The optics of core / shell nanowire solar cells was investigated. The optical wave propagation was studied by finite difference time domain simulations using realistic interface morphologies. The interface morphologies were determined by a 3D surface coverage algorithm, which provides a realistic film formation of amorphous silicon films on zinc oxide nanowire arrays. The influence of the nanowire dimensions on the interface morphology and light trapping was investigated and optimal dimensions of the zinc oxide nanowire were derived.
© 2014 Optical Society of America
The realization of core / shell nanowire solar cells is a promising route to enhance the energy conversion efficiency and short circuit current of solar cells utilizing materials that are limited by low charge carrier diffusion lengths [1–8]. The 3D architecture of the solar cells allows for the decoupling of electrical and optical properties, so that high conversion efficiencies can be achieved. Furthermore, the 3D arrangement of the nanowires (NWs) allows for an efficient incoupling and trapping of light in the solar cell structure leading to an enhanced quantum efficiency and short circuit current. Experimentally realized core / shell solar cell based on zinc oxide (ZnO) nanowires in combination with amorphous silicon overcoats exhibit high short circuit currents [1–7], while the photo-induced degradation (Staebler-Wronski effect) of the solar cells is reduced [6,9]. The combination of oxide semiconductor based nanowires with silicon thin film technology is a very promising route, since highly ordered oxide based nanowires can be grown at low temperatures on glass or plastic substrates [10–13]. Different growth processes of ZnO nanowires ranging from hydrothermal to electro-deposition and pulse laser deposition have been demonstrated [1,10–14]. The array of nanowires acts as substrate for the growth of the very thin solar cells. The ZnO nanowires are doped by aluminum or gallium, so that they form an electrical contact to the solar cell . Afterwards, the nanowires are over-coated by the thin amorphous silicon p-i-n diode. The deposition process used to cover the array of nanowires must be conformal to ensure all regions of the nanowire surface are covered with an equal amount of p-i-n layers, which would enable efficient generation of photocurrent across the entire surface area of the nanowires. Hence, atomic layer deposition and chemical vapor deposition processes are most favorable since they exhibit excellent surface coverage [15–18]. In most of the cases, the amorphous silicon films are prepared by plasma enhanced chemical vapor deposition [17,18].
Although promising experimental results have been demonstrated the optimal core/shell dimensions of the solar cell are unknown. The aim of the manuscript is to derive optimal device dimensions of core/shell solar cells. However, a realistic description of the surface and interface morphology is required to study the optical properties of such nanowire solar cells. We have developed a simple approach to determine realistic interface morphologies of the individual layers of the solar cells. The approach is described in section 2. The simulation results are presented and discussed in section 3 before summarizing the results in section 4.
2. Device structures and interface morphologies
In the following, the device model of the core/shell nanowire solar cell is described. The device structure was selected to be consistent with experimentally realized core/shell nanowire solar cells [1–7]. Figure 1 (left) shows the Scanning Electron Microscope (SEM) image of an array of zinc oxide nanowires synthesized from a thin Al-doped seed layer. The nanowires were subsequently coated with a thin amorphous silicon layer. A cross-section of the nanowire solar cell is shown in Fig. 1 (right). The amorphous silicon solar cells exhibited an excellent surface coverage of the ZnO nanowires . The silver back reflector is assumed to be flat to minimize parasitic absorption losses compared to a textured silver back reflector . On top of the silver reflector, a 50 nm thick back TCO ZnO film is defined to act as a seed layer for the growth of the ZnO nanowires. The dimensions of the zinc oxide nanowire array are described by the spacing of the nanowires (period of the unit cell, p), the diameter (d), and height of the nanowire (h). The cross section of the nanowire is assumed to be circular. To provide an analysis of the optics in core/shell nanowire arrays a detailed description of the nanowire geometry is required.
