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Modelling of interfaces for high performance solar cell materials

Final Report Summary - HIPERSOL (Modelling of interfaces for high performance solar cell materials)

Executive summary:

The resistance at the metal contact-semiconductor interface and recombination at the passivating layer-semiconductor interface are two important bottlenecks for improving the performance of current solar cells. These processes are quantum mechanical by nature, but so far most studies and attempts to improve the properties of solar cells have been at the device scale. A main reason for this is the great challenges faced by theoretical modelling. Accurate descriptions of the geometric and electronic structures are required, which necessitate the use of highly sophisticated methodologies based on first principles. At the same time, the interfaces extend in many cases well beyond the size limit of first principles methods, creating the need for more efficient methods, which can operate at larger time and size scales. HiperSol aimed at filling this knowledge gap by developing and implementing a multi-scale modelling environment, focusing on real interfaces and how the achieved knowledge can be used to enhance the present solar cell technology. The physics at the various scales was treated by a multitude of techniques, and the boundaries between these techniques were of utmost importance for the success of the project. Hence, considerable emphasis was laid on consistently connecting different methods and on experimental validation.

Project Context and Objectives:

The HiperSol (Modelling of Interfaces for High Performance Solar Cell Materials) project was a small- and medium scale project within the EU 7th framework programme. The overall aim of the project was to develop an integrated multi-scale modelling environment that is applicable to properties of real materials on length scales not accessible by ab initio modelling; and to use this environment to accurately describe and predict important parameters and properties of interfaces of contacting and passivation layers with silicon, in order to enable a drastic decrease of the cost/efficiency ratio of a solar cell device. This three year project started on December 1st 2009 and had a total budget of 4.5 million Euro of which the funding from the European Commission was 3.4 million Euro.

Motivation for the HiperSol project
Improvements in the field of materials science and nanostructured materials in particular, increasingly require fundamental understanding of important aspects like interfaces, and thus modelling at many different scales. The industrial shift towards a knowledge-intensive economy demanded radical innovation in the design of new material systems for specific highly-demanding applications. This implies that designs based on phenomenological and macroscopic material property measurements no longer suffice for this increasing demand. Engineering tools, associated with multi-scale modelling and simulation approaches, can help by including the microscopic, or even more accurate atomistic, structure and properties into materials design, in order to construct more reliable high performance materials, based on an accurate prediction of their in-service behaviour.

Solar cells were chosen both because of their modelling challenges, and also because of their relevance for the development of sustainable energy resources in Europe as well as in the rest of the world. In many energy scenarios, solar electricity will dominate electricity production within the coming 50 years. For this to become true, the costs have to be decreased while simultaneously realising high efficiencies. This requires in-depth knowledge about the behaviour of the most crucial processes in solar cell devices, enabling the optimisation of solar cell design and solar cell processing. Despite the conceptual simplicity of today's solar cells, a detailed understanding is still lacking, in particular of many of the interface-related mechanisms. In order to achieve the necessary breakthroughs in solar cell manufacturing, fundamental understanding and accurate predictions are required and can only be achieved by advanced modelling including all the relevant scales.

Project scope

The HiperSol project focused on two interfaces, the contacting interface between silicon and the silver finger and the passivating interface between silicon and the passivating layer since the resistive and recombination losses at these interfaces are responsible for the major loss mechanisms for the light generated carriers (electrons and holes) in standard Si-based PV. Even though the modelling framework developed in HiperSol is specifically designed for contacting and passivation interfaces in solar cells, the generic character of the methodology spreads the impact other fields within materials science and engineering.

HiperSol's objectives

The first objective of the HiperSol project was to develop general methodology and models on the atomistic level for theoretical studies of interfaces and other complex structures at the nano-scale.

To realise this it was necessary to develop a methodology capable of describing a macroscopic system, with properties determined on a quantum mechanical level. To create such a methodology, the following subgoals had to be met:

-Construction of inter-atomic potentials for empirical molecular dynamics (EMD) from first principles (FP) calculations.
-Determination of realistic and representative atomistic structure models as a basis for further ab initio calculations.
-Creation of semi-empirical pseudo-potentials (SEPP) based on first-principles calculations.
-Development of techniques for accurate calculation of electronic band structures in sub-systems large enough to include macroscopically relevant features.

In order to enhance the impact of this work, it was an important goal to make the solution generally applicable and accessible.

The second objective of HiperSol was to construct a validated multi-scale modelling environment specifically aimed at describing and predicting important properties of contact interfaces in silicon solar cells.

The integrated modelling environment for the contacting interface should provide realistic atomistic models of the dynamic metallization process as well as calculating conductivities of the static contacting interfaces from first principles with the following output:
-Diffusion parameters obtained from FP and EMD calculations.
-Surface and interface energies calculated from FP or EMD.
-Electric conductivities from FP calculations and Boltzmann theory.
-Detailed models of the metallization processes obtained with FEM simulations.
-Global conductance of a contacting finger from FEM simulations.

These results depend strongly on the development of a general methodology, and an essential goal was to successfully integrate the different length and time scales involved in the modelling approaches. Another essential goal was to obtain a systematic and reliable scheme for experimental validation of the theoretical tools.

The third objective of HiperSol was to create a validated and integrated multi-scale modelling environment for accurately calculating the most relevant properties of the passivation interface in silicon solar cells.

The integrated modelling environment for passivating interfaces should provide accurate band structure calculations and charge carrier recombination rates at the interface from first principles calculations. The expected output included the following:
-Electronic band structures of simple interfaces from FP calculations and of more complicated surfaces from SEPP calculations.
-Normalized (Kohn-Sham) wave functions from projector augmented wave-based calculations.
-A new scheme for calculating charge carrier lifetimes from first principles.
-A novel design for computing recombination rates using envelope function approaches.

Again, the integration of the various scales was an important common goal in these calculations. Also, a systematic validation scheme to test the modelling set using various experimental techniques on idealized interfaces was an important outcome.

The fourth objective of HiperSol was to apply the multi-scale modelling tools to predict improved structures and materials for contacting and passivation in solar cells.

