1. Introduction

Silicon solar cells made of thin films are exceptionally promising applicants used for generation of extremely efficient and lowest rate photovoltaic configurations. Several recent and developing thin film solar cell technologies including graphene based Schottky junction conformations, silicon-based nanowire/nanorod thin structures, applying thin optimal absorber and transparent layers, and highly reflective back metal reflectors to achieve maximum light trapping and high efficiencies have been introduced [1–6]. Graphene based thin cells which renovate optical to electric energy conversion efficiently with outstanding power adaptation efficiencies are utmost desirable applicants for renewable and sparkling energy power bases [2–8]. The power productivity of silicon solar (SC) devices depends on passivation of supported surface defects, extreme light available in active/absorber layer, efficient collection of photogenerated charge carriers, less passivistic absorption and total light reflections from rear side of solar cells [9–12]. Thin films in solar cells become most demanding in commercialisation and intense development research due to its tiny size of thin films up to 2 microns or less, efficient absorption and flexibility abilities. Light captivation is a scheme which is frequently used to increase light absorption in thin films by increasing the optical scattering by inner reflections within absorption layer [13–15]. Thus, better light trapping is crucial in µc-Si cells. For this concern, textured dielectric, Transparent conductive layers and substrates have been developed to scatter the incident light and increase the optical path length inside the cells [16]. Though, it is well known that the usage of excessively steep textures with V-shaped or rounded shaped valleys often encourages defective porous areas during the µc-Si growth, resulting in a poor photovoltaic performance. So, various wavelength-scale texture formation on substrate, transparent oxide layers or on metal reflectors are used to enhance light trapping through inner reflections [5,16,17]. Thus, in conventional thin silicon solar cells metal back reflectors are employed to increase rear optical reflections. In addition to the simple perception of metal back reflectors to improve reflections and exploit absorption, a thin dielectric layer is also inserted between silicon and back metal reflector layers [18,19]. Recent studies [19,20] presented that dielectric layers have assistance of minor cost, truncated temperature dispensation, extreme output, and low parasitic and plasmonic losses. In the earlier studies it was shown that previous solar cell reflectors with dielectric has limited bandwidth and inadequate light scattering because of shortage of plasmonic emissions [21,22]. Recently, passivated diffused solar cells were introduced in which rear passivation layers along with nanoparticles were employed to minimize surface recombination, significant optical scattering and surface plasmonic emissions [23,24]. However still the trade-off between passivation effects, low parasitic absorption and high optical captivation in thin absorber layers is not significantly heightened. Although there are several device parameters on which solar cell performance depends, as stated above, but light trapping, low passivation and parasitic absorption, and high light coupling in thin film solar cells are considered as vital aspects in thin solar cells. Several light trapping structures have been presented recently to increase performance of solar cell [4,5,6,16,17,25] where front surface textures/nanograting or front coatings aim to maximize surface reflections and rear-surface structures aim to maximize large optical scatterings from rear side [6,7,10].

We are mainly focusing on Front and rear located textured structure with fixed semiconductor surface area that increase optical conductivity, maximum light absorption in active layer and extreme coupling of light through graphene on top and increase inner scattering through back reflector with specific Nano scale textures. For this reason, dielectric films of SiO2, SiNx or ZnO or stacks of these constituents are employed in terms of optical possessions of back reflector integrating dielectric coatings. Nevertheless, rear dielectric layers joint with metal reflectors are assigned to passivate exterior interface and parasitic captivation in back metallization, and exploit light trapping. Graphene has remarkable progress in high conductivity, carrier mobility and transparency. Graphene is widely utilised in applications of optoelectronic and electronic devices. Therefore, graphene can be referred as an ideal electrode appropriate for thin solar cells [2,8,26] as well as graphene can extensively increase the optical conductivity by magnetic resonance effects in active layers of solar cell [25]. Graphene based scotkky junction or multijunction solar cells has been widely used where mono layer of graphene integrated on any semiconductor or oxide layer along with various texturing or photonic crystals schemes are synthesised to increase graphene based solar cells efficiency and light tricking [25].

For solar cell devices with metallic nanoparticles or gratings, in order to redirect maximum light in active layers of solar cells, identification of the passivation effects (ohmic losses) to produce minimum power losses is required. Moreover, in order to balance the trade-off between conductivity and transparency, the optimum number of graphene layers and specific thickness of each material stack is desired. Therefore, a similar idea is adopted for improving performance of thin film solar cell nanostructures and to address the urgent tasks in this field, thus to find effective ways to increase optical absorption, minimise parasitic losses and passivate the interface states. We integrated graphene material for optical conductivity improvements and Nano scale texturing to confine more light in active region through scattering or magnetic resonance/plasmonic effects. Moreover, back reflectors are used to reflect maximum light from rear stack so light path can be increased through many ways.

