Diffusion of Rb in polycrystalline Cu(In,Ga)Se₂ layers and effect of Rb on solar cell parameters of Cu(In,Ga)Se₂ thin-film solar cells

The positive effect of the alkali element sodium on the performance of Cu(In,Ga)Se₂ (CIGS) solar cells was first detected in 1993 by comparing different glass substrates.¹ The main electrical parameters affected by Na were the open-circuit voltage, V_oc, and the fill factor, FF.² It was found that the increase in V_oc was caused by an increase in the net acceptor concentration.³ However, despite the long history of research on alkali elements in CIGS, the question of whether the positive effect of sodium is due to passivation of defects at grain boundaries (GBs)⁴ or due to bulk related effects^5,6 has remained a subject of debate up to this day. Already at an early stage in the research of alkali elements in CIGS, the effect of the heavier alkali elements potassium and cesium on cell performance and CIGS layer properties was also investigated. But these heavier alkali elements were not found to be as relevant for CIGS solar cell performance as sodium⁷ and thus were not further investigated. The positive effect of potassium was re-discovered in 2012: CIGS solar cells on enameled steel substrates showed even higher cell efficiencies than cells on standard soda lime glass (SLG) substrates,⁸ which was at that time believed to be the best choice of substrate for CIGS solar cells. The reason for the improved cell performance was the higher amount of potassium in the CIGS layer grown on enameled steel compared to that grown on SLG substrate. One effect of K was the higher net charge carrier concentration caused by the additional K doping.⁸ Since then, application of the potassium fluoride postdeposition treatment (KF PDT)^9,10 led to a boost in cell efficiency up to 21.0%.^10–12 This trend in increase of cell efficiency was then continued by application of the PDT process with the heavier alkali elements rubidium (Rb) and cesium (Cs).^13,14 But until now, it is unclear whether the positive effect of Rb is a bulk- or a grain-boundary-induced effect, or both. Further, it is generally observed that the heavier alkali elements that are introduced by PDT into the already grown CIGS absorber tend to push out the lighter alkalis already present in the material (i.e., Na and K).^10,14 This so-called ion exchange mechanism is far from being understood. Recent atom probe tomography (APT) measurements have shown that Rb pushes the lighter alkali elements Na and K out of the grain boundaries.¹⁵ However, the concentration of Rb in the bulk of the grains could not be determined by APT, as the concentration of Rb in the grains was below the detection limit of 10 ppm.¹⁵ Hence, one main focus of this paper is to find out if Rb diffuses into the bulk of the grains as well as into the grain boundaries, as observed for sodium and potassium.^16–18 The second focus is to investigate the ion exchange mechanism and to find an answer to the question if Rb pushes Na out only from the grain boundaries or also out of the bulk of the grains. In the third part, the electronic effect of RbF PDT on cell parameters of formerly alkali-free CIGS thin-film solar cells is investigated.

Ferritic stainless steel foil with a thickness of 127 μm and zirconia (ZrO₂) substrates with a thickness of 90 μm were used as alkali-free substrates as their coefficient of thermal expansion (11 ppm/K) is similar to that of CIGS (7–9 ppm/K).¹⁹ After cleaning the zirconia and stainless steel substrates with organic solvents in an ultrasonic bath, the molybdenum (Mo) back contact was deposited by DC sputtering. A standard thickness of 500 nm of Mo was deposited on the zirconia substrates. To suppress diffusion of detrimental Fe into the CIGS layer, the Mo layer thickness was increased to 2.7 μm for the stainless steel substrates. The CIGS layers were grown by co-evaporation of the constituent elements in a high-temperature (HT) multi-stage in-line process²⁰ at a substrate temperature of about 600 °C or in a HT single-stage in-line process.²¹ The multi-stage in-line process produces coarse grained (cg) CIGS layers with a Cu content of [Cu]/([Ga] + [In]) = CGI = 0.86, a Ga content of [Ga]/([Ga] + [In]) = GGI = 0.33, and a thickness of d(CIGS) = 2.1 μm. The single-stage in-line process resulted in fine-grained (fg) CIGS layers with CGI = 0.75, GGI = 0.29, and d(CIGS) = 2.1 μm.

The CIGS layers on stainless steel were used for diffusion experiments since the thermal conductivity of steel is high enough to allow fast heating and cooling ramps. As the CIGS layers on stainless steel were stored in ambient air, they were etched with potassium cyanide (KCN, 10%) for 3 min directly before the NaF or RbF post-deposition treatment to remove the native oxide from the surface of the CIGS layer.²² For the RbF PDT, the RbF was evaporated in vacuum onto the unheated substrate at a crucible temperature of 500 °C for 20 min, which leads to a RbF layer thickness of about 300 nm to obtain a constant Rb diffusion source. (The thickness of the RbF layer was hard to measure as it immediately reacted with humidity from ambient air during transfer from the deposition chamber to the Scanning Electron Microscope.) For the NaF PDT, the NaF was evaporated in vacuum onto the unheated substrate at a crucible temperature of 670 °C for 20 min, which leads to a NaF layer thickness of about 30 nm to obtain a constant Na diffusion source. After coating the sample with the alkali-fluoride (AF), it was annealed in vacuum by moving the substrate holder under a heating zone for the duration of the diffusion annealing time and moving the sample out of the heating zone immediately after then. This technique allowed fast cooling and heating ramps. A thermocouple directly in contact with the back side of the sample was used to measure the sample temperature. Finally, the residual AF layer on the CIGS surface was removed with HCl (10%) and a CdS layer with a thickness of about 50 nm was grown onto the CIGS layer in a chemical bath deposition at 65 °C for about 10 min. The CdS layer serves as a capping layer to protect the sample surface against oxidation.

