Efficiency enhancement in a lensed nanowire solar cell

A solar cell with no losses^1,2 and ideal contacts will operate at the maximum efficiency predicted by the Shockley–Queisser limit, which is ∼33.7% for a cell with a bandgap of 1.34 eV. Under short-circuit conditions, it absorbs all sunlight with wavelengths shorter than the bandgap of the material and converts the absorbed photons into electricity. Under open-circuit conditions, the absorbed photons cannot contribute to the current and can either be radiatively re-emitted or recombine nonradiatively, causing the cell to heat up. An ideal solar cell without losses will re-emit all absorbed photons at open-circuit.^3–7 However, even when operating at the Shockley–Queisser limit, a traditional solar cell converts a highly directional beam of photons from the Sun into a random directional emission pattern. The random angular emission pattern significantly increases the entropy of the photons and is responsible for a voltage loss of ∼0.3 V. The addition of an external lens will collimate the emitted light and reduce this photon entropy loss. The concentrating lens will however also increase the solar illumination per unit area.

In this paper, we investigate an arrayed nanowire solar cell in which we focus the solar light onto a small number of nanowires, while leaving the majority of the nanowires unilluminated. The addition of external microlenses to a nanowire solar cell is expected to (i) create a nano-concentration solar cell in which the current generation in the illuminated nanowires increases significantly, thus also increasing the open-circuit voltage of the illuminated nanowires. In addition, the external lens will collimate the emitted light under open-circuit conditions, thus (ii) reducing the photon entropy loss. Finally, the concentration of the light into a small number of nanowires tends to (iii) saturate nonradiative losses. We will first explain these three different effects separately in Secs. I A–I C in order to subsequently assess the contribution of each of these effects for our lensed nanowire solar cell.

The photon entropy loss in a nanowire solar cell can be avoided if the emitted photons are directed into a narrow cone with a solid angle equal to the solid angle of the solar emission cone reaching the earth,⁸ as shown in Fig. 1(a). In this picture, the addition of a microlens prevents the increase in the photon entropy and eliminates this thermodynamic loss mechanism.

As compared to conventional solar cells, nanowire solar cells feature an almost deterministic light path for both the absorption of sunlight and the external emission of photoluminescence (PL) close to the bandgap under open-circuit conditions. In both cases, the light is mainly trapped into confined optical modes⁹ of the submicron nanowire cavity. Under open-circuit conditions, it has been shown¹⁰ that approximately 68% of the emitted light will be confined into the fundamental $H E 11$ guided mode. This guided mode is already somewhat directional, showing an open-circuit voltage above the radiative limit, as shown by the blue curve in Fig. 2. The presence of guided modes within the nanowire allows to employ microlenses to subsequently collimate the emitted light into a parallel output beam that can, in principle, be sent back to the Sun as shown in Fig. 1(a). For a lossless nanowire solar cell, this implies that while the impinging solar light can be treated as a parallel beam, the same amount of light will be re-emitted by the cell into a parallel beam under open-circuit conditions. For the photons emitted into the guided mode, the photon entropy is not increased in this process if the etendue of the externally emitted photoluminescence $ε o u t$ approaches the etendue of the incoming solar radiation $ε i n$⁠. In this case, the solar cell will approach the 46.7% efficiency ultimate limit.

In this paper, we have chosen the diameter of the microlenses to be 6 μm, which is 12× larger than the 500 nm nanowire pitch. We have chosen these relatively large lenses since very small microlenses with a diameter equal to the pitch of the nanowire array are not capable of effectively¹⁰ focusing or collimating the light due to the diffraction limit. A 500 nm diameter microlens will diffract the light in the same way as a 500 nm circular aperture. Previously published simulations show that a 4.6 μm (8 μm) diameter lens is capable of reducing the emission angle from 0.84 down to 0.024 sr (0.011 sr), allowing to increase the open-circuit voltage with 139 mV (159 mV) above the radiative limit for a lossless cell.¹⁰ These simulations, thus, emphasize that we need to employ relatively large diameter lenses to reduce the effect of diffraction and to be capable of effectively collimating the emitted light as shown in Fig. 1(a). Figure 2 shows $V o c$ for a lossless solar cell in which the guided mode is focused with an external lens of 4.6 or 8 μm diameter as calculated by Korzun et al.¹⁰ This shows that focusing of the emitted light provides a substantial improvement in the open-circuit voltage for a lossless cell.

