Heterosubstrate Illumination Effects in III-V Solar Cells

Abstract

Reference cell based current vs voltage (IV) measurements assume that the effect of an illumination spectrum on a solar cell’s performance can be fully captured by the multiplication of the spectrum with the device’s spectral response and subsequent integration. This is based on a fundamental understanding that sub-bandgap light will be minimally absorbed, if at all, in the active layers of the solar cell and therefore not contribute to the power generation. In this work we show a novel phenomenon in which illumination of the substrate is required for good performance in solar cells with III-V active layers and germanium substrates, despite negligible contribution to the short circuit current or open circuit voltage, or increase of generated power beyond that expected from the III-V junction. Discovered in the course of characterizing cells for low-light conditions, we confirm the observation with additional IV and electroluminescence measurements and modeling that reproduces experimental results. This phenomenon has implications for device characterization under non-standard light sources, the development of solar cells for conditions lacking long-wavelength light such as indoor photovoltaics under light-emitting diode illumination, and the prediction of device performance under spectra that differ from the test conditions.

I. Introduction

The development of photovoltaics has been largely focused on devices designed for use outdoors under a standardized terrestrial or extra-terrestrial solar spectrum, at 1000 W/m² or higher. However, there is now increased interest in and demand for indoor photovoltaics that make use of ambient light to run low-power devices including Internet of Things sensors and components [1]. These cells will operate not only at extremely low power densities (i.e., <0.5 W/m²) but also under spectra significantly different from the AM1.5G or AM0 standards [2]. The bandgap of silicon cells, which presently dominate the photovoltaic (PV) market, is poorly matched to many indoor and low-light spectra [3], so higher performance under these conditions has been achieved with III-V solar cells [4], [5] as well as organic and perovskite devices [6], [7], [8].

An extensive range of wide-bandgap novel and emerging PV technologies are being considered for low light applications, making accurate prediction of device performance under these varying conditions vital. There is a demand to be able to perform accurate measurements under conditions that are potentially significantly different from the conditions under which devices are deployed, and to be able to predict performance under conditions and spectra other than those which have been used in a measurement. Therefore, establishing equivalency between different conditions is essential.

It is common practice to, aside from any heating effects, consider only light above the active layers’ bandgap(s) in relation to a solar cell’s power generation. Measurements are taken with reference cells and calibration is dependent on the illumination spectra and the spectral responsivities of reference and test cells [9], [10]. Light of wavelengths that do not contribute to the short circuit current, where the spectral responsivity is negligible, is considered superfluous and irrelevant to the operation of the solar cell. The irradiance level and a reference spectrum (such as AM1.5G) are specified, but no distinction is necessarily made between differing test spectra beyond ensuring that they produce the same short circuit current.

However, in this work we demonstrate that sub-active-layer-bandgap illumination can substantially affect the performance of a solar cell with a substrate having a narrower bandgap than that of the active device layers.

Recently our group observed and reported that some devices measured under multiple conditions showed an apparently higher series resistance at lower illumination levels [10]. This work investigates that inconsistency through additional IV measurements under variable spectra and absolute electroluminescence (EL) measurements. We find that the apparent series resistance is affected not by the irradiance level but by the spectral composition of the light source which was used in the low-light measurements. To have a high fill factor and conversion efficiency, these devices require illumination below the bandgap of the III-V material, which is absorbed in the substrate. However, they lack many characteristics of a tandem cell, including those which could be used to identify a tandem from standard IV measurements. We demonstrate this and present an electrical model of the devices that reproduces the measured results and suggests a possible physical explanation. This requirement becomes important when predicting the performance of devices under different spectra and low-light conditions. These effects were observed in both GaAs and GaInP devices; this work will focus on GaAs devices, and observations in GaInP devices can be found elsewhere [11].

II. Methods

We obtained commercial GaAs n-on-p solar cells designed for AM1.5G or AM0 applications, grown on p-type germanium substrates, with contacts on each side of the stack (Fig. 1) from Cesi S.p.A., diced into 2 cm squares and packaged. Previous work determined the 1-sun efficiencies of these devices to be 23.9 %[12]. We further characterized the devices using current-voltage, spectral responsivity, and absolute electroluminescence (EL) measurements.

Fig. 1.

Basic structure of the devices studied in this work, consisting of III-V active layers and Ge substrates.