We benchmarked our study to recent research work [27–29] based on different back metal reflectors with/without textures strategies as well as silicon thin film solar cells where additional new features are required. In order to improve overall light trapping, low parasitic absorption in metal and high photon absorption effects in silicon absorber layers, the development of precise texture profile and back reflector material combinations are essential. Therefore, we proposed new graphene-based silicon thin film solar cell configuration to combine all those benchmark effects to develop innovative key design with graphene layer, specific texturing approach, and dielectric-metal back reflectors. Hence this structure achieved high photon absorption up to 90% and extreme light reflectance at bottom side of reflector.

In this study we investigate graphene/silicon thin solar cells through application of front and back random textures and SiO2 dielectric layers and in Back Ag metal reflector. Our aim is to maximize inner rear reflections and optical scattering in absorber layer and to facilitate maximum light trapping in absorber layer in order to absorb light and produce carrier generation. A single sheet of graphene is deposited on top of textured SiO2 dielectric material. P-i-n microcrystalline silicon (µc-Si) diode is sandwiched between top and bottom textured dielectric layer and back Ag layer is combined with dielectric serving as back-reflector to improve optical properties rear inner reflections and absorption of proposed solar cell. The thin graphene and textured SiO2 layers on top and silver layer combined with textured dielectric SiO2 as back reflector on rear side of solar cell assembly form a complete optical waveguide which enables maximum optical scattering inside absorber layer and light tricking. The proposed structure offers best optical absorption up to 90%, maximum rear optical reflections > 82%, maximum transparency by graphene layer, and good EM wave propagation through entire structure.

2. Simulation method and structure description

The film stack of graphene/Silicon solar cell device is illustrated in Fig. 1. The optical reflections, absorption and transmissions of light in G/Si/dielectric/metal stack signifying through inner front reflectance angle rf(θ) and inner rear reflectance angle rr(θ) of proposed solar cell structure, shown in Fig. 1, is calculated using Fresnel equations [30].

 

Fig. 1. (a) Schematic view of dielectric-metal reflector-based graphene/Silicon thin film solar cell. Here red ray denotes optical wave scattering and trapping through different angles at front reflectance angle (rr(θ)), and the rear reflectance angle (rf(θ)) denotes wavelength ranges λ=400nm-1200 nm. (b) Electrical schematically cross section view of proposed silicon thin film solar cell device structure with possible integration of Nickle (Ni) contacts inserted in top and bottom dielectric layers attached with semiconductor active layer.

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The layer specifications of proposed device are graphene layer of thickness 1 nm integrated on dielectric SiO2 layer of thickness 20 nm designed with explicit periodic textures. Recently it has been demonstrated that explicit combination of thin Graphene sheets (1 nm or <1 nm) with spacer dielectric and plasmonic assemblies can increase the overall performance of optical devices including solar cells, photo-sensors and detectors [31,32]. In our proposed simulation work we assumed graphene thickness to be 1 nm to attain appropriate model convergence. For the development of thin, doped silicon layers depending on the type of which is used for thin film solar cells applications, it is essential to have an accurate and fast scheme to limit the geometrical thickness and material properties of silicon sheets (microcrystalline or amorphous silicon) layers, because the growth rate and refractive index is not constant in the initial stage of the layer growth [33] and the material properties (both structural and electronic) are thickness dependent. In particular, thin µc-Si layers may have thickness dependent properties or even show a delayed inception of growth as well as the performance of devices with this material can be varied depending on thickness of microcrystalline silicon. For our simulations we have used microcrystalline silicon (µc-Si) as semiconductor active region and P-i-n Silicon diode is interleaved in between top and bottom textured dielectric layers with n = p = 20 nm and intrinsic layer 0.25um. The microcrystalline silicon substrate doping for p and n region are used 1e17[1/cm^3]. The edge to edge distance of pyramid shape texture is up to 0.45um where the semi-hexagonal shaped textures with depth of 80 nm and period 0.5um are designed next to each pyramidal texture.

To attain the accurate solar cell absorption, solar spectrum of AM 1.5 is employed to obtain the wavelength (λ) and incident angle (θ) dependant absorption (A) over the light EM spectrum with standard light intensity 1000W/m2.

