Abstract
We demonstrate through precise numerical simulations the possibility of flexible, thinfilm solar cells, consisting of crystalline silicon, to achieve power conversion efficiency of 31%. Our optimized photonic crystal architecture consists of a 15 μm thick cell patterned with inverted micropyramids with lattice spacing comparable to the wavelength of nearinfrared light, enabling strong waveinterference based light trapping and absorption. Unlike previous photonic crystal designs, photogenerated charge carrier flow is guided to a grid of interdigitated back contacts with optimized geometry to minimize Auger recombination losses due to lateral current flow. Front and back surface fields provided by optimized Gaussian doping profiles are shown to play a vital role in enhancing surface passivation. We carefully delineate the drop in power conversion efficiency when surface recombination velocities exceed 100 cm/s and the doping profiles deviate from prescribed values. These results are obtained by exact numerical simulation of Maxwell’s wave equations for light propagation throughout the cell architecture and a stateoftheart model for charge carrier transport and Auger recombination.
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Introduction
Photovoltaics provides a very clean, reliable and limitless means for meeting the everincreasing global energy demand. Silicon solar cells have been the dominant driving force in photovoltaic technology for the past several decades due to the relative abundance and environmentally friendly nature of silicon. Nevertheless, one of the drawbacks of crystalline silicon is the indirect nature of its electronic band gap, making it a relatively weak absorber of long wavelength sunlight. Traditionally, this has been offset using a relatively thick (100–500 μm) silicon structure. While enabling more solar absorption, thicker silicon adds to the materials cost for large area applications and renders the structure inflexible. Moreover, thick silicon solar cells suffer from unavoidable losses in power conversion efficiency due to nonradiative recombination of photogenerated charge carriers during their relatively long path to electrical contacts at the extremities of the cell. These deficiencies have sparked broad interest in a variety of thinfilm solar materials including CdTe, GaAs, perovskites and various polymers^{1,2,3}. Due to the indirect band gap nature of c–Si, thinfilm silicon has not been considered a viable competitor to these alternative materials.
In some recent papers^{4,5}, we have suggested a paradigm shift in solar science and technology, exploiting the wave nature of sunlight while retaining a realistic description of chargecarrier recombination. By designing suitable photonic crystal architectures that promote waveinterference based lighttrapping in the required frequency band, it is possible for c–Si thin films to absorb sunlight as effectively as a direct band gap semiconductor. In this paper we demonstrate how this enables a flexible, 15 μmthick c–Si film with optimized doping profile, surface passivation and interdigitated back contacts (IBC) to achieve a power conversion efficiency of 31%, higher than that of any other single material of any thickness.
The maximum possible roomtemperature power conversion efficiency of a single junction, c–Si solar cell under 1–sun illumination, according to the laws of thermodynamics, is 32.33%^{6}. This limit is based on the assumptions of perfect solar absorption and no losses due to nonradiative chargecarrier recombination. The best realworld silicon solar cell to date, developed by Kaneka Corporation, is able to achieve 26.7% conversion efficiency^{7,8}. A loss analysis of this 165 μmthick, heterojunction IBC cell shows that in absence of any extrinsic loss mechanism the limiting efficiency of such a cell would be 29.1%^{7}. The competing factors responsible for this upper limit of the conversion efficiency are rayoptics based lighttrapping and intrinsic loss due to Auger chargecarrier recombination^{9,10}. The thicker the cell, the more light is absorbed. Unfortunately, this is accompanied by increased bulk nonradiative recombination loss of chargecarriers. In the hypothetical case of ideal Lambertian lighttrapping, stateoftheart Auger chargecarrier recombination^{11} and the inclusion of band gap narrowing (BGN) in c–Si, a theoretical limit to power conversion efficiency of 29.43% has been proposed^{10}. In this case, the optimum balance between solar absorption and bulk losses is achieved for a cell of 110 μm thickness. In traditional light trapping structures, the Lambertian limit is not achieved and the optimum solar cell thickness is much greater than 110 μm, as witnessed by the worldrecordholding Kaneka cell. Moreover, the inclusion of nonzero bulk doping and surface charge carrier recombination effects further reduce the theoretical power conversion limit by at least another (additive) percentage point. For these reasons, lighttrapping concepts using rayoptics, applied to any conventional silicon solar cell architecture, are not expected to yield power conversion efficiencies beyond 28%.
The wave nature of light offers a powerful alternative paradigm for solar energy capture and conversion in silicon. This is evident in certain subwavelength scale waveguides^{12,13,14} and photonic crystal^{15,16} architectures with microstructure periodicity and feature sizes on the scale of nearinfrared light^{17,18,19,20,21,22}. Sunlight that would otherwise be weakly absorbed in a thin film is, instead, absorbed almost completely. The resulting photonic crystal solar cell absorbs sunlight well beyond the longstanding Lambertian limit. This, in turn, leads to a dramatic reduction in the optimum silicon solar cell thickness. Rayoptics is an approximation that cannot be applied to photonic crystals and accurate modeling of waveinterference based lighttrapping in a photonic crystal (PhC) due to multiple coherent scatterings from wavelengthscale microstructures requires rigorous numerical solution of Maxwell’s equations^{17,18,19,20,21,22,23} throughout the solar cell architecture. A coupled opticalelectronic approach and experimental study on a 3 μmthick cell in^{23} showed the possibility of enhanced lightabsorption and conversion efficiency in patterned silicon cells as compared to bare silicon cells. However, the lightabsorption in this study still falls well below the Lambertian lighttrapping limit.