We used two different experimental set-ups for IV measurements. First we used a class AAA solar simulator with a xenon (Xe) arc lamp source to characterize the cells under a spectrum similar to AM1.5G between 100 W/m² and 1000 W/m² (0.1 and 1 sun). Second, and crucially for this work, we use a lab-built multi-zone simulator, with a Xe lamp and 8 light emitting diodes (LEDs) coupled into a tapered glass waveguide with an output area sufficient to completely and uniformly illuminate the cells [13]. The LEDs can each be controlled individually and the broadband cool white LED and 940 nm LED were used to selectively illuminate layers of these devices. Illumination spectra are shown in Fig. 2. We took measurements with this system from 0.3 W/m² to 760 W/m². Both experimental set-ups use a calibrated silicon reference cell and a temperature-controlled stage. With the multi-zone simulator we were also able to measure the irradiance and spectrum of the incident light directly with an in-house calibrated UV-VIS-NIR spectroradiometer.

Fig. 2.

Spectra of LED and Xe sources which we measured cells under, overlaid by the spectral response of the GaAs junction.

Spectral response measurements were performed using the differential spectral resistivity method under DC bias light and AC probe light. Measurements performed out to 1800 nm confirmed negligible contribution (0.7 %) of the sub-GaAs-bandgap region to the short circuit current under an AM1.5G spectrum.

We measured absolute EL of the devices with a hyperspectral imaging system as described in detail in [12]. Images were averaged over their area to find the radiative efficiency of the device as a whole, which we then used in calculations of luminescent coupling from the III-V cell to the Ge substrate.

III. Results and Discussion

We first compare device performance under white LED and Xe lamp illumination at a range of illumination intensities. Current density-voltage (JV) curves taken under both sources are shown in Fig. 3. A second device showed the same trend in IV curves, and key parameters are presented in Fig. 4. The short circuit current is linear with respect to irradiance level, and open circuit voltage is essentially the same under each spectrum. However, the fill factor varies greatly. Under the Xe lamp, we see an expected slight decrease in fill factor with increased illumination due to series resistance. Under the white LED the fill factor is lower, with this device having a minimum fill factor of 0.44 at a short circuit current density (J_SC) between 5 and 7 mA/cm², increasing at both lower and higher illumination intensities.

Fig. 3.

JV curves measured on GaAs cells at varying irradiances a) under a white LED from 2.93 to 428 W/m² b) under a Xe lamp from 100 to 1000 W/m² and c) comparing the two at similar short circuit currents.

Fig. 4.

Short circuit current, open circuit voltage, and fill factor of a second GaAs-on-Ge solar cell as a function of irradiance level under white LED and Xe lamp spectra. V_OC and fill factor are plotted against J_SC to normalize for the different photon flux and spectrum utilization between the light sources.

The JV curves measured under white LED illumination (Fig. 3a) have an unusual shape featuring a complicated evolution with irradiance and a breakdown in superposition. In Fig. 3c, we directly compare JV curves taken under the two sources at nominally the same short circuit current, seeing significant differences between the two illumination spectra. The spectrum rather than the effective irradiance, is the key factor in the reduced performance of these devices under low-irradiance LED illumination.

The important difference between the Xe Lamp and LED spectra (Fig. 2) is the extension of the Xe Lamp spectrum past 890 nm. This is the portion of the spectrum containing light which passes through the GaAs active layers and is absorbed in the Ge substrate. As GaAs is a strongly absorbing direct-bandgap semiconductor, the light from the white LED, less than 0.5 % of which is at wavelengths longer than 750nm, is completely absorbed in the GaAs and does not reach the Ge substrate. To confirm that the missing IR light is what is causing the low fill factor under LED illumination, we used the multi-zone simulator to keep the irradiance from the white LED fixed while adding varying irradiance illumination from the 940 nm LED. Fig. 5 shows how this “repairs” the JV curve and increases the fill factor. We note that the slight increase in short circuit current with 940 nm LED illumination is due to the overlap between the spectral response of the GaAs cell and the short-wavelength tail of the 940 nm LED spectrum (see Fig. 2).

Fig. 5.

JV curves measured under constant irradiance (17.6 W/m²) white LED illumination with the addition of varying irradiance 940 nm LED illumination, showing that the addition of light that reaches the Ge substrate repairs the device fill factor. The slight increase in short circuit current is due to the short-wavelength tail of the 940 nm LED illumination, which is absorbed in the GaAs.