The incident angle was altered from 0 [deg] to 90 [deg] for optical absorption to stimulate EM light wave reaching at front and rearmost surfaces at entire angles for different wavelengths. Fresnel equations are used to calculate reflectance, transmittance and absorbance. The reflection constant ‘r’ is described as reflected amplitude (E_b) to incident amplitude (E_f1) and transmission coefficient ‘t’ is stated as relation of transmitted amplitude (E_f2) to incident amplitude (E_i). Thus, to describe expressions for ‘r’ and ‘t’ (The Fresnel equations) we define some boundary conditions for Electric field factor (E) and Magnetic field factor (H) E, H: Hx, Hy, Hz, Ex, Ey, and n²Ez are continuous over entire boundaries. Here two main clarifications exist (1) These boundary conditions denote components of total field E, H= (E, H)_f + (E, H)_b (where E_f = E₀, E_b = rE₀) and (2) these boundary conditions are continuous across boundaries where x-components of E and H are defined in terms of permittivity and permittivity values µ = µ₀, ɛ = n² ɛ₀. Thus, light traveling from air medium to silicon medium through graphene, the reflection and transmission waves are defined for s and p polarisation [34].

The absorption ‘A’ is considered through integration of power dissipation in silicon absorber active sheet as shown in Eqs. 6 and 7. Here ω denotes the angular frequency, λ specified the free-space wavelength, ɛ₀ is the vacuum permittivity, and ɛ″ is imaginary component of composite semiconductor dielectric constant. ‘E’ and ‘H’ represents electric and magnetic field vectors, respectively. The electric field amplitude of incident wave was taken 1 V/m. Time average power loss Q (x, y, z) in a node inside absorber domain was considered via electric field distribution by using following equation [38];

These equations help to estimate the optical absorption in the wavelength array 350-1200 nm along with incidence angle 0° to 90°. It is assumed that entire photons are absorbed to produce electron-hole pair and an individual light generated carrier can arrive at electrodes. Finite element method (FEM) is utilised to regulate the electromagnetic fields (optical arenas) to propagate through device structure. In this scheme, Maxwell’s and Fresnel equations, are defined in simulator for EM wave incidence and propagation, as well as Drude-Lorentz model and fermi-Dirac distribution models are discretised for graphene modelling in solar cell structure.

Graphene is essentially modelled in two regimes (linear and non-linear) where linear model of graphene is demonstrated by Kubo formulation [39]. For Fermi-Dirac distribution term (Ef >>KBT) the graphene conductivity depends on electrochemical potential (an equal parameter of Fermi energy Ef determined by number of valence electrons which occupy energy levels conferring to Pauli’s principle). Consequently, in terahertz frequency ranges graphene is more well-defined by Drude-like surface conductivity [39], For the graphene modelling we used surface conductivity term determined by Kubo formalisms and we consider graphene as a monolayer sheet of small thickness. For our numerical simulations, graphene is modelled by means of volumetric permittivity approach where graphene is characterised as a thin sheet of material of small thickness (1 nm) with an in-plane effective permittivity. Dielectric materials are essentially demonstrated by closed form of Drude-Lorentz Dispersion model and to study the properties of metals, Drude Lorentz classical model returns to Drude metal model with no resonance estimates. Hence, in our simulations we have defined graphene as a Drude-Lorentz model by means of a thin sheet with plasma frequency dependent on Fermi level [39], [40].

Bulk compound refractive indexes for µc-Si, Ag, Cu, SiO2, SiN, and ZnO were taken from literature for the calculations [41,42]. For the integration of such materials including SiO2 and µc-Si the complete ‘n’ and ‘k’ (extinction values) spectrum (n and k values vary for each wavelength) were used to derive optical and absorption constants for these materials. The moderated absorption bands effects have been studied by using 2D FEM approach, which mathematically resolves Maxwell’s equations under periodic boundary condition, Floquet boundary conditions, scattering boundary condition and open boundary settings (perfect matched layers). This study is focused on analysing light reflections and scattering effects by applying different back metal reflector and dielectric effects and absorption spectra investigation at different wavelength between incident angle 0° to 90 °. Since numerous silicon solar cell structures have been presented recently where the performance of device increase depending on different texturing or back mirror configuration schemes. Despite advances, silicon thin film solar cells have not yet reached their complete potential. Silicon has been utilized as the dominant cell material ever, with cell efficiency hampered by silicon’s inadequate optical absorption within the wavelength array around its band-edge, particularly for thinner sheets. Hence there is increased focus on improving light absorption in thin films and rear light trapping schemes would be crucial for such conformations, considering front textures would impede the growth process of the top cell. In this study, we undertook simulations exploring the relationship and analysis between enhanced absorption into the solar cell, maximum inner scattering and rear reflections due to decreased parasitic losses in the metal. We identify mechanisms linking dependence on rear dielectric and metal reflector material offering high rear reflectance and low parasitic losses and absorption enhancements in active layer, and found that by ensuring correct design and configuration of textures and layer geometries, the light trapping structures will have a positive impact on the overall solar cell performance. Our results clearly show that the large angle scattering provided by the graphene-based silicon solar cell nanostructure is the reason for the enhanced optical absorption. The proposed graphene-silicon solar cell device with back reflector configuration offers maximum rear reflections and inner scattering for high light trapping in absorber layer.