After validation of the modelling tools on simple systems, the methodology was employed on more realistic and practical systems. The HiperSol consortium used this to generate ideas for improving the contacting and passivation interfaces in silicon solar cells. In this way, new structures and materials were screened before conducting expensive and complicated experiments.

Thus the following subgoals had to be met:
-Obtain new fundamental insight into the role played by the contacting and passivation interfaces in solar cells (and other semiconductor materials), based on current materials.
-Formulate new structures and materials to improve contacting and passivation schemes.
-Assess the applicability of new materials to industrial production.

The ultimate goal was to combine these modelling efforts with engineering at the nano-scale for improved contacting and surface passivation to enable cheaper and/or more efficient silicon solar cells.

Project Results:

The structure and properties of the contact and passivation interfaces in solar cells have considerable effects on the cell behaviour. Examples include the electronic conductivity across the interface (for example, the effect of Schottky barriers) and the generation of recombination defects. Understanding and predicting these effects requires models of the interfaces at the atomic scale. In principle, it would be desirable to use ab initio quantum mechanics to calculate the properties of these interfaces. In practice the number of atoms required to model the interfacial structures adequately is too large (and the number of structures that need to be considered is too high), for this to be possible, even with the recent developments described below. We must therefore use a combined strategy of using simpler, classical models based on force-fields to investigate interfacial structures, reserving the use of ab initio methods for particular cases and also using the structures generated by the simpler models as a starting point for the more expensive ab initio calculations where possible. It is therefore necessary to develop models using classical force-fields that are of sufficient quality to do this using ab initio simulation data as a starting point. Such models must be compared both with further ab initio simulations and well-targeted experiments for validation. This is the purpose of the first work-package. The validated models can then be used elsewhere within the project. Models have therefore been developed for both the silicon/metal contacting interface (initially the metal was silver but other metals have also been considered) and silicon/silicon nitride passivation interfaces. This has required the determination of suitable models for the bulk materials and the interfaces from a combination of ab initio calculations and experimental data; the generation of suitable interfacial structures at the atomistic scale and the validation of the models using suitable experimental and ab initio data where possible. The silicon/silver and silicon/silicon nitride interfaces (the most important for this project) was validated against a combination of ab initio and experimental data. The other metals considered (Ni, Zn) were validated against a range of ab initio simulations.

For the contacting (metal/silicon) interface, we have used different models for the bulk materials and developed new models for the interfaces. For the metals we used an embedded atom model, which has been successfully employed for modelling the metals of interest. This takes account of the metallic bonding through a simple many-body function. For Si (and for the interaction between Si and metal) we used the Tersoff force-field that has been widely used for the modelling of Si and can account for the bond directionality characteristic of this covalent material.

The parameters of the model force-fields were first optimised to reproduce the results of ab initio simulations using the VASP code. For the Si/Ag interface, this ab initio data included the bond length and binding energy of the Si-Ag dimer, the optimized geometry obtained after replacing an Ag atom in the unit cell by a Si atom and the geometries and work of separation calculated for the interfaces Si(111)//Ag(111), Si(110)//Ag(110), Si(100)//Ag(100) and Si(100)//Ag(110). We also compared to structures obtained by ab initio methods for the Ag(110)//Si(110) interface and the Ag(100)//Si(110) interface and structural details of calculated AgSi structures taken from the literature. All of our calculated cluster bond lengths are within 5% of the ab initio values, although our potential was based primarily on condensed state data. For other metals, the validation set used was similar.

For the Si/Ag interface, we also compared to experimental data for the structure of the Ag(001) interface with the 2x1 reconstructed Si(001) surface, the Ag(011) interface with the 2x1 reconstructed Si(001) surface and recent high resolution electron microscopy (HREM) results for the spacing of the (111) planes at the Ag(111)//Si(111) interface. The relaxation of surfaces in contact with one another can be characterized by both the interatomic distances at the surface and the inter-layer distances of the surface to bulk layer atoms. These values are available experimentally for Ag surfaces in contact with the reconstructed Si(001)(2x1) surface. In all cases the calculated values are within 3% of the experimental ones. We ?nd the interatomic separations obtained from the force-field to be within 5% of the ab initio results and generally good agreement for bond angles. When we compare to recent HREM results for interlayer spacings at the Si/Ag interface in a crystalline Si solar cell, we ?nd that our values are within 0.2% of experiment (i.e. within the spatial resolution of HREM).

We also investigated the geometry of the two interfaces identified by Transmission Electron Microscopy (TEM) using a combination of empirical and ab initio methods. For both interfaces it was found that significant re-organization of the atomic positions compared to the ideal crystal positions (greater than 0.01 nm) occurred only within the ?rst 5 % either side of the interface. For the 111//111 interface there is very little distortion of the surface layer to back layer distances on either side of the interface, with both Si-Si and Ag-Ag bonds being within 0.001 nm of the ideal crystal values. For the 110//110 case, the Si-Si bond between the surface and back layer is slightly stretched relative to the perfect crystal, whilst the Ag-Ag bond is slightly compressed.

In order to provide input and feedback for the metallization process modelling and the calculation of the global conductance at the contact interfaces, the phenomenological reasons for good and bad contact resistance values were studied. Increasing the emitter sheet resistance causes an increased contact resistance. If the electrically inactive excess phosphorus-doping concentration in the emitter is further decreased, fewer Ag-crystallites are grown into the Si surface. As observed by TEM, the excess phosphorus results in considerable strain within the Si lattice that could facilitate Ag crystallite nucleation and growth. Additionally, different Ag-pastes result in different contact formation.

Further details of the use of this modelling can be found under WP3 and WP5.

The generation of the passivation layer on top of silicon, the firing process of the contacting layer and graded doping of silicon all lead to diffusion across interfaces and inside the bulk materials. It is thus particularly important to obtain knowledge of the geometric structure of these interfaces and related nearby structures, which will include defects or perturbations of the perfect crystalline bulk structure. Models for the silicon-silicon nitride interface were developed and applied to show the effects of different preparations of the interface (whether abrupt or gradual) on the interfacial defects and hence on the electronic properties.