To better describe the effect of sub-bandgap illumination on device performance, we plotted the voltage loss at a constant cell current as a function of the Ge illumination. It is important here to realize that the Ge illumination comes not only from the 940 nm LED. Observing the JV curves shown in Fig. 3c, we see that, especially with higher illumination intensities, voltage losses compared to the Xe-illuminated curves are low near V_OC. This is the result of luminescence from the GaAs junction into the Ge substrate. Internal recombination rates are higher when the GaAs junction is operating closer to V_OC (or rather, away from short circuit current), resulting in sufficient illumination of the Ge substrate to eliminate the voltage loss. At the lowest illumination intensities, the recombination rates and resultant luminescence are not sufficient for this. This is why the fill factor increases at short circuit current densities above a certain point (Fig. 4) - there is an increased range of extracted current over which luminescence from the GaAs is sufficient to mostly eliminate the voltage losses.

Therefore, in describing the voltage loss dependent on Ge illumination, we must consider and quantify two sources of illumination of the Ge substrate – the externally applied 940 nm LED illumination, and internal luminescence from the GaAs junction. We measured the LED irradiance directly with a spectroradiometer in the plane of the solar cell and converted it to photon flux. We calculated the photon flux of the GaAs luminescence (Φ_LC) from absolute EL measurements of the external radiative efficiency, y_ext, [12], [14] as:

$${\Phi }_{LC}=\frac{y_{ext}{n}^2{I}_j}{qA}$$ (1)

where A is the device area (4 cm²), q is the elementary charge, n is the refractive index of GaAs at 890 nm, and I_j is the current through the GaAs junction diodes. I_j is equal to I_L–I_t where I_L is the light generated current and I_t is the extracted terminal current. Since EL measurements of y_ext were taken at discrete injection currents, Φ_LC as a function of injection current was fit to provide Φ_LC at intermediate points (Fig. 6 inset).

Fig. 6.

Voltage loss as a function of Ge illumination level at fixed extracted terminal currents, from comparing JV curves in Fig. 5, with a fit logistic curve. Inset shows the fitting of Ge illumination from GaAs luminescence as a function of the GaAs diode current, based on absolute EL measurements of external radiative efficiency (y_ext). Contours show illumination for fixed values of y_ext.

For each curve in Fig. 5, at a set I_t, we calculated the voltage loss relative to the JV curve with full Ge illumination (rightmost, red curve in Fig. 5). The dependence of this voltage loss, which we denote V_C, on Ge illumination is shown in Fig. 6. We fit this data with a logistic function of the form:

$$V_C\left({\Phi }_{Ge}\right)=V_C\left(\mathit{\text{dark}}\right)\frac{1+e^{-M/s}}{1+e^{\left(qA{\Phi }_{Ge}-M\right)/s}}$$ (2)

in which s and M are fitting parameters. While this provided a slightly better fit and simpler implementation in our model than a Gaussian or Lorentzian curve, it is not a definitive physical description of the effect. We also find that s and M vary some with terminal current. In particular, M, which is correlated to the level of illumination required to eliminate losses, increases with the terminal current, up to a saturation point.

Having determined that illumination of the germanium substrate eliminates the voltage loss, we now consider the origin of that loss. We tested both a model based on a resistance-limited exponential shunt, such as might be present at device edges [15], [16], and a tandem model based on the presence of a second active Ge junction or Ge/GaAs heterojunction in series with the GaAs junction [17], [18], but found neither accurately described these results.

In the case of the tandem model, the use of a low shunt resistance and reverse bias breakdown voltage [19] improved qualitative agreement with measured data, but significant inconsistencies remained. First, we see completely repaired JV curves at photon fluxes much lower than would allow a Ge sub-cell to current-match the intentional GaAs junction. For example, with a GaAs junction short circuit current density of 10 mA/cm², the 940 nm illumination required to repair the JV curve is such that the photogenerated current in a bottom junction with a 100 % internal quantum efficiency (IQE) would be 4.4 mA/cm². This will increase to 6.5 mA/cm² near V_OC when GaAs luminescence is included, but this is still short of the current matching condition required by the tandem model. Furthermore, we have seen already in Fig. 5 that V_OC does not change with the addition of 940 nm illumination. Any tandem model predicts an increase in V_OC when the photocurrent in the bottom junction increases towards that of the top junction. Finally, we were not able to use the tandem model to fit JV curves at different white LED illumination levels without changing the parameters of the bottom junction, which is not illuminated by the white LED.

