Tin sulfide (SnS) is a candidate material for Earth-abundant, non-toxic solar cells. Here, we demonstrate the fabrication procedure of the SnS solar cells employing atomic layer deposition, which yields 4.36% certified power conversion efficiency, and thermal evaporation which yields 3.88%.
Tin sulfide (SnS) is a candidate absorber material for Earth-abundant, non-toxic solar cells. SnS offers easy phase control and rapid growth by congruent thermal evaporation, and it absorbs visible light strongly. However, for a long time the record power conversion efficiency of SnS solar cells remained below 2%. Recently we demonstrated new certified record efficiencies of 4.36% using SnS deposited by atomic layer deposition, and 3.88% using thermal evaporation. Here the fabrication procedure for these record solar cells is described, and the statistical distribution of the fabrication process is reported. The standard deviation of efficiency measured on a single substrate is typically over 0.5%. All steps including substrate selection and cleaning, Mo sputtering for the rear contact (cathode), SnS deposition, annealing, surface passivation, Zn(O,S) buffer layer selection and deposition, transparent conductor (anode) deposition, and metallization are described. On each substrate we fabricate 11 individual devices, each with active area 0.25 cm2. Further, a system for high throughput measurements of current-voltage curves under simulated solar light, and external quantum efficiency measurement with variable light bias is described. With this system we are able to measure full data sets on all 11 devices in an automated manner and in minimal time. These results illustrate the value of studying large sample sets, rather than focusing narrowly on the highest performing devices. Large data sets help us to distinguish and remedy individual loss mechanisms affecting our devices.
Thin film photovoltaics (PV) continue to attract interest and significant research activity. However, the economics of the PV market are shifting rapidly and developing commercially successful thin film PV has become a more challenging prospect. Manufacturing cost advantages over wafer-based technologies can no longer be taken for granted, and improvements in both efficiency and cost must be sought on an equal footing.1,2 In light of this reality we have chosen to develop SnS as an absorber material for thin film PV. SnS has intrinsic practical advantages that could translate into low manufacturing cost. If high efficiencies can be demonstrated, it could be considered as a drop-in replacement for CdTe in commercial thin film PV. Here, the fabrication procedure for the recently reported record SnS solar cells is demonstrated. We focus on practical aspects such as substrate selection, deposition conditions, device layout, and measurement protocols.
SnS is composed of non-toxic, Earth-abundant and inexpensive elements (tin and sulfur). SnS is an inert and insoluble semiconducting solid (mineral name Herzenbergite) with an indirect bandgap of 1.1 eV, strong light absorption for photons with energy above 1.4 eV (α > 104 cm-1), and intrinsic p-type conductivity with carrier concentration in the range 1015 – 1017 cm-3.3–7 Importantly, SnS evaporates congruently and is phase-stable up to 600 °C.8,9 This means that SnS can be deposited by thermal evaporation (TE) and its high-speed cousin, closed space sublimation (CSS), as is employed in the manufacture of CdTe solar cells. It also means that SnS phase control is far simpler than for most thin film PV materials, notably including Cu(In,Ga)(S,Se)2 (CIGS) and Cu2ZnSnS4 (CZTS). Therefore, cell efficiency stands as the primary barrier to commercialization of SnS PV, and SnS could be considered a drop-in replacement for CdTe once high efficiencies are demonstrated at the laboratory scale. However this efficiency barrier cannot be overstated. We estimate that the record efficiency must increase by a factor of four, from ~4% to ~15%, in order to stimulate commercial development. Developing SnS as a drop-in replacement for CdTe will also require growth of high quality SnS thin films by CSS, and the development of an n-type partner material on which SnS can be grown directly.
Below is described the step-by-step procedure for fabricating record SnS solar cells using two different deposition techniques, atomic layer deposition (ALD) and TE. ALD is a slow growth method but to-date has yielded the highest efficiency devices. TE is faster and industrially scalable, but lags ALD in efficiency. In addition to the different SnS deposition methods, the TE and ALD solar cells differ slightly in the annealing, surface passivation, and metallization steps. The device fabrication steps are enumerated in Figure 1.
After describing the procedure, test results for the certified record devices and related samples are presented. The record results have been reported previously. Here the focus is on the distribution of results for a typical processing run.