The different phases of Si3N4 were investigated using ab initio methods and the P63m found to be the most stable. Models were built for the crystalline-Si//amorphous-Si3N4 interface and electronic structure calculations performed for these models. The results are evaluated by detailed comparison of the force-field models with small models built using a full ab initio density functional treatment. In a first step, small amorphous models of the passivation layer were created using ab initio and force fields. We found that the previous Tersoff parameterizations result in a too high defect density in amorphous silicon nitride, in particular for stoichiometries different from Si3N4. To construct the models necessary to simulate the interface in this project we refined the force-field parameters. The fitting was done by employing the force-matching technique to fit these parameters to ab initio molecular dynamics simulations. The agreement with full ab initio simulations was satisfactory, in particular for structural properties. The final structures are usually relaxed using ab initio methods to guarantee that residual forces do not degrade the calculated electronic properties. The force-field parameterisation which resulted gave structures which, when geometry optimised by ab initio methods, gave wider band-gaps than those using published force-fields, indicating fewer defective centres and a better representation of the structure. Unfortunately it proved impossible to reproduce completely a structure that gave the same band gap as a structure generated solely from ab initio molecular dynamics. However the new potential parameterization gives more reliable structures than previous parameterizations and was used in the project for work on designing improved passivation layers.

The SiNx/Si interface was characterized with ellipsometry and SIMS to determine the effect of passivation. This shows that a gradient in composition is important for the passivating quality. The SiNx signal penetrates inside the first nanometres of the bulk c-Si, which can be interpreted as nitridation of the Si. The difference between passivating and standard SiNx expresses itself in the Si-N bond density as measured with bulk FTIR, lower for the former, and the refractive index, higher for the former. Both SiNx layers show a trend through the layer with increasing refractive index. A similar trend can be found with ellipsometry, in which an interface layer can be modelled. For this, different SiNx layers have been fabricated with similar refractive indices, but with varying Si-N bond densities. Both low and high levels of nitridation will give limited passivation, the optimum can be found in between. This might be related to the balance between the fixed charge (more nitridation will enhance the fixed charge) and induced strain or damage in the first nanometres of the crystalline Si bulk and thus the density of interface states.

Simulations of the nitridation effect show that with increasing nitridation the volume and fraction of important defects in the silicon (K and N centres) increase and are found within a few nanometres of the interface. This correlates well with the experimental results obtained. Further details may be found in other workpackages.

WP2: Atomistic band structures for large systems

Development of computational methods and tools:

The development effort within this work package strongly focused on three key issues that needed to be solved in order to calculate accurate band structures and wave functions for large atomistic models:

1.) A bandgap correction scheme. Since conventional density functional theory calculations massively underestimate the band gap in the materials considered within the project (Si, silicon nitride, glass). The band gap error greatly complicates the prediction of the properties of defects and interfaces and needs to be dealt with before we can seriously consider calculations for large models.

We have adopted a band-gap correction scheme, the modified Becke-Johnson local density approximation (MBJLDA), that has now been tested for III-V semiconductors as well as Si, silicon nitride and silicon oxide. The scheme yields accurate band gaps for all considered materials, although, as expected, it involves a grain of empiricism, requiring adjustment of the parameters against high level quasiparticle calculations such as GW. 2.) Development of fast iterative matrix diagonalization methods for the calculation of electron and hole band structures in large systems containing several hundred thousand atoms. This objective was achieved by constraining the calculations to selected orbitals around the valence band maximum and conduction band minimum. These states are relevant for the electronic and transport properties. We implemented a robust and very efficient scheme, the harmonic Davidson inner eigenvalue solver, and the method has been applied to and evaluated for systems containing up to 100 000 atoms.

3.) Effective semi-empirical potentials for non-selfconsistent calculations. When the calculations are constrained to few states close to the Fermi level, the potential created by the other valence electrons can no longer be calculated parameter free. This implies that we need to account for the effect of the other electrons be means of an effective screened semi-empirical potential. We achieved this goal by adopting a new charge-fit procedure, in which the electronic density distribution of the valence electrons is fitted to amorphous model structures.

In addition to the three points mentioned above, we have invested considerable effort in:
4.) The implementation of an efficient scheme to calculate Auger recombination rates from DFT orbitals. The ab initio calculation of Auger recombination rates requires a very dense sampling of the first Brillouin zone in reciprocal space, to such an extent even that the selfconsistent DFT calculations that serve as input become prohibitively expensive. Therefore, in addition to the evaluation of the Auger recombination rates, we have implemented an interpolation scheme that allows for the construction of the one-electron orbitals at a very dense mesh in reciprocal space from an underlying calculation on a coarse grid of points in reciprocal space. Both features (calculation of Auger recombination rates as well as the interpolation algorithm) will be useful in many application far beyond the scope of the HiperSol project.

Applications

In terms of the application of our computational methods and tools, the main achievement within this work package was the identification of the dominant defects in bulk amorphous-Si3N4-xHy and crystalline-Si/amorphous-Si3N4-xHy interfaces and the characterisation of the contributions of these defects to the density of states within the bandgap. The role of hydrogen as passivator of the dangling bonds of under-coordinated atoms has been elucidated. The mechanism that leads to so-called 'fixed-charges' at the silicon nitride side of the c-Si/ a-Si3N4-xHy interfaces is now understood at the atomistic level.

1.) Defects in bulk amorphous-Si3N4-xHy:

First of all, we constructed a statistically sound ensemble of amorphous-Si3N4-xHy structures (actually a-Si3N4, a-Si3N3.5H0.8 and a-Si3N3H0.8) using ab initio molecular dynamics (MD) techniques (roughly 1000 independent samples for each stoichiometry). These samples were analysed with respect to the number and the nature of the defects they contain, and the influence of these defects on the electronic structure.

Si in crystalline and amorphous Si exhibits tetragonal (four-fold) coordination (Si-Si4) and sp3 hybridization. Its electronic structure shows an energy gap (about 1.2 eV) between the valence band (Si sp3 bonding) and conduction band (Si sp3 anti-bonding). Si3N4 phases (α-, β- and the amorphous phases) are wide gap insulators (energy gaps greater than 5.0 eV). In Si3N4-x, Si atoms are still in a tetragonal coordination, and N atoms triangularly (three-fold) coordinated. The valence band is dominated by N sp2 hybrid (bonding) orbitals at lower energy and N lone-pairs (non-bonding) at the upper part of the valence band.

