy Ef at contacts: EfEv(p) = 0.1 eV and Ec(n)-Ef = 0.1 eV. Surface recombination speeds for holes and electrons at the front and back contacts are both set to be 1 × 107 cm s−1, and reflection for light impinging on front and back surfaces are ignored. In the simulated models, the energy distributed within the band gap contains mid-gap states and Urbach exponential tails coming out of both the conduction band and the valence band. The values of dielectric constant, carrier mobility, band gaps, Urbach band tails for silicon and Mg2Si are given according to reported data in literature, as listed in Table 1, wherein the effective conduction and valence band densities are calculated using effective masses from literature. For example, the effective conduction band density NC is related to the effective electron mass me∗ as, NC = 2{2πme∗ kT / h2} 2 , wherein T is absolute temperature, k and h are Boltzmann and Plank’s constant respectively. Furthermore, Gaussian like mid-gap defect states with different densities and distributions are introduced to assess their impact.
3. Results and discussion 3.1. Conduction band offset effect It has been recognized that the electron affinity (χ) of semiconductors determines the conduction band offsets in heterojunction solar cells, ΔEc (χMg2Si – χSi), and thus plays critical role on solar cell performance. However, the electron affinity of Mg2Si is still not well established. Through investigating the band diagram of the Mg2Si(n)/Si (n) heterojunction, the electron affinity of Mg2Si was determined to be 0.42 eV smaller than that of Si (Atanassov and Baleva, 2007), and thus the Mg2Si electron affinity is evaluated to be 3.59 eV. Taking the mean values of experimentally determined band gaps for bulk materials into account (1.1 eV for Si and 0.7 eV for Mg2Si), this leads to the valence band maximum (VBM) for Mg2Si being offset for 0.82 eV above that for Si. On the other hand, investigation on Schottky barrier height at Au/ Mg2Si(n) interface suggested a significantly bigger value of 4.61 eV for the electron affinity of Mg2Si, leading to an offset of 0.6 eV below the VBM of Si (Sekino et al., 2011). It is worth noting that the reported band offsets at the VBM are even opposite in signs. Theoretical calculation suggested that the work function of Mg2Si was in the range between 3.02 eV and 5.28 eV, which was dependent upon the exposed surfaces and terminating atoms, with surface containing more Si having bigger electron affinity (Qin and Wang, 2015). This indicates the great
Fig. 1. Schematic architecture of the p-i-n solar cell construction.
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Table 1 Simulation parameters for each layer, with available materials data taken from literature (Kato et al., 2011; Gao et al., 2011; Udono et al., 2013; Madelung, 2004). Parameters
Mg2Si
c-Si (Gao et al., 2011)
a-Si (Gao et al., 2011)
Relative permittivity Electron mobility (cm2 V−1 S−1) Hole mobility (cm2 V−1 S−1) Acceptor concentration (cm−3) Donor concentration (cm−3) Band gap (eV) Effective conduction band density (cm−3) Effective valence band density (cm−3) Electron affinity (eV) Band tail density of states (cm−3 eV−1) Characteristic energy for donor and acceptor like tails (eV) Capture cross section for acceptors states, e, h(cm2)
20 (Madelung, 2004) 550 (Madelung, 2004) 70 (Udono et al., 2013) 1 × 1014 1 × 1014 0.77 (Kato et al., 2011; Madelung, 2004) 7.8 × 1018a 2.06 × 1019a 4.37 1 × 1014 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
11.9 1350 500 1 × 1015–1 × 1021 1 × 1015–1×1021 1.12 2.8×1019 1.04 × 1019 4.05 1 × 1014 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
9.66 15 2 1 × 1015–1 × 1021 1 × 1015–1 × 1021 1.7 2.5 × 1020 2.5 × 1020 3.92 1 × 1021 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
Capture cross section for donors states, e, h(cm2)
a
Calculated according to experimentally determined effective carrier masses from Ref. Madelung (2004).
where λ and λ′ are the lengths of microscopic average on each side of the interface. Then the difference in potential across the heterostructure can be defined as
importance of the orientation relationship and atomic arrangement at the Si/Mg2Si interface, so as to permit practical assessment of band offset at the heterojunctions. The heterojunction model shown in Fig. 3 is built through full structural relaxation in DFT calculation using the GGA functional. The resultant stable structure is of fundamentally coherent lattice matching between the Mg2Si (1 1 0) and Si (1 1 1) planes. A vacuum layer over 1 nm is used to avoid interaction between images of the coupled Si/Mg2Si slabs. For the calculation of energy band structures, the non-local effect in the exchange-correlation functional is considered using the Heyd, Scuseria and Enrzerhof (HSE) hybrid functional (Heyd et al., 2003). A screen parameter w = 0.2 is used to produce reliable band gap values for both Si and Mg2Si.In order to determine the average potentials of a hetero-structure made of two bulk materials, the microscopic average potential can be considered in pseudopotential calculation by averaging the sum of the Hartree, exchange-correlation, and ionic potentials parallel to the interface, which is defined as Vtot (z) , a one-dimensional quantity along the perpendicular direction to the interface. The macroscopic average can then be defined as (Baldereschi et al., 1988; AlAllak and Clark, 2001)
Vtot (z) =
1 λλ′
z+λ/2
z′+ λ′/2
∫z−λ/2 ∫z′−λ′/2
Vtot (z″)dz″dz′,
ΔVtot = Vtot Si (z)−Vtot Mg 2Si (z).
(2)
The offset in the macroscopic average potentials, ΔVtot is however inadequate to describe the behaviour in moving electrons across the heterojunction, as the maximum of valence bands (VBM) of bulk materials for each side of interface (E VBMSi and E VBMMg2Si ) should be taken into account. After considering the valence band, the corrected band offset is given as
ΔE v = (VtotSi + E VBMSi)−(VtotMg2Si + E VBMMg2Si) = (VtotSi−VtotMg2Si) + (E VBMSi−E VBMMg2Si) = ΔVtot + ΔEVBM
(3)
where ΔEVBM is the difference in the energies of the valence-band maxima of the bulk Si and Mg2Si. Here we follow the convention in assigning signs to the valence and conduction band offset with respect to Si, such that downward offset is positive for ΔEC but positive forΔEV due to different signs for electrons and holes. The band offset at the CBM is defined as ΔEc = χMg2Si - χSi (the difference in the electron affinities between Mg2Si and Si). The band offset at the VBM (ΔEV ) is then related to the band gaps (Eg ) of the two materials as
(1)
Fig. 3. (a) The atomic configurations and lattice matching on the interface of heterostructure composed by 6 units of Mg2Si(1 1 0) and 7 units of Si(1 1 1), (b) the relaxed configurations of the Mg2Si/Si heterostructure.
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Fig. 4. Schematic summary of a band structure line-up at the heterojunction from DFT calculation.
ΔEV = Eg (Si)−Eg (Mg2 Si)−ΔEC . According to Eqs. (2) and (3), it is predicted by DFT calculation that the bottom of the valence band for Si is 0.35 eV higher than that for Mg2Si, with resultant data summarised in Fig. 4. This lies between the experimentally reported offset values at the valence bands with the same sign as that from Ref. Sekino et al. (2011). This is attributable to the coupling of the Mg2Si (1 1 0) surface with mixed Mg and Si atoms to the pure Si phase, which contributes to induce some enrichment of Si over the Mg2Si surface. Such surface enrichment in Si is to increase the electron affinity of Mg2Si surface, being consistent with the theoretical outcome of Ref. Qin and Wang (2015). Such theoretical observation is of fundamental implications, indicating a potential route in tuning the band offset, both value and signs, via interfacial adjustment of Mg2Si compositions. While the standard band offset at the VBM, ΔE v , is moderate (−0.35 eV), the offset at the conduction band minimum (CBM), ΔEC , is considerably larger. The sum of the valence and conduction band offset equals to the difference in band gap values of the two materials, i.e. ΔEV + ΔEC = Eg (Si)−Eg (Mg2 Si) . Taking into account of the average band gap values of 1.1 eV and 0.7 eV for bulk Si and Mg2Si phases respectively, we have the Si conduction band being 0.75 eV above that of Mg2Si. Interestingly, the experimental work of Ref. Atanassov and Baleva (2007) was indicative of capability in significant widening of the band gap of Mg2Si nanocrystals embedded in Si, enlarging to 1.01–1.07 eV in 4–6 nm nanocrystal, possibly owing to straining and quantum confinement. Such enlargement in Mg2Si band gap through nanostructural engineering could induce significant reduction of ΔEC down to 0.38 eV above the Si VBM. Also, chemical enrichment of Mg at the heterojunction is likely to reduce the electron affinity of Mg2Si, thus helping eliminate the valence band offset or even change its sign, which could lead to radical reduction of the offset at the conduction band (e.g. about 0.4 eV when valence offset is fully eliminated, and 0.3 eV when valence offset is +0.1 eV instead). In view of such considerable band offsets, it is therefore necessary to clarify the effect of Mg2Si electron affinity on the performance of Si(p)/ Mg2Si(i)/Si(n) heterojunction solar cells (At this stage, we focus on the
Fig. 5. The effects of conduction band offset ΔEc on the performance of Si(p)/Mg2Si(i)/Si (n) PV cells, ΔEc = χMg2Si - χSi (the difference in the electron affinities between Mg2Si and Si). The band offset at the top of the valence band is ΔEV = Eg (Si)−Eg (Mg2 Si)−ΔEC .
