UC Davis

While traditional c-Si solar cells still dominate the photovoltaic market, progress in further increasing their power conversion efficiencies or otherwise lowering operation costs has been relatively stagnant. As such, photovoltaic research focuses predominantly on novel solar technologies, also known as emerging solar technologies, each of which has demonstrated pathways toward a combination of high effiency and low cost which would allow them to supplant c-Si and change the solar technology landscape.

Two such novel solar technologies are nanoparticle and silicon heterojunction solar cells. The issues facing the widespread adoption of these two technologies are quite different. In nanoparticle solar cells, extraction of photogenerated carriers is inhibited by low carrier mobilities. Driving NP solids toward band-like transport is crucial to preventing electron/hole pairs from recombining before they can be collected. In contrast, silicon heterojunctions have already demonstrated very high conversion efficiencies, but exhibit high levels of unexplained performance degradation. Determining the degradation pathways and developing strategies for degradation minimization will be crucial to their widespread adoption.

This dissertation presents theoretical studies of both solar technologies. Beginning with NP solids, carrier transport studies are carried out in NP solids which examine the underlying physics governing transport, as well as determining the extent to which defects inhibit extended band-like transport. Continuing to silicon heterojunctions, comprehensive simulations model defect formation pathways and measure the corresponding energy barriers, in order to determine which pathways lead to the observed long-term degradation in these solar cells. The main chapters in this dissertation, apart from a section describing the NP simulation methods, are discussed briefly below.

First, we simulated electron transport across a binary nanocrystal solid (BNS) of PbSe NCs with diameters of 6.5nm and 5.1nm. We used our Hierarchical Nanoparticle Transport Simulator HINTS to model the transport in these BNSs. The mobility exhibits a minimum at a Large-NC-fraction f=0.25. The mobility minimum is deep at T = 80K and partially smoothed at T = 300K. We explain this minimum as follows. As the LNC fraction f starts growing from zero, the few LNCs act as traps for the electrons traversing the BNS because their relevant energy level is lower. Therefore, increasing the f concentration of these traps decreases the mobility. As increasing f reaches the percolation threshold f=f_P, the LNCs form sample-spanning networks that enable electrons to traverse the entire BNS via these percolating LNC networks. Transport through the growing percolating LNC networks drives the rapid growth of the mobility as f grows past f_P. Therefore, the electron mobility exhibits a pronounced minimum as a function of f, centered at f = f_P. The position of the mobility minimum shifts to larger LNC fractions as the electron density increases. We have studied the trends of this mobility minimum with temperature, electron density, charging energy, ligand length, and disorder. We account for the trends by a “renormalized trap model”, in which capturing an electron renormalizes a deep LNC trap into a shallow trap or a kinetic obstacle, depending on the charging energy. We verified this physical picture by constructing and analyzing heat maps of the mobile electrons in the BNS.

Next, we showed that nanoparticle (NP) solids are an exciting platform to seek new insights into the disordered Mott-Hubbard physics. We further developed HINTS to build from localized states to describe the Disorder-localized and Mott-localized phases, and the transitions out of these localized phases. We also studied the interplay between correlations and disorder in the corresponding multi-orbital Hubbard model at and away from integer filling by Dynamical Mean Field Theory. This approach is complementary to HINTS, as it builds from the metallic phase of the NP solid. The mobility scenarios and phase diagrams produced by the two methods are strikingly similar, and account for the mobilities measured in NP solids.

Third, we analyzed the 3D structure of a 120x38 nm disc-shaped region of a PbSe QD epi-SL using full-tilt high-angle annular dark-field electron tomography. The high spatial resolution of the tomographic reconstruction (0.65 nm) enables determination of the center-of-mass coordinates of all 1,846 QDs in the sample as well as the size and shape of the thousands of epitaxial connections (necks) between the QDs. The tomogram reveals the detailed crystallography and internal positional disorder of the three SL grains that constitute this sample. A map of the neck network is used to quantify relationships between neck number (the number of necks each QD possesses), average neck diameter, QD location in the film, and the nearest neighbor inter-QD distance and distance distribution. We found a strong positive correlation between neck number and local spatial order, suggesting that future improvements in neck connectivity are likely to simultaneously enhance the overall structural perfection of the epi-SLs. HINTS was employed to estimate the electron mobility of the tomography sample and assess the impact of grain boundaries on charge transport. The electron tomography study established a baseline for the quantitative statistical analysis of structural defects in 3D QD epi-SLs.