In Sec. I A, we employed a thermodynamic approach, which assumed that the combination of a nanowire solar cell and a lens acts as a single “thermodynamic engine,” which is converting a parallel beam of photons from the Sun into a collimated output beam and increases the output voltage at open-circuit. An alternative approach, which is shown in Fig. 1(b), is to only consider the nanowire solar cell as a “thermodynamic engine,” which is now illuminated by a converging light beam due to the nano-concentrating lens^8,12–14 with input etendue $ε i n= ε concentrator$⁠. Here, to approach the ultimate limit efficiency, the input etendue of the concentrated solar light should be matched^15,16 to the output etendue of the emitted light from the nanowire photonic cavity.

This shows that the two approaches shown in Figs. 1(a) and 1(b) yield identical results. The effect of a microlens can be interpreted by method outlined in either Fig. 1(a) or 1(b). The effects of both methods should, however, not be added.

We subsequently turn our attention to the lensed nanowire array solar cell as shown in Fig. 1(c). A nanowire array solar cell with a pitch of 500 nm and a surface area of 500 × 500 μm² is made up of ∼1 × 10⁶ individual nanowire solar cells that are connected in parallel to each other. In our nanowire solar cells with 6 μm diameter lenses on their surface, only a small fraction of the nanowires is exposed to light, as shown in Fig. 1(c). We assume $N N W$ nanowires below each microlens, with one illuminated wire and $N N W−1$ non-illuminated wires, where $N N W$ approaches 144. Under short-circuit conditions, the current flowing through the non-illuminated nanowires is almost zero, while the concentrated short-circuit current $J s c c o n c$ in the illuminated nanowire is N times larger $( J s c c o n c = N N W J s c n o − l e n s)$ due to the concentration of light.

The equivalent circuit for the lensed nanowire array solar cell is presented in Fig. 3.

By inspecting Eqs. (3) and (4), it is clear that the addition of microlenses to an arrayed nanowire solar cell does not increase the open-circuit voltage $( V o c c o n c = V o c n o − l e n s)$⁠. This can be easily understood since $I s c c o n c$⁠, $N N W I D , 1$ and $N N W I D , 2$ increase with the same nano-concentration factor $N N W$⁠. Since the approaches outlined in Figs. 1(a) and 1(b) are identical, neither nano-concentration nor focusing of the emitted light is expected to increase $V o c$ for the lensed nanowire array cell shown in Fig. 1(c).

In the last part of this equation, we merged the external radiative efficiency $η ext PL$ into an effective saturation current density $J 0$⁠, yielding the well-known textbook expression for the open-circuit voltage and showing that $J 0$ is dependent on the external radiative efficiency of the solar cell.

When increasing the nano-concentration factor $X c o n c$⁠, we increase the amount of emitted photoluminescence, but we do not change the currents $J s c c o n c$ or $J 0 r a d$⁠. We acknowledge that a thermodynamic approach might look somewhat unsatisfactory since, in a microscopic model, one would expect a voltage redistribution between the illuminated and the non-illuminated nanowires. We, however, note that the non-illuminated wires will also start emitting light in forward bias, thus implying that an equivalent circuit model that only treats currents is insufficient to treat the combined action of current and light generation of a solar cell under open-circuit conditions. Our thermodynamic model, however, treats all relevant effects. The case in which the PL-intensity increases as $I P L∝ I s u n β.$ with a slope $1≤β≤2$ is treated in the supplementary material.