Recent coupled opticalelectronic analysis of thinsilicon solar cells involving parabolic pore PhCs^{4} and inverted pyramid PhCs^{5} have shown that the previous theoretical efficiency limit obtained by rayoptics based Lambertian lighttrapping can be surpassed. In contrast to 165 μmthick Kaneka cell and 110 μmthick optimum Lambertian cell, photonic crystal solar cells are an order of magnitude thinner. The key mechanisms enabling nearly 30% efficiency using just 10 μmthick silicon are existence of longlifetime, slowlight resonances, paralleltointerface refraction (PIR) and the coupling into such modes from external plane waves^{24}. Slowlight modes exhibiting vorticity in the Poynting vector flow originate from waveinterference and cannot be achieved by rayoptics based Lambertian lighttrapping. They require silicon microstructures on the scale of the optical wavelength. The Lambertian limit involves a number of assumptions such as, a randomly rough top surface without any specular reflection and deflection of the incident rays according to a cosθ probability distribution, where θ is the angle between the rays inside the slab and the surface normal. According to this model, parallel to interface flow of light (i.e. deflection of light rays at nearly θ = 90°) is unattainable. Light waves in PhCs exhibit behavior beyond the realm of rayoptics with the potential to bridge the gap between the thermodynamic efficiency limit and rayoptics based limits. Although thinsilicon PhC solar cell designs with front contacts, discussed earlier^{4,5}, are capable of achieving efficiencies up to 30%, optical shadowing loss due to front contacts and power loss due to sheet resistance prevent them from substantially surpassing this limit.
In this article, we demonstrate that thinsilicon PhC solar cells with IBC can surpass the 30% power conversion efficiency barrier. We consider 3–20 μm thick, flexible c–Si IBC cells with a ptype bulk doping concentration of 5 × 10^{15} cm^{−3}. These inverted micropyramid photonic crystals are optimized for lighttrapping using an exact finite difference time domain (FDTD) simulation of Maxwell’s equations throughout the cell for each cellthickness. The optical generation profiles for the optimized PhCs are then used for carrier transport optimization. We show that each optimized silicon PhC is capable of achieving a photocurrent density well beyond Lambertian limit. We also present a physical explanation for the underlying waveinterference mechanism responsible for this unprecedented light trapping and absorption capability. The PhC solar cells exhibit multiple resonant peaks in the 900–1200 nm wavelength range of the absorption spectra, a region where conventional silicon solar cells and planar cells absorb negligible sunlight. These resonant peaks of PhCs are associated with PIR and vortex like flow of trapped solar energy that gives rise to effective path lengths much longer than the 4n^{2} pathenhancement associated with Lambertian limit. Our electronic optimization of the IBC cell involves realistic Gaussian doping profiles of emitter, back surface field (BSF) and front surface field (FSF) regions. We optimize contact geometry and widths through careful consideration of BGN, Auger recombination and practically feasible ShockleyReadHall (SRH) lifetimes. As the cellthickness increases, the shortcircuit current of the cell increases due to more lightabsorbing material. As expected, increased cellthickness reduces the opencircuit voltage of the cell due to increased bulkrecombination, leading to a new optimum IBC cellthickness. This balance between lightabsorption and bulk recombination suggests an optimum thickness slightly larger than that of the corresponding front contact solar cell^{5}. We consider a wide range of SRH lifetime and study the effect of lifetime variation on optimum cellthickness. Our results suggest that for SRH lifetimes exceeding 1 ms, the optimum PhC IBC cellthickness is 15 μm, in contrast to 110 μm optimum thickness of the hypothetical Lambertian cell. For SRH lifetimes 1 ms and 10 ms and contact SRV 10 cm/s, our optimum 15 μm PhC IBC cell yields power conversion efficiencies of 30.29% and 31.07%, respectively. Even when the contact SRV increases to 100 cm/s, our optimum cell delivers close to 31% conversion efficiency. Our thinfilm photonic crystal design provides a recipe for single junction, c–Si IBC cells with ~4.3% more (additive) conversion efficiency than the present worldrecord holding cell using an order of magnitude less silicon.
Raytrapping architectures in traditional silicon solar cells usually employ two types of surface textures: upright and inverted pyramids^{25,26,27,28,29,30,31}. Randomly distributed upright pyramid textures are widely used due to their easy maskless fabrication through KOH etching of the silicon surface. Despite easy fabrication, uprightpyramid, thinsilicon structures typically provide less effective lighttrapping than the optimized invertedpyramid PhC of the same thickness^{32}. On the other hand, a regular array of inverted pyramids has been used for lighttrapping in the previous recordholding, passivatedemitter, rear locally diffused (PERL) cell with 25% conversion efficiency and 400 μmthickness^{31}. However, the featuresizes of traditional inverted pyramid cells are typically 10 μm or more and lightabsorption in such cells falls below the Lambertian raytrapping limit. Traditional raytrapping architectures require thick silicon (~160–400 μm) to achieve sufficient light absorption, with concomitant bulk carrier recombination that usually limits the conversion efficiency to below 27%. In contrast, our lighttrapping geometry employs inverted pyramids with baselengths ranging between 1.3–3.1 μm. This allows our cells to achieve beyondLambertian lightabsorption through strong waveinterference effects. Using only 3–20 μmthick silicon, resulting in low bulkrecombination loss, our silicon solar cells are projected to achieve up to 31% conversion efficiency, using realistic values of surface recombination, Auger recombination and overall carrier lifetime.
Although the surface of our silicon solar cell is patterned along a plane that is perpendicular to the incident light, the lightpropagation characteristics are considerably richer than widelystudied gratingcoupled waveguides. Our photonic crystal refracts and diffracts incoming light to numerous wavevectors that are nearly parallel to the airsilicon interface. These wavevectors couple to and experience the longlifetime slowlight modes of the PhC. Vortexlike flow of the electromagnetic Poynting vector is evident in high density of optical resonances throughout the 800–1200 nm range. These modes are evidence of an enhancement of the overall electromagnetic density of states over this wavelength range and are characteristic of the higher bands of a photonic crystal. In contrast, the grating couplers exhibit a much narrower coupling bandwidth, typically about 10% of center frequency^{33,34,35,36,37}.