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recombine and thus reducing the establishment of a built-in voltage between the heterojunctions at both sides of the main optical absorbing material, the i-Mg2Si in the middle. One can see from Fig. 6(b), the smaller band offset barrier due to the 0.32 eV band offset is not to affect the Jsc, Voc, FF, and the Eff significantly, owing to evident slope in the bands within the optical absorber to help separate photo-induced electron-hole pairs. Fig. 7 demonstrates the typical aligned energy band diagrams at various doping concentrations, with band offset being set to be 0.32 eV. The sign of such an offset is consistent with the current theoretical prediction, with the value being experimentally achievable via nanostructural engineering of the silicide material. In line with established doping principles, the effect in reducing the space charge region of the band barriers through higher level of doping in Si leads to weakened offset peak with narrower peak width at Mg2Si(i)/Si(n) heterojunction. On the other hand, one notes from Fig. 7 that the slope in the energy band within the silicide layer does not change evidently with respect to the change in carrier concentrations in the Si layers, so long as the band barriers at the heterojunctions are not too big to hinder the separation of photo-induced carrier pairs. The dominant effect of increasing doping in Si is in mitigating the detrimental effect of band barriers. The other major effect, as shown in Fig. 5, is that higher doping levels in Si layers at both sides bring about evident enhancement in the open-circuit voltage. This is owing to shifting in the Fermi level closer to conduction band minimum in the Si(n) and the valence band maximum in the Si(p), leading to increased potential difference between the two heterojunctions. On the basis of the optimised doping level of 5 × 1019 cm−3 for both the n- and p-doped Si layers, one can examine the role of the Si layer thicknesses on the cell performance, as shown in Fig. 8. When the p-layer thickness increases from 10 nm to 600 nm, Jsc falls nearly linearly from 42.670 mA/cm2 to 37.755 mA/cm2. This is not hard to understand, since the depletion region for the separation of the photogenerated electron-hole pairs are largely confined within the intrinsic silicide layer, owing to the rather high doping level in the Si layers at both sides. The front Si(p) layer therefore will largely function as a window to let light through to the active silicide layer for useful PV effect, so that thicker Si(p) layer leads to loss of light due to unwanted absorption, thus resulting in reduction of Jsc together with Eff. On the other hand, the back Si(n) layer does not affect the Jsc. The effect of the Si layer thicknesses on the Voc reaches the plateau top value at about 100 nm, the Si(p) layer being more effective than the Si(n) layer. When the effect of the front p-Si thickness is simulated, the back n-Si thickness is set to be 100 nm (optimised choice according to Eff in Fig. 8). Likewise, when the effect of back n-Si thickness is simulated, the front p-Si thickness is 50 nm, in order to allow more light into the silicide. This gives rise to some slight difference in resultant Voc. Overall, the recommended thicknesses for the Si layers are within the range of 50–200 nm. As the main optical absorber layer, the thickness of intrinsic Mg2Si is dominant on Jsc, owing to the need in full optical absorption with adequate layer thickness, Fig. 9 (On the basis of the optimised doping level of 5 × 1019 cm−3 for Si, and the optimised thicknesses of 50 nm for the p-Si layer and 100 nm for the n-Si layer). The slight increase in Voc is attributed to the evidently enhanced Jsc. Further increase in the thickness leads to widening of depletion region in the silicide layer, which gives rise to enhanced carrier recombination and dark saturation current, so that both Voc and FF deteriorate while Jsc is saturated. The overall efficiency is then largely determined by Jsc, which increases significantly with Mg2Si thickness, resulting in sustaining improvement in Eff to 22.254% at 2000 nm in the thickness of the optical absorber layer. Further increase in thickness is not seen to have significant benefit in the Eff, as any slight enhancement in Jsc is offset by the loss in FF.
band offset effect without considering carrier interaction with any defect states). Fig. 5 shows the effect of Mg2Si electron affinity on the performance of Si(p)/Mg2Si(i)/Si(n) solar cells, with the doping concentration of p-type Si (NA) and n-type Si (ND) set to be the same value in the range from 1 × 1016 cm−3 to 5 × 1019 cm−3. The thickness for p, i and n layers are 50 nm, 2000 nm and 100 nm correspondingly, which are the optimised parameters to be discussed later, other parameters are kept the same as listed in Table 1. It is apparent that the ΔEc in the range of −0.45 to 0.7 eV has rather limited influence on Voc of the sandwiched solar cell. For the p-i-n heterojunction solar cells, Voc is mainly determined by the built-in voltage of the p-layer and n-layer after energy band alignment, which is determined by doping concentrations at both sides and as well as the band barriers after energy band alignment. This is because the band offsets within such a range have rather moderate effect on the overall built-in voltage difference between the p- and n-layers of Si at both sides of the silicide, as the spikes or valleys due to such offsets are well within the potential ranges defined by the doping conditions within the Si materials. Consequently, the Voc is largely determined by the doping levels in the Si layers, being gradually enhanced with increasing doping concentration from the usual range between 1016 and 5 × 1019 cm−3. On the other hand, the existence of band barriers due to the band offsets do exert significant effect on charge transport through the devices, as is characterised in the short-circuit current. At low doping concentration, Jsc decreases significantly when the band offset is lower than a negative threshold or higher than a positive threshold, leading to evident deterioration of the efficiency. As is shown, such thresholds of band offset are affected by the doping concentration of Si, with higher doping concentrations in Si layers reducing their effect. Fundamentally, higher doping in the Si material helps to confine the band barriers within the silicide material at the heterojunctions, leading to reduced barrier thickness to help transport of charged carriers through them. When the doping concentration is as high as 5 × 1019 cm−3, the band offset effect in reduction of Jsc is apparently overcome in the test range from −0.45 to 0.7 eV. This is in line with engineering practice in reducing the offset effect in heterojunction devices, with increased doping to help eliminating or reducing band barriers at the heterojunctions. Fill factor (FF) is generally affected by the series resistance and shunt resistance of the solar cell, wherein the series resistance is detrimentally impacted by the band barriers. For p-i-n structure, the band offsets and therefore the series resistances at p-i interface and i-n interface have different trends of variation against ΔEc, thus resulting in valleys in the FF when the combined offset effects are maximum. Apparently, higher doping in Si helps to reduce the band barriers and hence promote FF. This is in line with the aligned energy band diagrams at varied band offsets and doping levels in Si, as shown in Fig. 6(a–c) for some band diagrams under solar illumination, with doping concentration of p-type and n-type Si layers both set to a moderate level of 1 × 1016 cm−3 to reveal the offset effect. Considering photo induced carriers in the cells are the same, it is reasonable to attribute the deterioration of Jsc to severe carrier recombination in Mg2Si layer and near the interfaces, as seen from Fig. 6(d), when the junction barriers at either the p-Si side or the n-Si side is too large to permit the separation of electron-hole pairs. When the band offset is −0.45 eV, apparent spiking barriers appear in the valence band at the Si(p)/Mg2Si(i) interface, which will reflect holes and hinder their transport from i-Mg2Si to p-Si. On the other hand, a positive band offset leads to barriers in the conduction band at the Mg2Si/Si(n) interface, thus hinders electrons from transporting to the electrode and force them to recombine with holes in i-Mg2Si. It is worth pointing out that large band offset barriers at either side lead to flattened potential in the Mg2Si optical absorber. This is obvious through comparing the slops of the bands under illumination in Fig. 6(a–c), such that the band slope for an offset of 0.32 eV is steeper than that with an offset of −0.45 eV or 0.65 eV. Large barriers either for holes or electrons, Fig. 6(a,c), would hinder the separation of photoinduced electron-hole pairs in the silicide material, forcing them to 658
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Fig. 6. (a) Band diagrams with different band offsets, (b) total recombination rate versus position, under solar illumination, NA = ND = 1 × 1016 cm−3.