3. Results and discussions

The standardized reflections (R) and transmission graph for graphene/silicon solar cell with application of dielectric/metal back reflector for standard AM1.5 solar spectrum ranges is shown in Fig. 3, for three different metal base reflector structure settings, as shown in Fig. 2. In Fig. 3, we show the cell reflectance of three different solar cell configurations, with plane typical Ag back reflector, plane dielectric layer deposited on Ag rear reflector and an additional textured top and bottom dielectric SiO2/Ag back reflector shown in Fig. 2 (a), (b) and (c), respectively.

 

Fig. 2. Schematic of a thin film Graphene/Silicon solar cell with dielectric-metal back reflector a) plane Ag back reflector without front/back dielectric layer and textures b) plane dielectric-Ag metal back reflector without textures c) textured front and bottom dielectric-Ag metal back reflector. Graphene layer is 1 nm thick deposited on 20 nm thick SiO2 dielectric spacer. Ag rear reflector is detached from n-layer of silicon by 20 nm thick SiO2 dielectric layer (b) and finally 40 nm thick SiO2 layer is made textured by pyramid and semi-hexagonal shape textures.

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Fig. 3. Simulated reflectance of graphene/Silicon thin film solar cell with varying dielectric SiO2 reflector configurations for wavelength spectra.

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The initial structure geometry under study is illustrated in Fig. 2. The solar cell stacks containing only plane Ag metal back reflector is reported in Fig. 2a, while a plane dielectric layer with metal back reflector illustrated in Fig. 2(b), and the textured dielectric layer with metal back reflector is shown in Fig. 2(c). For periodic textures in dielectric layer with specific shape and geometry, the high reflection is due to rough surfaces at rear sides. For wavelength λ up to 650 nm, a minor fraction of light reaches rear side of device and get absorbed. For silicon solar cells with plane Ag back reflector without textures and dielectric layer, incident light has low scattering up to 60% reflectance at 700 nm wavelength (Fig. 3) which reveals the conditions of less inner scattering and high rear transmissions from back reflector at shorter wavelengths <700 nm and high reflections at longer wavelengths also demonstrated in reference structures [27,29].

For wavelengths longer then 600 nm both solar cells (Figs. 2(b), 2(c)) with SiO2/Ag back reflector, the rear reflections are higher than reflectance of solar cell device by plane silver reflector without dielectric and textures (Fig. 2(a)), signifying a better light trapping and absorption in the active intrinsic i-layer of silicon.

These high rear reflections for infrared wavelength ranges show that more light reaches the back contact and decrease parasitic absorption and reduced plasmonic absorption in silver occurs due to combined effect of dielectric and metal which comes up with the impression that more light reflected from back reflectors, less light transmissions from back contact and more light scattering and trapping in active layers. In order to further increase the rear reflections and reduced parasitic absorptions, we introduced a textures SiO2 dielectric layer separating Ag and silicon layers, as illustrated in Fig. 2(c). Despite the increase in photon absorption for these two cell configurations (middle and right), the rear cell reflection is reduced up to 50% at wavelength 350nm-550 nm for G/Si p-i-n solar cell by SiO2/Ag plane back mirror without textures, as shown in Fig. 3.