For combined PDT processes, first the NaF (RbF) was done at a temperature of 400 °C (350 °C) for 20 min to get a homogeneous alkali Na (Rb) concentration throughout the CIGS layer. The residual NaF (RbF) was then removed with HCl (10%), and then the second alkaliflouride was applied with PDT (RbF or NaF). After the second PDT, the residual AF was etched with HCl (10%) and a CdS capping layer was grown on the CIGS layer.

For preparation of solar cells, the CIGS layers were grown onto Mo coated zirconia substrates in a multi-stage in-line CIGS process. The reference sample without PDT was stored in an exsiccator. The sample with RbF PDT was immediately transferred into the PDT vacuum chamber after CIGS layer growth to minimize exposure to air as much as possible. Then, a RbF layer of about 150 nm (or 75 nm) was deposited onto the unheated substrate. The RbF PDT annealing was then done at 350 °C for 20 min in vacuum without intentional evaporation of Se (the presence of Se cannot be completely excluded as Se from the chamber walls could be evaporated during the annealing process). The residual RbF was removed in HCl (10%). Then, a CdS layer with a standard thickness of about 60 nm in thickness was grown on the RbF treated and the untreated reference sample in the same chemical bath. The solar cells were completed by RF sputtering of a thin intrinsic ZnO layer (about 80 nm), sputtering of a 350 nm thick ZnO:Al front contact layer, and electron beam evaporation of a Ni/Al/Ni contact grid through a shadow mask. Finally, cell separation was done by mechanically scribing (total cell area of approximately 0.5 cm²). All cells had no antireflective coating.

Current density voltage (jV) characteristics of the solar cells with and without the RbF treatment were measured under illumination with simulated AM 1.5 spectrum at standard test conditions. External quantum efficiency (EQE) measurements were done with additional bias illumination by measuring the short-circuit current generated with spectrally resolved monochromatic light. Capacitance voltage (CV) measurements were recorded with a HP 4192A LF Impedance Analyzer with a frequency of 100 kHz and a modulation voltage of 50 mV in the dark at room temperature.

The structure and cross section of the CIGS layers were investigated by scanning electron microscopy (SEM) measurements in a FEI XL-30 Sirion SFEG with 5 kV acceleration voltage. Atomic concentrations, relative Cu content CGI = [Cu]/([Ga] + [In]), relative Ga content GGI = [Ga]/([Ga] + [In]), and thicknesses of CIGS and Mo layers were determined using an energy dispersive X-ray fluorescence (XRF) spectrometer, the EAGLE XXL instrument from EDAX/Roentgenanalytik. For analysis, a Rh X-ray source was used, operating at 50 keV, with an aperture of 1 mm diameter. Depth profiling of the CIGS layers including the alkali elements was performed at liquid nitrogen temperature by Secondary Ion Mass Spectrometry (SIMS) by a LEYBOLD SSM200 system using 5 keV primary Ar⁺ ions. The sputtered area was 2 × 2 mm². The CdS capping layer on the CIGS surface was etched off in diluted hydrochloric acid (HCl) before the SIMS measurement. A TOF.SIMS 5 instrument from IONTOF was employed for laterally resolved 3D-TOF-SIMS measurements (TOF = time of flight). To achieve a good lateral resolution, the CIGS samples were measured in the fast imaging mode. The secondary ion beam delivers several information: the lateral position (x,y), the time of flight of ions, and the signal strength (intensity). The TOF-SIMS analyzer can be optimized to one of these parameters. For the fast imaging mode, lateral resolution reaches values of about 200 nm at cost of mass resolution. In this case, only species for each mass number can be distinguished. However, in the fast imaging mode, the ion current is high, and therefore an optimal sensitivity to measure low alkali concentrations in the CIGS layer is given. During detection, a Bi⁺ analysis beam records an image of 10 × 10 μm² with a resolution of 256 × 256 pixels. Depth profiling is achieved by switching between analysis and sputter sources. An oxygen ion beam is used as the sputter source. This beam scans over a larger area of 200 × 200 μm² to avoid sputter crater influences inside the measurement area of 10 × 10 μm². A ²³Na implanted (dose = 1 × 10¹⁵ cm⁻², energy = 150 keV) and a ³⁹K implanted (dose = 1 × 10¹⁵ cm⁻², energy = 150 keV) CIGS sample were used to calibrate the relative SIMS and TOF-SIMS profiles to obtain absolute Na and K concentration profiles, respectively. Several ⁸⁵Rb-implanted CIGS samples (dose = 5 × 10¹³ cm⁻² up to 1 × 10¹⁵, energy = 380 or 700 keV) were used to calibrate the relative SIMS and TOF-SIMS profiles to obtain absolute Rb concentration profiles.