The optimal device geometry of the nanowires can only be determined by a realistic description of the thin film growth on the ZnO nanowire array. Figure 2 shows interface morphologies of silicon films on ZnO nanowires for different growth models. Figure 2(a) shows the interface morphology of a silicon film in which the silicon film grows in the direction of the substrate normal. Such a growth model is commonly assumed when describing the silicon film growth on textured substrates. However, in the case of the ZnO nanowires array the substrate normal is zero for the side walls of the nanowires so that the side walls are not covered. A realistic description of the silicon film formation is given in Fig. 2(b). In order to provide a realistic description of the interface morphology a 3D surface coverage algorithm was developed. The algorithm assumes that the film grows in the direction of the local surface normal. A comparison of measured and calculated silicon thin film morphologies on textured substrates exhibits a very good agreement so that the algorithm enables a realistic interface description of silicon thin film formation. References 20,21 provide details on the surface growth algorithm. The same film formation mechanism was assumed for the front transparent conductive oxide layer. The calculated interface morphologies were used as input parameter in the optical simulations. For a device structure in which the spacing between the nanowires is larger than twice the thickness of the thin amorphous silicon diode and the length of the nanowire is much larger than the diameter of the nanowire the interface morphology can be approximated by the simple geometrical model as shown in Fig. 2(c).
The thin amorphous silicon p-i-n solar cell consists of a 10 nm n-layer, an intrinsic amorphous silicon layer (i-layer) and 10 nm p-layer. Since the solar cell is very thin it can be assumed that the diffusion length of the photo-generated carriers is larger than the solar cell thickness. The thickness of the front TCO (ZnO) layer was 100 nm.
3. Results and discussion
3.1 Electrical versus optical properties
Preparing very thin amorphous silicon solar cells on ZnO nanowire allows for decoupling of the electrical and optical properties of the solar cell. Due to the short diffusion length of carriers in nanowire solar cells, their electrical properties are similar to that of a solar cell of flat substrates. The same structure behaves optically like a much thicker solar cell due to efficient light trapping within the nanowire array . To describe the differences in the electrical and optical behavior of the solar cell, the “electrical thickness” and “optical thickness” need to be defined. The electrical thickness, telec, is defined as the maximum distance photo-generated electron/hole pairs have to travel, while the optical or effective thickness of i-layer, topt, is the averaged intrinsic layer thickness of the solar cell structure. The electrical thickness and optical thickness depend on the interface morphologies and/or silicon film growth [Figs. 2(b) and 3]. The electrical and optical thicknesses were compared to the nominal thickness of the intrinsic layer of the solar cell, which is given by ti. The optical thickness, topt, of the absorber/intrinsic (i) layer of the p-i-n diode was calculated byFig. 3. The interface morphology of the nanowire solar cell is determined by the diameter of the nanowire, height of the nanowire, period or spacing of the unit cell, and thickness of the silicon film, to . The influence of different dimensions of the ZnO array on the interface morphology is shown in Fig. 3. The diameter (d) and height (h) of the nanowire are 120 nm and 200 nm, respectively, while the thickness of the p-i-n diode or amorphous silicon solar cell is assumed to be to = 120 nm. If the period is smaller than 2 × to + d, the gap between the nanowires is completely filled [Fig. 3(a)] or partly filled [Fig. 3(b)]. For such structures, the electrical thickness increases from to to h + to. Since the height of the nanowires is usually distinctly larger than the nominal thickness of the solar cells, creating a maximum charge carrier transport distance that may exceed the carrier diffusion length. For the selected device geometries in Fig. 3, such an effect occurs for nanowire spacing smaller than 500 nm. As a consequence, we will not discuss the optics of these structures. We focused on wire spacings of unit cell period (p>500 nm) for which the electrical thickness of the solar cell is equal to the nominal thickness (to) of the amorphous silicon solar cell. Examples of such structures are shown in Figs. 3(c) and 3(d). The surface morphology for large nanowire spacing is shown in Fig. 3(d). Since the period is distinctly increased, a large fraction of the structure is flat. With increasing period, the optical thickness converges towards the nominal thickness of the solar cell [Fig. 3(d)]. The optical thickness for the structure shown in Fig. 3(c) is distinctly larger compared to structure shown in Fig. 3(d).