This effect probably results from concentrated captivation losses in dielectric sheet or decreased plasmonic absorption in silver or reduction in parasitic absorption inside front dielectric layer. We can see in Fig. 3, the rear reflections for SiO2/Ag plane back reflector without textures gradually increase up to 80% after wavelength 650 nm as compared to 60% reflectance for plane Ag back reflector solar cell without dielectric and textures (Figs. 2(a)–2(b)). After characterisation of back reflector layers the simulation of rear reflection and transmission were performed and cell reflectance and transmittance results are presented in Fig. 3. The graphene/Silicon solar cell rear reflections are higher for visible to infrared wavelength ranges (600nm-1200 nm) lead to rear reflections enhancement from 80% up to 90% (around 30% and 10% reflectance enhancement compared with plane Ag and dielectric/Ag back reflectors respectively. The low transmission and high reflections from back reflectors reveal the fact that low parasitic absorption occurs as for the case of linear dielectric-metal back reflector (Fig. 2(b)) which can further increase reflections by applying texturing technique. So, the light goes through several reflections from periodic textures in rear side and this increase the light trapping and absorption in i-layer of silicon. In fact, the topology of front and back dielectric layer with thicknesses 20 nm and Ag metal reflector offers good reflections and high light scattering due to less plasmonic absorption losses in rear rough metal interface. According to recent studies of thin solar cells with bottom detached mirrors, high rear optical reflectivity can arise due to textured dielectric/metal back reflectors, also the parasitic absorbance losses occur in rear dielectric as well as in metal films [43,44].

In order to well analyse and improve rear optical reflections and parasitic absorption losses at back side of thin film SC devices, utilisation of precise texturing techniques, dielectric thickness, and rear dielectric/metal material with appropriate refractive index is needed. In a recent study it has been analysed that the effect of dielectric thickness is very sensitive to the optical absorption of solar cell devices and an appropriate dielectric thickness of 20 nm could offer high light captivity [25]. Consequently, to increase optical reflections at back side of SC device we present a direct contrast of bulk variety of back mirrors depending upon back metal material and back dielectric material sheets on identical graphene/silicon SC and therefore produce a rapid and precise study on its influence on solar cell presentation. For this purpose, three varied forms of back contact metal materials and three types of back dielectric materials combined with metal are simulated as shown in Fig. 4(a)-4(b). The rear reflections of three different back contacts silver (Ag), copper (Cu) and gold (Au) combined with dielectric SiO2 layer (20 nm) are analysed by using Fresnel equations (1-5) as shown in Fig. 4(a). Similarly, optical reflections are simulated for varied plane dielectric materials Silicon dioxide (SiO2), zinc oxide (ZnO) and silicon nitride (SiN) with the combination of silver plane back metal reflector as shown in Fig. 4(b).

 

Fig. 4. Reflectance of thin film graphene-based silicon solar cell with a) three different kinds of back metal reflector materials Ag, Au and Cu and b) three different rear dielectric materials ZnO/Ag, SiN/Ag, and SiO2/Ag.

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As can be seen in Fig. 4, rear reflections for graphene/silicon thin film solar cell with the application of varied rear metal reflector materials are observed. To achieve high light absorption in active layer through high rear reflections from back reflector we analyse copper, gold and silver metal reflectors where the maximum reflections were resulted for silver back metal reflector. As illustrated in Fig. 4(a), maximum rear reflections up to 90% was achieved with the application of Ag back contact combined with rear dielectric SiO2 layer. However, minimum reflections were observed when copper or gold is used for metallic back reflector layer in graphene/silicon thin film solar cell. According to Fresnel equations [30,34] the reflections/transmissions or refractions of light strongly depends upon the refractive index (n) of dielectric and rear metal materials. Since ‘n’ reduces, the active reflectance at the boundaries among n-silicon layer and back dielectric film (dielectric medium) rises.