When determining the Rb concentration from the SIMS spectra by using the peaks at amu 85 and amu 87, care has to be taken as these peaks can be attributed to ⁸⁵Rb and ⁸⁷Rb as well as to ⁶⁹Ga¹⁶O and ⁷¹Ga¹⁶O. If the peak ratio of amu 85/amu 87 is ∼1.5, which corresponds to the isotopic ratio of Ga (1.55), then these two peaks can be attributed to gallium oxide, which was the case for Rb-free CIGS layers. If a peak ratio of amu 85/amu 87 ∼2.5 was observed, which corresponds to the isotopic ratio of Rb (2.59), then these two peaks can be attributed to the two rubidium isotopes. This was the case for all Rb depth profiles of CIGS layers measured by SIMS after a RbF PDT. Here, the Rb concentration in the CIGS layer could be directly determined from the intensity of the ⁸⁵Rb peak. If the peak ratio of amu 85/amu 87 is in the range between 1.7 and 2.4, a peak deconvolution has to be done to separate the Rb part from the GaO part of the spectra. This was the case when the Rb content in the CIGS layer was very low. A peak deconvolution was performed in order to correctly determine the Rb concentration in the bulk of the CIGS grains from the 3D-TOF-SIMS spectra.

The grain structure of the CIGS layers was investigated with an SEM (Fig. 1). The fine-grained (fg) CIGS layer from the single-stage CIGS process [Fig. 1(a)] shows grains with a size between 0.5 and 1 μm which are partly stacked over each other in some areas. The coarse-grained (cg) CIGS layer from the multi-stage CIGS process [Fig. 1(b)] exhibits a column-like shape with a grain height of about 2 μm, and the square width was estimated to range from 1 μm to 2 μm. Due to the fast diffusion of Rb through the CIGS layer, only short diffusion annealing times from 6 to 22 min could be used in the temperature range from 150 to 310 °C in order to get useful diffusion profiles for extracting diffusion coefficients. At such short time scales, the heating and cooling periods cannot be neglected. The effective diffusion time t_eff was estimated from the temperature-time profile for each diffusion process (see Fig. 2) as explained in Ref. 23 

In order to separate diffusion into grain boundaries from diffusion into the grain bulk, a fine- and a coarse-grained CIGS layer were annealed in the same RbF PDT process at 148 °C for 14.9 min. The corresponding Rb diffusion profiles are shown in Fig. 3 by black and red symbols for the coarse- and fine-grained samples, respectively. Both samples show a fast decline of the diffusion profile up to a depth of 0.7 μm and a slow declining tail at a larger depth. As this tail is much more pronounced for the fine-grained sample, this part can be attributed to diffusion into GBs. The strong declining part can be attributed to diffusion into the bulk of the grains as was done in the case of Na diffusion profiles in Ref. 16.

As diffusion takes place along grain boundaries as well as into the grain volume, the diffusion profiles were fit according to the following equation:

where x describes the penetration depth, t is the diffusion annealing time, D_V and D_GB are the diffusion coefficients in the CIGS volume and the grain boundaries (GBs), respectively, and C_V0 and C_GB0 are the average Rb concentration in the grain volume and the effective concentration at grain boundaries at the CIGS surface, respectively, and C₀ is for a background level. The first part in Eq. (1) describes the direct volume diffusion and the second part describes the diffusion along the GBs. The diffusion profile of the coarse-grained sample (black symbols and curve in Fig. 3) could be well fit according to Eq. (1) by two complementary error function (erfc) shaped curves with D_V(cg) = 3.2·10⁻¹³ cm²/s and D_GB(cg) = 2.3·10⁻¹² cm²/s. The complementary error function curve is the solution of the diffusion equation for the boundary condition of a constant Rb source.²⁴ This means that for the cg sample the RbF layer acts as a constant or infinite source for the supply of Rb during the diffusion process. However, for the fine-grained sample (red symbols in Fig. 3), the grain boundary part of the diffusion profile could only be fit by a Gaussian-shaped profile as follows:

and

Here, only the “right hand part” of the Gaussian profile is used for x > x_i and a constant concentration plateau C_GB0 for x < x_i. This means that for the fine grained sample the Rb supply was too low so that it could be better described by the model of an instantaneous, limited Rb source, as the Gaussian function is the solution of the diffusion equation for the boundary condition of an instantaneous source.²⁴ The fit of the fine-grained samples resulted in D_V(fg) = 2.9·10⁻¹³ cm²/s and D_GB(fg) = 2.0·10⁻¹² cm²/s, which nicely agrees with the values for the coarse grained sample. The value C_GB0—diffusion into the grain boundaries (dotted lines in Fig. 3)—is nine times higher for the fine grained sample than for the coarse grained sample. This result was expected due to the higher density of GBs. Whereas C_V0—diffusion into the grain volume (dashed lines in Fig. 3)—is similar for the fg sample with a lower Cu content (see also Table I). This could be an indication that the higher amount of Cu vacancies in the fine-grained sample, a result of its lower Cu content, does not lead to a stronger diffusion of Rb into the bulk of the grains. The fit with Eq. (1) or (2) means that the diffusion takes place mainly along the GBs and leakage from the GBs into the adjacent grain interiors (GIs) is negligible, i.e., it indicates type C diffusion according to Harrison²⁵ with additional direct diffusion into the grain bulk.