1. Substrate Selection and Cutting
2. Substrate Cleaning
3. Mo Sputtering
4. SnS Deposition
Note: The ALD deposition technique is described in sub-section 4.1, and the TE deposition is described in sub-section 4.2. The ALD deposition system is shown in Figure 2, and TE deposition system is shown in Figure 3.
5. SnS Annealing
Note: This step is performed slightly differently for ALD and TE solar cells. The annealing procedure for ALD solar cells is described in sub-section 5.1, and the procedure for TE solar cells is described in sub-section 5.2. The purpose of annealing is discussed in the Discussion section.
6. SnS Surface Passivation with a Native Oxide
Note: This step is performed slightly differently for ALD and TE solar cells. In sub-section 6.1 the surface passivation procedure for ALD solar cells is described, and the procedure for TE solar cells is described in sub-section 6.2. The function of this step is further discussed in the Discussion section.
7. Deposition of the Zn(O,S) / ZnO Buffer Layer
Note: This step is performed in the same ALD chamber that is used for SnS growth by ALD.
8. Deposition of the Transparent Conducting Oxide (TCO), Indium Tin Oxide (ITO)
9. Metallization
10. Device Characterization
In Figures 6-8 results are shown for two representative “baseline” TE-grown samples as described above. Illuminated J–V data for these two samples is plotted in Figure 6. The first sample (“SnS140203F”) yielded the device with certified efficiency of 3.88% that was reported previously.9 Representative J-V distributions are also shown for each sample. For a given bias voltage, these distributions are calculated as where <J> is the average of the current density measured for all devices, σJ is the standard deviation of these measurements, and N is the total number of measurements. In other words, the average and the standard error are graphically represented. This representation helps with comparing results from different samples, and for visually assessing the impact of changes in device fabrication on the resulting device performance.
The J–V data suggest that the samples suffer from problems with shunt resistance that varies between devices on a sample. This conclusion is further reinforced by Figures 7 and 8. In Figure 7 the standard solar cell parameters are plotted — open circuit voltage (VOC), short circuit current density (JSC), fill factor (FF), and power conversion efficiency — for all the same devices shown in Figure 6. The bar graph representation helps to visually identify correlations between parameters. For these samples the most apparent correlation is between efficiency and the FF, as expected for devices that suffer from shunt or series resistance losses. For the second device there is also an apparent correlation between efficiency and VOC, as expected for shunt resistance losses.
These correlations are made explicit by the multivariate plots shown in Figure 8. Here, VOC, JSC, and FF are plotted against the series (Rs) and shunt (Rsh) resistances. Rs and Rsh are calculated using linear fits to the J–V data near 0.5 and 0 V, respectively. In many cases it would be better to extract Rs and Rsh as parameters in a diode model which can be fit to the J–V data. However, for relatively low efficiency solar cells there are many sources of loss, and diode models that succeed for higher efficiency devices are not reliable. Therefore it is preferred to extract Rs and Rsh by a more robust technique. Although the resulting values may not be accurate, the trends are still instructive and can be used to guide development. The data in Figure 8 confirm that shunt resistance is a major source of loss. This can be seen most clearly in the rising trend in FF (Rsh). The data show that, at the present stage of device development, the shunt resistance must be maintained greater than approximately 200 Ω cm2 in order for efficiency gains from other process improvements to become apparent. Rs appears not to limit the devices reported here. The values for Rs are typically 0.5 Ω cm2, and only rarely venture above 1 Ω cm2.
Results for one representative “baseline” ALD-grown sample as described above are shown in Figure 9. The ALD devices show better performance than the TE devices, with the best device showing 4.6% efficiency. Besides the different SnS growth techniques, the two fabrication procedures differ in the SnS surface passivation by oxidation. In addition, the TE samples are exposed to laboratory air in between film growth and annealing, while the ALD samples are annealed in the growth chamber without an air break. The ALD-grown samples appear to suffer less from shunt resistance losses than the TE-grown samples. The reason for this difference is not known. It is possible that the ALD-grown SnS films are more compact, due to the self-limiting growth mode and slow growth rate, than the TE-grown films.
The certified device tests are reproduced in Figure 10.9,10 On the left is shown the certified record device using an ALD-grown SnS layer. The certified efficiency for this sample was 4.36%, and devices up to 4.54% efficient have been measured using the same fabrication procedure. On the right is shown the certified record device using a TE-grown SnS layer. The certified efficiency for this sample was 3.88%, and devices up to 4.1% have been measured with the same procedure. Note that the 3.88% certified test result is well within the range measured for the same sample, for which the average ± standard deviation is 3.5% ± 0.4%, as shown in Figure 7.
