Simulation Analysis on Photoelectric Conversion Characteristics of Silicon Nanowire Array Photoelectrodes.

Semiconductor nanowire photoelectrochemical cells have attracted extensive attention in the light-conversion field owing to the low-cost preparation, excellent optical absorption, and short distance of carrier collection. Although there are numbers of experimental investigations to improve the device performance, the understanding of the detailed process of photoelectric conversion needs to be further improved. In this work, a thorough optoelectronic simulation is employed to figure out how the nanowire diameter, doping concentration, and illumination wavelength affect the photoelectric conversion characteristics of the silicon nanowire array photoelectrodes. We find that two balances should be carefully weighted between optical absorption and photogenerated-carrier collection, along with between short-circuit photocurrent density and open-circuit voltage. For the small-diameter nanowire array photoelectrodes, the overall absorption is higher than that of the larger-diameter ones with the most contribution from the nanowires. However, the substrate shows increasing absorption with increasing illumination wavelength. Higher doping density leads to a larger open-circuit voltage; while lower doping density can guarantee a relatively higher short-circuit photocurrent. To obtain high-light-conversion-efficiency photoelectrodes, the doping density should be carefully chosen with considerations of illumination wavelength and surface recombination. Suppressing the surface recombination velocity can effectively enhance the short-circuit photocurrent (open-circuit voltage) for the lightly (heavily) doped nanowire array photoelectrodes. Our systematical results provide a theoretical guidance for the photoelectrochemical devices based on semiconductor nanostructures.

Background

Owing to the unique intrinsic morphology (e.g., large specific surface area and length-diameter ratio) and the resultant light-harvesting capability, semiconductor nanowire arrays (SNWAs) have attracted considerable attention and exhibit bright prospects in the optoelectronic fields [1-5]. Various device configurations have been proposed and richened and can be reduced into two main categories, i.e., solid-state [6, 7] and solid-liquid junctions [8-12]. The solid-state junction is a traditional configuration widely employed for the SNWAs in the form of p-n, p-i-n, or Schottky junctions [13-15]. The other prototype is usually constructed by immerging the SNWAs into an electrolyte, leading to a 3-D heterojunction which can orthogonalize the directions of the incident photons and the photogenerated-carrier collection [8–12, 16–18]. There are numbers of advantages in the latter configuration, such as uncomplicated preparation process, low cost, high efficiency of carrier collection, and so on.

The present investigations of the SNWA photoelectrodes (i.e., solid-liquid junction devices) in the applications of solar cells [9–12, 16–18], photocatalytic water splitting [19], and photon detection [10] are mostly focused on experiments. Simulation/theoretical analysis is scarce but significant for understanding the photoelectric response and improving the photoelectric conversion efficiency. Recently, Foley et al. extensively simulated the performances of silicon nanowire array (SiNWA) photoelectrode through the finite element method and declared that the SiNWA photoelectrodes exhibit much larger short-circuit photocurrent density (Jsc) and photoelectric conversion efficiency (η) than those of the film counterpart [20]. However, the light scattering and diffraction effects are not involved in their work, where the light absorption in the NWs is simplified into according to the Lambert-Beer law. Therefore, further analysis/simulation of SNWA photoelectrodes considering the realistic light effects is meaningful to reveal the veritable photoelectric conversion process.

In this work, we intensively analyze the photoelectric conversion characteristics of SiNWA photoelectrodes by way of studying the influences of NW diameters (d), doping concentrations (Nd), surface recombination, and illumination wavelengths (λ). Our results show that the photoelectric conversion characteristics are strongly dependent on the above four parameters. To achieving high-η SiNWA photoelectrodes, (1) the Nd should be high as soon as possible if the surface recombination can be effectively suppressed, (2) the d should not be too small for merely maximizing the optical absorption, and (3) the absorption enhancement should be preferentially taken into account for the long-λ illumination.