Solar cell Geometry and Numerical Details
Figure 1 shows the schematic of our PhCIBC cell. The front surface of the solar cell is textured with a square lattice of inverted micropyramids of lattice constant a. Such inverted pyramids are fabricated by KOH etching of the (100) surface of silicon, exposing the (111) surfaces and resulting in a pyramid sidewall angle of 54.7°^{21}. The cell has a duallayer antireflection coating (ARC) of refractive indices n_{1} and n_{2} and thicknesses t_{1} and t_{2}, respectively. This ARC layer also acts as part of the front passivation of the cell. We consider c–Si cells with thickness (H) ranging over 3–20 μm. The ptype bulk is assumed to have a uniform doping concentration of 5 × 10^{15} cm^{−3}. Both the front surface field (FSF) and the base consist of highly doped pregions (denoted by p^{+}) with Gaussian doping profiles. Similarly, the emitter contains a highly ndoped region (n^{+}) with Gaussian doping profile. The peak doping concentrations of n^{+} and p^{+} regions are denoted by N_{n0} and N_{p0}, respectively. The corresponding Gaussian doping profiles are \({N}_{i0}\exp (\,{z}^{2}/2{\sigma }_{i}^{2})\), where i = n, p. Here, z refers to the direction of the Gaussian variation and σ_{i} denotes the depth of the doping profile. The widths of the base and emitter regions are assumed to be w_{pdop} and w_{ndop}. The separation between the edges of emitter and base is w_{pn}. A rear passivation layer covers all back surfaces of the cell where the electrode fingers do not make direct contact with the n^{+} and p^{+} regions. The width of the base (emitter) contact, touching the p^{+} (n^{+}) region, is denoted by w_{pcon} (w_{ncon}). The emitter and base contacts extend below the rear passivation and acts as backreflector for the cell.
A stable FDTD scheme, implemented using open source software package Electromagnetic Template Library (EMTL)^{38}, is used to simulate Maxwell’s equations and optimize the lighttrapping performance of the c–Si solar cell. A unit cell of the c–Si inverted pyramid PhC is used for 3D FDTD computations. Perfectly matched layers (PML) are applied at the top and bottom boundary planes (normal to zdirection) of the computation domain. Periodic boundary conditions are assumed along the x and y− directions. The top of the inverted pyramids are coated with dual ARC layers. The bottom of the c–Si is coated with a 50 nm SiO_{2} passivation layer (with refractive index 1.45), backed by a perfect electric conductor (PEC), acting as a backreflector to the sunlight. The use of SiO_{2} buffer layer reduces parasitic absorption losses in realworld back contact such as silver^{39} and justifies the use of a PEC to simulate the backreflector. Calculation of absorbed photon density in our PhC solar cell is a twostep process. In both steps, the cell is illuminated with a broadband plane wave, incident from +zdirection. In the first step, the incident wave has significant energy in the 300–1100 nm spectral range. In the second step, we accurately model solar absorption in the 1100–1200 nm range. This latter absorption in c–Si involves both electronic bandgap narrowing (BGN)^{40} and phononassisted optical absorption comprising the Urbach edge^{41,42,43,44}. As we show in sec. 3, the second effect is insignificant in conventional Lambertian lighttrapping based solar cells but contributes significant subgap solar absorption in our PhC solar cell. In the second FDTD computation, we use an incident plane wave with significant energy in the 1100–1200 nm spectral range. A detailed model of the complex refractive index of c–Si in the 1100–1200 nm wavelength range appears in the “Methods” section.
Combining the results of the separate FDTD computations, we calculate the absorption coefficient of the c–Si over 300–1200 nm wavelength range as A(λ) = 1 − R(λ) − T(λ), where R(λ) and T(λ) are the reflection and transmission coefficients of the structure. The maximum achievable photo current density (MAPD) of the cell under AM1.5G illumination is given by:
Here, I(λ) is the intensity of the AM1.5G spectrum. We assume that each absorbed photon creates a single electronhole pair. The shortcircuit current (J_{SC}) of an ideal cell, without any surface and bulk recombination losses, coincides with J_{MAPD}.
The left panel of Fig. 2 shows a sample optical generation profile for a 10 μmthick cell obtained through our FDTD calculation. The actual 3D profile has been integrated along the ydirection and converted into an equivalent 2D profile. This 2D profile is then repeated over many unit cells of the inverted pyramid PhC to cover the entire width of the 2D transport model of the IBC cell (shown in the right panel of Fig. 2). For the purpose of clarity, the carrier generation profile only over 3 unit cells is shown. The 2D carrier transport calculations are performed using Sentaurus^{45} assuming a temperature of 25 °C. In all the calculations, the ShockleyReadHall (SRH) lifetime, τ_{SRH}, is assumed to be 10 ms (except for the cases where we study the performance and optimum thicknesses of our solar cell as a function of τ_{SRH}) according to the experimental results obtained in^{11}. The Auger recombination in our carriertransport calculations is implemented using the stateoftheart improved Auger model^{11}. The surface recombination at the Si − SiO_{2} interface is implemented using a microscopic, SRH recombination statisticsbased model^{46} (more details are given in the “Methods” section) that complies with the experimental data of^{11,47,48,49}. In all our computations involving invertedpyramid PhC solar cells, the contact SRVs are chosen to be 10 cm/s. This low contact SRV allows us to compare the performance of our solar cell to the benchmarks that completely neglect surface recombination^{10}. In addition, recent experimental developments suggest that passivated contacts allow realization of IBC cell with much lower contact SRVs than conventional contacts^{50}. Nevertheless, we discuss the effect of higher contact SRVs on the performance of our cell in sec. 4.
One approach to achieve low SRVs is through passivated carrierselective contacts using highly doped polycrystalline Si (polySi) thin films. Experimental study^{51} has shown that a 20 nmthick polySi frontcontact leads to parasitic absorption loss of ~1.1 mA/cm^{2}. In contrast, in our IBC design, polySi layers with similar thickness would be placed at the back of the cell. As shown by the integrated optical generation profile of Fig. 2, our photonic crystal architecture captures the vast majority of sunlight in the upper parts of the cell. Two orders of magnitude more photogenerated carrier density appears in the upper regions relative to the bottom of the cell. Accordingly, we expect that parasitic absorption in polySi bottom contacts is negligible in our PhCIBC cell.