Fig. 7. Band diagrams for different doping concentration in Si, at a conduction band offset of 0.32 eV.
3.2. Cell architecture Fig. 10(a) compares the illuminated current density-voltage (J-V) curves of the optimised p-i-n heterojunction Si/Mg2Si/Si cell and single junction cells, wherein n- or p-doping for Mg2Si can be achieved via specific impurity incorporation (Han and Shao, 2012; Akasaka et al., 2008; Udono et al., 2013; Tamura et al., 2007). For comparison, the doping levels for n- or p-doped materials are all set to be 5 × 1019 cm−3, and the detailed thicknesses for each function layer are summarized in Table 2. The benefit of the p-i-n junction cell is remarkable in enhancing both Voc and Jsc, particularly in the former due to the
Fig. 8. The thickness effects of p- and n-layers of Si on the performance of Si(p)/Mg2Si(i)/ Si(n) PV cells.
utilisation of a wider gap Si(p) to promote the overall built-in potential over the cell (Gao et al., 2011; Zhu et al., 2013). For example, using Mg2Si as the optical absorber, the highest Voc for the single-junction cells is 0.410 V with the structure of Si(p)/Mg2Si(n), which is less than two thirds of the 0.654 V value from the Si(p)/Mg2Si(i)/Si(n) cell. Therefore, Eff achieved by single-junction cells are rather low due to 659
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Table 2 Performance of simulated PV cells under illumination. Structure
Thickness(μm)
Voc (V)
Jsc (mA/ cm2)
FF
Eff (%)
Mg2Si(n)/Mg2Si(p) Si(n)/Mg2Si(p) Si(p)/Mg2Si(n) Si(p)/Mg2Si(i)/Si(n) Si(n)/Mg2Si(i)/Si(p) Si(p)/Si(i)/Si(n) a-Si(p)/Mg2Si(i)/aSi(n)
0.05/2.0 0.05/2.0 0.05/2.0 0.05/2.0/0.1 0.1/2.0/0.05 0.05/200/0.1 0.05/2.0/0.1
0.297 0.353 0.410 0.654 0.654 0.678 0.730
29.041 33.572 33.527 41.981 41.365 38.370 41.463
0.716 0.749 0.772 0.810 0.810 0.834 0.754
6.178 8.872 10.613 22.254 21.905 21.695 22.828
Fig. 9. Effect of Mg2Si layer thickness on the performance of Si(p)/Mg2Si(i)/Si(n) PV cells.
low Voc, as shown in Table 2: 6.178% for Mg2Si(n)/Mg2Si(p), 8.872% for Si(n)/Mg2Si(p) and 10.613% for Si(p)/Mg2Si(n). With regard to p-i-n heterojunction PV cells, both front and back illumination give rise to similar efficiency of 22.254% and 21.905% (emboldened in Table 2). It is worth stressing that the proposed p-i-n heterojunction structure with total thickness of 2.15 μm has comparable Voc, higher Jsc as well as Eff to those of Si solar cells of 200.15 μm as (highlighted in itallic in Table 2) shown in Table 2, suggesting that replacing Si by Mg2Si as optical absorber can decrease the thickness of solar cells radically for about a hundred times and thereby reduce material cost significantly (considering that Mg is a lot cheaper than Si). By replacing crystalline Si with amorphous Si of larger band gap, the Voc can be enhanced further to 0.730 V. It is worth pointing out that the advantage of the p-i-n cells over crystalline Si cells is analysed here on the basis of simple planar devices, without consideration of more sophisticated device designs such as those adopting optical trapping technics to enhance efficiency at reduced thickness of optical absorbers.
Fig. 11. The effect of deep-level defect states on the performance of the Si(p)/Mg2Si(i)/Si (n) cells.
reduced via adequate annealing, due to their higher formation energy with respect to the interstitial Mg state. Processing materials under a Siricher condition is helpful to reduce donor states from the interstitial Mg. While shallow defect states provide mobile carriers, deep defect states will act as recombination centres to trap photo-induced carriers. Here, both donor-like and acceptor-like defect levels in Mg2Si are studied respectively with defect state density ranging from 1 × 1015 cm−3 to 5 × 1017 cm−3, with the assumption of Gaussian like defect levels with peak energy located at 0.1 eV below the conduction band or above
3.3. Effect of defects Defects are well known detrimental factors for solar cells. The Mg2Si is a very interesting semiconductor material, for which natural defects tend to be interstitial Mg that are fortunately the origin for effective ntype conductivity owing to associated shallow donor states (Han and Shao, 2015). Other defects such as vacancies in the Si sites can be
Fig. 10. Illuminated J-V curves of PV cells with different structures.
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which is much higher than the intrinsic carrier density (∼1014 cm−3) (Madelung, 2004) in the silicide material at room temperature. The recombination is higher next to the front junction due to higher local intensity of light. As to the potential profile in the silicide layer, it is seen that higher defect concentration leads to flattened profile, Fig. 12(a), with associated weakening of the electric field, Fig. 12(b). It is understandable that low defect density below 1013 cm−1 does not considerably impact on either the depletion region in terms of either potential field or recombination rate. Although the AMPS code does not take into account of the interface recombination loss, one can still investigate the role of interface defects by artificially inserting between Mg2Si/Si a very thin layer containing a large number of defect states distributed evenly in the band gap, so as to simulate a more realistic device (Liu et al., 2014). Fig. 13(a) shows the simulated results for Voc and Eff as a function of the density of such interfacial traps. In this case, the two interfacial trap layers between Si and Mg2Si are set to be 4 nm in thickness, with the donor/acceptor switching-over energy corresponding to the mid-gap energy of Mg2Si. Electron and hole capture cross sections are set to be the same as those in band tails of the optical absorber. Apparently, both Voc and Eff would suffer from high carrier recombination rates near the interfaces as seen from Fig. 13(b), suggesting the importance of interfacial quality preferably with good epitaxial orientation relationship between Si and Mg2Si. Fortunately, coherent lattice match can exist between the two phases, as is shown in the DFT simulated relaxed structural model, Fig. 3. Furthermore, such an epitaxial relationship was experimentally realised (Wang et al., 2007). An additional and yet important advantage in the proposed Si(p)-Mg2Si(i)-Si(n) cell architecture is that it is not necessary to dope the Mg2Si material. This helps to avoid the difficulty in doping the silicide into p-type, as the natural tendency in forming interstitial Mg and associated donor states offers killers to doped holes. Such a fundamental problem in p-type doping of Mg2Si makes it necessary to rely on heavier p-type doping and associated coupling with native defects, leading to significantly reduced hole mobility (Han and Shao, 2015).
Fig. 12. (a) Equilibrium band diagrams, (b) electric field, (c) recombination profile versus position for the Si(p)/Mg2Si(i)/Si(n) PV cells.
the valence band. The standard deviation of the dopant level is 0.01 eV, and electron and hole capture cross sections are the same as those in band tails. The defect effects on the performance of the typical Si(p)/ Mg2Si(i)/Si(n) PV cell as a function of defect density are presented in Fig. 11. It is seen that both donor-like and acceptor-like defects have similar influence on the solar cell performance that Voc deteriorates severely from 0.652 V to 0.357 V when the defect density increases from 1 × 1012 cm−3 to 5 × 1017 cm−3, resulting in significant degradation of Eff to 9.954% for donor like defects and 11.018% for acceptor like defects. In addition to the effect on carrier recombination rate, the presence of deep-level defects, either acceptor like or donor like, contributes to deteriorate the potential field in the optical absorber. Generally speaking, such effect would be significant only if the defect density is comparable to or higher than the doping concentration in the absorber layer. Taking acceptor like defects as example, the equilibrium band diagrams and acceptor recombination rate versus position are plotted in Fig. 12(a,c). It is evident that the whole recombination rate in Mg2Si shoots up rapidly with the increase of defect density up to 1017 cm−3,
4. Conclusions First principle calculations suggest that fundamentally the Mg2Si phase can form coherent interface with Si, thus making it easier to engineer high quality interface for efficient solar cells. While the valence band offset is moderate, the offset at the conduction band can be significant. This could be mitigated either through nano-structural engineering of the silicide phase or adjustment of junction composition to change the sign of the valence band offset.
Fig. 13. (a) Voc and Eff against interface trap density, (b) recombination profile versus position, for PV cells with different interfacial defects.