Methods

Uniform SiNWs are assumed to be periodic on the homogeneous substrate, i.e., the NWs are etched from the substrate. The calculation unit is shown in Fig. 1, with the diameter-to-period ratio of 0.5. In this simulation, the NW length (substrate thickness) is fixed to 4.5 (5.5) μm with consideration of the finite computation and the representative values in experiments, while the diameter varies. Optical absorption and spatial distribution of photogenerated carriers are obtained by the finite-difference time-domain method. Drift-diffusion carrier transport at 300 K is simulated by a commercial electronic design automation software (Synopsys TCAD Sentaurus Device), considering doping-dependent carrier mobility and minority-carrier lifetime, and Auger, Shockley-Read-Hall (SRH), and surface recombinations. Optical absorption and photovoltaic characteristics of SiNWA photoelectrode with different d, Nd, λ, and minority-carrier lifetime in the surface layer (τsur) are investigated in sequence.

Fig. 1

Schematic. One calculation unit of the SiNWA photoelectrode is shown with the main feature sizes. The dashed square indicates the details at the SiNWA/electrolyte interfaces. The incident illumination is along the Z direction

The solid-liquid heterojunction between Si and electrolyte is assumed to be a Schottky junction with an interfacial equilibrium barrier height of 1.0 eV [11, 20]. Ohmic contact is employed on the bottom of the substrate. A 3-nm-thick surface layer in the outmost region of the front side of SiNWA photoelectrode is supposed to be rough and work as surface combination region (i.e., shell layer), where the carrier recombination occurs in the process of injecting into electrolyte. The τsur is usually smaller than that in the bulk (core) region from the surface recombination. The minority-carrier lifetime in the bulk (τbulk) is dependent on the Nd in the Scharfetter relation [21]:

In our model for n-type Si (default by the employed software), τmin is 0 s, τmax is 2.08 × 10−6 s, γ is 1, and Nref is 3 × 10−6 cm−3. The surface recombination is approximated to be a SRH process, which is present through deep defect levels in the gap. The surface recombination velocity (SRV) in unit of cm−2 s−1 in this model can be obtained from the τsur via following equation:

where tsur is the shell thickness.

Results and Discussion

Influence of Nanowire Diameter

The NW sizes play a determinative role in the overall light absorption and the spatial photongenerated-carrier distributions [1, 11]. For this, we firstly assess the photoelectric conversion properties of the SiNWA photoelectrodes with different d (i.e., 100, 150, and 250 nm) and Nd. The Nd values of the phosphor-doped Si substrates are chosen as 2.19 × 1014, 2.34 × 1015, 3.07 × 1016, 4.0 × 1017, and 1.31 × 1018 cm−3, i.e., the corresponding resistivities are around 20, 2, 0.2, 0.037, and 0.02 Ωcm, respectively. In this section, the 590-nm-λ illumination with the power density of 41.75 W/m2 is employed according to our previous experiments [10-12]. The non-polarized light is implemented by averaging two polarized lights with the angles of 0° and 90°.

Figure 2a–c shows the profiles of photogenerated carriers inside a quarter of the periodical calculated unit. The overall absorption percentage (Abs) of the 100-nm-d SiNWA photoelectrode is 96.65 %, among of which 82.98 % is attributed to the SiNWAs (i.e., the Abs of the substrate is 13.67 %). The distributions along the NW radial direction are relatively uniform; while there are obvious attenuations along the longitudinal direction, especially inside the substrate, the carrier concentrations are close to 0 at the bottom. The Abs of the 150-nm-d SiNWA photoelectrode is 99.21 %, while only 66.09 % arises from SiNWAs. Inside the NWs, the distribution along the NW radial direction is not uniform, i.e., alternative peaks and valleys appear along the NW axial direction. It can be ascribed to the Fabry-Perot resonances between the substrate and the top surface of SiNWAs. The overall Abs of the 250-nm-d SiNWA photoelectrode reaches 96.39 % and that of the SiNWAs is up to 94.4 %. To some extent, the distributions are similar to that of the moderate-d SiNWA photoelectrode. Moreover, the carriers inside the substrate distribute relatively even in the NW radial direction while gradually fall off along the longitudinal direction. Thus, it can be clear that the Abs of the three photoelectrodes shows relatively small differences, but the spatial distributions of photogenerated carriers display marked differences.