To prove the reliability of a real diffusion process, Rb diffusion profiles should be measured at a fixed temperature for different annealing times to check if the diffusion coefficient is constant. As the diffusion of Rb is very fast, we chose a lower annealing temperature of 175 °C and two different annealing times t_eff = 11.2 min and 21.9 min. The corresponding diffusion profiles and the corresponding fits with Eq. (1) are shown in Fig. 4. The fit for t_eff = 11.2 min resulted in D_V(11.2 min) = 4.3·10⁻¹³ cm² s⁻¹ and D_GB(11.2 min) = 3.3·10⁻¹² cm² s⁻¹ and that for t_eff = 21.9 min in D_V(21.9 min) = 4.0·10⁻¹³ cm² s⁻¹ and D_GB(21.9 min) = 3.4·10⁻¹² cm² s⁻¹. The diffusion coefficients are similar within the measurement uncertainty. Hence, we have an indication that the diffusion of Rb follows the diffusion law. The increase of Rb concentration toward the Mo back contact (bumps at 2 μm in Fig. 4) is caused by a mixture of a SIMS matrix effect and a real Rb segregation at the CIGS/Mo interface. At the CIGS/Mo interface, the ionization probability of the alkali metals strongly increases when reaching the Mo surface due to a change from the CIGS matrix to the molybdenum-oxide matrix (the surface of the Mo layer is always oxidized). This leads to a strong increase in signal intensity and is a measurements artefact. Hence, from the SIMS measurements alone it is not possible to determine the alkali concentration at the CIGS/Mo interface. The second effect is that the CIGS/Mo interface is also a GB of the CIGS grains, where Rb can segregate. NanoXRF measurements have revealed that Rb segregates at the CIGS/Mo interface.²⁶ 

A distinct proof of our interpretation that the first strong decline of the diffusion profiles in Figs. 3 and 4 can be assigned to diffusion into the grain bulk could be given by atom probe tomography (APT) measurements. Unfortunately, the detection limit of APT was too low (10 ppm) to measure the Rb concentration in the grain interior.¹⁵ Therefore, we analyzed the local distribution of Rb on a coarse grained sample (RbF PDT at 311 °C, t_eff = 6.3 min) by a locally resolved 3D-TOF-SIMS measurement as shown in Fig. 5. A clear segregation of Rb at grain boundaries and at the Mo/CIGS interface can be observed, which is in accordance with nanoXRF measurements by Schöppe et al.²⁶ When analyzing the Rb concentration in the region of interest (ROI) marked as an ellipse in Fig. 5(b), a Rb concentration of C_GI(Rb) = 4 ppm was found in the grain interior (GI). Hence, the TOF-SIMS measurement proves that Rb diffuses into the GI. This Rb concentration is lower than the mean value of the volume part of the diffusion profile of C_V(mean) = 10 ppm determined from the fit of the Rb diffusion profile, but the deviation could be explained by local variations of the Rb bulk concentration from grain to grain. The value for the Rb concentration in the grain interior (4 ppm) is much lower than the Na concentration of C_V(Na) = 13 ppm measured by APT¹⁶ even after a NaF PDT at 157 °C. This is a hint that diffusion of Rb into the GI is hindered compared to Na. For the rectangular ROI in Fig. 5(b), which corresponds to a GB, one can extract a Rb concentration of 134 ppm. In the TOF-SIMS measurement, the GB [rectangular ROI in Fig. 5(b)] is smeared out over a width of about 350 nm due to the limited resolution. In order to have a more precise value, which is independent from the smear-out effect and which can better be compared to the literature data, the Gibbsian interfacial excess Γ, a GB area density, is calculated. By using the particle density of CIGS of 4.26·10²² at/cm⁻³, the Gibbsian interfacial excess of Rb at the GB is estimated to Γ(TOF-SIMS) = 4.26·10²² at/cm⁻³ * 134 ppm * 350 nm = 2.0 at/nm², which nicely corresponds to the value measured by APT of Γ(APT) = 1.6 at/nm².¹⁵ Assuming that the GB is distributed over an area of about 1 nm, we can estimate a GB concentration of C_GB(TOF-SIMS) = 4.6 at. %. Together with the Rb concentration in the volume C_V = 4 ppm, we can estimate the segregation factor s, which is defined as the ratio of C_GB and C_V just near the GB,²⁷ 

to s = 11 500. With s, the parameter α could be determined

where δ = 1 nm is the GB width, D_V = 9.0·10⁻¹² cm² s⁻¹ is the volume diffusivity of Rb, and t_eff = 6.3 min is the diffusion time. For the lowest diffusion temperature of 148 °C, one gets α(148°) = 34.0, when assuming the same segregation factor s. (This approximation is allowed as alkali metals strongly segregate at GBs even at low temperatures.¹⁶) The parameter α describes the leakage of Rb from a GB into the grain volume and its value indicates the diffusion type. If α < 0.1, type B diffusion is present. Here, the diffusion into the volume takes place in parallel to the diffusion along GBs with leakage from the GB into the adjacent grain volume (see Fig. 7 in Ref. 16). The interval 0.1 < α < 1 describes an intermediate regime of GB diffusion.²⁷ On the other hand, α > 1 indicates type C diffusion, where diffusion takes place mainly along the GBs and leakage from the GBs into the adjacent grain interiors is negligible. Knowing that α > 1, type C diffusion is indicated here with additional direct volume diffusion. Hence, the 3D-TOF-SIMS measurement proves that our interpretation of the diffusion profiles with a volume part and a GB part is correct.