To develop a more representative circuit model, we noted that the lack of change in V_OC indicates a series effect with voltage loss dependent on terminal current. We therefore plotted the same voltage loss, V_C, as shown in Fig. 6, but this time as a function of terminal current for a fixed Ge substrate illumination. As the luminescent coupling between the GaAs and Ge means that Φ_Ge varies as a function of GaAs junction current, this required the use of multiple IV measurements. We chose a fixed value of I_j, and therefore fixed (low level) luminescence from GaAs to Ge, and extracted the terminal current (I_t) and voltage loss (V_C) at that point for each in a series of measurements at different white LED intensities (i.e., the curves in Fig. 3a). These are plotted in Fig. 7 and represent the JV characteristic of the series loss element. This curve is well fit by a parallel combination of a linear ohmic element and an exponential diode element. Fig. 7 shows each of these as well as the combined fit. It is clear that neither element alone would result in a good fit, as the extracted data have a linear characteristic at lower voltages and an exponential characteristic at higher voltages. Therefore, our model, pictured in Fig. 8, consists of an additional shunted diode in series with the standard double-diode solar cell equivalent circuit that represents the GaAs junction. The model is similar to that of a tandem solar cell, but does not include a light-generated current source in parallel with D_C, as a tandem model would. Instead, the characteristics of the additional shunted diode are directly modulated by Φ_Ge.

Fig. 7.

Current and voltage loss curve at a fixed GaAs diode current, and therefore constant Ge substrate illumination, fit to inform the development of a circuit model. The shape of the measured curve informed the choice of an ohmic and an exponential component in parallel to fit the data and describe the loss element.

Fig. 8.

Equivalent circuit diagram representing IV characteristics of GaAs-on-Ge solar cell. The dashed box indicates the loss element, which is added to a standard double-diode model of a solar cell. The parameters of the diode and resistor which comprise this element are dependent on the illumination of the Ge substrate, which is accounted for in the model by multiplying voltage loss across this element by a parameter dependent on the Ge illumination (Eqn. 2).

We modeled the circuit in a mathematical programming environment. The voltage drop across the loss element, consisting of the parallel combination of the resistance R_C and the diode D_C, with saturation current I_0,Dc and ideality factor n_Dc, is a function of the current through each element as:

$$V_C\left(\mathit{\text{dark}}\right)=I_{Rc}{R}_C=\frac{n_{Dc}kT}{q}ln\left(I_{Dc}/I_{0,Dc}+1\right)$$ (3)

with k being the Boltzmann constant, T the device temperature, and where

$$I_t=-\left(I_{Rc}+I_{Dc}\right)$$ (4)

The root of these equations was solved numerically. To quickly plot an IV curve, the extracted terminal current (I_t) is calculated based on the two-diode model using an internal GaAs junction voltage, V_j:

$$I_t=I_{0,1}\left(e^{q{V}_j/kT}-1\right)+I_{0,2}\left(e^{q{V}_j/2kT}-1\right)+V_j{R}_{sh}-I_L$$ (5)

with I_0,1 and I_0,2 being the saturation currents of the two diodes and R_sh is the shunt resistance. The external terminal solar cell voltage (V_t) was then calculated by subtracting the voltage losses from the standard series resistance and the Φ_Ge-modulated loss element described by Eqns. 2 through 4 as:

$$V_t=V_j-V_C\left(\mathit{\text{dark}}\right)\frac{1+e^{-M/s}}{1+e^{\left(qA{\Phi }_{Ge}-M\right)/s}}-I_t{R}_s$$ (6)

We then plotted I_t against V_t. The rapid calculations enabled adjustment of parameters and visual fitting of the experimental measurements. The model uses the dependence of V_C on Φ_Ge found in Eqn. 2 to capture the effect which the illumination of the germanium substrate has on the parameters of R_C and D_C. This approach is convenient as Φ_Ge varies with the current within a single IV curve due to luminescence from the GaAs cell. Visual fits are depicted in Fig. 9 with parameters listed in Table I. As several of these parameters are correlated (e.g., n_Dc and I_0,DC), these are not definitive parameters, but they demonstrate that this model reproduces the IV characteristics seen under LED illumination over a wide range of illumination intensities.

Fig. 9.

Visual fit (lines) of circuit model parameters to measured GaAs-on-Ge JV curves (circles) under white LED illumination at three different total irradiances, varying only I_L and M between each.

TABLE I.

Parameters For Visual Fits

parameter	2.93 W/m2	2.93 W/m2	173 W/m2
IL	0.525 mA	4.26 mA	31.0 mA
I0,1	9e-16 mA
I0,2	6.5e-8 mA
Rs	<1Ω*
Rsh	>40 kΩ*
I0,Dc	6.3e-3 mA
nDc	3.2
Rc	240 Ω
s	*	0.3 mA
M	*	−.765 mA	.75 mA

^*Further specificity of these parameters does not noticeably affect the IV curve at this irradiance level.