In amorphous (a-)Si3N4-x, both Si and N atoms would prefer, topologically speaking, to keep their tetragonal- and triangular-coordinations in a distorted Si-N network, respectively. Naturally the distortions causes states to tail into the band gap increasing the number of states in the gap. The major structural defects in a-Si3N4 are under-coordinated Si (Si-N3) and N (N-Si2), which are known as K-defects and N-defects, respectively. The K-defects contribute dominantly to the defect states in the middle of the energy gap. With decreasing N concentration in a-Si3N4-x, Si-Si pairs or Si-clusters appear due to the deficiency of N atoms.

2.) Defects near the crystalline-Si/amorphous- Si3N3.5H0.8 interface

Again, by means of ab initio MD we constructed over 1000 c-Si/a-Si3H3.5H0.8 interface structures. The ensemble of interface structures was carefully analyzed with respect to (i) the number and nature of the defects in the silicon nitride part of the system, and in the c-Si near the interface, (ii) the electronic properties of these defects, foremost their contribution to the density of states within the gap, (iii) the spatial distribution of H, and (iv) the influence of the presence of H on the density of states in the gap.

The defects that we find in these interface structures are of the same nature as the defects we encountered in the bulk a-Si3N4-xHy structures: undercoordinated Si (threefold) and N (twofold), and ideally coordinated but strongly distorted SiN4 and NSi3 units. The undercoordinated defects are in part passivated by H.

Two thickly drawn red lines indicate the top of the valence band (left thick red line) and the bottom of the conduction band (right thick red line) on the c-Si side of the interface. The defect states between these lines (almost exclusively located at the silicon nitride side of the interface) play an important role in the defect assisted carrier recombination of electrons and holes created on the c-Si side of the interface.

In practice, of course, the Fermi-levels on both sides of the interface will be equilibrated: charge will flow from the silicon nitride side of the interface into the silicon part, depleting a number of defect states near the interface and injecting electrons into the c-Si conduction bands.

These depleted defect states at the silicon nitride side of the interface represent positive charges (often called the 'fixed charge').

WP3. Modelling of contacting interface

Atomistic calculations:

DFT based molecular dynamics (MD) was used to simulate the various phases and interfaces relevant for the FEM study. Since most of the phases were in the liquid state, it was possible to use elevated temperatures for many of the systems. Nevertheless, we have obtained results for all relevant diffusion parameters at 1000 K, which is a relevant temperature for the firing process.

Diffusivities were calculated by first-principles molecular dynamics.. The diffusivities of each element were fitted to an Arrhenius behaviour;
(1)
where D0 is the prefactor, Eb is the energy barrier, R is the gas constant, and T is the temperature.

The force fields obtained from WP1 (D1.2) were used to simulate the Si/Ag contacting interface. The (111//111) and (110//110) interfaces, which were identified in samples as part of D1.1 were simulated. The potentials were used to search through a large number of possible starting configurations and identify the most suitable candidates for simulation using density functional theory (DFT). The DFT simulations reveal metal-induced gap states (MIGS) in the density of states plots at the Si/Ag interface.

The Schottky barriers were calculated for silver contacting to pure Si and to Si doped with phosphorus, highlighting the role of phosphorus for reducing the SBH. The SBHs were also calculated for Si/Ni (silicide) interfaces and Si/Zn interfaces. It was found that the Schottky barriers vary considerably with the type of Ni silicides. Zn was found to have a higher SBH, even in the presence of doping.

We also investigated the role of P for promoting the formation of Ag crystallites at the Si surfaces. Using classical nucleation theory (CNT) we were able to show that the P stabilises the Si/Ag interface. We show that the rate of nucleation depends on the nature of the glass frit used.

Continuum calculations:

The work has consisted of:
i) establishing necessary thermodynamic model input, phase-diagrams and Gibbs free energies;
ii) solving the diffusion equation in the liquid phase for equilibrium and non-equilibrium surface conditions and solving the mass balance at the particle surface; and
iii) establishing and solving the phase-field model in the commercial software Comsol Multiphysics.

Qualitative agreement between the models ii) and iii) has been obtained. Quantitative correspondence will be discussed below.

The physical process for the metallization process that has been investigated is the thermodynamic non-equilibrium situation that allows for a solid substance to be dissolved into a liquid at temperatures below the melting temperature of the solid.

The driving force of dissolution is the temperature dependent chemical potential gradient. The same mechanism allows for precipitation of solids from the liquid phase.

To study the metallisation process, a simplified approach is taken. It is assumed that silver particles are initially residing on top of the SiN layer. It is assumed that the liquefied glass etches away the SiN layer, such that the silver particles are separated from the silicon wafer by a liquid film consisting of liquid glass. Further simplification considers the silver particles as an infinite continuous solid silver body. Eqs. (1) and (2) can now be solved in 1-dimensional Cartesian coordinates to simulate the metallisation process.

To facilitate the precipitate growth at the silicon surface, when the firing temperature is dropping, an artificial nucleation site is introduced by specifying the existence of a solid silver phase (boundary condition) at the silicon surface.

To enable modelling of complex liquid mixtures, a thermodynamic procedure was developed to reducing the multicomponent glass phase to a single pseudo component. Output from the procedure was the concentration and phase dependent Gibbs free energy and saturation point for a mixture of solute and the glass phase.

Experimental validation and input:

Phenomenological studies were conducted to generate input parameters for the FEM model of the contacting interface to predict the global contact resistance. This part was done in close connection to WP5. To evaluate the relative importance of the possible current transport paths from the Si emitter into the Ag-finger bulk, microscopic contact characterization by SEM was combined with liquid conductive silver application to different stages of etched-back contacts.

Comparative experiments on flat Si reveal a very sparse direct contact density as the source for the high contact resistivities measured. We conclude that the observed direct contacts are essential for the current transport in silver thick film metalized Si solar cells and the first parameter to calculate for modelling the current transport is therefore the Si-Ag interface resistivity of the observed geometries. Besides the already calculated crystal orientation dependence of the Schottky barrier, its value will also be depth-dependent because of the varying P-doping concentration in the emitter where the Ag-crystallites penetrate up to ~80 nm in average.