The diffusion coefficients D_V and D_GB have been determined for different annealing temperatures and annealing times (see Table I) and are plotted in Fig. 6 against the inverse diffusion temperature T. The error in the diffusion coefficients D_V and D_GB was estimated to be within 30% and mainly caused by the uncertainty in the fit procedure and the uncertainty in the diffusion time t_eff. The diffusion coefficients D_V for the fine grained samples (filled down triangles in Fig. 6) are similar to those of the coarse grained samples (filled up triangles in Fig. 6) even though the fined grained samples have a lower copper content. Hence, the higher concentration of copper vacancies in the fine grained samples, which is a result of their lower copper content, does not lead to stronger diffusion of Rb into the grain interior of the fg samples. The GB diffusion coefficients D_GB for Rb (open triangles in Fig. 6) are about one order of magnitude (factor of 3 to 8) higher than the volume diffusion coefficients D_V for Rb (filled triangles), which agrees well with the expectation that the diffusion along GBs is much faster than the direct volume diffusion. The experimental data of the volume diffusion constant D_V (filled triangles in Fig. 6) can be fit by the Arrhenius equation (black solid line in Fig. 6)

with the Boltzmann constant k_B, the activation energy E_A(V, Rb) = 0.44 eV, and a pre-exponential factor D_0V(Rb) = 3.8·10⁻⁸ cm² s⁻¹. The standard deviation in the activation energy is 0.03 eV, while the error in the pre-exponential factor D_0V is 3.4·10⁻⁸ cm² s⁻¹.

The experimental data of the GB diffusion constant D_GB (open triangles in Fig. 6) can be fit by the Arrhenius equation (black dashed line in Fig. 6)

with the activation energy E_A(GB, Rb) = 0.29 eV and a pre-exponential factor D_0GB(Rb) = 5.7·10⁻⁹ cm² s⁻¹. The standard deviation in the activation energy is 0.02 eV, while the error in the pre-exponential factor D₀ is 4.2·10⁻⁹ cm² s⁻¹.

For comparison, the Arrhenius plots for the volume (red solid line in Fig. 6) and GB diffusion of Na (red dotted line in Fig. 6) from the literature¹⁶ are also shown in Fig. 6. The volume diffusion coefficient of Rb is slightly lower than that of Na, as expected for the heavier alkali element, but the activation energy for the volume diffusion of Rb is only 0.08 eV higher than that of Na [E_A(V, Na) = 0.36 eV].¹⁶ Hence, Rb can diffuse into the volume of the grains even though it is much larger than Na, which is an unexpected result. The activation energy of 0.44 eV for the volume diffusion of Rb found here is comparable to the migration barrier of 0.24 eV calculated for the vacancy diffusion mechanism.²⁸ This could be a hint that Rb diffuses via copper vacancies. The grain boundary diffusion coefficient of Rb is one order of magnitude lower than that of Na. But the activation energy for the GB diffusion of Rb is only 0.08 eV higher than that of Na [E_A(GB,Na) = 0.21 eV].¹⁶ The pre-exponential factor D₀ for Rb diffusion into the volume is three times higher than that of Na diffusion into the volume [D_0V(Na) = 9.7·10⁻⁹ cm² s⁻¹].¹⁶ This means that at a temperature of 400 °C the diffusion of Rb into the volume is the same as that of Na. The pre-exponential factor D_0GB for Rb diffusion along the GB is comparable to that of Na diffusion along GBs [D_0GB(Na) = 6.5·10⁻⁹ cm² s⁻¹].¹⁶ Hence, in alkali-free CIGS layers, Rb can easily diffuse into the grain interior similar to Na. However, the grain boundary diffusion of Rb is hindered compared to Na.

The Rb concentration in the grain bulk C_V0 and the effective concentration of Rb in the grain boundaries C_GB0 at the surface of the CIGS layer resulting from fitting of the diffusion profiles are shown in Fig. 7 over the inverse temperature. In general, C_V0 is larger than C_GB0. Hence, at the surface of the CIGS layer, the concentration of Rb in the bulk of the grains is larger, which further confirms type C diffusion. For fg samples, the C_GB0 is about a factor of 10 larger compared to cg samples as expected.

For cg samples, C_V0 (filled triangles in Fig. 7) is thermally activated and can be fit by the Arrhenius equation (black solid line in Fig. 7)

with the activation energy E_A(V0, Rb) = 0.16 eV and a pre-exponential factor of 1975 ppm. The standard deviation in the activation energy is 0.05 eV, while the error in the pre-exponential factor is 4149 ppm.

The data points C_GB0 for cg samples (open triangles in Fig. 7) also show thermal activation and can be fit by the Arrhenius equation (black dashed line in Fig. 7)

with the activation energy E_A(GB0, Rb) = 0.22 eV and a pre-exponential factor of 824 ppm. The standard deviation in the activation energy is 0.06 eV, while the error in the pre-exponential factor is 3016 ppm.

Hence, the solubility of Rb in the CIGS matrix is comparable to that in the grain boundaries. One must however take into account that at temperatures higher than 250 °C the grain boundary part could not be extracted reliably from the fit of the diffusion profiles any more. Hence, this conclusion is only valid for the temperature range below 250 °C.