For all our chargecarrier transport calculations, we assume that the the contacts are ideal (i.e. zero resistivity). The resistive losses in the bulk and along the highly doped n^{+} and p^{+} regions depend on the doping concentrations and are automatically considered in our 2D driftdiffusion calculations. We account for the losses at the semiconductordielectric and semiconductormetal interfaces through SRH recombination statistics^{46} and contact surface recombination velocities, respectively.
LightTrapping Optimization
C–Si thinfilms with low doping can provide solar cells with high opencircuit voltage due to reduced bulk recombination, but usually suffer from poor solar absorption. Maximization of lighttrapping capability in c–Si thinfilm is one of the most important aspects of highefficiency, ultrathin silicon solar cell design. We show below that 3–20 μmthick c–Si inverted micropyramid PhCs are highly effective for waveinterference based lighttrapping leading to solar absorption, comparable to (and in some cases more than) that of the 165–400 μmthick conventional cells. Our simulations reveal that a duallayer ARC with n_{1} = 1.4, t_{1} = 45 nm, n_{2} = 2.6 and t_{2} = 100 nm exhibits the best antireflection behavior, irrespective of the cellthickness. Figure 3 shows the optimization results for the lattice constant, a, of c–Si invertedpyramid PhCs with H = 3, 5, 7, 10, 15 μm for MAPDs over 300–1100 nm wavelength range. We also note from Fig. 3 that for a 3 μmthick cell, the MAPD corresponding to a = 400 nm is 31.9 mA/cm^{2} in comparison to the MAPD of 39.05 mA/cm^{2} at the optimum lattice constant of 1300 nm. However, as the cell becomes thicker, this difference progressively decreases. For a 20 μmthick cell, the difference between MAPD at a = 2900 nm and a = 400 nm is only 0.34 mA/cm^{2}. For H = 15 μm, the MAPD shows a maximum variation of 0.25 mA/cm^{2} over the 1700–3200 nm lattice constant range. The lighttrapping performances of 15–20 μmthick inverted PhC solar cells are extremely robust with respect to lattice constant variation. The total MAPD over the entire 300–1200 nm wavelength range, for the optimum cases of different cellthickness, are shown in Table 1. The 1100–1200 nm absorption is calculated according to an accurate Lorentz model of experimental c–Si dispersion data as discussed in the “Methods” section. Table 1 also shows that waveinterference based lighttrapping in our optimized thinsilicon inverted pyramid PhCs surpasses the rayoptics based Lambertian lighttrapping limit. The MAPDs corresponding to the Lambertian limits of different cellthicknesses are calculated using absorption coefficient from^{9} and eq. 1.
As illustrative examples of our optimized inverted pyramid PhC solar cells, we show two absorption spectra in Fig. 4 over the 300–1200 nm wavelength range: a thin cell with H = 5 μm and a relatively thicker cell with H = 15 μm. These absorption spectra exhibit multiple resonance peaks and significant absorption in the 900–1200 nm wavelength range, whereas Lambertian cells and planar silicon are weak absorbers of sunlight. These peaks in the absorption spectra originate from purely waveinterference effects, absent in Lambertian lighttrapping. To illustrate this point, we show a magnified view of the absorption spectrum of the 5 μmthick, optimized inverted pyramid PhC cell over the 850–1200 nm wavelength range in Fig. 5(a). The red circles correspond to resonant absorption peaks located at λ = 1110, 1130 and 1176 nm. Figure 5(b–d) show the inplane Poynting vector plots over the central xzslice of the inverted pyramid PhC unit cell at these resonances. The energy flowpattern reveals multiple regions with vortexlike flow and parallel to interface flow of light at these resonances leading to very long dwelltime of photons in the solar cell. On the other hand, Lambertian light trapping assumes that the distribution rays in the cell obeys a probability distribution f(θ) = 1/π cosθ, where θ is the angle that a ray within the cell makes with the cellsurface normal. According to this distribution, propagation of energy near θ = 90° (i.e. parallel to the interface) is insignificant. However, direct solutions of Maxwell’s equations show that a significant amount of energy flows close to θ = 90° due to waveinterference based lighttrapping in our PhC. Moreover, a rayoptics based picture cannot provide vortices in the powerflow pattern shown in Fig. 5(b–d).
Electronic Optimization
Collection of the photogenerated carriers, before they recombine, is crucial for high power conversion efficiency in solar cells. Accordingly, the emitter, base and FSF regions of the IBC cell require higher doping levels in order to deflect minority carriers from contacts and other surfaces. However, high doping levels in these regions lead to high Auger recombination. Higher doping also reduces the opencircuit voltage due to larger BGN. Therefore, a careful balance between the peak doping concentration and depths of the Gaussian doping profiles is paramount to exploiting the full potential of waveinterference based lighttrapping. For carriertransport optimizations, we use a 2D model of the IBC cell (shown in Fig. 2). The design parameters such as the details of the Gaussian doping profiles and contact widths turn out to be independent of the PhC cellthickness. For concreteness, we describe in detail the optimization process for a 10 μm thick cell.
Figure 6 shows the optimization map for the Gaussian doping profile of the n^{+} emitter region. For this optimization, the peak doping concentration (N_{p0}) and doping depth (σ_{p}) of p^{+} regions are kept fixed at 5 × 10^{18} cm^{−3} and 100 nm (corresponding to a total p^{+} region depth of 370 nm). The specific contact geometry and other parameters used for emitter optimization calculations are given in Table 2. Figure 6 shows that our 10 μmthick IBC cell achieves a conversion efficiency of 30.74% for a peak emitter doping concentration N_{n0} = 2 × 10^{18} cm^{−3} and emitter doping depth σ_{n} = 220 nm, corresponding to a total emitter depth of 760 nm. This plot reveals that if we increase σ_{n} to 300 nm (keeping N_{n0} fixed at 2 × 10^{18} cm^{−3} which corresponds to an emitter depth of 1.038 μm), the cell efficiency exhibits a negligible drop of 0.01% (additive). Clearly, N_{n0} = 2 × 10^{18} cm^{−3} allows a large tolerance toward emitterfabrication.