Fourth, we developed TRIDENS: the Transport in Defected Nanoparticle Solids Simulator, that adds three more hierarchical layers to our HINTS code for nanoparticle solar cells. In TRIDENS, we first introduced planar defects, such as twin planes and grain boundaries into individual NP superlattices (SLs) that comprised the order of 10^3 NPs. Then we used HINTS to simulate the transport across tens of thousands of defected NP SLs, and constructed the distribution of the NP SL mobilities with planar defects. Second, the defected NP SLs were assembled into a resistor network with more than 10^4 NP SLs, thus representing about 10^7 individual NPs. Finally, the TRIDENS results were analyzed by finite size scaling to explore whether the percolation transition, separating the phase where the low mobility defected NP SLs percolate from the phase where the high mobility undefected NP SLs percolate, drives a low-mobility-to-high-mobility transport crossover that can be extrapolated to genuinely macroscopic length scales. For the theoretical description, we adapted the Efros-Shklovskii bimodal mobility distribution percolation model. We demonstrated that the ES bimodal theory's two-variable scaling function is an effective tool to quantitatively characterize this low-mobility-to-high-mobility transport crossover.

All four of these NP projects provided crucial insight into our understanding of transport mechanisms in NP solids, and the crucial role that defects play. Collectively this work is important for developing strategies for driving NP solids into the metallic regime and band-like transport.

The rest of the dissertation switches focuses to silicon heterojunction solar cells, which exhibit notable performance degradation. While the exact defect formation pathways are unknown, all degradation pathways can be modeled by electronic defects getting generated by thermal activation across energy barriers over time. To analyze the physics of this degradation, we developed the SolDeg platform to simulate the dynamics of electronic defect generation. First, femtosecond molecular dynamics simulations were performed to create a-Si/c-Si stacks, using the machine-learning-based Gaussian approximation potential. Second, we created shocked clusters by a cluster blaster. Third, the shocked clusters were analyzed to identify which of them supported electronic defects. Fourth, the distributions of energy barriers that control the generation of these electronic defects were determined. Fifth, an accelerated Monte Carlo method was developed to simulate the thermally activated time dependent defect generation across the barriers. -- Our main conclusions are as follows. (1) The degradation of a-Si/c-Si heterojunction solar cells via defect generation is controlled by a broad distribution of energy barriers. (2) We developed the SolDeg platform to track the microscopic dynamics of defect generation across this wide barrier distribution, and determined the time dependent defect density N(t) from femtoseconds to gigaseconds, over 24 orders of magnitude in time, achieved by connecting the results of the femtosecond molecular dynamics simulations to the long time scale kinetic simulations. (3) We have shown that a stretched exponential analytical form can successfully describe the defect generation N(t) over at least ten orders of magnitude in time. (4) We found that in relative terms the open circuit voltage degrades at a rate of 0.2\%/year over the first year, slowing with advancing time. (5) We developed the Time Correspondence Curve to calibrate and validate the accelerated testing of solar cells. We found a compellingly simple scaling relationship between accelerated and normal times. (6) We ourselves carried out experimental studies of defect generation in a-Si:H/c-Si stacks. We found a relatively high degradation rate at early times, that slowed considerably at longer time scales.

Finally, we developed a Si-H Gaussian approximation potential in order to add H to our simulations of degradation of silicon heterojunctions. The Si-H GAP is able to closely match DFT measurements of microscopic quantities such as energies, forces and virial stresses, and is also able to reproduce structural characteristics such as partial pair correlation functions and the vibrational spectra. Reference structural data taken from Tersoff MD calculations highlights the improvement that is gained by adopting the non-parameterized model and more accurately matching the target potential energy surface. The Si-H GAP is more accurate than any interatomic potential which has come before it, and will be readily usable for the next phase of the project.