We have first grown the layer stack of the p–n junction InP solar cell using metalorganic vapor phase epitaxy (MOVPE). The details of the fabrication process are presented in the supplementary material. We subsequently etch an array of nanowires by using a SENTECH inductively coupled plasma (ICP) reactor. The nanowires have a length of 1.2 μm and have conical shape with a top diameter of 170 nm, a bottom diameter of 250 nm, and a pitch of 500 nm. The nanowires subsequently receive three digital etching steps^6,19 to improve their sidewall quality and are subsequently covered with a 20 nm SiO₂ layer to promote the adhesion of benzocyclobutene (BCB). The sample is planarized with BCB and a 300 nm indium tin oxide (ITO) layer is deposited for the front contact. The back contact is fabricated by first growing a strongly p-doped InGaAs layer on the back of the substrate and subsequently evaporates Ti/Au metallization.

The microlenses are fabricated using a resist reflow process.^20–24 We use a polymethyl methacrylate (PMMA) resist, which is a highly viscous and transparent positive electron beam lithography (EBL) resist that is suitable for thermal reflow. This resist features a low light absorption and a refractive index of ∼1.5. We first spin a resist layer of 3.4 μm thickness, which is subsequently patterned by electron beam lithography, providing cylindrical pillars as shown in Fig. 4(a). These cylindrical pillars are subsequently converted into 6 μm diameter microlenses by a thermal reflow process at 125 °C, the details of which are outlined in the supplementary material. The lenses are shown in Fig. 4(b) and show high quality, low surface roughness, and hemispherical shape with good uniformity between individual lenses, which is partly due to the EBL fabrication process. The final solar cell structure can be seen from Fig. 4(c).

The working principle of our microlenses can be understood by the photonic nanojet effect,^10,25 which is due to Mie scattering in an object that is larger than the wavelength of light. Our microlenses can be considered plano–convex truncated spherical lenses, which show a tight focus with high peak intensity as shown in Fig. 5(a) by finite difference time domain FDTD simulations using the Lumerical software package. The special property of the nanojet effect is that the focal width is nearly constant for increasing diameter of the lens, while the peak intensity within the focus linearly increases with the lens diameter, as shown in Fig. 5(b). This panel also shows that the FWHM of the focus is ∼0.7 μm in diameter, implying that the lens is capable of focusing most of the excitation light onto a single nanowire as schematically indicated in Fig. 1(c).

We assess the focusing quality of the microlens by using the configuration presented in Fig. 1(a). Here, the purpose of the lens is to effectively collimate the emitted light. We, thus, simulate the collimation of the light emitted by the nanowire in the far field. The result is presented in Fig. 5(c), showing a strong collimation. A more detailed analysis is presented in Fig. S1 of the supplementary material. There, we show the focusing properties of an elliptical lens, which, by definition, does not have any spherical aberration. These elliptical lenses show diffraction patterns in which the first minima for lenses of 2, 4, and 6 μm diameter are observed at 30.5°, 15.9°, and 10.2°, while the theoretical diffraction limit is calculated to be 32.2°, 16.1°, and 10.7°. The close agreement between the simulated far-field patterns and the diffraction limit shows that the focusing properties are predominantly determined by the diffraction of the light through the circular aperture defined by the perimeter of the microlens.

We use spherical microlenses, which are not expected to be free of aberrations. By comparing the simulated size of the focal spot of our 6 μm diameter spherical microlens [Fig. 5(c)], we observe that it is slightly larger than the focal spot size of the 6 μm diameter elliptical lens [Fig. S1(c) in the supplementary material] but clearly smaller than the size of a 4 μm diameter elliptical lens [Fig. S1(b) in the supplementary material]. We conclude that although spherical aberrations are clearly observable, the increase in the diameter of the light pattern in the far field due to spherical aberration is acceptable for our purposes.

Our fabricated microlenses obtain their final shape by the reflow process. It is, thus, a priori not known whether our PMMA microlenses have a perfect spherical shape. We, thus, have to investigate the quality of the microlenses experimentally. A first idea of this quality is provided by the scanning electron microscopy (SEM) image of the completed solar cell presented in Fig. 4(c). The image shows the path of the light below the microlenses. This light path is visible by breaking the bonds in the BCB spacer layer induced by the high intensity light below the lenses. We have artificially highlighted the light path in yellow and the illuminated nanowire in red, showing that the microlenses are capable of focusing the light predominantly onto a single InP nanowire.