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C 3, 530–537. Heyd, J., Scuseria, G.E., Ernzerhof, M., 2003. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215. Kato, T., Sago, Y., Fujiwara, H., 2011. Optoelectronic properties of Mg2Si semiconducting layers with high absorption coefficients. J. Appl. Phys. 110, 063723. Kosyachenko, L.A., 2011. Solar Cells Thin Film Technologies. InTech. Liu, F., Zhu, J., Wei, J., Li, Y., Lv, M., Yang, S., Zhang, B., Yao, J., Dai, S., 2014. Numerical simulation: toward the design of high-efficiency planar perovskite solar cells. Appl. Phys. Lett. 104, 253508. Madelung, O., 2004. Semiconductors: Data Handbook. Springer. Messenger, R.A., Ventre, J., 2004. Photovoltaic Systems Engineering. CRC Press LLC. Ok, Y.W., Kang, M.G., Kim, D., Lee, J.C., Yoon, K.H., 2009. Understanding of a-Si:H(p)/cSi(n) heterojunction solar cell through analysis of cells with point-contacted p/n junction. Curr. Appl. Phys. 9, 1186–1190. Oladejia, I.O., Chowa, L., Ferekidesb, C.S., Viswanathanb, V., Zhao, Z., 2000. Metal/ CdTe/CdS/Cd1−xZnxS/TCO/glass: a new CdTe thin film solar cell structure. Sol. Energy Mater. Sol. Cells 61, 203–211. Qin, Y., Wang, S., 2015. Ab-initio study of the role of Mg2Si and Al2CuMg phases in electrochemical corrosion of Al alloys. J. Electrochem. Soc. 162, 503–508. Scouler, W.J., 1969. Optical properties of Mg2Si, Mg2Ge, and Mg2Sn from 0.6 to 11.0 eV at 77 K. Phys. Rev. 178, 1353–1357. Sekino, K., Midonoya, M., Udono, H., Yamada, Y., 2011. Preparation of Schottky contacts on n-type Mg2Si single crystalline substrate. Phys. Proc. 11, 171–173. Shah, A.V., Meier, J., Vallat-Sauvain, E., Wyrsch, N., Kroll, U., Droz, C., Graf, U., 2003. Material and solar cell research in microcrystalline silicon. Sol. Energy Mater. Sol. Cells 78, 469–491. Shah, A.V., Schade, H., Vanecek, M., Meier, J., Vallat-Sauvain, E., Wyrsch, N., Kroll, U., Droz, C., Bailat, J., 2004. Thin film silicon solar cell technology. Prog. Thin-Films Sol. Cells 12, 113–142. Tamura, D., Nagai, R., Sugimoto, K., Udono, H., Kikuma, I., Tajima, H., Ohsugi, I.J., 2007. Melt growth and characterization of Mg2Si bulk crystals. Thin Solid Films 515, 8272–8276. Udono, H., Yamanaka, Y., Uchikoshi, M., Isshiki, M., 2013. Infrared photoresponse from pn-junction Mg2Si diodes fabricated by thermal diffusion. J. Phys. Chem. Solids 74, 311–314. Vantomme, A., Mahan, J.E., Langouche, G., Becker, J.P., Bael, M.V., Temst, K., Haesendonck, C.V., 1997. Thin film growth of semiconducting Mg2Si by codeposition. Appl. Phys. Lett. 70, 1086–1088. Vantomme, A., Langouche, G., Mahan, J.E., Becker, J.P., 2000. Growth mechanism and optical properties of semiconducting Mg2Si thin films. Microelectron. Eng. 50, 237–242. Wang, Y., Wang, X.N., Mei, Z.X., Du, X.L., Zou, J., Jia, J.F., Xue, Q.K., Zhang, X.N., Zhang, Z., 2007. Epitaxial orientation of Mg2Si(110) thin film on Si(111) substrate. J. Appl. Phys. 102, 126102. Zhu, L., Shao, G., Luo, J., 2013. Numerical study of metal oxide hetero-junction solar cells with defects and interface states. Semicond. Sci. Technol. 28, 055004.
Numerical simulation has been carried out to study the feasibility in designing high-efficiency thin film solar cells based on the low-gap semiconducting silicide Mg2Si, which is a cheap material of vast natural resources. It is found that the Si(p)/Mg2Si(i)/Si(n) architecture offers great benefit in achieving large short circuit current and high open circuit voltage at the same time. The optimised Si(p)/Mg2Si(i)/Si(n) cell of only 2.15 μm in total thickness has potential efficiency ravelling that of crystalline Si cells about 100 times thicker, Acknowledgments This work is partially supported by the NSFC (No. 11504277, 11174256, 91233101), the Natural Science Foundation of Hubei Province (2015CFB229), the Zhengzhou University, and the Zhengzhou Materials Genome Institute. References Akasaka, M., Iida, T., Yamanaka, K., Matsumoto, A., Takanashi, Y., Imai, T., Hamada, N., 2008. The thermoelectric properties of bulk crystalline n- and p-type Mg2Si prepared by the vertical Bridgman method. J. Appl. Phys. 104, 013703. Al-Allak, H.M., Clark, S.J., 2001. Valence-band offset of the lattice-matched β-FeSi2(100)/ Si(001) heterostructure. Phys. Rev. B 63, 033311. Atanassov, A., Baleva, M., 2007. On the band diagram of Mg2Si/Si heterojunction as deduced from optical constants dispersions. Thin Solid Films 515, 3046–3051. Au-Yang, M.Y., Cohen, M.L., 1969. Electronic structure and pptical properties of Mg2Si, Mg2Ge, and Mg2Sn. Phys. Rev. 178, 1358–1364. Avrutin, V., Izyumskaya, N., Morko, H., 2011. Semiconductor solar cells: recent progress in terrestrial applications. Superlatt. Microstruct. 49, 337–364. Baldereschi, A., Baroni, S., Resta, R., 1988. Band offsets in lattice-matched heterojunctions: a model and first-principles calculations for GaAs/AlAs. Phys. Rev. Lett. 61, 734. Chaure, N.B., Samantilleke, A.P., Burton, R.P., Young, J., Dharmadasa, I.M., 2005. Electrodeposition of p+, p, i, n and n+-type copper indium gallium diselenide for development of multilayer thin film solar cells. Thin Solid Films 472, 212–216. Gao, Y., Liu, H.W., Lin, Y., Shao, G., 2011. Computational design of high efficiency FeSi2 thin film solar cells. Thin Solid Films 24, 8490–8495. Han, X., Shao, G., 2012. Origin of n-type conductivity of Sn-doped Mg2Si from first principles. J. Appl. Phys. 112, 013715. Han, X., Shao, G., 2015. Interplay between Ag and interstitial Mg on the p-type characteristics of Ag-doped Mg2Si: challenges for high hole conductivity. J. Mater. Chem.
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Simulation of planar Si/Mg2Si/Si p-i-n heterojunction solar cells for high efficiency Quanrong Denga,b,1, Zhuo Wanga,c,1, Shenggao Wangb, Guosheng Shaoa, a b c
MARK
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State Centre for International Cooperation on Designer Low-Carbon & Environmental Materials (CDLCEM), Zhengzhou University, Zhengzhou 450001, China Hubei Key Laboratory of Plasma Chemistry and Advanced Materials, Wuhan Institute of Technology, Wuhan 430073, China School of Physics and Electronic Technology, Hubei University, Wuhan 430062, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Silicide solar cells Mg2Si Theoretical modelling p-i-n heterojunctions
A novel Si(p)/Mg2Si(i)/Si(n) PV cell architecture is proposed on the basis of numerical simulation and ab intio calculation in the framework of the density functional theory (DFT). First-principles calculations on the basis of the relaxed Mg2Si(1 1 0)/Si(1 1 1) heterojunction suggest that the valence band offset is about −0.35 eV with respect to the valence band maximum (VBM) of Si. The effect and corresponding mechanism of band offsets, doping concentration, layer thickness, as well as defect states on the performance of solar cells have been studied and discussed in detail. The optimised ideal Si(p)/Mg2Si(i)/Si(n) heterojunction solar cell with a total thickness of 2.15 μm of active materials is predicted to provide a large open-circuit voltage of 0.654 V and a high conversion efficiency up to 22.254%, which is much higher than single junction cells and rivals the performance of crystalline silicon solar cells over 100 times thicker. This work demonstrates great potential to develop Mg2Si based low-cost and environmentally friendly solar cells on the ground of the well-established silicon technology.