It was found that during PDT, the heavier alkali elements reduce the concentration of the lighter alkali elements in the CIGS layer^10,14 and push them somehow out of the CIGS layer. In the following part, this ion exchange mechanism will be investigated. In a first experiment, a RbF PDT followed a NaF PDT. In a second experiment, it was done vice versa, i.e., a NaF PDT followed a RbF PDT. In the first experiment, two pieces from a coarse-grained sample were taken. One part was left Na-free. The second part was doped with Na by a NaF PDT at a substrate temperature of 400 °C for 20 min to get a homogeneous Na concentration throughout the CIGS layer,¹⁶ which will in the following be called Na-doped layer. Both samples—the Na-free and the Na-doped one—were then treated by a RbF PDT at 251 °C for 6.6 min and finally investigated by SIMS (Fig. 8). The Rb profiles of both samples could be well fit by Eq. (1) [solid lines in Fig. 8(a)]. For the Na-doped sample, the fit results in D_V(Rb, Na doped) = 8.2·10⁻¹⁴ cm² s⁻¹ and D_GB(Rb, Na doped) = 9.1·10⁻¹² cm² s⁻¹. For the Na-free sample, the fit results in D_V(Rb, Na free) = 3.0·10⁻¹² cm² s⁻¹ and D_GB(Rb, Na free) = 1.2·10⁻¹¹ cm² s⁻¹ (see also Table II). Hence, the volume diffusion coefficient for the Na-doped sample is two orders of magnitude lower than that for the Na-free sample, but the GB diffusion coefficient is similar. For the Na-doped sample [black in Fig. 8(a)], the volume part [black dashed line in Fig. 8(a)] is one order of magnitude lower than for the Na-free sample [red dashed line in Fig. 8(a)], and the GB part of the Na-doped sample [black line in Fig. 8(a)] is 5 times higher than that of the Na-free sample [red dotted line in Fig. 8(a)]. From this, we conclude: If Na is already present in the CIGS layer, it hinders the diffusion of Rb into the grain interior so that Rb mainly has to diffuse along the GBs. Further, diffusion of Rb along the GBs is promoted if Na is already present in the GBs.

In Fig. 8(b), the corresponding Na and K profiles of the Na-doped sample after the RbF-PDT are shown [thick lines in Fig. 8(b)] together with the Na and K profiles from that part of the sample which was capped by a polyimide foil during the RbF-PDT and only annealed [thin lines in Fig. 8(b)]. Potassium has also diffused into the CIGS layer as the NaF powder (Puratronic 99.995%) used here contains KF as the main impurity. The RbF-PDT leads to a small decrease of the Na profile and a decrease in the K profile. The lower decrease of the Na and K profiles observed here compared to the literature data^10,14 could be explained by the lower temperature (251 °C) and the shorter treatment time (6.6 min) used here compared to the literature (350 °C and 15 min).¹⁰ This result shows that the ion exchange mechanism even works at a temperature of 251 °C and only 6.6 min of annealing.

We repeated the former experiment also for a fine-grained CIGS layer. Here, a Na-free and a Na-doped fine-grained CIGS layer were treated with RbF at a temperature of 205 °C for 7.8 min. The Rb profile of the Na-doped layer (black circles in Fig. 9) lies above that of the Na-free CIGS layer (red circles in Fig. 9). This means that diffusion of Rb is somehow enhanced due to the presence of Na. The Rb profile of the Na-free CIGS layer (red circles in Fig. 9) could be fit by Eq. (2) as a combination of an erfc-shaped and a Gaussian-shaped profile resulting in D_V(Na-free) = 7.2·10⁻¹³ cm² s⁻¹ and D_GB(Na-free) = 4.0·10⁻¹² cm² s⁻¹, respectively. The fit of the Rb profile of the Na-doped sample (black circles in Fig. 9) could be fit by Eq. (1) by an erfc-shaped profile resulting in D_erfc(Na-doped) = 4.9·10⁻¹² cm² s⁻¹ and C₀ = 21 ppm for the background level. This value for D_erfc(Na-doped) fits well to the nominal GB diffusion coefficient at 205 °C calculated with Eq. (6) as D_{GB, Nominal}(205 °C) = 5.0·10⁻¹² cm² s⁻¹ (see also Table II). We therefore interpret the erfc-shaped part of the Rb profile of the Na-doped CIGS layer (dotted black line in Fig. 9) as diffusion along grain boundaries. A diffusion part attributable to diffusion into the grain volume cannot be found for this fine-grained Na-doped CIGS layer.

The Rb concentration at the surface of the CIGS layer C_V0 and C_GB0 for the volume and the GB part, respectively, for the Na-doped samples is also shown in Fig. 7 (red symbols) and Table II. The value of C_V0 for the Na-doped coarse grained sample (red up triangle in Fig. 7) is 5 times smaller than that for the Na-free sample (black up triangle in Fig. 7 at 250 °C). In contrast, C_GB0 is enhanced by a factor of 5 for the Na-doped samples compared to the Na-free samples.