In this study, we focused on structures which exhibit an increased optical thickness while the electrical thickness is equal to the nominal thickness. Hence, we focused our investigation on structures where the p-i-n diode is wrapped around the individual nanowires. Furthermore, it is assumed that the height of the nanowire is larger than the nominal thickness of the p-i-n diode. The structures where the height of the wire is smaller than the nominal thickness of the p-i-n diode correspond to solar cells with textured contact layers [22–27].
3.2 Optics of core/shell nanowire solar cells
The optical wave propagation within the core/shell nanowire solar cells was determined by Finite Difference Time Domain (FDTD) simulations [19,23,26,27]. The Maxwell’s equations were rigorously solved in 3D and the electric fields within the solar cells and absorption of light in individual layers of the solar cell were calculated. To compare the different solar cell structures, the power loss profiles, the quantum efficiency (QE) and the short circuit current were calculated. Firstly, the electric field was calculated in the 3D FDTD simulations for circularly polarized incident light. Secondly, the time average power loss within the amorphous silicon solar cells was calculated from the electric fields for the incident light with amplitude of 1 V/m. Afterwards, the quantum efficiency was calculated and is defined as the ratio of the power absorbed in the i-layer with respect to the total power incident in the unit cell. In the simulations, it was assumed that all photo-generated charge carriers are collected, i.e. internal quantum efficiency was assumed to be 100%. Finally, the short circuit current was calculated from the quantum efficiency of the i-layer. References 19,25 give details on the calculation of these parameters. The calculated power loss profile for a solar cell [Fig. 4(a)] with an i-layer thickness of 100 nm is shown in Figs. 4(b)-4(d). The power loss profile of the solar cell was calculated in 3D and Fig. 4(a) exhibits the power loss profile in the center of the unit cell. The power loss profiles for Figs. 4(b)-4(d) are shown for an incident wavelength of 360 nm, 560 nm and 620 nm, respectively. For a shorter wavelength of 360 nm, the absorption of light mainly occurs in the front TCO due to the high absorption coefficient of ZnO close to the band edge. Longer wavelengths (560 nm and 620 nm) is scattered and diffracted by the nanowire array to enhance absorption of light in absorber layer of the solar cell.
The influence of the ZnO nanowire diameter on the quantum efficiency is shown in Fig. 5(a) for a solar cell with a period of 600 nm, a height of 200 nm and i-layer thickness of 100 nm. The diameter of the nanowire was varied from 60 nm to 150 nm. As a reference the QE of a solar cell on the flat substrate is shown in Figs. 5 and 6(b).A comparison of different simulations shows that the diameter of the ZnO nanowire has only a minor influence on the quantum efficiency. The incoupling of light in the array of the solar cell is not affected. Furthermore, the scattering of longer wavelengths light remains almost unchanged. The short circuit current of the solar cell increases from 15.0 mA/cm2 to 15.6 mA/cm2 with increasing diameter. The reference solar cell on the flat substrate exhibits a short circuit current of 7.6 mA/cm2. The optical thickness of i-layer was calculated to be 126 nm for a 50 nm ZnO nanowire diameter and 140 nm for a nanowire diameter of 150 nm for the nominal i-layer thickness of 100 nm.