Figure 11 shows results demonstrating the stability of TE-grown SnS solar cells in ambient conditions. For select samples J–V tests were performed before and after storing for up to eleven months. The samples were stored in air and exposed to ambient light without encapsulation. All four samples shown in Figure 11 were processed slightly differently than the procedure reported here; this is for historical reasons, and there is no reason to think that the devices reported here would have different stability characteristics. The processing differences are described in the figure caption, and they account for the varying performance of the devices. The main point is that minimal degradation is observed over a year. It remains to be seen how SnS solar cells would survive more accelerated lifetime testing, such as damp heat or prolonged full spectrum illumination.
Figure 1. Device fabrication process. Enumeration of the device fabrication process, from substrate cutting (#1, bottom) to metallization (#9, top).
Figure 2. Atomic layer deposition (ALD) system overview. (Top) ALD system schematic drawing. (Bottom) ALD system photograph, with critical components numbered and labeled. This system can perform SnS deposition, SnS annealing, and buffer layer deposition and sits in the Gordon group at Harvard University. It consists of a hot-wall deposition tube, two ovens used to store precursor, gas deliver and control system, temperature controlling system and a rotary vane mechanical vacuum pump. The substrate holder can put at most eight 1” × 1” square substrates. Please click here to view a larger version of this figure.
Figure 3. Thermal evaporation (TE) system overview. Critical components are numbered and labeled. This system is dedicated to SnS deposition and sits in the Buonassisi group at MIT. The system consists of a process chamber and a load lock. The process chamber is typically kept under high vacuum conditions (1 × 10-8 Torr) and includes a shuttered substrate stage with sample rotation and radiative heating, and a shuttered effusion cell for source evaporation. The chamber also has a retractable quartz crystal monitor (QCM) located directly underneath the substrate plate to measure growth rate, and a pyrometer to measure substrate temperature. Commercially purchased SnS powder is used for the precursor, with a thermal pre-treatment described previously.9 The substrate plate holds one large device substrate (1 × 1 in2) and one smaller substrate (1 × 1/3 in2) which is used for SnS film measurements. The distance from the substrate to the source orifice is 10 cm. Please click here to view a larger version of this figure.
Figure 4. Metallization pattern and sample photograph. The drawing at left shows the metallization pattern for 0.25 cm2 devices. For clarity the TCO footprint is outlined on only one device. Also shown is the location of the larger TCO pad that is used for optical reflectivity measurements. The photograph at right shows a real sample with TE-grown SnS. The scratched region at the left provides contact to the underlying Mo layer for testing. Photograph: KJ Wang. Please click here to view a larger version of this figure.
Figure 5. Device testing with probe card. This top-down image shows a sample mounted on the test station chuck with multiple devices contacted simultaneously with the custom probe card. Only half of the sample is visible in this image. Please click here to view a larger version of this figure.
Figure 6. J–V tests for devices on two different “baseline” TE samples. For clarity, all 12 devices on a given sample are plotted in the same color (grey or red). Also plotted are representative J–V envelopes (average ± standard error) for all devices on each sample, as described in the text. These measurements were performed without an area-defining light aperture. Please click here to view a larger version of this figure.
Figure 7. Solar cell test parameters for two baseline TE samples. The test results are plotted on a single line for each device tested — 11 devices each for “SnS140203F” (top) and “SnS140306H” (bottom) — to make correlations more apparent. Above each plot is reported the best, average, standard deviation (SD), and standard error (SE) for each distribution. Note that the best Voc (for example) is the highest measured Voc, not the Voc of the most efficient device. These measurements were performed without an area-defining light aperture. Please click here to view a larger version of this figure.
Figure 8. Series and shunt resistance multivariate plots for two baseline TE samples. The devices represented are the same reported in Figures 6-7. The series (Rs) and shunt (Rsh) resistances are calculated as described in the text. Please click here to view a larger version of this figure.
Figure 9. J-V tests and test parameters for one baseline ALD sample. (Top) The J-V curves show good peak performance, but some devices clearly suffer from low shunt resistance. (Bottom) The test parameters show a strong correlation between efficiency and the FF, consistent with shunt resistance losses. These measurements were performed without an area-defining light aperture. Please click here to view a larger version of this figure.