For the optimization of p^{+} regions (shown in Fig. 7), we choose N_{n0} = 2 × 10^{18} cm^{−3} and σ_{n} = 220 nm. For both p^{+} base and FSF regions, we assume the same Gaussian doping profile, characterized by peak doping concentration N_{p0} and depth σ_{p}. Other simulation parameters used in our base doping optimization are given in Table 2. Our cell achieves 30.75% conversion efficiency for N_{p0} = 4 × 10^{18} cm^{−3} and σ_{p} = 100 nm.
The PERC cell described in^{4}, has an emitter with N_{n0} = 3 × 10^{18} cm^{−3} and a total depth of 730 nm. This is very similar to the optimized emitter of our IBC cell. However, the emitter optimization in^{4} does not involve BGN and is a result of the balance between Auger recombination and sheet resistance. In contrast, the carriers in our IBC cells travel at most 70 μm lateral distance, unlike PERC cells where, the electrons inside the emitter region travel several hundreds of microns laterally before they reach front contacts. Consequently, sheet resistance is much less in our IBC cell. In addition to Auger recombination, we have included BGN in the present optimization study. This unavoidable effect limits N_{p0} and N_{n0} in a practical cell. The BGNmediated drop in the opencircuit voltage reduces the power conversion efficiency for large N_{p0} and N_{n0}.
Figure 8(a,b) show the optimization maps for p and ncontact widths with contact SRVs 10 cm/s and 100 cm/s, respectively. The IBC cell is assumed to be 10 μm thick with optimized p^{+} and n^{+} dopings. Table 3 shows the details of all the simulation parameters used in our contact optimization study. Figure 7(a) reveals that for contact SRV = 10 cm/s and 10 μm emittercontact width, the optimum value of base contact width, w_{pcon}, is 140 μm. As w_{pcon} increases from 10 μm to the optimum value of 140 μm, the cell efficiency increases by 0.2% (additive). In comparison to this, the variation of the emitter contact width (w_{ncon}) has even less influence on the power conversion efficiency of the cell. For w_{pcon} = 140 μm, as w_{ncon} increases from 10 μm to 100 μm, the power conversion efficiency of the photonic crystal IBC cell drops only by 0.08% (additive). As we increase the contact SRV to 100 cm/s, Fig. 8(b) shows that the relative influences of the variations in w_{pcon} and w_{ncon} on the cell efficiency remain approximately the same as for contact SRV 10 cm/s. However, the optimum base contact width and maximum power conversion efficiency now have lower values, 110 μm and 30.49%, respectively. Although the contact SRV increased by an order of magnitude, the cell efficiency changes only by 0.25% (additive).
Using the optimum contact widths and doping profiles obtained above, we now study the optimum thickness of our inverted pyramid PhC IBC cell. A thicker cell leads to a higher shortcircuit current due to more light absorption but has a lower opencircuit voltage due to increased bulk recombination of photogenerated carriers. This tradeoff leads to an optimum cellthickness for each choice of τ_{SRH}. The SRH lifetime, determined by bulk defects in the c–Si wafer, can vary widely depending upon the quality of the fabrication process. A higher SRH lifetime or lower bulk recombination allows larger solar absorption by using thicker c–Si layer without losing much photocurrent in the recombination process. It follows that for a higher SRH lifetime, the optimum cellthickness is larger and vice versa. In Fig. 9, we consider τ_{SRH} = 0.1,0.5,1 and 10 ms to study the optimum cellthickness (other simulation parameters appear in Table 4). Figure 9(b–d) show the variation of V_{OC}, J_{SC} and FF with cellthickness. As the cellthickness is increased from 3 to 20 μm, the FF of the IBC cell drops by 4% (additive) for τ_{SRH} = 0.1 ms. As τ_{SRH} increases, the drop in the FF becomes smaller for the same range of cellthickness variation. For τ_{SRH} = 10 ms, the FF becomes almost independent of cellthickness.
Figure 9(a) shows the variation of power conversion efficiency of our IBC cell with cellthickness for various choices of τ_{SRH}. For τ_{SRH} = 0.1 ms and 0.5 ms, the optimum IBC cells are 7 μm and 12 μm thick with conversion efficiencies 27.35% and 29.63%, respectively. For both τ_{SRH} = 1 ms and 10 ms, the optimum cellthickness becomes 15 μm with power conversion efficiencies 30.29% and 31.07%, respectively.
It is instructive to compare the optimization of our realistic IBC cell with that of a hypothetical, ideal Lambertian cell. Here, we include the same surface recombination mechanism and SRH lifetime as used in our best IBC cell. The hypothetical Lambertian cell is also endowed with the same doping levels as the ptype bulk, n^{+} and p^{+} regions of our IBC cell. The optimum thickness of the Lambertian cell is found to be 90 μm with a maximum conversion efficiency of 28.37% (shown in Fig. 10). Thus, our thinSi photonic crystal solar cell offers 2.7% (additive) higher conversion efficiency than the limiting efficiency of a Lambertian cell with practical doping configurations and loss mechanisms. Table 5 compares the performance of our inverted pyramid PhC IBC solar cell with the hypothetical Lambertian solar cell.
Lifetime measurements of wellpassivated c–Si samples (Fig. 5 in^{11}) have shown that the effective lifetime (τ_{eff}) of ptype samples with a bulk doping concentration of 5 × 10^{15} cm^{−3} is approximately 10 ms. Since, τ_{SRH} > τ_{eff} (as a result of the relation: τ_{eff} = (1/τ_{SRH} + 1/τ_{Aug})^{−1}), τ_{SRH} = 10 ms is practically attainable. We now consider our 15 μmthick IBC PhC cell, with optimized lighttrapping, to study the degradation of performance with lower quality electronic parameters. We delineate below, how higher SRH lifetime, poor contact quality and nonoptimized FSF, lower the efficiency of our PhC IBC cell.