To determine whether Rb has also diffused into the grain interior in the case of the Na-doped coarse-grained CIGS layer sample, we performed 3D-TOF-SIMS measurements on this sample. The overall Rb content in this sample was too low to obtain good statistics in the 3D-TOF-SIMS imaging mode. Therefore, we selected a CIGS layer from a very high efficiency solar cell on glass substrate with an efficiency of η = 20.4%, where a RbF PDT was applied at 350 °C after the CIGS growth. The CIGS layer was grown on an alkali-aluminosilicate glass in a multi-stage process (for details, see Ref. 14) so that the layer was doped with Na and K before the RbF PDT. From the 3D-TOF-SIMS measurement (not shown here), we extracted a concentration of c(Na,GI) = 60 ppm, c(K,GI) = 34 ppm, and c(Rb,GI) = 16 ppm for Na, K, and Rb in the grain interior (GI), respectively (see Table III). This result proves that Rb can diffuse into the grain interior during the PDT even when Na and K are already inside the grains. It further shows the high sensitivity of 3D-TOF-SIMS measurements as it is so far the unique method to detect K and Rb in the GI. The integral concentration of alkali elements in the whole CIGS layer as determined from the 3D-TOF-SIMS measurement is c(Na) = 59 ppm, c(K) = 31 ppm, and c(Rb) = 111 ppm. Hence, for Na and K, the amount of alkalis located in the GI is comparable to that in the GBs after a RbF-PDT. In contrast, most of the Rb is located at GBs. The Gibbsian interfacial excess Γ values at the GBs determined roughly from the 3D-TOF-SIMS measurements are also shown in Table III and compared to the values from APT measurements. Even though the absolute values of the 3D-TOF-SIMS measurements are much higher compared to those of the APT measurements, they confirm the APT results: Rb is much more segregated at the GBs compared to Na and K which indicates that Rb pushes Na and K out of the GBs.

We conclude that both the results of the coarse- and the results of the fine-grained CIGS layers can be interpreted by the following model: In the case of Na-free CIGS layers, Rb diffuses into the grain bulk as well as into the GBs [Fig. 10(a)]. If Na is already present in the CIGS layer [see Fig. 10(b)], diffusion of Rb into the grain interior is strongly hindered—but still takes place—and therefore, Rb mainly diffuses into the GBs. Diffusion of Rb along the GB is strongly promoted by the presence of Na at the GBs. Here, Rb pushes the Na, which is segregated at the GBs, out of the GBs as was observed in APT measurements.¹⁵ 

In the second experiment, two pieces from a coarse-grained sample were taken. One part was left Rb-free. The second part was doped with Rb by a RbF PDT at a temperature of 355 °C for 20 min to get a homogeneous Rb concentration throughout the CIGS layer. Both samples—the Rb-free and the Rb-doped one—were then treated in a NaF PDT at 316 °C for 6.7 min and finally investigated by SIMS (Fig. 11). One half of the Rb-doped sample was capped by a polyimide foil during the NaF PDT so that it was only heat treated during the NaF PDT [Fig. 11(a)] to see the effect of the thermal load during the NaF PDT on the Rb profile. The Rb profile of the Rb-doped layer with NaF PDT [black dashed line in Fig. 11(b)] is similar to that of the capped sample part [black dotted line in Fig. 11(b)]. Hence, the Na PDT had no effect on the Rb profile, i.e., Na did not push Rb out of the CIGS layer. The Na profile of the Rb-doped layer [red dashed line in Fig. 11(b)] is one order of magnitude lower than that of the Rb-free layer [red solid line in Fig. 11(b)]. Hence, Rb hinders the diffusion of Na into the CIGS layer. The Na profiles of the Rb-free and Rb-doped layer could be well fit by diffusion into the volume of the grains [dashed curves in Fig. 11(c)] and diffusion along GBs [dotted curves in Fig. 11(c)] with D_V(Na) = 4·10⁻¹² cm² s⁻¹ and D_GB(Na) = 9·10⁻¹¹ cm² s⁻¹ (see Table IV). These values correlate well to the nominal value of the volume diffusion coefficient of Na at a temperature of D_V(Na, 316 °C) = 8.1·10⁻¹² cm² s⁻¹ and to the GB diffusion coefficient of Na at a temperature of D_GB(Na, 316 °C) = 1.0·10⁻¹⁰ cm² s⁻¹ (calculated according to Ref. 16). For the Rb-doped layer, diffusion into the volume is strongly reduced compared to the Rb free layer. The diffusion along the GBs is also reduced if Rb is already present at the GBs. Hence, in the case of the Rb-doped CIGS layer, diffusion of Na along grain boundaries is partly hindered whereas diffusion into the grain interior is strongly hindered.

We conclude that in the case of a Rb-free CIGS layer, Na can diffuse into the grain interior as well as into the GBs [see Fig. 10(c)], whereas in a Rb-doped layer, the diffusion of Na can take place along the grain boundaries, but is hindered, and diffusion into the volume of the grains is strongly hindered as Rb already occupies the places in the grain interior [Fig. 10(d)]. Hence, Na does not push Rb out of the CIGS layer. Only the heavier alkali element Rb can replace the lighter alkali elements Na and K, but not vice versa. These ion exchange results were confirmed by density functional theory calculations.²⁸ 

For two samples where a NaF PDT was performed, the diffusion coefficients of Na and K could be extracted from the diffusion profiles (see Table V). K also diffused into the samples as the NaF powder (Puratronic 99.995%) used here contains KF as the main impurity. The diffusion coefficients of K are very similar to that of Na (see Table V and Fig. 6). This is a first hint that diffusion of K is similar to that of Na.

