Nanostructure-based solar cell device concepts


The demand for higher PV energy conversion efficiencies has in the past decade led to the emergence of a whole new generation of solar cell concepts, which all aim at exceeding the single junction efficiency limit through the reduction of fundamental losses. Popular representatives are the concepts based on enhanced spectrum utilization and reduced thermalization losses via the use of multiple junctions, intermediate bands, multiple exciton generation or hot carrier effects. While these concepts differ widely in the physical mechanisms exploited, they have in common that they are largely based on artificially engineered materials with designed optoelectronic properties, like semiconductor nano- structures such as quantum wells, wires and dots, offering size-, geometry- and composition-tunable characteristics. This deviation from bulk behaviour needs to be taken into account at the time of describing the device operation mechanisms, a requirement which may preclude the use of standard macroscopic device simulation models commonly used in bulk photovoltaics. Similar issues are encountered in the field of nanostructure based light emitting and amplifying devices, however, the regime of operation is inverted in solar cells, since the light needs to be trapped and the charge carriers are to be extracted. While light-trapping techniques have been successfully implemented, leading to a substantial efficiency enhancement, the increase of collection efficiency remains a critical issue, mainly due to the strong interaction of charge carriers with their environment and the large number of interfaces associated with the nanostructures.


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Quantum-kinetic theory of photovoltaics at the nanoscale


The conventional approach to the theoretical description of nanostructure based solar cell devices consists of a combination of microscopic models for the electronic structure and optical transitions in the nanostructure with a macroscopic framework for charge transport. This kind of hybrid approach can be used to reproduce experimental device characteristics with remarkable accuracy. However, any situation requiring energy resolution, non-locality or coherence in the transport process cannot be described properly, e.g., non-thermalized carrier distributions or resonant tunneling. To include such processes in a consistent description, a truly
microscopic picture of carrier transport is to be used.
Hence, for an accurate description of the physics of these novel solar cells based on quantum effects in low dimensional absorbers, the optical transitions and associated carrier generation and recombination processes between the states of the low dimensional absorber are to be treated on equal footing with the processes that provide charge transport in extended states, which amounts to the need for a unified picture of quantum optics and dissipative quantum transport.
The challenge in using a microscopic approach resides in the fact that many modelling requirements that were automatically met by the macroscopic approach, such as, e.g., open boundary conditions, carrier relaxation and non-equilibrium occupation, are very hard to satisfy in a quantum-mechanical picture and have to be addressed explicitly on the basis of scattering states, which results in an adequate description to be found only at the quantum-kinetic level. There, the non-equilibrium Green's function formalism (NEGF), popular in nano- electronics and quantum optics, provides an ideal framework for the formulation of a comprehensive quantum theory of nanostructure based photovoltaic devices.

Essentially, the macroscopic steady-state photovoltaic balance equations are replaced by their microscopic quantum-kinetic counterparts in terms of Green's functions and self-energies for charge carriers, based on a general expression of the total scattering rate (intra- and interband). The Green's functions as the basic quantities are determined by the steady-state Dyson and Keldysh equations. While the retarded and advanced Green's functions are related to the density of states, the correlation functions additionally contain information on the
(non-equilibrium) occupation of these states. The self-energies on the other hand are scattering functions describing the renormalization of the Green's functions due to coupling to the the environment, in the form of interactions with photons (→ photogeneration, radiative recombination), phonons (→ relaxation,indirect transitions) and other carriers (→ excitons, Auger processes). An additional self-energy term describes injection and extraction of carriers at contacts with arbitrary chemical potential, enabling the treatment of an open non-equilibrium system. The macroscopic photovoltaic device characteristics are obtained from the Green's functions via the respective expressions for steady-state carrier and current densities.
As for the models based on the macroscopic transport equations, the computation of the Green's functions needs to be coupled self-consistently to the determination of the electrostatic potential from Poisson's equation, using the expressions for the carrier densities. Similar sets of equations can also be formulated for the optical and vibrational degrees of freedom (i.e., for photons and phonons), which then provides the desired comprehensive microscopic theory of nanostructure based optoelectronic devices.

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Ultra-thin absorber solar cells


Many high-quality absorber materials such as the direct-gap III-V semiconductors provide the high energy conversion efficiencies at considerable cost only. One approach to mitigate such expense are the increasingly popular ultrathin-film architectures, where almost complete absorption of the incident light is achieved in <100 nm via the use of nanophotonic light-trapping. While rigorous optical simulation has been instrumental for the development of such devices, no attention was paid to the fact that at such reduced spational extension, the consideration of the solar cell as electronically bulk-like object becomes increasingly questionable. Indeed, comparison of the semiclassical device characteristics based on bulk physics with rigorous quantum-kinetic simulations reveals significant discrepancies in both dark curent and photocurrent. There are two deviations from the bulk situation that together explain the observed discrepancies. On the one hand, the strongly reduced thickness of the space charge region leads to a strong enhancement of the built-in field, which induces electroabsorption effects and the associated redshift and broadening of the emission spectra. On the other hand, the contact regions span a significant fraction of the entire device and have a sizable impact on the physical processes in the absorber. For instance, the carrier blocking layers not only prevent leakage currents, but also suppress absorption in the vicinity of the electrodes.