The fact that the JV characteristic of the voltage loss includes an exponential component which must be represented by a diode (i.e. junction) of some kind, along with the knowledge that the device structure consists of multiple material types, suggests that either the heterojunction III-V/Ge interface or the Ge/Au interface, or both, form a barrier to current extraction. This makes V_C the voltage across this barrier. Considering the high work function of the Au contacts, and the charge neutrality level near the valance band in Ge [20], [21] along with the fact that the absorption coefficient of germanium [22] between 880 and 940 nm indicates that 99 % of light incident on the Ge will be absorbed in the first 2 μm, the III-V/Ge interface seems more likely to be at fault than the Ge/Au interface.

Measurements of spectral response under voltage and DC light bias (Fig. 10) indicate the involvement of the Ge substrate. However, unlike in conventional multijunction devices, an apparent external quantum efficiency of greater than 100 % can be measured. As in any differential spectral response measurement, the application of the AC probe beam results in an AC component of the device’s terminal current as the device operating condition changes. Unlike in a tandem device, the change in terminal current is not due to the extraction of carriers photogenerated in the Ge by the AC probe beam, but by the modulation of the characteristics of the III-V/Ge interface such that carriers photogenerated in the GaAs by the bias light are more efficiently extracted at the points in the cycle when the AC probe beam is on. The device operating point moves, for example, from a location on the leftmost blue curve in Fig. 5 to the same voltage on the rightmost red curve. This can increase the terminal current by more than the photon flux from the AC probe beam, consistent with our observations that the IV curves are fully repaired with lower illumination levels than would be required for current-matching in a tandem device.

Fig. 10.

Spectral response of GaAs on Ge solar cells measured under different bias voltages (Vbias) and bias lights (specified by current generated in the solar cell). Apparent EQE greater than 100 % is due to the influence of substrate illumination on efficient extraction of bias-light generated carriers from the GaAs, as explained in the text.

Previous work on GaAs cells on Ge have shown the possibility of an active junction in the Ge - either a GaAs/Ge heterojunction or a Ge p-n homojunction, formed in some cases by indiffusion of Ga or As into the Ge substrate, resulting in p-type or n-type doping, respectively [17], [18], [23], [24]. Of the two species, As has a higher diffusion coefficient and has been more difficult to eliminate [23], [24]. Given the p-type Ge substrates in these devices, As indiffusion may also play a role in the effects observed in this work. However, the previously reported active junctions have all resulted in a standard tandem cell, even if the bottom cell is poor quality. They require current matching to avoid power losses from the bottom cell, and are evident under broadband illumination due to increases in V_OC.

The parasitic heterojunction barrier in the devices we characterize in this work on the other hand does not exhibit the behavior of a subcell in a tandem device. The lack of a current-matching requirement or change in V_OC means the JV curves are not repaired by means of a photogenerated current in this junction. Instead, illumination of the Ge substrate serves to directly impact junction parameters, possibly by either adjusting the band bending such that the barrier height is reduced, or altering the occupancy of traps near the interfaces to increase lossless tunneling currents. This also means that in contrast to previously observed active Ge substrates, this effect is not detectable solely from JV characterization under a broadband spectrum such as a standard AM1.5G or AM0 calibrated solar simulator.

IV. Conclusions and Implications

We have shown in this work that some III-V solar cells with heterosubstrates require illumination of the substrate in order to achieve high efficiencies. The substrate is not acting as a second junction in a multijunction device would, and does not contribute directly to power generation. It also does not produce an increased V_OC under broadband illumination, which could generally be used to identify a tandem device formed from an active Ge substrate. Our circuit analysis suggests the presence of energy barriers, which long wavelength illumination eliminates or increases tunneling through. Further work with temperature-dependent IV measurements will allow for more insight into the nature of these barriers.

The observation of this phenomenon is important in informing the way devices are measured and potentially developed. Devices which operate under spectra that do not include sub-bandgap light, such as indoor LED illumination or in spectrum-splitting systems, may perform poorly under those conditions compared to in laboratory measurements under an AM1.5 or similar spectrum. Conversely, measuring devices intended for use under a spectrum containing long wavelength light using only an LED illumination source could result in some devices which would perform well being discarded or identified as performing poorly due to the lack of sub-bandgap illumination during the measurement. In both these cases, the measurement may appear to be correctly calibrated based on reference and test cell short circuit currents. These effects also may not be readily apparent from measurements under a single condition, as we have seen that they can appear as a simple high series resistance under indoor illumination levels. Based on the devices we have observed this effect in, this will be most relevant when considering III-V solar cells with Ge or other heterosubstrates, and could be an important phenomenon to be aware of when developing devices using new materials, particularly if they also incorporate heterosubstrates.