Figure 10. Certification results for ALD- and TE-grown devices. Certification performed by the PV Performance Characterization Team at the National Renewable Energy Laboratory, USA. (Left) The ALD certified record is 4.36%, as reported in Sinsermsuksakul et al.10 (Right) The TE certified record is 3.88%, as reported in Steinmann et al.9 Please click here to view a larger version of this figure.
Figure 11. Long-time stability of SnS solar cells. J–V tests of samples that were repeatedly measured over a period of nearly a year, while being stored in air and being exposed to ambient light without encapsulation. For each panel the black curves show the initial measurement, the red curves show the final measurement, and dashed curves show. The thin lines show the best device for each test, and the thick curves are representative J–V envelopes (average ± standard error) for all devices on each sample as described in the text. All four panels show TE-grown samples that were processed as described in this manuscript except for the following differences: (a) No H2S annealing step. (b) Thinner absorber layer, 650 nm thick; no H2S annealing step; air exposure performed at 200 °C for 30 min. (c) Thinner absorber layer, 650 nm thick; no H2S annealing step; buffer layer with higher sulfur content and no nitrogen doping. (d) Antireflection coating deposited on top of device stack. The time between measurements was 50 weeks, 48 weeks, 48 weeks, and 28 weeks for panels a, b, c, and d, respectively. Please click here to view a larger version of this figure.
Figure 12. Visualization of spatial non-uniformity across two baseline TE samples. Results are the same as reported in Figure 6-8. There are 11 devices on each sample, and each device is color coded according to the measured efficiency; the colormap is the same for both samples. Black-and-white hatching indicates either that the device was not measured, or no device was present (as one corner of each sample).
Figure 13. Illustrated example of hypothesis testing in the presence of common cause variance. Fictional characters Angela and Nessi are separately testing the hypothesis that Process B yield higher efficiency solar cells than Process A. Angela has superior process control but a slightly lower baseline efficiency than Nessi. (A,D,G) True probability distributions for Angela and Nessi’s results. (B,E,H) Individual measurements. (C,F,I) Measured distributions. With only 6 samples, Angela can reject the null hypothesis but Nessi cannot. See text for full description. Please click here to view a larger version of the figure.
Substrate selection cleaning
Oxidized Si wafers are used as substrates. The substrates are the mechanical support for the resulting solar cells, and their electrical properties are not important. Si wafers are preferred to glass because commercially purchased Si wafers are typically cleaner than commercially purchased glass wafers, and this saves time in substrate cleaning. Si substrates also have higher thermal conductivity than glass, which leads to more even heating during growth and annealing. With commercially purchased glass wafers it was found that it was necessary to clean the substrates with detergent, including a manual rub with gloved fingers followed by a warm ultrasonic bath, in order to remove all visible traces of contamination, and even then substrate cleanliness could not be guaranteed. It was experimentally confirmed that the choice of glass or Si substrates has no impact on device performance. However, this comparison was performed with devices were in the 2% – 3% efficient range, and repeated comparisons will be worthwhile as the baseline efficiency improves.
Typically 10 or more substrates are cleaned at a time using a custom designed quartz wafer carrier. This yields more reproducible results than handling wafers individually with tweezers.
Mo sputtering
It was decided to deposit the Mo back contact (the cathode) in-house rather than purchase Mo-coated substrates after disappointing results were obtained with the substrates available from several different vendors. With purchased substrates (sputtered Mo on glass) problems were encountered with cleanliness, delamination, or both. The Mo film is deposited by DC magnetron sputtering in two layers, one for adhesion to the Si / SiO2 substrate and one for high conductivity, according to the results published by Scofield et al.13
Typical Mo films are 720 nm thick with a sheet resistance of approximately 1 Ω/sq. The sheet resistance is measured on a sacrificial substrate using a four point probe system after each Mo growth run. In addition, the adhesion to the substrate is tested using a scalpel blade. Well-adhered films can withstand scratching by hand with a scalpel at moderate pressure without de-laminating. Poorly adhered films will de-laminate with only slight pressure. It was observed that a short substrate plasma cleaning step in the sputtering chamber before Mo growth is important to obtain good adhesion. Typical parameters for this cleaning step are 20 mTorr Ar, 20 W RF, and 60 sec.