In the following, the effect of RbF PDT on the electrical properties of CIGS solar cells will be studied. For this, CIGS layers were grown on alkali free zirconia substrates. One sample was left Rb-free as a reference sample, whereas another sample was treated with a RbF PDT at 350 °C for 20 min. Then, both samples were processed to complete solar cells in the same CdS and ZnO runs. In Fig. 12, the current density voltage (jV) curves of these samples are shown. The open-circuit voltage V_oc and the fill factor FF of the Rb-doped sample (red dashed curve in Fig. 12) are much higher than that of the Rb-free reference sample (black solid curve in Fig. 12). The short-circuit current density J_sc of the Rb-doped sample is slightly smaller than that of the Rb-free reference (see also Table VI). In Fig. 13, the external quantum efficiency of both samples is shown. The quantum efficiency of the undoped reference (black solid curve in Fig. 13) shows higher charge carrier collection in the infrared range of the spectrum compared to the Rb-doped sample (red dashed curve in Fig. 13). To find out the reason for this lower charge carrier collection, capacity voltage (CV) measurements were performed on both samples at room temperature (Fig. 14). From the CV curve of the undoped sample (black solid curve in Fig. 14), one can extract a doping concentration of 1.0·10¹⁴ cm⁻³ and a space charge width of 2230 nm whereas for the Rb-doped sample (red dashed curve in Fig. 14) one gets corresponding values of 6.2·10¹⁵ cm⁻³ and 453 nm. Hence, Rb doping enhances the charge carrier concentration in a similar way as Na or K^9,29 (see Table VI). The higher doping of the Rb-doped sample leads to a smaller space charge width and hence to a lower charge carrier collection in the infrared region as observed in EQE and a lower short-circuit current density J_sc.

In Table VI, the gains obtained in cell parameters due to a RbF PDT are compared to the gains of a NaF²⁹ and KF PDT⁹ performed on samples from the same CIGS setup and to the literature data.^30,31 The gain in efficiency η due to a pure RbF PDT amounts up to 50% and is comparable to the gain achieved by a pure NaF or KF PDT (see Table VI). Remarkable is that the gain in efficiency for Rb is comparable to that of the other alkali elements even though the concentration of Rb in the CIGS layer is only 32 ppm which is much lower compared to that of Na (65 ppm) and K (121 ppm) after a NaF or KF PDT, respectively. This shows the high impact Rb has on cell efficiency. For the gain in V_oc and FF, a preliminary trend can be observed (see Fig. 15): The gain in V_oc due to the alkali PDT increases for heavier alkali elements. In contrast, the gain in FF decreases for heavier alkali elements. This trend could be explained by the different effects of the alkali elements on the grain interior compared to the GBs.

APT measurements on very high efficiency CIGS solar cells have shown that Rb pushes Na and K out of the grain boundaries¹⁵ and thereby strongly enhances V_oc. Further, the strong accumulation of Rb at the GB was accompanied by a very strong Cu depletion at the GB compared to the Rb free case.¹⁵ This strong Cu depletion leads to a higher hole barrier at the GB³² and thereby to a better passivation of GBs and finally to a stronger increase in V_oc in case of RbF PDT compared to KF or NaF PDT. The higher FF observed for NaF PDT compared to the heavier alkali elements could be caused by a higher conductivity of the CIGS layer when it is doped with Na. Hence, the lighter alkali element Na leads to a higher conductivity in the CIGS layer compared to K and Rb. The heavier alkali element Rb leads to a better GB and surface passivation. Nevertheless, an effect of Rb on the bulk properties cannot be excluded, as Rb was also detected in the bulk of the grains by 3D-TOF-SIMS. In conclusion, these results confirm the results of Pianezzi et al.³¹ that the alkali metals act in a different way in the CIGS layer and that a combination of light and heavy alkali elements is necessary to realize very high efficiency solar cells.

The effect of a pure RbF PDT on alkali-free CIGS layers was investigated. 3D-TOF-SIMS measurements revealed that Rb diffuses into the GBs as well as into the bulk of the grains. In alkali-free CIGS layers, the bulk diffusivity of Rb is comparable to that of Na, but the GB diffusivity of Rb is reduced compared to that of Na. In Na-doped CIGS layers, the diffusion of Rb into the bulk of the grains is hindered, whereas the diffusion of Rb into the GBs is even enhanced due to Na at the GBs. The heavier alkali element Rb pushes the lighter alkali elements out of the GBs. In contrast, in Rb-doped CIGS layers, Na does not push Rb out of the CIGS layer, and the diffusion of Na along GBs is hindered and that into the grain interior is even strongly reduced. Preliminary results show that diffusion of K in alkali-free CIGS is similar to that of Na. The cell efficiency of alkali-free CIGS layers could be enhanced up to 54% by a pure RbF PDT, which is comparable to the effect of a NaF or a KF PDT. The gain in V_oc is even more pronounced in case of Rb compared to the lighter alkali elements Na and K.

This work was supported by the European Union’s Horizon 2020 research and innovation programme under Grant No. 641004 (Sharc 25) and by German Federal Ministry for Economic Affairs and Energy under the speedCIGS project (Contract No. 0324095E), which are hereby gratefully acknowledged. We thank all colleagues at ZSW involved in the sample preparation and technical support. We thank Wolfram Hempel and Jonas Hanisch for SIMS and 3D TOF SIMS measurements. We thank B. Hollaender and U. Reislöhner for Na, K, and Rb implantation.