1. Introduction Photovoltaic (PV) devices have been extensively investigated and exploited to address worldwide energy crisis and associated environmental problems due to the dependence on fossil fuel. Current PV market is mainly dominated by silicon solar cells, including bulk crystalline silicon (c-Si) solar cells and thin film amorphous silicon (a-Si) solar cells. However, the low optical absorption coefficient of crystalline silicon makes it necessary for silicon solar cells to be rather thick, generally hundreds of microns and thus relatively costing in materials consumption (Avrutin et al., 2011). Besides, photo-generated carriers have to travel for a long distance to reach the electrodes, so that the material has to be of a very high purity and of high crystalline perfection to avoid carrier recombination and scattering, resulting in high manufacturing cost with extensive energy drainage. Although a-Si offers a much higher optical absorption coefficient that a layer about 1 μm thick can absorb sufficient sunlight to enable efficient solar cell operation, the high defect state density in amorphous phase limits the typical carrier motilities and diffusion lengths, resulting in much lower efficiency (Kosyachenko, 2011). Moreover, a-Si solar cells also suffer from the problem of performance degradation due to poor material stability (Shah et al., 2003, 2004).
⁎
1
In order to achieve high energy conversion efficiency at low cost, researchers around the world have endeavoured to exploit new semiconducting materials with high optical absorption coefficients, suitable band gap and electrical properties. Semiconducting Mg2Si is recognized as an attractive alternative on account of its reported narrow band gap ranging from 0.66 to 0.80 eV (Scouler, 1969; Au-Yang and Cohen, 1969; Kato et al., 2011; Tamura et al., 2007), high optical absorption coefficient over 105 cm−1 at 500 nm, irrespective of its indirect bandgap, and high carrier mobility (Au-Yang and Cohen, 1969), which makes it suitable for light absorption layer in solar cells. Mg and Si are abundant in natural sources and environmentally friendly. This makes Mg2Si quite promising in enabling thinner solar cells to reduce materials cost, while maintaining the benefit of a-Si solar cells particularly for flexible applications. Considering that the narrow band gap of Mg2Si could result in lowered open circuit voltage (Voc), it is envisaged to be necessary in combining Mg2Si and Si films into p-i-n heterojunctions, in order to improve the Voc while maintaining large short circuit current (Jsc) on the basis of recent theoretical work (Gao et al., 2011; Zhu et al., 2013). In addition, Mg2Si and Si are in thermodynamic equilibrium, so that good and clean interface of the two materials can be readily achieved. This helps to realize novel practical solar cells using sustainable resources (Vantomme et al., 1997, 2000; Wang et al., 2007).
Corresponding author. E-mail address: [email protected] (G. Shao). Authors with equivalent contribution.
http://dx.doi.org/10.1016/j.solener.2017.10.028 Received 10 January 2017; Received in revised form 30 September 2017; Accepted 9 October 2017 0038-092X/ © 2017 Elsevier Ltd. All rights reserved.
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This work is dedicated to carry out systematic theoretical simulation and thus optimise the architecture of Mg2Si based solar cells for high energy conversion efficiency. The input materials parameters are largely based on available experimental data. First principle calculation is carried out to assess the electronic structure and band offset at the heterojunction, so as to provide reliable insight essential for improved accuracy of numerical simulation. It will be demonstrated that on the basis of established Si technology in fine-tuning n- and p-type doping levels in Si, thin films Si/Mg2Si/Si p-i-n heterojunction solar cells only 2.15 µm in total thickness could deliver high energy conversion efficiency ravelling that of p-i-n Si solar cells about 100 times thicker.
2. Methods First principles simulation of the heterojunction between Mg2Si and Si is carried out in the framework of the density functional theory (DFT), using the Vienna Ab initio Simulation Package (VASP) with the ionic potentials including the effect of core electrons being described by the projector augmented wave (PAW) method. On the basis of extensive test in recent DFT work (Han and Shao, 2015), the Brillouin zone integration is performed on well-converged Monkhost–Pack k-point grids, using 8 × 1 × 1 K-mesh for the heterojunction. A plane-wave energy cutoff of 500 eV is used in all calculations. All structures are geometrically relaxed until the total force on each ion was reduced to be less than 0.01 eV Å−1. Non-local effect in the exchange-correlation functional is considered for band structure calculations. The AMPS-1D (Analysis of Microelectronic and Photonic Structures,) code, which solves one dimensional dipolar problems according to Poisson’s and continuity equations, is used for numerical modelling under the standard solar spectrum illumination (AM1.5). The proposed device consists of sequentially stacked layers of Si(p)/Mg2Si (i)/Si(n), wherein a middle layer of intrinsic Mg2Si is used as the main optical absorption material, Fig. 1. Both the p- and n-type silicon films, with wider band gap than that for Mg2Si, can act as windows for the solar spectrum to be harvested by the Mg2Si absorber. Herein, silicon layers could be both crystalline (c-Si) and amorphous (a-Si), which can be readily doped to adequate carrier concentrations, using the established Si technology. For simplicity in description, here in this work Si refers to c-Si unless otherwise defined. Initially, such sandwiched architecture is envisaged to be useful not only in avoiding the difficulty in doping Mg2Si to adequate carrier concentration for p-type (Han and Shao, 2015), but also in making use of a p-type material with wider gap to enhance the open-circuit voltage while maintaining large short-circuit current, as was demonstrated by our recent work that the Voc is promoted by using wider gap materials on both sides (Gao et al., 2011; Zhu et al., 2013). Experimentally, such p-i-n heterojunction structures were employed in the well-known a-Si/ c-Si/a-Si (Ok et al., 2009), CIGS (Chaure et al., 2005), and CdTe based solar cells (Oladejia et al., 2000). To clarify the effect of p-i-n heterojunctions, devices made of Si/Mg2Si heterojunction and Mg2Si/Mg2Si homojunction are also studied for comparison.Experimentally measured optical absorption spectra of c-Si, a-Si, and Mg2Si are used as input in this work are shown in Fig. 2 (Kato et al., 2011; Messenger and Ventre, 2004). The spectral response range for the quantification of the external quantum efficiency for device simulation is in line with the range for experimental optical data in Fig. 2, being 380–1600 nm.
Fig. 2. Optical absorption spectra of Mg2Si, c-Si and a-Si used in simulation.
Optical model for the photo-induced free charge populations (electrons and holes) in the Poisson’s equation are inscribed in the continuity equation, and readers are referred to Section 2.2 of the AMPS-1D User Manual for details (http://www.ampsmodeling.org/). In addition, the following assumptions are made between the valence band top Ev, the conduction band bottom Ec and the Fermi energy Ef at contacts: EfEv(p) = 0.1 eV and Ec(n)-Ef = 0.1 eV. Surface recombination speeds for holes and electrons at the front and back contacts are both set to be 1 × 107 cm s−1, and reflection for light impinging on front and back surfaces are ignored. In the simulated models, the energy distributed within the band gap contains mid-gap states and Urbach exponential tails coming out of both the conduction band and the valence band. The values of dielectric constant, carrier mobility, band gaps, Urbach band tails for silicon and Mg2Si are given according to reported data in literature, as listed in Table 1, wherein the effective conduction and valence band densities are calculated using effective masses from literature. For example, the effective conduction band density NC is related to the effective electron mass me∗ as, NC = 2{2πme∗ kT / h2} 2 , wherein T is absolute temperature, k and h are Boltzmann and Plank’s constant respectively. Furthermore, Gaussian like mid-gap defect states with different densities and distributions are introduced to assess their impact.
3. Results and discussion 3.1. Conduction band offset effect It has been recognized that the electron affinity (χ) of semiconductors determines the conduction band offsets in heterojunction solar cells, ΔEc (χMg2Si – χSi), and thus plays critical role on solar cell performance. However, the electron affinity of Mg2Si is still not well established. Through investigating the band diagram of the Mg2Si(n)/Si (n) heterojunction, the electron affinity of Mg2Si was determined to be 0.42 eV smaller than that of Si (Atanassov and Baleva, 2007), and thus the Mg2Si electron affinity is evaluated to be 3.59 eV. Taking the mean values of experimentally determined band gaps for bulk materials into account (1.1 eV for Si and 0.7 eV for Mg2Si), this leads to the valence band maximum (VBM) for Mg2Si being offset for 0.82 eV above that for Si. On the other hand, investigation on Schottky barrier height at Au/ Mg2Si(n) interface suggested a significantly bigger value of 4.61 eV for the electron affinity of Mg2Si, leading to an offset of 0.6 eV below the VBM of Si (Sekino et al., 2011). It is worth noting that the reported band offsets at the VBM are even opposite in signs. Theoretical calculation suggested that the work function of Mg2Si was in the range between 3.02 eV and 5.28 eV, which was dependent upon the exposed surfaces and terminating atoms, with surface containing more Si having bigger electron affinity (Qin and Wang, 2015). This indicates the great
Fig. 1. Schematic architecture of the p-i-n solar cell construction.