Regarding the dynamic contact formation, the most relevant experiments shedding lights on the metallization process have been already done, mostly by Gunnar Schubert:

Silver - silicon: Pure silver is able to grow Ag-crystallites into Si with the typically observed geometrical shapes, but only at much higher temperatures and longer times than the ones used in a standard firing process.

Glass - silicon: Lead borosilicate glass is observed to etch into Si and results in metallic lead precipitates in the glass: 2PbO + Si → 2Pb + SiO2. Interestingly, instead of the well-defined Si crystal orientation dependent geometrical shapes in which the Ag crystallizes into the Si surface, lead borosilicate glass alone etches Si isotropically leaving round etch pits. Because metallic lead does not wet silicon, the lead precipitates move away from the Si surface in form of spherical crystallites.

Silver - glass → Silver containing glass - silicon: Lead silicate glass is able to dissolve silver. Thus silver saturated lead borosilicate glass on silicon is fired. Instead of the round etch pits from silver-free glass only, the usual pyramidal etching behaviour is observed. Thus, a possible silver growth mechanism could be an anisotropic redox reaction of the silver ions in the glass with silicon, similar to the PbO-Si reaction. As simultaneously Pb precipitates are observed in the bulk of the glass, both redox reactions could occur during the firing process. However, the dissolution of Ag in glass is slow and thus the silver growing in Si must mainly be transported through the glass, as occurring by liquid lead melting silver and forming the experimentally detected liquid silver-lead phase.

Silver - glass - silicon: Again, only minor Ag amounts added to glass are necessary to anisotropically etch silicon. The lead content of the resulting crystallites grown into Si decreases with increasing Ag content in the paste, and crystalline lead is not present in the glass any more.

These experimental observations (Schubert's PhD) including measurements of reaction temperatures during firing (also in Horteis' PhD) are an excellent database to validate the metallisation process model, not only as a whole but also in its subsystems.

As we observed the glass-freeness of the standard monocrystalline Si pyramid tips to be crucial for direct contact formation and thus current conduction, the Ag-paste's wetting properties on different Si surface topographies, are experimentally investigated.

WP4: Modelling of the passivation interface

Several models were generated for studies of Si/SiNx interfaces regarding the number of potential defects which can act as charge carrier recombination centres. The bonding at the interface between amorphous SiNx and crystalline Si with various values of nitrogen content x for topological information were investigated using these models. We demonstrated how the concentration of geometric defects at the interface depends on the stoichiometry of the SiNx layer. It was further shown that a nitrogen concentration gradient across the interface can significantly lower the number of under-coordinated Si defects in the interface region. These results have implications for the design of SiNx layers for use as passivation/anti-reflective layers in solar cell devices. The information will be further used for solar-cell optimization.

Solid state diffusion across the passivation interface and inside the bulk materials of solar cells can take place both during steady-state operation and accelerated during the firing process of the contacting layer. This will cause defects and modifications to the interfaces. We have combined Nudged Elastic Band (NEB) and First-principles molecular dynamics (FPMD) methods to study the detailed diffusion mechanisms and defect formation processes. We further investigated the impact of various defects on the performance of the solar cell for which we needed detailed knowledge of the defect-free bulk and interface structures. In this respect we wanted to obtain knowledge of the electronic properties of Si3N4. The studies are very demanding, but also valuable, since they complete the view of the conduction process, e.g. defect levels, exciton effects, screening, etc. These results will be important for the lifetime calculations and are benchmark studies in the field of solid-state calculations.

As we concentrated on studying the recombination losses of photocarriers at the passivation interface, it is noticed that the photocarriers are normally mobile and thus rather extended, while various recombination centres (mostly defects) at the passivation interface are quite localized, e.g. K centres with Si atoms bounded to three N atoms instead of four. FP methods are necessary for properly describing localized defects, while in most cases; only solid-state based envelope function approach has been able to describe the mobile photocarriers under device operation conditions (their photogeneration and transport under external bias). Therefore, for the recombination time calculations two approaches have been used about single particle wave functions of extended photocarriers and localized defects. One is to extract the total wave functions directly from the FP calculations from WP2. The other approach is to match the base functions used in solid-state envelope function theory and the ones in FP calculations. This is believed to be more suitable when states of wave functions extended over 10 nm are involved. We are now programming intensively the corresponding numerical codes, which will be used in the following task.

We have formulated the principal recombination processes, i.e. radiative recombination, electron-electron interaction (Auger recombination and impact ionization), and electron-phonon interaction. Model calculations based on solid-state envelope function approach have been performed for recombination processes in semiconductor quantum dots placed at various distances from the interface. Numerical results agree with relevant experimental data of quantum-dot based solar cell. We are now trying to replace the quantum dots by the real potentials of defects at the passivation interface and the extracted single-particle wave functions to calculate the recombination times of photocarriers at the passivation interface. We have further tried to have a close look at experimental indications about effects of defects at the passivation interface on solar cell performance. The first check is the lifetime of minority carriers measured using photoconductance decay.

The major results of the period were that computable expressions could be derived and used to give numerical values for the most important mechanisms of recombination processes occurring at interfaces. A highly interesting result was the prediction of a dominant radiative coupling over the non-radiative channels (electron- electron scattering and phonon coupling). An important ramification of this result is that structure-property relations can be achieved by virtue of the comparative simplicity of the radiative coupling over the other processes, motivating that also even more advanced calculations should be applied for that very purpose. There indeed seems to be a possibility to design cells optimal for anti-quenching this way.

WP5: Application of the modelling set to improve contacting

Recent commercial Ag-pastes are able to form contacts with emitters with significantly lower phosphorous surface-concentrations. To understand the reasons we formed contacts with four differently doped emitters with three of the most recent Ag-pastes. On the microscopic level, Ag-crystallites grown into the emitter in direct contact with the bulk of the Ag-finger play a major role in current transport. Here we find that while partially glass-free pyramid tips leading to such direct contacts are observed no matter what the level of the emitter doping, the Ag-crystallite density and depth grown into Si resulting from a specific paste mainly depend on the electronically inactive P-content in the Si emitter within the so-called dead-layer.