We, subsequently, use Fourier microscopy^26–29 to measure the directional emission of our lensed nanowires. For a fixed 6 μm lens diameter, the main parameter defining the quality of the collimated beam in the far field is the spacer layer thickness [shown as “SL” in Fig. 1(c)] in between the microlens and the ITO top contact positioned on the top of the nanowires. We varied the spacer layer thickness between 1.2 and 9.2 μm as shown in Fig. S2 (Sec. 5 of the supplementary material). We obtain an optimum spacer layer thickness of ∼4 μm. The optimum focusing is shown by the Fourier images of our lensed nanowires [Fig. 5(e)] in comparison with a nanowire sample without any microlenses in Fig. 5(d). We observe a strong collimation of the emitted light with the addition of a microlens. Moreover, by comparing our experimentally obtained far-field pattern in Fig. 5(e) with the simulated pattern in Fig. 5(c), we conclude that our fabricated PMMA microlenses show excellent focusing properties.

Out of the total 49 fabricated nanowire solar cells, a subset of nine cells was chosen based on the initial results, unlike other cells that displayed very low short-circuit current $( J s c)$ or open-circuit voltage $( V o c)$ values. These nine cells were electrically connected, and their efficiency, series resistance, and shunt resistance exhibited realistic values. The I–V curves were measured before and after placing lenses on the cells, and again after removing the lenses following a period of time. From these I–V curves, the values for the $V o c$ are shown in Fig. 7(b).

It is observed that the addition of randomly positioned microlenses leads to a significant increase in $V o c$ for half of the cells, while a slight drop in $V o c$ is noted for the remaining cells. We attribute the decreased $V o c$ to damage of the cells since we had to push the probe tip firmly through the BCB spacer layer to make contact to the AuGeNi metallization, thereby taking the risk of partially damaging the nanowire solar cell. The interesting data points are those where we observe an increase in $V o c$⁠. An increased $V o c$ is very unlikely to be a result of damage. On the contrary, the cells with the lowest $V o c$ before lens placement clearly show improved $V o c$ after lens placement. The increased values of the $V o c$ after the placement of the microlenses are, therefore, attributed to the saturation of nonradiative recombination in the illuminated nanowires as discussed in Sec. III. We emphasize that the microlenses are positioned randomly. This implies that the amount of light concentration onto a single InP nanowire varies due to changes in the relative alignment of the focal spots with respect to the tips of the nanowires.

III/V compound semiconductor solar cells are known to feature the highest photon conversion efficiency solar cells,³² but they are made of expensive and scarce materials, which makes them too expensive for terrestrial applications. In our lensed nanowire solar cell, we use tapered nanowires with an average diameter of 210 nm, which can be spaced 6 μm apart by only positioning a nanowire in the focal spot of each microlens, as shown in Figs. 1(a) and 1(b). When we assume that such a strongly diluted nanowire array can still be grown bottom-up by the vapor–liquid–solid (VLS) growth method,^33–37 the amount of reduction in the expensive epitaxially grown InP is already as much as a factor (6 μm/210 nm)² = 816. On top of the reduction in the amount of epitaxially grown material, we also consider heteroepitaxial growth on a masked silicon substrate,^38–41 allowing to further reduce the amount of expensive III/V semiconductor material.

An alternative approach to reduce the amount of expensive III/V semiconductor material is ultrathin III/V solar cells in which the light absorption is enhanced by light trapping strategies.^42,43 In our case, the “thickness” of the cell is given by the nanowire length. InP nanowire solar cells with cylindrical nanowires require a nanowire length of 2 μm to absorb 94% of the solar light.⁴⁴ Tapered nanowires even feature a slightly better light absorption allowing 98% light absorption in 3 μm length conically tapered nanowires.⁴⁵ Our microlenses will focus the light to the top of the nanowires. Figure 8(a) shows an FDTD simulation of the light absorption at 555 nm in an array of InP nanowires. This simulation shows that most of the light is absorbed into the top part of a single nanowire, thus suggesting that it is possible to further decrease the required length of the nanowires below 2 μm.