SnS growth by thermal evaporation
SnS is evaporated from source powder using a commercially purchased low temperature effusion cell with a pyrolytic boron nitride crucible with volume 32 cm3. When the source is first loaded it is a fine powder and dark grey in color. Typically 3 4 g of powder is loaded. With new source powder, the source temperature is approximately 540 °C in order to maintain a growth rate of 1 Å/sec on a substrate heated to 240 °C. With an increasing number of growth runs, the source temperature must be increased to maintain a constant growth rate. When the required source temperature reaches 610 °C the powder is exchanged.
Closely connected to the source temperature is the issue of SnS flakes. When the growth rate is increased to over 10 Å/sec, large SnS flakes can be observed in the growing film. It is unknown whether these originate from the main source, or from secondary sources such as the effusion cell shroud or the source shutter.
One remarkable observation is that when a batch of source powder is exhausted it leaves behind a white, porous residue at the bottom of the crucible. X-ray diffraction confirms that this is SnO2. The weight of this residue is typically 0.01 g.
SnS growth by ALD
A critical parameter in this process is the pressure of the nitrogen carrier gas that flows to the Sn(amd)2 precursor. The pressure is maintained near 250 Torr, but may vary a little bit from time to time. Given that the volume ratio of the Sn(amd)2 precursor bubbler and N2 gas trap is 5:1, the pressure inside the bubbler is around 50 Torr. If this value becomes too large, the evaporation of Sn precursor will be significantly suppressed. On the other hand, if the pressure inside the bubbler is too small, there would not be a sufficient pressure drop between the bubbler and the reaction furnace (which has a pressure of ~10 Torr) to enable a smooth gas flow. Either of these scenarios will result to inadequate Sn precursor in the ALD reaction. An indication of this problem is that film thickness near the outlet of the reaction furnace is much thinner than that near the inlet. During each deposition, the pressure inside the reactor is monitored to make sure that the system pressures sit in the correct range.
To ensure a uniform temperature distribution within the reaction zone, the inlet and outlet of the hot-wall deposition tube are wrapped with heating tapes. Under the heating tapes, a pair of thermocouples are inserted to measure the temperature. A non-uniform temperature distribution inside the reaction zone will result to different SnS film morphologies at different regions. At higher deposition temperature, films tend to be rougher and have a lighter color. At low temperatures below 200 °C, films have a higher reflectivity, as can be examined by eye.
SnS annealing in an H2S tube furnace
The purpose of the annealing step is to optimize the morphology, crystallinity, and electrical properties of the SnS films. For the TE-grown solar cells, the annealing step is performed in a dedicated tube furnace. This 2” diameter quartz tube furnace is capable of flowing mixtures of 4% H2S (balance N2), 4% H2 (balance N2), pure N2 and pure Ar. Temperatures are controlled by external Nichrome heating elements and monitored using a quartz-encased thermocouple located in the hot zone. Gas is evacuated using an oil pump filled with inert oil. Seals are made using H2S resistant elastomers. Typical base pressure is 8 20 mTorr.
The annealing temperature of 400 °C is a balance between secondary grain growth and film re-evaporation. In principle, higher annealing temperature might be beneficial for device performance, and could be achieved without significant film loss by using higher furnace pressure. This is the subject of active investigation.
SnS surface passivation with a native oxide
The purpose of the passivation step is to reduce the density of electronic trap states at junction between the absorber and the buffer layers, and to serve as a diffusion barrier to prevent unwanted mixing of the constituent elements of the absorber and buffer layers.14 It has been observed that samples processed with this oxidation step have higher VOC values than samples processed without.
At this time, the oxidation step has not been extensively studied and is probably not optimized. Using X-ray photoelectron spectroscopy results (not shown) it is estimated that the oxide should be less than 1 nm thick for good performance and to avoid current blocking.
Deposition of the transparent conducting oxide (TCO), indium tin oxide (ITO)
Prior to this point care is taken to control the total air exposure of the samples at each step. However, after the buffer layer deposition air exposure is no longer limited and the samples are stored and transported in ambient air.
Prior to this point, all depositions have been “blanket” films, covering the entire substrate. From this point on the depositions are patterned to define individual devices. For both the ITO and metallization steps the depositions are defined using laser-cut metal shadow masks. For the ITO deposition it is very important that the area of the deposited pad is sharply defined by the shadow mask. If the area is not sharply defined, for example due to flexing of the mask in the mask aligner, then the active area of the resulting devices may be significantly larger than the nominal size of 0.25 cm2. This can lead to erroneous over-reporting of the current density.