With most recent best-performing pastes the resulting Ag crystallite densities grown into Si are considerably less dependent on the dead-layer, thus good contacts can be formed to advanced emitters.

Based on the experimental confirmation of the existence and importance of direct contacts between the Ag finger and the cell surface, realistic models of the solar cell contact formation were established. The model of the conductance thus contains such direct contacts within the observed geometries and the metallisation process model focuses on the amount of silver crystallized at the silicon surface.

Detailed mathematical models have been implemented in realistic geometries for the Ag-Si contacting interface based on Schottky barrier models for the local resistivity. An idealized geometry is generated based on detailed investigation of real contacting interfaces (textured surface) by SEM. The models allow for identification of conductivity losses related to surface fraction, orientation and shape of silver crystallites. The conductance model predictions of contact resistivity changes with varying doping type and profiles, Si etch depth, removal of glass, as well as temperature, are in agreement with our experimental data and result in deeper and more fundamental understanding of contact formation. The contact resistivity resulting from identical microscopic contact configurations on typically used higher and lower phosphorous doped solar cell emitters varies only slightly, e.g. only by a factor of two when reducing emitter doping from 60 to 80 O/sq within typical industrial emitter doping profiles. The experimentally observed trend of reduction of contact resistance upon reduction of temperature is found to be related to the improved conductivity of the emitter layer with lower temperature and it is accentuated by the doping profile variation. When contacting boron-doped emitters, despite the presence of some directly contacted Ag-crystallites at the pyramid tips, measured contact resistivities are two orders of magnitude higher. From modelling we conclude that despite the lower p-type Schottky barriers, also with identical microscopic contact configuration, contact resistivity would be increased by one order of magnitude because of less efficient hole transport and significantly reduced peak doping of the boron doping profile.

A mathematical dissolution-transport model was developed for solids in liquid solvents, at temperatures below the melting temperature of the solid. A thermodynamic procedure was developed to prepare input for the dissolution-transport model, enabling simplified modelling of complex liquid mixtures. This metallisation process model was employed to study the crystallization of silver at the silicon surface, in dependence of realistic firing temperature/time profiles, and liquid layer thicknesses separating the silver body and the Si surface. The modelled trend of silver content in Si as resulting from simple experimental glass frit composition (only PbO, B2O3 and SiO2) together with different experimental firing profiles is in agreement with the equivalent experimental data.

The use of silver in the rapidly growing solar cell industry is problematic, due to high price and eventually to availability. Replacement of silver is a very challenging task: Equally well conducting metals are like gold even more expensive, or like copper detrimental for long-term solar cell performance. Because Cu, the only sufficiently conducting and cheap alternative metal cannot be put in direct contact with Si, we focused on splitting up the current Ag-based pastes bi-functionality of forming good contact to Si and simultaneously transporting the collected current in well conducting lines. Nickel builds a good contact to silicon because of Ni silicide formation and is a good Cu diffusion barrier. While Ni and Cu are equally fast diffusers in Si, Cu has a higher solubility in Si than Ni and Cu precipitates (Cu3Si) fit worse into the Si lattice than Ni precipitates (NiSi2). Therefore Ni is less detrimental for the solar cell efficiency. Also Zn could be a possible material to substitute Ag because of low cost and alike properties. Despite the large temperature/time parameter space tested, neither with Ni- nor with Zn-paste could good contact to Si be formed. The microscopic interfaces resulting from high-temperature fast-firing are identical for Ni- and Zn-paste: Pb-crystallites with small Ni respectively Zn content grow into Si. Their shapes are the same as those of the Ag-crystallites. Tempering of Ni-paste only leads to insufficient Ni silicide formation).

WP6: Application of the modelling set to improve passivation

The work carried out in this workpackage contains four main topics:
1.Research and development of improved passivating layers based on SiNx:H
2.Research and development alternative layers for passivation
3.Application of improved passivating layers in an industrial environment
4.Relate the modelling results to the experimental ones.

There was a close cooperation between the partners that performed the experimental work and the partners that carried out the modelling and theoretical part of the project.

The main results of this workpackage have been published or will be published later this year.

Research and development of improved passivating layers based on SiNx:H

In the first part of the project different characterization techniques were evaluated within workpackages 1 and 4. High resolution Transmission Electron Microscopy (TEM), Fourier Transform InfraRed (FTIR) spectroscopy, X-ray Photoelectron Spectroscopy (XPS), spectroscopic ellipsometry and Time of Flight Secondary Ion Mass Spectroscopy (SIMS) were used for detailed characterization of the layers. In the second part of the project the physical properties of the layers were related to passivating properties. The passivating properties were measured by Quasi Steady State Photoconductance (QSSPC) and Capacitance-Voltage Metal-Insulator-Semiconductor (CV MIS) measurements. With the first method the effective lifetime of the minority charge carriers can be determined. From this lifetime the effective surface recombination velocity Seff can be calculated. With the latter the density of states at the interface Dit and the number of fixed charges in the layers (Qf) can be determined. Dit is a measure for the so-called chemical passivation and Qf is the one for the so-called field effect passivation. Both Dit and Qf determine the overall passivating quality. The number of fixed charges Qf can be related to defects in the SiNx:H layer (for example the so-called K and N centres).

Furthermore it can be seen that Dit and Qf follow the same trend (the higher Qf, the higher Dit). For solar cell applications the effect of Dit and Qf are competing with each other. Lower Dit will result in better chemical passivation, while a lower Qf will result in reduced field effect passivation. Good passivation is found for n values above 2.1. However, for the higher n values absorption in the SiNx:H layers becomes limiting, and those layers cannot be applied to solar cells (it will result in lower efficiencies).

Based on this information we have improved the passivating quality by using layers with a gradient in composition (and therefore n). At the Si-SiNx:H interface the layer is more Si rich (higher n) and at the interface with air the layer is more N rich. On completed solar cells a clear improvement in blue response was observed which resulted in an efficiency gain of about 0.2% absolute.

More details can be found in M.W.P.E. Lamers, K.T. Bulter, P.E. Vullum, J.H. Harding, A.W. Weeber, "Characterization of a-SiNx:H layer: Bulk properties, interface with Si and solar cell efficiency", accepted by Physica Status Solidi A, (2012).