Fig. 2

Influences of nanowire diameter. Spatial distributions of photogenerated carriers inside a quarter of the calculated unit (a–c) with the same color bar, J-V curves (d–f), and IQE and η as a function of N d (g–i) for SiNWA photoelectrode with d = 100 nm (a, d, g), 150 nm (b, e, h), and 250 nm (c, f, i)

Figure 2d–f plots the photocurrent density versus voltage (J-V) curves of the three photoelectrodes with different Nd. Since the specific surface area of SiNWAs is quite large, the resulting surface recombination leads to τsur obviously smaller than τbulk [11]; we assume that τsur = τbulk/10 in this section. For the small-D SiNWA photoelectrode, the Jsc gradually increases with increasing Nd, and open-circuit voltage (Voc) goes up first and declines later with increasing Nd. The largest Jsc (Voc) is 1.640 mA/cm2 (0.559 V) when Nd = 1.31 × 1018 cm−3 (3.07 × 1016 cm−3). For the moderate-d SiNWA photoelectrode, Jsc goes down slowly before rising up with the increase of Nd and reaches the peak (1.751 mA/cm2) at Nd = 4.0 × 1017 cm−3, while Jsc shows a slight decline as Nd further increases. Voc rises first and declines later when the Nd increases from 2.19 × 1014 cm−3 to 4.0 × 1017 cm−3 and reaches the peak (0.560 V) at Nd = 4.0 × 1017 cm−3. For the large-d SiNWA photoelectrode, Jsc and Voc have relatively smaller differences than the other two cases.

Internal quantum efficiency (IQE) defined by the ratio of the numbers of the carriers contributing to Jsc and the absorbed photons is employed to evaluate the collection efficiency of the photogenerated carriers. Figure 2g–i summarizes IQE and η for the three cases under different Nd. As D = 100 nm, IQE goes up with the increase of Nd, giving rising to the maximal IQE of 0.856 at Nd = 1.31 × 1018 cm−3. It implies that a higher Nd leads to a higher IQE for the small-D SiNWA photoelectrode. Meanwhile, η rises first and then decreases with the increase of Nd, with the maximum of 13.06 % around Nd = 3.07 × 1016 cm−3. As d is 150 nm, IQE goes down slowly before going up, then goes down eventually. Moreover, η goes up before going down and reaches the maximum (15.37 %) when Nd = 3.07 × 1016 cm−3. As D is 250 nm, IQE has a similar change tendency with that of the 150-nm-d case. The maximum IQE (0.89) is achieved when Nd = 4.0 × 1017 cm−3, while η goes up before going down and reaches the peak (15.66 %) when Nd = 2.34 × 1015 cm−3. These results reveal that the maximal IQE and η cannot be simultaneously achieved for the SiNWA photoelectrodes with different d and Nd. To get a high η, more factors (e.g., Voc and fill factor) should be involved and balanced besides the IQE and Jsc.

The 150-nm-d SiNWA photoelectrode is taken as an example to unveil the underlying physics of the Nd influences. We dissect the profiles of electrostatic potential and energy band inside the SiNWA photoelectrode. The cross-sectional electrostatic potential profiles are plotted in Fig. 3. The depletion layer widths become thicker with decreasing Nd, and leading to that, the built-in barrier between the NW-electrolyte heterojunction cannot be built completely. The energy band diagrams in the axial and radial directions are presented in Fig. 4. One can see that NWs are fully depleted as Nd < 3.07 × 1017 cm−3. The IQE of the photoelectrode sustaining high can be explained by the following: once NWs are immersed into the electrolyte, a similar p-n junction is formed at the outmost region of the substrates (as shown in Fig. 4a), which can effectively separate the photogenerated carriers in the axis direction. When Nd increases from 2.19 × 1014 to 3.07 × 1016 cm−3, Jsc drops slightly because of the low-efficiency collection of photogenerated carriers and the increase of SRH recombination. The increase of Voc is mainly caused by the noticeable rise of the built-in potential in the axial direction. When Nd increases to 4.0 × 1017 cm−3, the depletion layer widths are smaller than the NW radius, leading to an obvious barrier in the radial direction (as shown in Figs 3d and 4b). In addition, the increase of Nd shortens the τbulk and raises J0 (i.e., exchange current density across the herterojunction interface without bias voltage), resulting in the declination of Voc (∝1/lnJ0) [20, 22]. When Nd further increases to 1.31 × 1018 cm−3, the τbulk is further shorten, leading to a lower Jsc than that of the case with Nd = 4.0 × 1017 cm−3 and a sustaining decrease of Voc.