The influence of the nanowire spacing or unit cell period on the quantum efficiency is shown in Fig. 5(b). The ZnO nanowire height was assumed to be 200 nm, while the period was varied from 600 nm to 800 nm. The quantum efficiency was calculated for a nominal i-layer thickness of 100 nm. The optical thickness of i-layer decreases from 136 nm (for a 600 nm period) to 120 nm (for 800 nm period) with increasing period. The increasing period results in a drop of the short circuit current from 15.6 mA/cm2 to 12.3 mA/cm2. For smaller periods, the gap between the nanowires is filled and the electrical thickness exceeds 100 nm nominal i-layer thickness. For larger periods, the optical thickness and the short circuit current steadily decrease. Furthermore, light is diffracted in smaller angles leading to a drop in the short circuit current. For very large periods the quantum efficiencies and short circuit currents converge towards that of the flat substrate and as a result, the nanowire solar cells with larger nanowire spacing behave like a flat solar cell.
The influence of i-layer thickness on the quantum efficiency is shown in Fig. 6(a). The quantum efficiency increases with increasing thickness of the i-layer. The short circuit currents increase from 13.8 mA/cm2 for an i-layer thickness of 50 nm to 15.8 mA/cm2 for a thickness of 150 nm. The height, diameter and period of the ZnO nanowire were 200 nm, 120 nm and 600 nm, respectively. The optical thickness of nominal i-layer thickness of 50 nm is estimated to be 65 nm. For the nominal thickness of 150 nm the approximated optical thickness of 208 nm was calculated. The increased optical thickness leads to the higher quantum efficiency for wavelengths larger than 520 nm. The nominal thickness of the i-layer also influences the front contact morphology and the incoupling of the shorter wavelength light (360-520 nm). The best light incoupling is achieved for the i-layer thickness of 125 nm.
The influence of the nanowire height on the quantum efficiency is shown in Fig. 6(b). The height of the wires was varied from 100 nm to 400 nm. For shorter wavelengths (<360 nm), the quantum efficiency is not affected by the nanowire heights. For wavelengths longer than 360 nm, increased quantum efficiencies were observed with increasing nanowire height. The QE is increased due to the improved absorption of the green and red parts of the optical spectrum. The improved absorption is due to the gain in the optical thickness and efficient photon management leading to an increased short circuit current [Figs. 7(a) and 7(b)].
The optical thickness of the absorber (i) layer as a function of the nanowire height for i-layer thickness of 100 nm, n-layer thickness of 10 nm, diameter of 120 nm, and period of 600 nm is shown in Fig. 7(a). While the optical thickness of the i-layer for the realistic interfaces is calculated by Eq. (1), and the value can be approximated by a simple geometrical model as shown in Fig. 2(c):Equations (1) and (2) show that for the given period and nanowire diameter the optical thickness depends linearly on the height of the nanowire [Fig. 7(a)]. However, the optical thickness calculated using Eq. (2) is slightly higher than that calculated from Eq. (1). It is due to the over estimation of the geometrical model in the region of the tip of the nanowire. Figure 7(b) exhibits the short circuit current as a function of the nanowire height. The short circuit current increases from 7.6 mA/cm2 for a flat solar cell up to 16.6 mA/cm2 for a nominal absorber thickness of 100 nm. The short circuit current starts to saturate at a nanowire height of 300 nm.
A comparison of the calculated short circuit current with short circuit current for amorphous silicon solar cells prepared on textured substrates shows that comparable short circuit currents can be achieved for significantly thinner diode. Amorphous silicon solar cell on randomly textured substrates exhibit short circuit currents ranging from 14 to 16 mA/cm2 using i-layer thicknesses of 300 nm [19,27–30]. However, our simulations show that high short circuit current of 16 mA/cm2 can be obtained for a nominal absorber thickness of only 100 nm (optical thickness of i-layer of 150 nm). This high short circuit current is achieved by the gain in the optical thickness and efficient light trapping properties governed by the nanowire array. To estimate the contribution of the optical thickness on the short circuit current, additional optical simulations were carried out. Increasing the nanowire heights up to 400 nm results in an increase of the optical thickness of i-layer from 100 nm to 177 nm. The corresponding gain in short circuit current for a flat solar cell with a thickness equal to the optical thickness was determined [Fig. 7].