Therefore, less light reaches back reflector. By decreasing ‘n’ the refractive index of rear dielectric region from 2 -1.45 and rear metallic contact medium from 0.7–0.05, an increase in an optical light reflection from rear side of graphene/silicon thin film solar cell could be observed. As we can see in Fig. 4a, when Cu metallic back reflector with refractive index ‘n’ 0.63 is utilised with the combination of dielectric SiO2 layer, low rear reflections around 40% is observed starting from wavelength ranges 650 nm to longer wavelengths. This low reflectance compared with gold metal back reflector still offers high reflections up to 60% starting from mid-visible wavelength region up to infrared spectrum. It can be clearly seen that silver rear reflector with refractive index ‘n’ 0.05 improves reflections by 90%. It is observed that metal reflector materials with low refractive index reduce parasitic absorption losses and deliver high rear reflections so the light coming in active silicon layer scatter and absorb efficiently. We observed that as refractive index for metal reflector ‘n’ declines, the plasmonic captivation losses are shifted to smaller wavelengths or we can say for cupper reflector the rear reflections increased for longer wavelengths, likewise for Au reflector the parasitic absorption losses shifted to shorter wavelengths and an appropriate rear reflectance improved for silver reflectors. Therefore, light trapping is significantly improved with the selection of low refractive index back metal reflector materials. Simulations were performed for proposed SC device with varied rear dielectric materials zinc oxide (ZnO), Silicon nitride (SiN) and Silicon dioxide (SiO2) with the combination of silver metal back reflector. It can be observed from Fig. 4(b); rear dielectric reflections are quite low around 35%- 65% for SiN and ZnO respectively. However parasitic absorption is reduced with SiO2 dielectric material and reflectance is enhanced by 30% compared with ZnO dielectric material. In this series, again this particular trend was observed, by lowering the dielectric medium refractive index (from 2.0-1.35) an increase in rear reflectance and reduced light absorption in rear dielectric-metal reflector medium could be observed. The increased ‘R’ may also consequence from decreased parasitic absorption losses in anterior dielectric layer.

Internal absorbance was intended to assess the fraction of light trapped and fascinated in the active intrinsic silicon sheet and so to approximate the parasitic absorption losses in the non-active layer (dielectric and metal layers). The reflectance of device with SiO2 as back dielectric medium joint with silver back mirror is significantly amplified up to 90% from mid-visible region to wavelengths longer than 700 nm. Considering the structure illustrated in Fig. 1. The possible configuration of electrical circuit is presented in Fig. 1. The presence of dielectric layer is necessary and enables the incident TM wave with magnetic field oscillating along z direction strongly localize and restore in substrate. The graphene located at top of dielectric spacer plays an important role in absorbing the incoming energy and thus causing the enhanced absorption at the Magnetic resonance wavelength. In general, the large quantity of interface states existing at the dielectric– semiconductor interface will lead to a high surface recombination probability, which will accordingly reduce the energy conversion efficiency. We placed SiO2 dielectric layer in between silicon diode and graphene. The presence of electrode at top of SiO2 can really affect the collectability of carriers and is difficult for carriers to tunnel though this thickness so we can introduce Nickle (Ni) as less resistance and good ohmic contact at top of silicon layer also to reduce shading we can use small radius of contacts. Our intention is to sustain stability between thickness of each layer and to produce best combination in between texture period and width and spacer thickness to increase generation of strong light propagation and absorption effects in silicon thin films.

We simulate the ultimate absorption in graphene/silicon thin film solar cell with dielectric-metal back reflector. We initiate the analysis by establishing a link between rear reflectance (Rr) (also the measure of parasitic absorption losses), optical trapping and ultimate absorption in intrinsic silicon active layer depending upon inner dielectric texture shapes, period and depth. The absorption was measured by varying incident angle (θ) from 0° to 90° as can be seen in Fig. 5. Rear reflectance varies equally with front internal reflection r_f (θ) and rearmost internal reflection angle r_r (θ) [27]. Rear reflection angle r_r (θ) actually explains the amount of light lost in parasitic absorption (optical absorption in non-active layers of solar cell) per total internal reflections. Although r_f (θ) essentially determines the lifetime of absorbed photons and the lifetime of photons inside the cell and therefore the path length/lifetime of rear internal reflections they experience with rear dielectric reflector material is analysed. We can say that both of these internal angles (r_f (θ) and r_r (θ)) are dependent on incident angle (θ) and textured mediums. Whereas the dispersion of these angles (at which the light photons reach out of the interfaces) depends on both top and bottom texture profile as well as the outlook of these textures might take part in light trapping and multiple scattering inside absorber layer, hence, reflectance (Rr) depends on textures. Figure 5 demonstrates the correlation between absorption (A) and light trapping for wafers of varying texture shapes, period and depth with varying absorption peaks. Absorption and Electric field distribution were calculated from equations (6-8) and light trapping visualisation was simulated for incoming electromagnetic wave propagating through proposed graphene/ silicon solar cell with varied textures under standard AM1.5 solar cell spectrum [28].

 

Fig. 5. Absorption as a function of incident angle (θ) for different texture shape, period ‘p’ and depth ‘d’. Light trapping visualization in active region of graphene/silicon solar cell for a) pyramid shape textures b) semi-hexagon shape textures c) pyramid and semi hexagon shape textures. The red legend represents the maximum magnetic field distribution (visualization of the magnetic field |H|), and total magnitude of current density (A/m).