Research and development alternative layers for passivation.

Surface passsivating properties can be changed by varying Dit and/or Qf. We aimed to increase Qf for SiNx:H layers for layers with lower n, and thus lower absorption, combined with good bulk passivation. In our case we applied (homogeneous) SiNx;H layers with n below 2.1 and before the actual deposition an NH3 plasma pre-treatment was carried out. With this pre-plasma Qf could be increased to much higher values, and thus to improved surface passivating properties. The higher the temperature the more nitrogen will be introduced in the Si lattice resulting in more defects, and thus higher Qf. This was confirmed by MD (see WP4).

More details can be found in M.W.P.E. Lamers, K.T. Butler, J.H. Harding, A.W. Weeber, "Interface properties of a-SiNx:H/Si to improve surface passivation", Solar Energy Materials & Solar Cells 106, 17-21 (2012). Oral presentation at SiliconPV 2012 (Leuven, Belgium).

Application of improved passivating layers in an industrial environment

SiNx:H layers with a gradient and layers with NH3 plasma pre-treatments were applied to solar cells processed in an industrial environment. In both cases an efficiency gain has been observed. For gradient layers the efficiency gain was about 0.3% absolute, and performing a plasma pre-treatment resulted in a gain of about 0.1% absolute. The improved passivation process will enable both Sunways and Isofoton to improve their cell manufacturing process resulting in better efficiencies.

Relate the modelling results to the experimental ones.

Experimental data of thoroughly characterized SiNx:H layers (high resolution TEM, XPS) were used as input for MD and ab initio Density Functional Theory (DFT) studies. Both MD and DFT show that Qf and Dit can be related to defects and distortions. With DFT it is shown that the K centers are the dominating defects resulting in higher Dit., which will result in higher Qf. SiNx:H layers with lower x will result in an increase of Qf. These results correspond to the experimental ones. More results on DFT studies can be found in WP2.

More results on MD can be found in WP4.

More details will be presented by M.W.P.E. Lamers et al. during the SiliconPV 2013 in Hamelin (so-called extended oral presentation), and will be published in Solar Energy Materials & Solar Cells.

Acknowledgements
In addition to the HiperSol grant from the European 7th Framework programme (Grant No. 228513) we acknowledge the Norwegian NOTUR high-performance computing facilities and the UK's national high-performance computing service HECToR (through USFD's membership of the UK's Materials Chemistry Consortium, which is funded by EPSRC grant EP/F067496) for providing needed supercomputer resources. Significant high performance compute time was also made available on the Vienna Scientific Cluster (VSC).

Potential Impact:

HiperSol is a fundamental project with an impact covering many fields of materials science as well as improvements in processing and properties of silicon solar cells.

4.1.4.1 Scientific impact

The phrase, the interface is the device, first coined by Herbert Kroemer (Nobel Prize Winner for Physics, 2000), is becoming increasing true as nanotechnology advances. However, if the interface is to become the device, then understanding at the atomic scale is essential. Moreover, this nanoscale understanding must then be linked to the other relevant length-scales in the system. The enduring necessity of using models with classical force-fields arises from two factors: modelling an interface requires a large number of atoms and it is always necessary to model a range of interfaces to understand a system. This work demonstrates that it is possible to generate suitable force-fields and use them to construct models of complex hetero-interfaces that can be linked to experiment and device performance. The strategies and methodologies developed here have much wider application than to the specific case of solar cells. For example, the rapidly growing field of adaptive oxide electronics requires the understanding of charge transport mechanisms, particularly at interfaces between interconnects and devices where band alignment influences whether Schottky barriers or ohmic contacts form.

As electronic devices shrink in size, scattering at defects and interfaces plays an increasing role and an atomistic description becomes important, maybe even mandatory. Hence, classical electronic device simulations, which are nowadays usually based on Boltzmann's transport equation, will ultimately be replaced by simulations that take into account the one-electron Schrodinger equation (treating non-interacting electrons) with a suitably parameterized weak interaction between electrons and interactions between the electrons and the lattice.

On the other hand, ab-initio (parameter-free) methods are available aiming to solve the true many electron Schrödinger equation (treating strongly interacting electrons). But the solution of the many electron Schrödinger equation is only possible for very small systems.

Our efforts contribute to the merger between classical electronic device simulation (aimed at macroscopic models containing billion of atoms) and full ab-initio simulations (aimed at few atoms). It aims to bridge this gap addressing systems and models containing typically 100.000 atoms. If we achieve our ambitious goal, we can enduringly change the methods used to simulate electronic devices. This might yield new insight in solar cells, but the methods developed here are broadly applicable to other electronic devices and nanostructures.

One major achievement of HiperSol it that it has been able to address all these three decay mechanisms in one formulation, another achievement is that it could associate numerical values to the formulation under certain assumptions or parameterization relevant for the real device situation. Through HiperSol we could thus put numbers on these processes and could relate those numbers rather closely to the design of the device in terms of materials and geometrical configuration. The understanding this gives, and will give through further extensive application of the derived formulas is a strategic accomplishment of the network which can give future impact, improvement and possible breakthrough in this important technology area.

4.1.4.2 Impact on PV

The insight acquired through the modelling activities can have valuable impact on the choice of future metallization schemes. The results have confirmed our hypothesis that metal transport through glass may be a rate limiting step in the contact formation, and this can be of important assistance when developing improved schemes for screen printing excluding the use of Pb or other unwanted elements in the paste. Also, the microscopic understanding of the electrical conductivity through various interfaces between Ag and Si can have significant impact on future metallization technologies, both those utilizing screen printing and other methods.

The PV industry has developed very fast in recent years in terms of market size and of reduction of cost per watts for the complete PV-system. It is expected that the growth of PV will continue for the next year and the search for implementing new technologies to reduce cost and to increase system efficiency will intensify. The main focus will lie on the replacement of the screen printed aluminium on the rear side of the solar cell for surface passivation by a dielectric layer and the reduction or even replacement of the use of silver for the contact formation. The assessment of these technologies requires a deep understanding of the underlying physical properties. As the project contributed a lot in the understanding passivation metallisation the results have the potential to help decision takers in PV-industry to decide for the investment in the appropriate technology.