Metallization
The metallization pattern is designed to enable the illumination spot of the quantum efficiency measurement tool to fall completely on the ITO without overlapping with the metal. This constraint results in 2 fingers separated by 1.5 mm, each 7 mm long, and a 1 x 1 mm2 contact pad, see Figure 4. This pattern is less than optimal from a device-performance standpoint. A pattern optimized for device performance would use more fingers with smaller spacing.
Ag has been used for TE-grown cells and Ni / Al has been used for ALD-grown cells. This division is historical and is not grounded in an experimental outcome. It is possible that Ni / Al provides superior resistance to corrosion during long storage times. In fact, it has been observed that Ag contacts have a tendency to corrode during extended storage in air (for example, longer than a year).
Device characterization
Finished devices are characterized using current-voltage (“J–V”) measurements collected and external quantum efficiency (EQE) measurements collected with and without white light and voltage bias. To-date solar cells have been measured by contacting individual devices one-at-a-time, using probe micromanipulators in a typical probe station configuration. The solar simulator and EQE systems were physically disconnected, so the sample needed to be re-contacted for each measurement. As a result, it would take approximately 4 – 5 hr to measure J–V and EQE on all 11 devices.
An integrated high-throughput test station that combines J–V and EQE using a single sample chuck and a probing card that contacts all devices simultaneously was recently installed at MIT, see Figure 5. The electrical connections are controlled by a programmable multiplexer, and the motorized X-Y chuck stage is computer controlled. In this way, J–V and EQE measurements can be performed sequentially on all 11 devices in under 1 hr.
For routine device testing an area-defining light aperture is not used. Therefore the active device area may be under-estimated, resulting in over-estimates of the current density. However an aperture is used by certification laboratories, often resulting in lower efficiencies (c.f. Figures 7, 9 and 10). Using an area-defining light aperture is always desirable, but for routine testing it is often neglected due to practical concerns such as to minimize physical contact with the top of the sample. Systematic error due to under-estimating the active device area can be mitigated by using larger device areas. For the work described here, the rather small (0.25 cm2) size was chosen as appropriate for early stage technology development (at earlier stages an even smaller device of 0.03 cm2 with no metallization was used). Now that the devices are in the range of 4% efficient and are repeatable, it is worth increasing to a size of 1 cm2 or more.
In addition to the standard characterization techniques described above, on occasion samples are also tested using techniques including temperature-dependent J–V, Suns-VOC, capacitance-voltage profiling, and lock-in thermography. These techniques are used to understand and quantify specific loss mechanisms such as interface recombination and series resistance loss.
The significance of sharing device fabrication protocols
In publications on inorganic thin film PV the results of device tests are never (with experience) accompanied by sufficient experimental details to reproduce the experiment. This situation leads to unnecessary frustration among individual researchers, and hampers the progress of the whole field. This situation also makes it difficult to compare the procedures described herein to those used by other research groups. The techniques described in this manuscript were developed with the aid of numerous conversations with researchers in thin film PV (mainly in the United States), and a lot of trial-and-error. The authors hope that this work helps others avoid unnecessary frustrations, and sets a precedent for details reporting of experimental methods in thin film PV.
Future applications of the described protocol
The protocol described herein is used to establish a “baseline” SnS solar cell. The most important feature of a baseline fabrication protocol is repeatability; the absolute efficiency number is less important. In the authors’ experience, repeatability is the key attribute that will enable ongoing research to improve efficiency, such as by improving surface passivation or reducing bulk defect density. Without a repeatable baseline protocol it is extremely difficult to judge the effects of changes to the fabrication protocol. This is fully described in the section below on hypothesis testing.
Ongoing and future work on SnS solar cells will leverage the baseline protocol described here to optimize the individual fabrication steps with the goal of increasing device efficiency. Of particular interest are the H2S annealing and the surface passivation steps, since these directly impact the defect density in the bulk of the absorber and at the p–n junction.
Data ensembles enable hypothesis testing
In a field that idolizes champion efficiencies, it is tempting to overlook the ensemble — the >99% of (non-champion) devices — and the useful information it provides. This section motivates ensemble data analysis, and presents facile approaches for visualizing and extracting useful insights from ensemble data. It is presupposed that the reader has a working understanding of experimental statistics (hypothesis testing), and is comfortable calculating a Gaussian distribution, standard deviation, standard error, and 95% confidence intervals for a given data set.