The effect of higher τ_{SRH} is shown in Fig. 11. Other simulation parameters are same as given in Table 4. As shown in Fig. 11(d), J_{SC} exhibits little variation with τ_{SRH} (only ~0.22 mA/cm^{2} over the entire range of 0.1 ms ≤ τ_{SRH} ≤ 15 ms). In contrast, V_{OC} and FF of the cell increase significantly as τ_{SRH} changes from 0.1 ms to 1 ms. Within this range of τ_{SRH}, V_{OC} increases from 768 mV to 792 mV and FF increases from 79.95% to 86.24%. For τ_{SRH} > 3 ms, V_{OC} of our IBC cell falls very close to its saturation value of 794.1 mV. Similarly, FF of the cell almost reaches its saturation value of 88.2% as τ_{SRH} becomes larger than 5 ms. Overall conversion efficiency of our 15 μmthick IBC cell increases steeply from 27.12% at τ_{SRH} = 0.1 ms to 30.3% at τ_{SRH} = 1 ms. Power conversion efficiency of our cell crosses the 31% threshold for τ_{SRH} > 5 ms. Clearly, τ_{SRH} > 1 ms is a prerequisite for photonic crystal IBC cells to achieve efficiency beyond 30%.
We now consider the effect of increased contact SRV and nonoptimized FSF/BSF on our 15 μmthick photonic crystal IBC cell. Apart from τ_{SRH} = 10 ms and a variable contact SRV, all other simulation parameters are given by Table 4. Figure 12(a) shows that the power conversion efficiency of our IBC cell with optimized FSF and BSF (i.e. N_{p0} = 4 × 10^{18} cm^{−3} and σ_{p} = 100 nm) undergoes only 0.3% (additive) drop leading to 30.77% efficiency when the contact SRV is increased from 10 cm/s to 100 cm/s (red curves in Fig. 12). In contrast, the blue curve in Fig. 12(a) shows a 5% (additive) drop in the conversion efficiency for the same change in contact SRV, in a cell with inadequate FSF and BSF (N_{p0} = 1 × 10^{17} cm^{−3} and σ_{p} = 100 nm in this particular example). When the contact SRVs are extremely high (~10^{6} cm/s), the IBC cell with optimum FSF/BSF doping retains ~20% power conversion efficiency. This is in sharp contrast to the cell with inadequate FSF/BSF where the conversion efficiency drops to ~5%.
Conclusions
Through detailed and precise design optimization, we have identified a route to 31% power conversion efficiency in thinfilm crystalline silicon solar cells. The architecture consists of a flexible 15 μmthick c–Si sheet patterned as a squarelattice, inverted micropyramid photonic crystal with a grid of interdigitated back contacts. By choosing the micropyramid lattice spacing comparable to the wavelength of nearinfrared light, it is possible to achieve remarkable waveinterferencebased lighttrapping throughout the 800–1200 nm wavelength range. Together with an optimized antireflection coating, this leads to overall solar absorption in the 300–1200 nm range, well above the so called Lambertian limit. This unprecedented amount of light absorption in a thinfilm, indirect band gap semiconductor, exploits the wave nature of light and suggests a paradigm shift in solar cell design. It leads to the remarkable conclusion that thin, flexible, silicon solar cells may outperform their traditional, thick, inflexible counterparts. Given the advanced technologies available for silicon surface passivation, it suggests that thinfilm silicon may provide higher power conversion efficiency than any other single material of any thickness.
Our predictions remain robust over a reasonable range of photonic crystal structure parameters as well as a viable range of surface recombination velocities at the siliconcontact interfaces. The vital role of front and back surface fields obtained by realistic doping profiles was delineated. Major deviations from the prescribed profiles were shown to cause rapid degradation of solar cell performance. By elucidating the optimized photonic and electronic architecture, together with deviations from the optimum parameter choices, we provide a detailed roadmap for experimental efforts to realize power conversion efficiency beyond 30% in a thinsilicon solar cell.
Methods
Long wavelength absorption in crystalline silicon
Subgap absorption in c–Si arises from two distinct mechanisms. The first is electronic bandgap narrowing (BGN), denoted by ΔE_{g} (in eV). This allows c–Si to absorb subgap photons with energies less than E_{g} but above (E_{g} − ΔE_{g}), where E_{g} is the bandgap energy (in eV) of unperturbed c–Si. In Sentaurus, ΔE_{g} is estimated using Schenk’s model^{40} and leads to a slight drop in V_{OC}. The second mechanism allows c–Si to absorb photons with energies less than (E_{g} − ΔE_{g}) and originates from the exponentially decaying Urbach tail below the continuum band edge^{41,42}. For noncrystalline solids, static disorder contributes to an exponential band tail of localized states below the electronic band edge. In c–Si, a similar tail of phononassisted optical absorption gives rise to mobile electronhole pairs^{43,44}. The subgap absorption is characterized by an exponential of the form: α(ν) ~ exp[{hν − E_{G}(T)/E_{0}(T)}], where ν is the optical frequency, E_{G}(T) is the downshift of the continuum band edge corresponding to BGN and E_{0}(T) is the Urbach slope.
In order to model the subgap absorption, we take the frequency dependent dielectric constant of Si over the 1000–1200 nm wavelength range from^{52} and fit it to a sum of Lorentz oscillator terms: \(\varepsilon (\omega )={\varepsilon }_{\infty }+{\sum }_{j}\frac{{\rm{\Delta }}{\varepsilon }_{j}{\omega }_{pj}^{2}}{({\omega }_{pj}^{2}2i\omega {\gamma }_{j}{\omega }^{2})}\). The fitting parameters ε_{∞}, ω_{pj}, Δε_{j} and γ_{j}, given in Table 6, are obtained using an open MATLAB program^{53}. We compare the absorption length λ/4πk (where k is the imaginary part of the refractive index) calculated form our fit and that obtained from^{52} in Fig. 13. The measured value of Urbach slope of c–Si at 300K is 8.5 ± 1.0 meV^{54}. In comparison to this experimental data, microscopic modeling of the opticalabsorption edge due to acoustic and optical phonons yields a slope of 8.6 meV^{43,44}. The inset shows that the experimental data from^{52} exhibits an Urbach slope of 8.6 meV over the 1160–1190 nm wavelength range.