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Table 1 Simulation parameters for each layer, with available materials data taken from literature (Kato et al., 2011; Gao et al., 2011; Udono et al., 2013; Madelung, 2004). Parameters
Mg2Si
c-Si (Gao et al., 2011)
a-Si (Gao et al., 2011)
Relative permittivity Electron mobility (cm2 V−1 S−1) Hole mobility (cm2 V−1 S−1) Acceptor concentration (cm−3) Donor concentration (cm−3) Band gap (eV) Effective conduction band density (cm−3) Effective valence band density (cm−3) Electron affinity (eV) Band tail density of states (cm−3 eV−1) Characteristic energy for donor and acceptor like tails (eV) Capture cross section for acceptors states, e, h(cm2)
20 (Madelung, 2004) 550 (Madelung, 2004) 70 (Udono et al., 2013) 1 × 1014 1 × 1014 0.77 (Kato et al., 2011; Madelung, 2004) 7.8 × 1018a 2.06 × 1019a 4.37 1 × 1014 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
11.9 1350 500 1 × 1015–1 × 1021 1 × 1015–1×1021 1.12 2.8×1019 1.04 × 1019 4.05 1 × 1014 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
9.66 15 2 1 × 1015–1 × 1021 1 × 1015–1 × 1021 1.7 2.5 × 1020 2.5 × 1020 3.92 1 × 1021 0.01 1 × 10−17, 1 × 10−15 1 × 10−15, 1 × 10−17
Capture cross section for donors states, e, h(cm2)
a
Calculated according to experimentally determined effective carrier masses from Ref. Madelung (2004).
where λ and λ′ are the lengths of microscopic average on each side of the interface. Then the difference in potential across the heterostructure can be defined as
importance of the orientation relationship and atomic arrangement at the Si/Mg2Si interface, so as to permit practical assessment of band offset at the heterojunctions. The heterojunction model shown in Fig. 3 is built through full structural relaxation in DFT calculation using the GGA functional. The resultant stable structure is of fundamentally coherent lattice matching between the Mg2Si (1 1 0) and Si (1 1 1) planes. A vacuum layer over 1 nm is used to avoid interaction between images of the coupled Si/Mg2Si slabs. For the calculation of energy band structures, the non-local effect in the exchange-correlation functional is considered using the Heyd, Scuseria and Enrzerhof (HSE) hybrid functional (Heyd et al., 2003). A screen parameter w = 0.2 is used to produce reliable band gap values for both Si and Mg2Si.In order to determine the average potentials of a hetero-structure made of two bulk materials, the microscopic average potential can be considered in pseudopotential calculation by averaging the sum of the Hartree, exchange-correlation, and ionic potentials parallel to the interface, which is defined as Vtot (z) , a one-dimensional quantity along the perpendicular direction to the interface. The macroscopic average can then be defined as (Baldereschi et al., 1988; AlAllak and Clark, 2001)
Vtot (z) =
1 λλ′
z+λ/2
z′+ λ′/2
∫z−λ/2 ∫z′−λ′/2
Vtot (z″)dz″dz′,
ΔVtot = Vtot Si (z)−Vtot Mg 2Si (z).
(2)
The offset in the macroscopic average potentials, ΔVtot is however inadequate to describe the behaviour in moving electrons across the heterojunction, as the maximum of valence bands (VBM) of bulk materials for each side of interface (E VBMSi and E VBMMg2Si ) should be taken into account. After considering the valence band, the corrected band offset is given as
ΔE v = (VtotSi + E VBMSi)−(VtotMg2Si + E VBMMg2Si) = (VtotSi−VtotMg2Si) + (E VBMSi−E VBMMg2Si) = ΔVtot + ΔEVBM
(3)
where ΔEVBM is the difference in the energies of the valence-band maxima of the bulk Si and Mg2Si. Here we follow the convention in assigning signs to the valence and conduction band offset with respect to Si, such that downward offset is positive for ΔEC but positive forΔEV due to different signs for electrons and holes. The band offset at the CBM is defined as ΔEc = χMg2Si - χSi (the difference in the electron affinities between Mg2Si and Si). The band offset at the VBM (ΔEV ) is then related to the band gaps (Eg ) of the two materials as
(1)
Fig. 3. (a) The atomic configurations and lattice matching on the interface of heterostructure composed by 6 units of Mg2Si(1 1 0) and 7 units of Si(1 1 1), (b) the relaxed configurations of the Mg2Si/Si heterostructure.
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Fig. 4. Schematic summary of a band structure line-up at the heterojunction from DFT calculation.
ΔEV = Eg (Si)−Eg (Mg2 Si)−ΔEC . According to Eqs. (2) and (3), it is predicted by DFT calculation that the bottom of the valence band for Si is 0.35 eV higher than that for Mg2Si, with resultant data summarised in Fig. 4. This lies between the experimentally reported offset values at the valence bands with the same sign as that from Ref. Sekino et al. (2011). This is attributable to the coupling of the Mg2Si (1 1 0) surface with mixed Mg and Si atoms to the pure Si phase, which contributes to induce some enrichment of Si over the Mg2Si surface. Such surface enrichment in Si is to increase the electron affinity of Mg2Si surface, being consistent with the theoretical outcome of Ref. Qin and Wang (2015). Such theoretical observation is of fundamental implications, indicating a potential route in tuning the band offset, both value and signs, via interfacial adjustment of Mg2Si compositions. While the standard band offset at the VBM, ΔE v , is moderate (−0.35 eV), the offset at the conduction band minimum (CBM), ΔEC , is considerably larger. The sum of the valence and conduction band offset equals to the difference in band gap values of the two materials, i.e. ΔEV + ΔEC = Eg (Si)−Eg (Mg2 Si) . Taking into account of the average band gap values of 1.1 eV and 0.7 eV for bulk Si and Mg2Si phases respectively, we have the Si conduction band being 0.75 eV above that of Mg2Si. Interestingly, the experimental work of Ref. Atanassov and Baleva (2007) was indicative of capability in significant widening of the band gap of Mg2Si nanocrystals embedded in Si, enlarging to 1.01–1.07 eV in 4–6 nm nanocrystal, possibly owing to straining and quantum confinement. Such enlargement in Mg2Si band gap through nanostructural engineering could induce significant reduction of ΔEC down to 0.38 eV above the Si VBM. Also, chemical enrichment of Mg at the heterojunction is likely to reduce the electron affinity of Mg2Si, thus helping eliminate the valence band offset or even change its sign, which could lead to radical reduction of the offset at the conduction band (e.g. about 0.4 eV when valence offset is fully eliminated, and 0.3 eV when valence offset is +0.1 eV instead). In view of such considerable band offsets, it is therefore necessary to clarify the effect of Mg2Si electron affinity on the performance of Si(p)/ Mg2Si(i)/Si(n) heterojunction solar cells (At this stage, we focus on the
Fig. 5. The effects of conduction band offset ΔEc on the performance of Si(p)/Mg2Si(i)/Si (n) PV cells, ΔEc = χMg2Si - χSi (the difference in the electron affinities between Mg2Si and Si). The band offset at the top of the valence band is ΔEV = Eg (Si)−Eg (Mg2 Si)−ΔEC .