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Multi-quantum-well solar cells


The most widely developed and commercially sucessful photovoltaic device relying on quantum effects in semiconductor nanostructures is the quantum well solar cell. In this device, the absorption edge is red-shifted via the insertion of thin layers of low-band gap material. The additional photocurrent comes at the cost of increased recombination in the device regions of reduced band gap. However, the tunability of the absorption edge allows for a optimized matching to the solar spectrum in both single and multijunction configurations.
One of the main challenges of the concept is the extraction of carriers at large bias voltage and corresponding low field condition, where carrier escape from deep QW becomes critical. Numerical simulation based on the NEGF formalism provide insight into the role of inelastic scattering and tunneling in the escape process at arbitrary illumination and bias conditions.



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Quantum-well superlattice solar cells


In the absorber designs based on quantum well superlattices, the latter do not only provide tunable absorption for charge carrier generation, but also extended states for charge carrier extraction. However, internal fields and any kind of disorder result in the breaking of the miniband structure and corresponding localization of the carrier wavefunctions, with severe consequences for the transport properties. The presence of inelastic interactions mitigates some of the detrimental effects by enabling relaxation between misaligned energy levels in adjacent wells. The NEGF formalism provides a realistic picture of current flow from the ballistic regime in extended superlattice states to sequential tunneling and Wannier-Stark hopping.



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Quantum-dot superlattice solar cells


For certain absorber materials, such as silicon, one-dimensional confinement does not provide the required design degree of freedom for proper tunability of the optical properties, not least due to the fact that carrier extraction demands the relaxation of carrier confinement in transport direction. In this situation, nanocrystals absorber designs are a suitable alternative to the layer systems, as they possess confinement in three dimensions. However, as in the QWSL case, carrier localization in the presence of finite fields, i.e. away from the flat band situation, represents a severe problem, which can only be partially mitigated by inelastic scattering, as the electron-phonon interaction is much weaker due to the sparse density of QD states.
Simulation of extended systems with 3D confinement is demanding, wherefore novel multi-scale approaches need to be developed.



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Fluorescent emission of QD


A special type of novel solar cell concepts is based on spectral tuning of light to a certain absorber frequency, e.g., for up-conversion devices. For that purpose, luminescent dyes or nanocrystal QDs are used. Due to the importance of the spectral shape of emission, adequate theories for QD fluorescence should provide physical lineshape. The line shape is naturally obtained by using the NEGF formalism to compute the luminescent response of an electronically closed nanosystem.


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Novel tunnel junction architectures


Most multijunction devices are operated under massive optical concentration, resulting in high currents. In this regime, losses at tunnel junctions between single component cells can become significant. Novel concepts for the optimization of the tunnel junction characteristics include architectures based on quantum wells. In these devices, current flow is strongly affected by the energetic alignement of bound and quasibound states in the junction region. Again, the NEGF formalism provides an ideal framework for the investigation of these nanostructure induced effects.



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Photonic solar cells


A wide range of novel solar cell concepts is based on nanophotonic absorption enhancement, especially in thin film architectures where insufficient light absorption is a major cause for efficiency limitation. In the subwavelength regime, the strength of absorption and emission can be largely tuned via the density and spatial structure of optical modes. Since solar cell devices are optically open structures, the relevant resonances are those associated with leaky modes. However, internal emission couples to all modes available, and consideration of the full mode structure is essential for a comprehensive assessment of photon recycling effects.
Extending the NEGF formalism to photon states, the density and occupation of the electromagnetic modes can be determined for arbitrary dielectric structures on equal footing with the optoelectronic properties.



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Multi-scale simulation of passivated contacts in high-efficiency solar cells


A common aspect of novel silicon solar cell architectures with efficiencies exceeding 25% - such as the silicon heterojunction solar cell (SHJ) and the tunnel-oxide passivated contact solar cell (TOPCon) - is the central role played by thin-film passivation layers. In the case of the SHJ concept, the passivation of crystalline silicon wafer surfaces is commonly mediated by a combination of ultra-thin layers of intrinsic hydrogenated amorphous silicon (a-Si:H →chemical passivation) with highly doped contact layers of hydrogenated microcrystalline silicon(-carbide/oxide) (muc-Si:H, muc-SiC:H or muc-SiOx:H →field effect passivation). In the TOPCon concept, a-SiOx:H tunnel oxides provide the desired carrier selectivity at high optical transparency for solar irradiation.
In order to reach efficiencies eta>25%, the physical mechanisms that can potentially limit the photovoltaic performance need to be understood in detail. Hence, device simulation is required to resolve the multilayered solar cell architecture in all its complexity, including intricated textures for light trapping and three-dimensional patterns for interdigitated contacts. Most importantly, however, an accurate picture of the amorphous-crystalline interface is required regarding transport and recombination of photogenerated charge carriers in dependence on configurational parameters such as energies and density of defects, band offsets or doping-induced band bending. Such parameters, on the other hand, should be obtained from a microscopic resolution of the material at the interface, as provided by first-principle calculations.
Our multi-scale simulation of passivated contacts in high-efficiency solar cells reflects the above requirements. It starts with the determination of the atomic and electronic structure from first principles, based on input from structure and composition and the use of tools such as molecular dynamics and density functional theory. Conventionally, the microscopic information on the device states is then processed into rates for generation and recombination as well as mobilities using something like Fermi's Golden Rule, which are then used for macroscopic device simulation on drift diffusion level. In our case, we insert an additional level of description at the mesoscale, where the microscopic information provides a parametrization of an effective model for the carrier dynamics based on quantum-kinetic theory (NEGF formalism).

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