Surface recombination at insulatorsilicon interface
For all our transport calculations, we use SRH statistics for the insulatorSi interface. According to this model, the recombination rate at the Siinsulator interface is given by^{46}:
where, S_{j0} = v_{th,j}σ_{j}D_{interface} with j = n,p (v_{th,j} is the thermal velocity, σ_{j} is the capture crosssection, D_{interface} is the interface trap density at the oxidesemiconductor interface), n_{s} and p_{s} are electron and hole concentration at the Si surface and \({n}_{i}=\sqrt{{N}_{e}{N}_{h}}\exp (\,{E}_{g}(T)/2{k}_{B}T)\). Here, T is the temperature (in K) and E_{g}(T) denotes the bandgap of Si. N_{e} and N_{h} are defined in terms of the electron/hole effective mass \({m}_{e}^{\ast }/{m}_{h}^{\ast }\) and Planck’s constant h as: \({N}_{j}=2{(\frac{2\pi {m}_{j}^{\ast }{K}_{B}T}{{h}^{2}})}^{3/2}\) with j = e and h for electrons and holes, respectively. For electrons, \({v}_{th}=\sqrt{\frac{3KT}{{m}_{e}^{\ast }}}=1.12\times {10}^{7}cm/s\) for \({m}_{e}^{\ast }=1.08{m}_{e}\) and T = 298K. The thermal velocity of holes is slightly lower due to higher effective mass \((\, \sim \,1.5{m}_{e}^{\ast })\). We set D_{interface} = 3 × 10^{9} cm^{−2} according to the measured value of the nearmidgap trap density at the Siinsulator interface in^{47}. We take σ_{p} = 6 × 10^{−17} cm^{2} for these traps from the measured data on capture crosssections (Fig. 6 in^{48}). This figure also shows that the measured value of σ_{n} varies over a large range. The choice of σ_{n} = 6 × 10^{−16} cm^{2} results in a S_{n0} that closely approximates the effective SRV of the state of the art measurements in^{11}. Accordingly, we choose S_{n0} ≈ 20.16 cm/s and S_{p0} ≈ 1.7 cm/s for all our transport calculations.
References
Guo, D., Brinkman, D., Shaik, A. R., Ringhofer, C. & Vasileska, D. Metastability and reliability of CdTe solar cells. J. of Phys. D: Appl. Phys. 51, 153002 (2018).
Yamaguchi, M., Lee, K. H., Araki, K. & Kojima, N. A review of recent progress in heterogeneous silicon tandem solar cells. J. of Phys. D: Appl. Phys. 51, 133002 (2018).
Chen, Y., Zhang, L., Zhang, Y., Gaoa, H. & Yan, H. Largearea perovskite solar cells – a review of recent progress and issues. RSC Adv. 8, 10489 (2018).
Bhattacharya, S. & John, S. Designing highefficiency thin silicon solar cells using parabolicpore photonic crystals. Phys. Rev. Applied 9, 044009 (2018).
Bhattacharya, S., Baydoun, I., Lin, M. & John, S. Towards 30% power conversion efficiency in thinsilicon photonic crystal solar cells. Phys. Rev. Appl. 11, 014005 (2019).
Shockley, W. & Queisser, H. J. Detailed balance limit of efficiency of pn junction solar cells. J. of Appl. Phys. 32, 510 (1961).
Yoshikawa, K. et al. Silicon Heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%. Nature Energy 2, 17032 (2017).
Green, M. A. et al. Solar cell efficiency tables (version 51). Prog. Photovolt. Res. Appl. 26, 3 (2018).
Tiedje, T., Yablonovitch, E., Cody, G. & Brooks, B. Limiting efficiency of silicon solar cells. IEEE Trans. on Electron Devices 31, 711 (1984).
Richter, A., Hermle, M. & Glunz, S. W. Reassessment of the limiting efficiency for crystalline silicon solar cells. IEEE J. of Photovoltaics 3, 1184 (2013).
Richter, A., Glunz, S. W., Werner, F., Schmidt, J. & Cuevas, A. Improved quantitative description of Auger recombination in crystalline silicon. Phys. Rev. B 86, 165202 (2012).
Stuart, H. R. & Hall, D. G. Thermodynamic limit to light trapping in thin planar structures. J. of Optical Society of America A 14, 3001–3008 (1997).
Munday, J. N., Callahan, D. M. & Atwater, H. A. Light trapping beyond the 4n2 limit in thin waveguides. Appl. Phys. Lett. 100, 121121 (2012).
Yu, Z., Raman, A. & Fan, S. Fundamental limit of nanophotonic light trapping in solar cells. PNAS 107, 17491–17496 (2010).
John, S. Strong localization of photons in certain disordered dielectric superlattices. Phys Rev. Lett 58, 2486 (1987).
Yablonovitch, E. Inhibited spontaneous emission in solidstate physics and electronics. Phys. Rev. Lett. 58, 2059 (1987).
Demsey, G. & John, S. Solar energy trapping with modulated silicon nanowire photonic crystals. J. Appl. Phys. 112, 074326 (2012).
Deinega, A. & John, S. Solar power conversion efficiency in modulated silicon nanowire photonic crystals. J. Appl. Phys. 112, 074327 (2012).
Eyderman, S., John, S. & Deinega, A. Solar light trapping in slanted conicalpore photonic crystals: Beyond statistical ray trapping. J. Appl. Phys. 113, 154315 (2013).
Eyderman, S. et al. Lighttrapping optimization in wetetched silicon photonic crystal solar cells. J. Appl. Phys. 118, 023103 (2015).
Mavrokefalos, A., Han, S. E., Yerci, S., Branham, M. S. & Chen, G. Efficient Light Trapping in Inverted Nanopyramid Thin Crystalline Silicon Membranes for Solar Cell Applications. Nano Lett. 12, 2792 (2012).