Fig. 3

Electrostatic potential distributions. X axis is the NW radial direction, and X = 0 corresponds to the NW center; Y axis is the NW longitudinal direction, and Y = 0 corresponds to the interface between the NWs and substrate. a–e The N d is 2.19 × 1014, 2.34 × 1015, 3.07 × 1016, 4.0 × 1017, and 1.31 × 1018 cm−3, respectively

Fig. 4

Energy band diagrams. a Along the NW axial direction. b Along the NW radial direction. Solid (broken) lines are the energy levels of conduction (valence) bands. Along the arrow, the N d is 2.19 × 1014, 2.34 × 1015, 3.07 × 1016, 4.0 × 1017, and 1.31 × 1018 cm−3, respectively

Influence of Illumination Wavelength

To fairly compare the performance and figure out the λ influence, we set three lights (i.e., ultraviolet (UV) light with λ = 365 nm, visible light with λ = 590 nm, and near-infrared light with λ = 800 nm) sharing the same photon flux of 1.24 × 1016 cm−2 s−1 with the corresponding power densities of 67.49, 41.75, and 30.79 W/m2, respectively. The spatial distributions of photogenerated carriers are presented in Fig. 5a–c. For the 365-nm-λ illumination, almost all of the photogenerated carriers for the 150-nm-d SiNWA photoelectrode are located inside the NWs and show a rapid falloff along the incident direction, which is also certified by the Abs of the entire photoelectrode (95.11 %) and the SiNWAs (95.08 %). When the illumination turns to visible (near-infrared) light, the Abs of the photoelectrode is 99.21 % (66.54 %) and that of SiNWAs is 66.09 % (35.82 %). As λ increases, the Abs fraction of the substrate and the entire photoelectrode increases obviously. It can be ascribed to the smaller optical absorption coefficient at longer λ. As a result, the photogenerated-carrier concentration inside the NWs is noticeably higher than that inside the substrate; meanwhile, the profile differences between the NWs and substrate are gradually diminished.

Fig. 5

Influences of illumination wavelength. Spatial distributions of photogenerated carriers inside a quarter of the calculated unit (a–c) with the same color bar, J-V curves (d–f), and IQE and η as function of N d (g–i) for the 150-nm-d SiNWA photoelectrode under the illumination of λ = 365 nm (a, d, g), 590 nm (b, e, h), and 800 nm (c, f, i). The three lights possess the same photon flux of 1.24 × 1016 cm−2 s−1

Figure 5d–f shows the J-V characteristics of the SiNWA photoelectrodes with various Nd under the three kinds of illumination. The Jsc and Voc exhibit a similar variation trend with increasing Nd, i.e., Jsc first decreases then increases and finally decreases (a peak around Nd = 4.0 × 1017 cm−3), Voc first increases and then decreases (a peak around Nd = 3.07 × 1016 cm−3 ). Under the near-infrared light, Jsc is the minimum on the whole (with the highest value of only 0.873 mA/cm2), which can be explained by the smallest Abs. Electrostatic potential distribution in the photoelectrode is mainly determined by Nd that accounts for the week effect of illumination λ on the variation trends of Jsc and Voc. Figure 5g–i summarizes IQE and η of the SiNWA photoelectrodes with different Nd under the three lights. Since IQE is obtained from the photocurrent density divided by the incident power density, it shows the same variation trend as that of Jsc. Moreover, η displays different variation trends with increasing Nd under the three lights. Under the UV light, η goes up before going down, and then again rising up before declining, giving rise to the maximum of 7.16 % when Nd = 4.0 × 1017 cm−3. Under the visible light, η first goes down then rises up, leading to the maximum of 15.37 % when Nd = 3.07 × 1016 cm−3. Under the near-infrared light, η shows the same variation tendency as that under the visible light, resulting in the maximum of 9.50 % when Nd = 2.34 × 1015 cm−3.

As a whole, Jsc, IQE, and η under the visible light are obviously higher than those under the other two lights. Under the UV light, though Jsc and IQE are relatively large under the high-Nd conditions, η is low because of small Voc and fill factor. In contrast, Jsc and η are always relatively small under the near-infrared light. These results imply that the NW sizes and Nd, along with photoactive materials, should be re-optimized to obtain high-performance photoeletrodes under different-λ illuminations.