At the industry-scale experiments at Isofoton on shallow low-doped emitters based on results from WP5, an improvement in the efficiency could be shown, essentially due to the reduction in superficial recombination, above all in the emitter. With these new cells, the efficiency over the current cells is increased by a factor of 3.6%, with the process intervals being sufficiently large, which we consider to be an important result.

4.1.4.3 Dissemination activities and exploitation

The dissemination activities for WP1 were publications in the academic literature and conference presentations. Exploitation is in conjunction with other work packages that used results from this one and is discussed below. At the university of Sheffield, a postdoc (Keith Butler) was funded by the HiperSol project and has applied a range of simulation methods to problems in photovoltaics. He will continue to work in this area. An MSc student (Tong Long) also did his project in the area of interfaces in solar cells.

As for WP1, the dissemination activities for WP2 were mainly publication in the peer-reviewed academic literature, and several presentations at international conferences. In addition, an appreciably part of the work at University of Vienna was performed by the PhD-student Leif-Eric Hintzsche, who will defend his thesis at the beginning of 2014. Furthermore, all algorithmic development within WP2 has been absorbed into the Vienna Ab-initio Simulation Package (VASP). VASP is a very prominent software package within the computational materials science community, with more than 2000 license holders world-wide. As such, the progress and algorithmic developments on the ab-initio side of WP2 of the HiperSol project will be directly available to a large and diverse part of the computational materials science community.

SINTEF educated two master students in WP3; Dan Michael Olsen Heggo and Astrid Marie Flattum Muggerud. They have achieved a broad overview of solar cell technology in addition to detailed scientific competence within DFT calculations and TEM characterization. Also, Espen Flage-Larsen worked as a postdoc at SINTEF, funded by the HiperSol project. He is now permanently employed in SINTEF, and is attached to several new and relevant projects.

At ECN internships of one bachelor student (Bart Teussink from Fontys University of Applied Sciences) and one master (Le Thang Nam from the Technical University of Munich and Nanyang Technological University) student were carried out. Le Thang Nam performed detailed characterization on passivating layers using FTIR, Kelvin Probe measurements, CV MIS and Spectroscopic Ellipsometry. Bart Teussink carried out process optimization on different passivating layers applied by PECVD (silicon oxide, silicon nitride, stack layers, etc.). With these studies more fundamental knowledge on the physical properties of the layers with respect to the passivating quality was gained. PhD student Machteld Lamers will finish her PhD thesis in 2013. The main part of her thesis, which will be made available in the public domain, will contain R&D results obtained in the HiperSol project. Several papers (a large part of these papers were written together with partners) have been published already. Together with industry partners Sunways and Isofoton improved processes that were developed based on the HiperSol results were evaluated and an efficiency gain was observed. ECN will use (or actually is already using) these improved processes in its baseline processing, and also in future processing schemes for high efficiency solar cells.

At ISC Konstanz the PhD-student Enrique Cabrera was recruited for the HiperSol project, generating a new doctorate, with a thesis submitted in the field of solar cell metallisation. This scientist is a valuable project contribution for both scientific fields in need of highly educated and trained researchers and for an industry sector in a process of rapid growth. His thesis produced in the HiperSol project will be made available in the public domain.

Isofoton have worked closely together with ISC and ECN in preparing and analyzing samples from industrial processes. Nitridation process for passivation improvement has been investigated, and the contacting for low resistivity emitter has been improved. Isofoton industrial solar cell efficiency has increased about 5.7% from HiperSol project beginning and the manufacturing cost has been reduced about 5.4%.

Dissemination of the network results have occurred through user contact, conferences and through normal academic channels. At KTH HiperSol results have been ventilated and discussed in the forum of the recently inaugurated research centre JINGLE - Joint institute of Nanotechnology for Global Energy, where Hans Ågren is director, and during the kick-off meeting of that centre in May 3-5, 2012, where a session dedicated to solar energy was included. Network results and the network as such have also been connected to or discussed with respect to other energy initiatives at KTH, n.b.

-The KTH Platform for energy research.
-The common KTH - UU energy consortium STANDUP, funded by the government strategic initiative, and with Escience aspects to eSSENCE and SeRC, the two strategic e-science initiatives in Sweden.
-The KTH platform and STANDUP connect to solar cell constellations in EIT energy, the European Institute of Technology. Here HiperSol has played a non-negligible role.
-The HiperSol work has been conducted in line with the KTH policy of strengthened international collaboration, as exemplified by the agreement between KTH and the China Scholarship Council for student and researcher exchange, in which energy research has a central role. A Chinese senior as well as a PhD student has been enrolled in HiperSol as results of this exchange.

List of Websites:

The HiperSol project has an open website available on http://www.sintef.no/Projectweb/HiperSol/ and http://cordis.europa.eu/projects/rcn/92605_en.html On these, information about the project vision, goals, consortium publications and events are published. The coordinating organisation was SINTEF, and the coordinator was Jesper Friis (jesper.friis@sintef.no +47-98230458). The logo of the project is shown below.

HiperSol consortium

The HiperSol project was executed by 8 partners from 7 European countries. The involved organisations are listed below:

Research institutes
Stiftelsen SINTEF, Norway
Contact person: Jesper Friis
E-mail: jesper.friis@sintef.no

Stichting Energieonderzek Centrum Nederland (ECN), the Netherlands
Contact person: Arthur Weeber
E-mail: weeber@ecn.nl

International Solar Energy Researchcenter Konstanz (ISC), Germany
Contact person: Sara Olibet
E-mail: sara.olibet@isc-konstanz.de

Industrial partners
Sunways Aktiengesellschaft, Germany
Contact person: Daniel Reinke
E-mail: daniel.reinke@sunways.de

Isofoton, Spain
Contact person: Miguel Ángel Vázquez
E-mail: m.vazquez@isofoton.com

Universities
Universitat Wien, Austria
Contact person: Georg Kresse
E-mail: georg.kresse@univie.ac.at

The University of Sheffield
Contact person: John Harding
E-mail: j.harding@sheffield.ac.uk

KTH (Kungliga Tekniska Högskolan), Sweden
Contact person: Hans Ågren
E-mail: hagren@kth.se