Simply put, ensemble data analysis is the study of variability, which when reduced, enables better hypothesis testing. Variability, colloquially “noise,” obfuscates the “signal” during hypothesis-driven process engineering and scientific research. As noise increases, more experiments are rendered inconclusive. Inconclusive experiments are a waste of time, resources, and optimism. Ensemble data can help reduce variability in two ways:
First, ensemble data reveal process non-uniformities in space and time. This type of variability is systematic (e.g., caused by temperature- or flow-rate-gradients within a given thin-film deposition chamber), yielding a clear spatially resolved pattern of performance variation, exemplified by Figure 12. The spatial or temporal variation embodies the “fingerprint” of the offending process step. In-situ metrology and control samples can help identify and troubleshoot sources of systematic process variability.
Second, ensemble data reveal “luck-of-the-draw” or “common-cause” variance, i.e., statistical variability that affects all ensemble elements equally. This variability is more difficult to troubleshoot, because it is the aggregate result of multiple coupled processing steps. Common-cause variance can best be minimized by stringent process controls and standard operating procedures at each step — admittedly a challenging proposition in a fast-changing and minimally staffed academic environment. Nevertheless, the following exercise illustrates why reducing common-cause variance is essential.
The impact of common-cause variance exemplified: A friendly, fictional scientific competition between Dr. Meticulous and Dr. Messy: Angela and Nessi are researchers from two different laboratories. They are engaged in a friendly scientific competition to test the hypothesis that Process B generates better devices than a well-accepted baseline Process A. Both researchers employ a standard hypothesis-testing procedure, which assumes that common-cause variance results in Gaussian efficiency distributions (more representative statistical distribution functions include log-normal for distributions without outliers, and the more statistically robust log-Cauchy-Lorenzian for distributions with strong outliers).
Angela is known to her colleagues as “Dr. Meticulous.” She endeavors to reduce process variability. Angela does not share her beakerware with others, employs chamber pre-conditioning routines before thin-film deposition, incorporates control samples with every fabrication run, and prefers IC-grade silicon substrates with thermal oxide surfaces instead of the more variable glass surfaces. She produces baseline (Process A) devices with a “true” (i.e., actual) mean efficiency of 10% and a true standard deviation (σtrue) of 0.5%. Device fabrication and measurements are time consuming, and she is only able to fabricate and measure six devices (N = 6) per process.
In another lab, Nessi is hard at work. To her colleagues, Nessi is known as “Dr. Messy.” Her fabrication and metrology tools are located in a shared-use facility. When it’s her turn to use them, she doesn’t take the necessary precautions to ensure low common-cause variance. But because of her sloppiness, her true standard deviation is 1.5% absolute (3× greater than Angela’s). This higher σtrue reflects less well-controlled experimental conditions. However, because Nessi uses higher-purity feedstock materials, her baseline Process A achieves a true mean of 10.6%. Nessi fabricates and measures N = 6 devices per process.
Let’s suppose that Process B improves “true” device efficiency by 10% relative (i.e., 10% improves to 11%; 10.6% improves to 11.7%). Both Angela and Nessi apply the central limit theorem to the N = 6 devices they each fabricate, as shown in Figure 13. Note that the “true” distributions (Figures 13A, D, G) are hidden to the researchers; they only observe their experimental data (Figures 13B, E, H) and the resulting Gaussian fits, standard errors, and confidence intervals (Figures 1C, F, I).
On one hand, Angela’s tighter process control (lower variability, smaller σtrue) allows her to reject the null hypothesis, concluding with >95% confidence that Process B is superior to Process A (Figure 13C). On the other hand, Nessi, who has higher σtrue, cannot conclude that Process B is better than Process A (Figure 13F) with N = 6. Even though Nessi is lucky to make two devices with efficiencies that are higher than any of Angela’s (Figures 13B, E), Angela is winning the race to publish the scientific paper that will revolutionize the way her field thinks about Process B.