Branham, M. S. et al. 15:7% Efficient 10mmThick Crystalline Silicon Solar Cells Using Periodic Nanostructures. Adv. Mater. 27, 2182–2188 (2015).
Boroumand, J., Das, S., VázquezGuardado, A., Franklin, D. & Chanda, D. Unified ElectromagneticElectronic Design of Light Trapping Silicon Solar Cells. Sci. Rep. 6, 31013 (2016).
Chutinan, A. & John, S. Light trapping and absorption optimization in certain thinfilm photonic crystal architectures. Phys. Rev. A 78, 023825 (2008).
Campbell, P. & Green, M. A. Light trapping properties of pyramidally textured surfaces. J. Appl. Phys. 62, 243 (1987).
Zhao, J., Wang, A., Campbell, P. & Green, M. A. 22.7% Efficient silicon photovoltaic modules with textured front surface. IEEE Trans. Electron. Dev. 46, 1495 (1999).
Chen, H. Y. et al. Enhanced performance of solar cells with optimized surface recombination and efficient photon capturing via anisotropicetching of black silicon. Appl. Phys. Lett. 104, 193904 (2014).
Abdullah, M. F. et al. Research and development efforts on texturization to reducethe optical losses at front surface of silicon solar cell. Renew. Sust. Energy Rev. 66, 380 (2016).
Borojevic, N., Lennon, A. & Wenham, S. Light trapping structures for silicon solar cells via inkjet printing. Phys. Status Solidi A 211, 1617 (2014).
Chen, H. Y. et al. Enhanced photovoltaic performance of inverted pyramidbased nanostructured blacksilicon solar cells passivated by an atomiclayer deposited Al2O3 layer. Nanoscale 7, 15142 (2015).
Zhao, J., Wang, A. & Green, M. A. 24.5% efficiency silicon PERT cells on MCZ substrates and 24.7% efficiency PERL cells on FZ substrates. Prog. Photovolt: Res. Appl. 7, 471 (1999).
Bhattacharya, S. & John, S. To be published.
Taillaert, D., Bienstman, P. & Baets, R. Compact efficient broadband grating coupler for silicononinsulator waveguides. Opt. Lett. 29, 2749–2751 (2004).
Na, N. et al. Efficient broadband silicononinsulator grating coupler with low backreflection. Opt. Lett. 36, 2101–2103 (2011).
Marchetti, R. et al. Highefficiency gratingcouplers: demonstration of a new design strategy. Sci. Rep. 7, 16670 (2017).
Hoffmann, J. et al. Backscattering design for a focusing grating coupler with fully etched slots for transverse magnetic modes. Sci rep. 8, 17746 (2018).
Sapra, N. V. et al. Inverse Design and Demonstration of Broadband Grating Couplers. IEEE. J. Sel. Top. Quant. 25, 6100207 (2019).
Electromagnetic Template Library. http://fdtd.kintechlab.com/en/download (2017).
Cui, H., Campbell, P. R. & Green, M. A. Optimization of the Back Surface Reflector for Textured Polycrystalline Si Thin Film Solar Cells. Energy Procedia 33, 118–128 (2013).
Schenk, A. Finitetemperature full randomphase approximation model of band gap narrowing for silicon device simulation. J. of Appl. Phys. 84, 3684 (1998).
Urbach, F. The LongWavelength Edge of Photographic Sensitivity and of the Electronic Absorption of Solids. Phys. Rev. 92, 1324 (1953).
Martienssen, W. The optical absorption edge in ionic crystals. Phys. Chem. Solids 2, 257 (1957).
Grein, C. H. & John, S. Temperature dependence of the fundamental optical absorption edge in crystals and disordered semiconductors. Solid State Commun. 70, 87 (1989).
Grein, C. H. & John, S. Temperature dependence of the Urbach optical absorption edge: A theory of multiple phonon absorption and emission sidebands. Phys. Rev. B 39, 1140 (1989).
Synopsys TCAD. Release M  2016:12 (2016).
Cuveas, A. Surface recombination velocity of highly doped ntype silicon. J. of Appl. Phys. 80, 3370 (1996).
Robinson, S. J. et al. Recombination rate saturation mechanisms at oxidized surfaces of high efficiency silicon solar cells. J. Appl. Phys. 78, 4740–4754 (1995).
Aberle, A. G., Glunz, S. & Warta, W. Impact of illumination level and oxide parameters on ShockleyReadHall recombination at the Si−SiO2 interface. J. of Appl. Phys. 71, 4422–4431 (1992).
Collett, K. A. et al. An enhanced alneal process to produce SRV < 1 cm/s in 1−cm ntype Si. Solar Energy Materials and Solar Cells 173, 50–58 (2017).
Haase, F. et al. Laser contact openings for local polySimetal contacts enabling 26:1% efficient POLOIBC solar cells. Solar Energy Materials and Solar Cells 186, 184–193 (2018).
Reiter, S. et al. Parasitic absorption in polycrystalline Silayers for carrierselective front junctions. Energy Procedia 92, 199–204 (2016).
Schinke, C. et al. Uncertainty analysis for the coefficient of bandtoband absorption of crystalline silicon. AIP Advances 5, 067168 (2015).
Fitting of dielectric function, http://fdtd.kintechlab.com/en/fitting (2012).
Cody, G. D., Tiedje, T., Abeles, B., Brooks, B. & Goldstein, Y. Disorder and the OpticalAbsorption Edge of Hydrogenated Amorphous Silicon. Phys. Rev. Lett. 47, 1480 (1981).
Acknowledgements
This work was supported by the United States Department of Energy DOEBES in a subcontract under award DEFG0206ER46347, the Natural Sciences and Engineering Research Council of Canada and the Ontario Research Fund.
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Bhattacharya, S., John, S. Beyond 30% Conversion Efficiency in Silicon Solar Cells: A Numerical Demonstration. Sci Rep 9, 12482 (2019). https://doi.org/10.1038/s4159801948981w
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DOI: https://doi.org/10.1038/s4159801948981w
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