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Generally incoming p- polarised light above critical angle can be strongly absorbed only if the dielectric layer is thinner then wave penetration medium depth. The optical absorption loss is utmost harmful to cell efficiency because it arises at extensive range of incidence angle. For this concern, specific thickness of dielectric medium is considered along with suitable texture shape and depth for high light absorption in cell. The air medium is kept to be λ/2 and perfect matched layer (PML) surrounds the solar cell which can undirect the incoming waves to penetrate and absorb strongly under varied incident angle conditions and to analyse the optimal angle of incidence that can increase inner scattering angles (r_f (θ) and r_r (θ)).

In the proposal of thin SC devices, light tricking is essential, by means of increasing the optical engagement. Sunlight trapping actually happens due to existence of good back reflectors, graphene on topmost, Ag on lowermost, specific texture profile at front and rear side of cell. Although plasmonic/photonic crystal structure can be good idea to increase optical trapping [28], otherwise front and rear textures in dielectric and rear dielectric-metal mirrors are an attractive key for light trapping in intermittently structure device. In Fig. 5, the cell absorption is illustrated by using three different texture profiles at a range of incident angles from 0° to 90°. With small pyramid periods, the incoupling of light into the solar cell is enhanced, but almost no optical scattering or no diffraction of light at longer wavelengths is observed. By identifying the key losses in the solar cell structure, we can derive potential approaches to minimize these optical losses. For thin film solar cells, the period and height of the pyramids must be reduced so that the diffracted light can interfere with light from neighbouring unit cells. The incoupling of the incident light can also be enhanced by using a double texture scheme. The regular surface texture is covered with spikes of significantly smaller dimensions then the incoming wavelength, such that the blue light can be efficiently coupled into the absorber layer. The smaller spikes act as an effective refractive index matching layer for the shorter wavelengths. The larger surface texture diffracts the longer wavelength light. The double texture or combination of both shapes combines the advantages from both of the regimes. This means that even though the randomized surface texture leads to a distinct increase of the short circuit current, however it is very challenging to optimise the scattering and reflections causing from randomised textures then for periodic textures. It can be expected that a periodic structure will provide a higher efficiency and light trapping then a random textured surface. Recent results for periodically patterned solar cells with very thin silicon absorber layers have previously shown very promising results as well as some optical losses resulting from only pyramid shaped textures [45].

We developed periodically textured dielectric with combination of pyramid and semi-hexagonal arrays and integrated in graphene based µc-Si cells with the p-i-n substrate uniform configuration in order to mitigate the trade-off as much as possible, recently reported for hexagonal textured solar cells previously [46,47]. Because of their simplicity and uniformity in texture morphology, periodic structures have the advantage of far clearer correlations between texture structures and the photovoltaic performance in solar cells. In addition, periodic textures have the potential to overcome the limitations of the optical path enhancement with randomly textured substrates. Furthermore, the periodicity allows for the use of periodic boundary conditions in optical calculations, which reduces the calculation cost significantly. By choosing a proper period and an aspect ratio of pyramid and hexagonal textures with respect to the cell thickness, a proficient percentage of 90% optical coupling and absorption was attained in a µc-Si solar cell with monolayer graphene sheet. Therefore, in this study we choose to simulate proposed µc-Si solar cell device with 1 nm thick graphene by combining both regimes of periodic pyramid and semi hexagon textures to improve light trapping effects and maximum inner scatterings.