Nessi realizes that she needs to increase her confidence intervals, which requires her to reduce her standard measurement error (SE), i.e.,
. [1]
Nessi can pursue one of two approaches to match Angela’s 3× smaller SE: Nessi can reduce her true variability (σo) by a factor of 3, or increase N by a factor of 32 = 9. Nessi gains access to a high-throughput device-measurement apparatus, increasing N by 9×. This improvement offsets her 3× greater process variability, and she is able to detect a statistically significant difference between Processes A and B, rejecting the null hypothesis with >95% certainty (Figure 13I). She is back in the race for publication.
Higher baseline efficiencies increase the odds of successful hypothesis testing: Focusing on the equation for SE (Equation 1), it can be seen how increasing baseline performance increases the odds of successful hypothesis testing. If the aforementioned Process B were tested on a 5%-efficient baseline device instead of 10%, the absolute efficiency improvement would be only 0.5% instead of 1%. Assuming σo is unchanged, the minimum number of samples required to reject the null hypothesis increases by 4×. Thus, improving baseline device performance has the same mathematical effect as reducing σ, i.e., a 1-to-1 improvement in confidence intervals.
Final word: Reducing standard error is essential to minimize the risk of inconclusive hypothesis tests. Standard error can be reduced by decreasing common-cause variance, manifest in σo, which results in a 1-to-1 reduction in SE. Improving baseline performance has an equivalent effect. One can also increase sample size N, but this will have a weaker impact on SE because of the square root (increasing N also increases the risk of systematic variation).
The importance of applying experimental statistics is widely accepted in biology and physics (c.f. standing statistics committees at all high energy experiments).15 To improve the quality of data reporting in PV, it is recommended that researchers pay attention to the 99% of devices they fabricate, and adopt hypothesis testing with data ensembles.
The authors have nothing to disclose.
The authors would like to thank Paul Ciszek and Keith Emery from the National Renewable Energy Laboratory (NREL) for certified J-V measurements, Riley Brandt (MIT) for photoelectron spectroscopy measurements, and Jeff Cotter (ASU) for inspiration for the hypothesis testing section. This work is supported by the U.S. Department of Energy through the SunShot Initiative under contract DE-EE0005329, and by Robert Bosch LLC through the Bosch Energy Research Network under grant 02.20.MC11. V. Steinmann, R. Jaramillo, and K. Hartman acknowledge the support of, the Alexander von Humboldt foundation, a DOE EERE Postdoctoral Research Award, and Intel PhD Fellowship, respectively. This work made use of the Center for Nanoscale Systems at Harvard University which is supported by the National Science Foundation under award ECS-0335765.
Quartz wafer carrier | AM Quartz, Gainesville, TX | bespoke design | |
Sputtering system | PVD Products | High vacuum sputtering system with load lock | |
4% H2S in N2 | Airgas Inc. | X02NI96C33A5626 | |
99.5% H2S | Matheson Trigas | G1540250 | |
SnS powder | Sigma Aldrich | 741000-5G | |
Effusion cell | Veeco | 35-LT | Low temperature, single filament effusion cell |
diethylzinc (Zn(C2H5)2) | Strem Chemicals | 93-3030 | |
Laser cutter | Electrox | Scorpian G2 | Used for ITO shadow masks |
ITO sputtering target (In2O3/SnO2 90/10 wt.%, 99.99% pure) | Kurt J. Lesker | EJTITOX402A4 | |
Metallization shadow masks | MicroConnex | bespoke design | |
Electron Beam Evaporator | Denton | High vacuum metals evaporator with load-lock | |
AM1.5 solar simulator | Newport Oriel | 91194 | 1300 W Xe-lamp using an AM1.5G filter |
Spectrophotometer | Perkin Elmer | Lambda 950 UV-Vis-NIR | 150mm Spectralon-coated integrating sphere |
Calibrated Si solar cell | PV Measurements | BK-7 window glass | |
Double probe tips | Accuprobe | K1C8C1F | |
Souce-meter | Keithley | 2400 | |
Quantum efficiency measurement system | PV Measurements | QEX7 | |
Calibrated Si photodiode | PV Measurements | ||
High-throughput solar cell test station | PV Measurements | bespoke design | |
Inert pump oil | DuPont | Krytox | PFPE oil, grade 1514; vendor: Eastern Scientific |
H2S resistant elastomer o-rings | DuPont | Kalrez | compound 7075; vendor: Marco Rubber |
H2S resistant elastomer o-rings | Marco Rubber | Markez | compound Z1028 |
H2S resistant elastomer o-rings | Seals Eastern, Inc. | Aflas | vendor: Marco Rubber |