The increased optical thickness results in a gain of the short circuit current of 2.2 mA/cm2 over the flat substrate which exhibits a short circuit current of 7.6 mA/cm2. The remaining gain of the short circuit current, 6.8 mA/cm2 is caused by efficient light trapping. Hence, it can be concluded that the gain in the optical thickness and efficient photon management technique lead to gain of the short circuit current of 9 mA/cm2 as compared to the flat substrate [Fig. 7(b)].
A comparison of the calculated nanowire solar cells with solar cells with textured contact layers shows that distinctly higher short circuit current can be achieved for nanowire solar cell architectures using very thin solar cells. By using thin solar cells the extraction of photo-generated charges can be improved and the influence of photo induced electronic defect creation (Staebler-Wronski-Effect) on the solar cell properties can be reduced . A comparison of Figs. 6(a) and 6(b) shows very similar sets of quantum efficiency curves. In Fig. 6(a), the thickness of the absorber layer was increased, while in Fig. 6(b), the height of the nanowire was increased. The comparison of these two graphs reveals that the effect on the quantum efficiency is comparable. This result would now lead to the conclusion that high short circuit currents and conversion efficiencies can be achieved for very thin amorphous silicon solar cells. However, this is not completely correct. The increased surface of the ZnO nanowire array leads to an increase of the saturation current of the solar cell, which has a negative influence on the open circuit voltage and fill factor. This is confirmed by experimental results [1,5,7,8,31]. Most of the experimental results show excellent absorption properties for nanowire solar cells resulting in high short circuit currents, while the open circuit voltage and fill factor are relatively low. Most of the structures in literature use very long nanowire, so that the optical thickness of the solar cells is very large. Such large optical thicknesses are not required to efficiently absorb most of the incident light. The large nanowire surface area leads to a distinct increase of the saturation current (saturation current density × surface area) and a drop of the open circuit voltage and fill factor. Hence, the use of nanowire solar cells allows for a partial decoupling of the optical and electrical properties of the solar cells. Furthermore, the optical properties of the nanowire changes with decreasing diameter of the nanowire and thickness of the amorphous silicon p-i-n diode. For very small nanowire diameters (<30 nm) and very thin diodes (<30nm) the number of modes that propagate in the individual nanowire drops. For such small structures the optics is dominated by waveguide modes in the nanowires. As a consequence a distinct drop of the quantum efficiency and short circuit current is observed.
For nanowire solar cells investigated in this study a large number of modes can propagate in the nanowires resulting in high quantum efficiencies and short circuit currents. The use of nanowire arrays as substrate for the preparation of solar cells introduces new parameters in designing and optimizing solar cells. However, the influence of the 3D surface on all three solar cell parameters; short circuit current, open circuit voltage and fill factor has to be considered when deriving optimal device geometries. Our study shows that high short circuit currents can already be achieved for ZnO nanowire heights of less than 500 nm. Subsequently, the open circuit voltage and the fill factor are rarely affected.
The optics of core / shell nanowire solar cells was investigated using realistic interface morphologies. The interface morphology of the amorphous silicon solar cells based on zinc oxide nanowires was calculated by using a 3D surface coverage algorithm. The interface morphologies and nominal film thicknesses were used as input parameters to calculate the optical wave propagation using Finite Difference Time Domain simulations. High short circuit currents can be comparable to the best solar cells prepared on textured contact layers. However, the high short circuit currents can be achieved for very thin absorber layers. The high short circuit current is achieved by a combination of light trapping and an increased optical thickness of the solar cell. The optical simulations show that very high short circuit currents can already be achieved for nanowires with a height of less than 500 nm. Therefore, the nanowire solar cell architecture allows for a partial decoupling of the electrical and optical properties of the solar cells. Such an approach is of major interest for materials systems which exhibit low carrier or exciton diffusion lengths. Further investigations are needed to study the effect of the nanowire architecture on the open circuit voltage and the fill factor.
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