Primarily pyramid textures with period ‘p’ 0.65um and depth ‘d’ 60 nm were designed at front and rear dielectric medium layers as can be seen in light trapping visualisation solar cell configuration in Fig. 5(a). This texture solar cell profile exhibit absorption (A) up to 40% at incident angle 50°, which confirms low optical scattering comparatively inside absorber layer and high parasitic absorption losses due to less reflections for rear medium reflection angle ‘r_f (θ)’. This texture outline may decrease rear reflectance (Rr) and therefore light trapping and absorption becomes low in active region. Textures with excessively symmetric or intervallic outlines like plane textures or textures with less depth might offer high reflectance but then sunlight travels through active layers on critical perspectives and simply outflows through the anterior interface. Although for pyramid textures with extensive symmetric outlook or less depth ‘d’ 60 nm, the light has less reflectance and minimum absorption in absorber layer because most light might have reflected back through front interface. Conversely arbitrary/inverted pyramids, or random vertical trenches result in high front reflectance angle r_f (θ) and high rear angle r_r (θ), because even an average light photon can hit the back reflector many times to produce photon trapping [48]. Accordingly, we used semi-hexagonal shaped textures with depth ‘d’ 70 nm and same period as for pyramid textures, to analyse rear reflections and absorption in cell. We detected rather virtuous variation in the simulated optical absorption for this textures profile, where highest absorption peak was observed at 20° incident angle with 70% photon absorption. Another two small absorption peaks were found at 40° and 65° for same texture outline which confirms that this texture figure and depth offers high light scattering at different incident angles and maximum scattering up to 70% with high rear reflectance angle and low parasitic absorption losses results at 20°. Fortunately, for dielectric mediums thinner then coarsely 100 nm, the optical harm is moderated, since the optical tendency traveling through active layers influences the metal individually for positions nearby critical angle. Beneath this critical perspective, parasitic captivation in metal layers increased conferring to interface surroundings at angle of incident. If dielectric refractive index will be low and texture depth and outline will be asymmetric, the critical angle will change accordingly, so the EM wave penetration complexity and interaction strength mutually affect photon lifetime inside absorber layer [29]. Also, we can observe the significant discrepancy in absorption with perspective of incidence revealed in Fig. 5. It can be finely identified that device textures change Absorption (A) and rear medium reflection angle and together these determine the light trapping (entire typical path length of photons trapped inside absorber region in the absence of parasitic captivation). We can clearly see in Fig. 5 the pyramid and semi-hexagonal profile of textures offers highest photon absorption around 90% and light trapping at 40° angle of incidence. The specific period ‘p’ and depth ‘d’ of these periodic textures were kept 0.5um and 80 nm respectively where the rear dielectric thickness was taken 40 nm. The absorption peak at this angle of incident might increase front r_f (θ) and rear reflectance angle r_r (θ) which accordingly increase inner optical scatterings and photon pathlength as illustrated in Fig. 5(c). This texture configuration increase photon absorption where several short absorption peaks can be observed depending upon texture depth and incident angle. Since the parasitic absorption depends on angle and top and bottom textures actually control the optical dispersal function inside the absorber layer, rear medium reflectance angle r_r (θ) is also texture dependant. The distributed optical wave has a supreme propagation distance over solar cell assembly at the incidence angle 40° consequences extreme light trapping while it reduces to minimum values on 50°, 65° and 90°. As we can observe from above illustrations, how textures strongly effect the reflections, absorption and light trapping so it is obvious to choose specific textured solar cell configuration with the selection of precise dielectric thickness, graphene on top, dielectric material and back metal reflector material. Although silver is best reflector material with silicon dioxide dielectric medium. Therefore, we must specify front and rear textures to estimate perfect optical absorption and reduce parasitic absorption losses. Therefore, this design demonstrates a considerable increment in light absorption, rear inner reflections, low parasitic interest losses and maximum light tricking in absorber layer with respect to planar graphene-based silicon solar cells.

4. Conclusion

Rear reflections from solar cell back mirrors and light absorption in silicon thin film solar cells is sensitive to top and bottom texture profiles, back dielectric/metal material and depth. An inclusive study in which the influence of these parameters was varied and explored a general method to maximize light trapping and absorption in graphene-based silicon thin film solar devices is demonstrated. We proposed a new design of thin film graphene/silicon solar cell with application of dielectric-metal back reflector of SiO2-Ag with an array of periodic textures. Low refractive index textured dielectric-metal reflector is utilized instead of plane back metal reflector or plane back dielectric-metal reflector and influence of both the textures profile and dielectric/metal reflector material is considered for high rear reflections and light trapping. We achieved maximum inner scattering and photon absorption at angle of incidence 40° where the light reflections and absorptions was analyzed with varied incidence angle from 0° to 90°. Excellent photon absorption is achieved in visible to infrared wavelength region with no major drop in rear reflectance for longer wavelengths. Extreme light trapping and captivation in absorber layer is improved from 80% to 90% and optical reflectance from rear side >89% is achieved in contrast to the previous studied reference structures [25,27]. We presented a precise geometry with graphene sheet 1[nm] thick, silver as metal reflector, random pyramid and semi-hexagonal shaped textures, SiO2 as dielectric medium textured from front and bottom with period ‘p’ 0.5[um] and depth ‘d’ 80[nm] with dielectric thickness 40 nm. The proposed design demonstrates a substantial light absorption and maximum inner light reflections when compared to silicon solar cells with planar back reflector geometries.