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recombine and thus reducing the establishment of a built-in voltage between the heterojunctions at both sides of the main optical absorbing material, the i-Mg2Si in the middle. One can see from Fig. 6(b), the smaller band offset barrier due to the 0.32 eV band offset is not to affect the Jsc, Voc, FF, and the Eff significantly, owing to evident slope in the bands within the optical absorber to help separate photo-induced electron-hole pairs. Fig. 7 demonstrates the typical aligned energy band diagrams at various doping concentrations, with band offset being set to be 0.32 eV. The sign of such an offset is consistent with the current theoretical prediction, with the value being experimentally achievable via nanostructural engineering of the silicide material. In line with established doping principles, the effect in reducing the space charge region of the band barriers through higher level of doping in Si leads to weakened offset peak with narrower peak width at Mg2Si(i)/Si(n) heterojunction. On the other hand, one notes from Fig. 7 that the slope in the energy band within the silicide layer does not change evidently with respect to the change in carrier concentrations in the Si layers, so long as the band barriers at the heterojunctions are not too big to hinder the separation of photo-induced carrier pairs. The dominant effect of increasing doping in Si is in mitigating the detrimental effect of band barriers. The other major effect, as shown in Fig. 5, is that higher doping levels in Si layers at both sides bring about evident enhancement in the open-circuit voltage. This is owing to shifting in the Fermi level closer to conduction band minimum in the Si(n) and the valence band maximum in the Si(p), leading to increased potential difference between the two heterojunctions. On the basis of the optimised doping level of 5 × 1019 cm−3 for both the n- and p-doped Si layers, one can examine the role of the Si layer thicknesses on the cell performance, as shown in Fig. 8. When the p-layer thickness increases from 10 nm to 600 nm, Jsc falls nearly linearly from 42.670 mA/cm2 to 37.755 mA/cm2. This is not hard to understand, since the depletion region for the separation of the photogenerated electron-hole pairs are largely confined within the intrinsic silicide layer, owing to the rather high doping level in the Si layers at both sides. The front Si(p) layer therefore will largely function as a window to let light through to the active silicide layer for useful PV effect, so that thicker Si(p) layer leads to loss of light due to unwanted absorption, thus resulting in reduction of Jsc together with Eff. On the other hand, the back Si(n) layer does not affect the Jsc. The effect of the Si layer thicknesses on the Voc reaches the plateau top value at about 100 nm, the Si(p) layer being more effective than the Si(n) layer. When the effect of the front p-Si thickness is simulated, the back n-Si thickness is set to be 100 nm (optimised choice according to Eff in Fig. 8). Likewise, when the effect of back n-Si thickness is simulated, the front p-Si thickness is 50 nm, in order to allow more light into the silicide. This gives rise to some slight difference in resultant Voc. Overall, the recommended thicknesses for the Si layers are within the range of 50–200 nm. As the main optical absorber layer, the thickness of intrinsic Mg2Si is dominant on Jsc, owing to the need in full optical absorption with adequate layer thickness, Fig. 9 (On the basis of the optimised doping level of 5 × 1019 cm−3 for Si, and the optimised thicknesses of 50 nm for the p-Si layer and 100 nm for the n-Si layer). The slight increase in Voc is attributed to the evidently enhanced Jsc. Further increase in the thickness leads to widening of depletion region in the silicide layer, which gives rise to enhanced carrier recombination and dark saturation current, so that both Voc and FF deteriorate while Jsc is saturated. The overall efficiency is then largely determined by Jsc, which increases significantly with Mg2Si thickness, resulting in sustaining improvement in Eff to 22.254% at 2000 nm in the thickness of the optical absorber layer. Further increase in thickness is not seen to have significant benefit in the Eff, as any slight enhancement in Jsc is offset by the loss in FF.
band offset effect without considering carrier interaction with any defect states). Fig. 5 shows the effect of Mg2Si electron affinity on the performance of Si(p)/Mg2Si(i)/Si(n) solar cells, with the doping concentration of p-type Si (NA) and n-type Si (ND) set to be the same value in the range from 1 × 1016 cm−3 to 5 × 1019 cm−3. The thickness for p, i and n layers are 50 nm, 2000 nm and 100 nm correspondingly, which are the optimised parameters to be discussed later, other parameters are kept the same as listed in Table 1. It is apparent that the ΔEc in the range of −0.45 to 0.7 eV has rather limited influence on Voc of the sandwiched solar cell. For the p-i-n heterojunction solar cells, Voc is mainly determined by the built-in voltage of the p-layer and n-layer after energy band alignment, which is determined by doping concentrations at both sides and as well as the band barriers after energy band alignment. This is because the band offsets within such a range have rather moderate effect on the overall built-in voltage difference between the p- and n-layers of Si at both sides of the silicide, as the spikes or valleys due to such offsets are well within the potential ranges defined by the doping conditions within the Si materials. Consequently, the Voc is largely determined by the doping levels in the Si layers, being gradually enhanced with increasing doping concentration from the usual range between 1016 and 5 × 1019 cm−3. On the other hand, the existence of band barriers due to the band offsets do exert significant effect on charge transport through the devices, as is characterised in the short-circuit current. At low doping concentration, Jsc decreases significantly when the band offset is lower than a negative threshold or higher than a positive threshold, leading to evident deterioration of the efficiency. As is shown, such thresholds of band offset are affected by the doping concentration of Si, with higher doping concentrations in Si layers reducing their effect. Fundamentally, higher doping in the Si material helps to confine the band barriers within the silicide material at the heterojunctions, leading to reduced barrier thickness to help transport of charged carriers through them. When the doping concentration is as high as 5 × 1019 cm−3, the band offset effect in reduction of Jsc is apparently overcome in the test range from −0.45 to 0.7 eV. This is in line with engineering practice in reducing the offset effect in heterojunction devices, with increased doping to help eliminating or reducing band barriers at the heterojunctions. Fill factor (FF) is generally affected by the series resistance and shunt resistance of the solar cell, wherein the series resistance is detrimentally impacted by the band barriers. For p-i-n structure, the band offsets and therefore the series resistances at p-i interface and i-n interface have different trends of variation against ΔEc, thus resulting in valleys in the FF when the combined offset effects are maximum. Apparently, higher doping in Si helps to reduce the band barriers and hence promote FF. This is in line with the aligned energy band diagrams at varied band offsets and doping levels in Si, as shown in Fig. 6(a–c) for some band diagrams under solar illumination, with doping concentration of p-type and n-type Si layers both set to a moderate level of 1 × 1016 cm−3 to reveal the offset effect. Considering photo induced carriers in the cells are the same, it is reasonable to attribute the deterioration of Jsc to severe carrier recombination in Mg2Si layer and near the interfaces, as seen from Fig. 6(d), when the junction barriers at either the p-Si side or the n-Si side is too large to permit the separation of electron-hole pairs. When the band offset is −0.45 eV, apparent spiking barriers appear in the valence band at the Si(p)/Mg2Si(i) interface, which will reflect holes and hinder their transport from i-Mg2Si to p-Si. On the other hand, a positive band offset leads to barriers in the conduction band at the Mg2Si/Si(n) interface, thus hinders electrons from transporting to the electrode and force them to recombine with holes in i-Mg2Si. It is worth pointing out that large band offset barriers at either side lead to flattened potential in the Mg2Si optical absorber. This is obvious through comparing the slops of the bands under illumination in Fig. 6(a–c), such that the band slope for an offset of 0.32 eV is steeper than that with an offset of −0.45 eV or 0.65 eV. Large barriers either for holes or electrons, Fig. 6(a,c), would hinder the separation of photoinduced electron-hole pairs in the silicide material, forcing them to 658
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Fig. 6. (a) Band diagrams with different band offsets, (b) total recombination rate versus position, under solar illumination, NA = ND = 1 × 1016 cm−3.
Fig. 7. Band diagrams for different doping concentration in Si, at a conduction band offset of 0.32 eV.
3.2. Cell architecture Fig. 10(a) compares the illuminated current density-voltage (J-V) curves of the optimised p-i-n heterojunction Si/Mg2Si/Si cell and single junction cells, wherein n- or p-doping for Mg2Si can be achieved via specific impurity incorporation (Han and Shao, 2012; Akasaka et al., 2008; Udono et al., 2013; Tamura et al., 2007). For comparison, the doping levels for n- or p-doped materials are all set to be 5 × 1019 cm−3, and the detailed thicknesses for each function layer are summarized in Table 2. The benefit of the p-i-n junction cell is remarkable in enhancing both Voc and Jsc, particularly in the former due to the
Fig. 8. The thickness effects of p- and n-layers of Si on the performance of Si(p)/Mg2Si(i)/ Si(n) PV cells.
utilisation of a wider gap Si(p) to promote the overall built-in potential over the cell (Gao et al., 2011; Zhu et al., 2013). For example, using Mg2Si as the optical absorber, the highest Voc for the single-junction cells is 0.410 V with the structure of Si(p)/Mg2Si(n), which is less than two thirds of the 0.654 V value from the Si(p)/Mg2Si(i)/Si(n) cell. Therefore, Eff achieved by single-junction cells are rather low due to 659
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Table 2 Performance of simulated PV cells under illumination. Structure
Thickness(μm)
Voc (V)
Jsc (mA/ cm2)
FF
Eff (%)
Mg2Si(n)/Mg2Si(p) Si(n)/Mg2Si(p) Si(p)/Mg2Si(n) Si(p)/Mg2Si(i)/Si(n) Si(n)/Mg2Si(i)/Si(p) Si(p)/Si(i)/Si(n) a-Si(p)/Mg2Si(i)/aSi(n)
0.05/2.0 0.05/2.0 0.05/2.0 0.05/2.0/0.1 0.1/2.0/0.05 0.05/200/0.1 0.05/2.0/0.1
0.297 0.353 0.410 0.654 0.654 0.678 0.730
29.041 33.572 33.527 41.981 41.365 38.370 41.463
0.716 0.749 0.772 0.810 0.810 0.834 0.754
6.178 8.872 10.613 22.254 21.905 21.695 22.828
Fig. 9. Effect of Mg2Si layer thickness on the performance of Si(p)/Mg2Si(i)/Si(n) PV cells.
low Voc, as shown in Table 2: 6.178% for Mg2Si(n)/Mg2Si(p), 8.872% for Si(n)/Mg2Si(p) and 10.613% for Si(p)/Mg2Si(n). With regard to p-i-n heterojunction PV cells, both front and back illumination give rise to similar efficiency of 22.254% and 21.905% (emboldened in Table 2). It is worth stressing that the proposed p-i-n heterojunction structure with total thickness of 2.15 μm has comparable Voc, higher Jsc as well as Eff to those of Si solar cells of 200.15 μm as (highlighted in itallic in Table 2) shown in Table 2, suggesting that replacing Si by Mg2Si as optical absorber can decrease the thickness of solar cells radically for about a hundred times and thereby reduce material cost significantly (considering that Mg is a lot cheaper than Si). By replacing crystalline Si with amorphous Si of larger band gap, the Voc can be enhanced further to 0.730 V. It is worth pointing out that the advantage of the p-i-n cells over crystalline Si cells is analysed here on the basis of simple planar devices, without consideration of more sophisticated device designs such as those adopting optical trapping technics to enhance efficiency at reduced thickness of optical absorbers.
