Authors
Christoph Freysoldt, Gernot Pfanner
Motivation
Conventional silicon-wafer-based solar cells achieve reasonable conversion of light to electrical power, but are expensive, heavy, and consume significant resources in the production process. The active conversion region, however, is much thinner than the real solar cell. An alternative technology are thin film solar cells, which consist of a few μm-thick layers of microcrystalline or amorphous silicon only. Yet, their long-term conversion rates are still significantly behind their wafer -based counterparts.
Since the initial conversion rates are much better, a key to systematic improvements is to understand the processes that deteriorate the performance. An elegant technique is electron-paramagnetic resonance (EPR), that may detect paramagnetic defects in low concentration. The EPR spectra contain information about the local atomic structure, but it cannot be straightforwardly derived from the experiments alone. Here, theory can provide a link between the microscopic structure and the EPR spectra.
In this project, the computational methods to calculate EPR spectra are being implemented into our DFT library, and will consequently be improved to meet the increased accuracy of the new EPR experiments developed by our cooperation partners. This will then serve to set up a catalogue of relevant defects in Si-based solar cells that can be used to identify the atomic structures behind the experimentally observed signals.
The most important defect in this context is the "dangling bond". It originates from an unsaturated valence of the 4-valent silicon atom, which then captures a single electron. The defect is detected in EPR spectroscopy, but little is known about the atomic structure in the immediate environment.
Models
- Silicon dangling bond models. The spin density is shown in yellow.
Methods
We use density-functional theory to compute the electronic structure and EPR parameters of various dangling-bond models. We believe that a solid-state environment is a crucial point, and therefore use periodic boundary conditions and the supercell approach. This allows us to use well-tested and efficient computer codes, in our case SPHInX.
Our code uses a plane-wave basis set, which has the advantage that we can systematically improve the accuracy with respect to spatial resolution. The disadvantage is that we are forced to use pseudopotentials to make the calculation feasible. Pseudopotentials replace the core region close to the nucleus by a smooth counterpart, thereby removing the core electrons (which usually do not contribute to chemical bonds) and the oscillations of the valence functions (which cause trouble with low plane-wave cutoffs). This approach works fine for all effects that take place in the interatomic region, notably chemical binding, valence electronic structure, and many more. Unfortunately, EPR parameters do not fall into this class. EPR hyperfine parameters are determined by the spin density close to the nucleus. EPR g-Tensors depend in part (namely the spin-orbit contribution) on the gradient of the potential, which again is largest close to the nucleus. Thus, a pseudopotential approach seems fatal!
Fortunately, P. Blöchl invented the projector-augmented wave method, which is a strict scheme to reconstruct the full wave function from its pseudoized version. This reconstruction is achieved through a set of projectors (hence the name).
Method for EPR hyperfine parameters
The hyperfine interaction is the coupling between the electron spin and the nuclear spin (if the nucleus has one). The hyperfine interaction then consists of an isotropic part, the Fermi contact interaction
a = 2/3 μ0 geμegNμNρe(RN)
where μ is the magnetic moment, g the gyromagnetic ratio, ρ the spin density of electron or Nucleus. μ0 denotes the magnetic susceptibility constant, and RN the position of the nucleus.
The anisotropic tensor comes from the dipole-dipole interaction
(3rαrβ - δαβ)/r5
where r is the distance between the nucleus and the electron and rα a cartesian component of the distance vector. The symmetry of the anisotropy corresponds to a d-function. If only s and p states are important, this gives a very interesting rationale of the hyperfine tensor: the isotropic part is sensitive to the s-like component only, since all other angular momentum components have a node at the nucleus. The anisotropic part, on the other hand, measures the p-like character of the spin-carrying state (since the density is given by the wave function square, and p×p gives a d-like symmetry.
g-Tensors
The g-tensor describes the Zeeman splitting between the electron spin and the external magnetic field. In vacuum, the value is 2.0023. In real compounds, the external magnetic field is partly screened, which may enhance or reduce the local magnetic field. This changes the Zeeman interaction, which is best absorbed into the g factor, i.e.,
S gvac Bloc = S g Bext
In DFT calculations, one actually computes the local B field by perturbation theory. In our approach,there are two main challenges: the pseudopotential problem mentioned above, and the difficulty to combine periodic boundary conditions with a constant magnetic field. The solution to this are gauge-including projector augmented waves (GIPAW). We intend to implement the GIPAW method into our S/PHI/nX code.
There is an open position available for this project!