We have tested the focusing of the light toward the top of the nanowires by using 1.2 μm length nanowires, which are too short to absorb all solar light. When we add the microlenses to our nanowire solar cell with a relatively short nanowire length, we observe an increase in the short-circuit current of 12 mA/cm² on average, as shown experimentally in Fig. 8(b). This effect is mainly attributed to the focusing effect of the microlenses, which effectively reduces the required nanowire length. It is, however, possible that the increase in the short-circuit current is also partly due to the saturation of nonradiative recombination centers. The nonradiative recombination losses are, however, moderate since the short-circuit current is already approaching its limiting value of 33.7 mA/cm². Unfortunately, we observe a few cells with a short-circuit current above this limit, which is due to an increased active area as explained in Sec. 6 of the supplementary material.

We have investigated the arrayed nanowire solar cells on which we fabricated 6 μm diameter PMMA microlenses to focus the light only on a single nanowire positioned within the focal spot of the microlens. We first simulated the microlenses and found that the quality of the focal spot is mainly determined by the diffraction limit, as determined by the perimeter of the lens. We subsequently assessed the quality of the microlenses with Fourier microscopy. We observe a high degree of collimation of the light in the far field, showing that our microlenses have sufficiently high optical quality. The main effect of the microlenses is to increase the light intensity on the central nanowire with a factor equal to the square of the lens diameter divided by the nanowire pitch, which is a concentration factor $X c o n c=144$ in our case. Since the photoluminescence intensity in our InP nanowires scales as $PL∝ I β$ with $β=1.72$⁠, the external radiative efficiency increases with a factor $X c o n c β − 1=34$⁠, corresponding to an increase in the open-circuit voltage of 92 mV. Our fabricated arrayed nanowire solar cells indeed show an increased open-circuit voltage due to the randomly positioned microlenses on top. We finally observe that the microlenses also increase the short-circuit current of the cells since the microlenses increase the amount of light absorption in the top part of our relatively short nanowires. This unexpected observation suggests that it is possible to decrease the nanowire length and, thus, to further limit the amount of expensive semiconductor material by using microlenses.

As an outlook, we finally like to revisit the lensed nanowire solar cell design as presented in Figs. 1(a) and 1(b). Such a design would combine the enhanced $V o c$ due to the reduced loss of entropy by collimating the emitted light with a microlens. In addition, such a cell will reduce the loss due to the usually small external radiative efficiency in current generation nanowire solar cells due to the saturation of nonradiative recombination as explained in Secs. II D and V. Finally, such a design reduces the amount of expensive III/V semiconductor material, provided that the cells are grown bottom-up on a silicon substrate. The drawback of this design is, however, a reduced absorbance since not all light within the focus of the microlens will be absorbed by a single nanowire, as shown in Fig. S4(a) in the supplementary material. We, however, show in Fig. S4(b) in the supplementary material that a small group of 3 × 3 nanowires is already capable of increasing the light absorption toward a value that is similar to the light absorption in a large nanowire array [Fig. S4(c) in the supplementary material]. We propose a lensed nanowire solar cell in which a group of 3 × 3 nanowires is positioned below each microlens, as shown in Fig. 9. Additional information is provided in the supplementary material.

See the supplementary material for details about the calculation of the V o c for arbitrary β-values, the fabrication of the solar cell and the microlenses, images of the focusing properties of elliptical microlenses and Fourier microscopy images of the directional light emission as a function of spacer layer thickness, and finally calculations of the absorbance for a single nanowire below each microlens, small arrays of 3 × 3 nanowires below each lens, and a full nanowire array.

This work was supported by the Dutch Organization for Scientific Research NWO (No. TTW 15971 and 16PR1043) and Solumineus.

The authors have no conflicts to disclose.

E. B., P.A.L.M.K., and K. K. contributed equally to this article.

Emanuele Bochicchio: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Philemon A. L. M. Koolen: Formal analysis (equal); Investigation (equal); Methodology (lead); Validation (equal); Writing – original draft (equal). Ksenia Korzun: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). Simon V. Quiroz Monnens: Investigation (supporting). Bas van Gorkom: Investigation (supporting). Jaime Gómez Rivas: Conceptualization (equal); Supervision (lead); Writing – review & editing (equal). Jos E. M. Haverkort: Conceptualization (equal); Supervision (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.