Influence of Surface Recombination

The surface roughness and τsur are actually/closely related to the preparation condition of SiNWAs as well as Nd. Thus, it is significant to calculate the J-V curves of the SiNWA electrodes with different τsur (i.e., SRV). Here, the 150-nm-d SiNWA photoelectrode under the 590-nm-λ illumination with the power density of 41.75 W/m2 is employed. Besides, a 400-μm-thick film photoelectrode under the same illumination is included as a comparison. The profile of photogenerated carrier in the film is produced by normal irradiation in the Beer-Lambert law, and τsur is supposed to equal τbulk for the film photoelectrode.

Figure 6 plots the J-V curves of the SiNWA photoelectrodes with two presentative Nd values (i.e., 2.19 × 1014 and 1.31 × 1018 cm−3), with the corresponding τbulk of 2.035 × 10−6 and 1.576 × 10−8 s. It can be seen that the τsur decrease leads to a remarkable drop of Jsc for the low-Nd case. The Jsc of the SiNWA photoelectrode (1.55 mA/cm2) under τsur = τbulk/10 is much higher than that of the film photoelectrode (1.17 mA/cm2). When the τsur reduces to τbulk/1000, the Jsc (1.21 mA/cm2) is slightly higher than the film counterpart; but as τsur further decreases to τbulk/10,000, the Jsc (0.65 mA/cm2) is substantially lower than that of the film counterpart. In contrast, the Voc shows a slight decrease with decreasing τsur. The Jsc variation of the SiNWA photoelectrode can be explained by the fully depleted SiNWs with low Nd and large τbulk (i.e., there is no radial Schottky formed in the SiNWA configuration), which brings about the collection efficiency of the photogenerated carriers in the SiNWA photoelectrode lower than that in the film photoelectrode. For the heavily doped case (i.e., Nd = 1.31 × 1018 cm−3), the Jsc slightly declines while the Voc remarkably drops with decreasing τsur. When τsur = τbulk/10, the Jsc is 1.69 mA/cm2, much higher than that of the film counterpart (0.60 mA/cm2), while the Voc is obviously lower. When τsur = τbulk/10,000, the Jsc nearly shows no decrease; yet, the Voc decreases from 0.53 to 0.33 V. The large margin of the Voc falloff can be ascribed to the remarkable increase of J0. Since the NWs are partially depleted when the Nd is high, the photogenerated carrier can be rapidly separated and collected via the radial built-in electric field.

Fig. 6

Influence of surface recombination. J-V curves of the SiNWA photoelectrodes with N d = 2.19 × 1014 cm−3 (a) and 1.31 × 1018 cm−3(b) as the τ sur varies. A film photoelectrode with the same N d are shown in gray-diamond curve for a reference

The above results reveal that the τsur change under different Nd has a preferential influence on different photoelectric parameters, i.e., the Jsc (Voc) of the SiNWA photoelectrode with low (high) Nd suffers great attenuation with decreasing τsur. It suggests that the surface recombination should be suppressed to be as low as possible for the high-performance SiNWA photoelectrode in the preparation, as well as improving light absorption and Schottky barrier height.

Conclusions

We have numerically investigated the influences of d, Nd, λ, and τsur on the photoelectric conversion performance of the SiNWA photoelectrode. We find that (1) when the d is small, the overall optical absorption is up to 99 % with most contribution from the NWs, while the NWs without large Nd are totally depleted, resulting in a substantial small Jsc. (2) When the d is large, the overall optical absorption is usually worse than that of the small-d one, yet the substrate contribution is larger; moreover, the NWs are partially depleted under low Nd, leading to higher Jsc and η than those of the small-d SiNWA photoelectrode under the same Nd. (3) Higher Jsc and IQE do not guarantee higher η, and photogenerated voltage and filled factor have to be involved. (4) The SiNWA photoelectrode exhibits worse light-conversion performance under the UV light than that under the near-infrared light, because under the short-λ illumination, most incident photons are absorbed in the near surface region, where recombination is remarkable and larger than that in the bulk. (5) An increase in the surface recombination mainly induces a great decrease in the Jsc (Voc) for the low (high)-Nd SiNWA photoelectrode. Our systematical/thorough simulation reveals the important influencing factors in the photoelectric conversion process of the SiNWA photoelectrode and gives a theoretical guidance to preparing the high-performance semiconductor nanostructure optoelectronic devices.