Fig. 11. The effect of deep-level defect states on the performance of the Si(p)/Mg2Si(i)/Si (n) cells.
reduced via adequate annealing, due to their higher formation energy with respect to the interstitial Mg state. Processing materials under a Siricher condition is helpful to reduce donor states from the interstitial Mg. While shallow defect states provide mobile carriers, deep defect states will act as recombination centres to trap photo-induced carriers. Here, both donor-like and acceptor-like defect levels in Mg2Si are studied respectively with defect state density ranging from 1 × 1015 cm−3 to 5 × 1017 cm−3, with the assumption of Gaussian like defect levels with peak energy located at 0.1 eV below the conduction band or above
3.3. Effect of defects Defects are well known detrimental factors for solar cells. The Mg2Si is a very interesting semiconductor material, for which natural defects tend to be interstitial Mg that are fortunately the origin for effective ntype conductivity owing to associated shallow donor states (Han and Shao, 2015). Other defects such as vacancies in the Si sites can be
Fig. 10. Illuminated J-V curves of PV cells with different structures.
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which is much higher than the intrinsic carrier density (∼1014 cm−3) (Madelung, 2004) in the silicide material at room temperature. The recombination is higher next to the front junction due to higher local intensity of light. As to the potential profile in the silicide layer, it is seen that higher defect concentration leads to flattened profile, Fig. 12(a), with associated weakening of the electric field, Fig. 12(b). It is understandable that low defect density below 1013 cm−1 does not considerably impact on either the depletion region in terms of either potential field or recombination rate. Although the AMPS code does not take into account of the interface recombination loss, one can still investigate the role of interface defects by artificially inserting between Mg2Si/Si a very thin layer containing a large number of defect states distributed evenly in the band gap, so as to simulate a more realistic device (Liu et al., 2014). Fig. 13(a) shows the simulated results for Voc and Eff as a function of the density of such interfacial traps. In this case, the two interfacial trap layers between Si and Mg2Si are set to be 4 nm in thickness, with the donor/acceptor switching-over energy corresponding to the mid-gap energy of Mg2Si. Electron and hole capture cross sections are set to be the same as those in band tails of the optical absorber. Apparently, both Voc and Eff would suffer from high carrier recombination rates near the interfaces as seen from Fig. 13(b), suggesting the importance of interfacial quality preferably with good epitaxial orientation relationship between Si and Mg2Si. Fortunately, coherent lattice match can exist between the two phases, as is shown in the DFT simulated relaxed structural model, Fig. 3. Furthermore, such an epitaxial relationship was experimentally realised (Wang et al., 2007). An additional and yet important advantage in the proposed Si(p)-Mg2Si(i)-Si(n) cell architecture is that it is not necessary to dope the Mg2Si material. This helps to avoid the difficulty in doping the silicide into p-type, as the natural tendency in forming interstitial Mg and associated donor states offers killers to doped holes. Such a fundamental problem in p-type doping of Mg2Si makes it necessary to rely on heavier p-type doping and associated coupling with native defects, leading to significantly reduced hole mobility (Han and Shao, 2015).
Fig. 12. (a) Equilibrium band diagrams, (b) electric field, (c) recombination profile versus position for the Si(p)/Mg2Si(i)/Si(n) PV cells.
the valence band. The standard deviation of the dopant level is 0.01 eV, and electron and hole capture cross sections are the same as those in band tails. The defect effects on the performance of the typical Si(p)/ Mg2Si(i)/Si(n) PV cell as a function of defect density are presented in Fig. 11. It is seen that both donor-like and acceptor-like defects have similar influence on the solar cell performance that Voc deteriorates severely from 0.652 V to 0.357 V when the defect density increases from 1 × 1012 cm−3 to 5 × 1017 cm−3, resulting in significant degradation of Eff to 9.954% for donor like defects and 11.018% for acceptor like defects. In addition to the effect on carrier recombination rate, the presence of deep-level defects, either acceptor like or donor like, contributes to deteriorate the potential field in the optical absorber. Generally speaking, such effect would be significant only if the defect density is comparable to or higher than the doping concentration in the absorber layer. Taking acceptor like defects as example, the equilibrium band diagrams and acceptor recombination rate versus position are plotted in Fig. 12(a,c). It is evident that the whole recombination rate in Mg2Si shoots up rapidly with the increase of defect density up to 1017 cm−3,
4. Conclusions First principle calculations suggest that fundamentally the Mg2Si phase can form coherent interface with Si, thus making it easier to engineer high quality interface for efficient solar cells. While the valence band offset is moderate, the offset at the conduction band can be significant. This could be mitigated either through nano-structural engineering of the silicide phase or adjustment of junction composition to change the sign of the valence band offset.
Fig. 13. (a) Voc and Eff against interface trap density, (b) recombination profile versus position, for PV cells with different interfacial defects.
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Numerical simulation has been carried out to study the feasibility in designing high-efficiency thin film solar cells based on the low-gap semiconducting silicide Mg2Si, which is a cheap material of vast natural resources. It is found that the Si(p)/Mg2Si(i)/Si(n) architecture offers great benefit in achieving large short circuit current and high open circuit voltage at the same time. The optimised Si(p)/Mg2Si(i)/Si(n) cell of only 2.15 μm in total thickness has potential efficiency ravelling that of crystalline Si cells about 100 times thicker, Acknowledgments This work is partially supported by the NSFC (No. 11504277, 11174256, 91233101), the Natural Science Foundation of Hubei Province (2015CFB229), the Zhengzhou University, and the Zhengzhou Materials Genome Institute. References Akasaka, M., Iida, T., Yamanaka, K., Matsumoto, A., Takanashi, Y., Imai, T., Hamada, N., 2008. The thermoelectric properties of bulk crystalline n- and p-type Mg2Si prepared by the vertical Bridgman method. J. Appl. Phys. 104, 013703. Al-Allak, H.M., Clark, S.J., 2001. Valence-band offset of the lattice-matched β-FeSi2(100)/ Si(001) heterostructure. Phys. Rev. B 63, 033311. Atanassov, A., Baleva, M., 2007. On the band diagram of Mg2Si/Si heterojunction as deduced from optical constants dispersions. Thin Solid Films 515, 3046–3051. Au-Yang, M.Y., Cohen, M.L., 1969. Electronic structure and pptical properties of Mg2Si, Mg2Ge, and Mg2Sn. Phys. Rev. 178, 1358–1364. Avrutin, V., Izyumskaya, N., Morko, H., 2011. Semiconductor solar cells: recent progress in terrestrial applications. Superlatt. Microstruct. 49, 337–364. Baldereschi, A., Baroni, S., Resta, R., 1988. Band offsets in lattice-matched heterojunctions: a model and first-principles calculations for GaAs/AlAs. Phys. Rev. Lett. 61, 734. Chaure, N.B., Samantilleke, A.P., Burton, R.P., Young, J., Dharmadasa, I.M., 2005. Electrodeposition of p+, p, i, n and n+-type copper indium gallium diselenide for development of multilayer thin film solar cells. Thin Solid Films 472, 212–216. Gao, Y., Liu, H.W., Lin, Y., Shao, G., 2011. Computational design of high efficiency FeSi2 thin film solar cells. Thin Solid Films 24, 8490–8495. Han, X., Shao, G., 2012. Origin of n-type conductivity of Sn-doped Mg2Si from first principles. J. Appl. Phys. 112, 013715. Han, X., Shao, G., 2015. Interplay between Ag and interstitial Mg on the p-type characteristics of Ag-doped Mg2Si: challenges for high hole conductivity. J. Mater. Chem.
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