Efficiency limiting factors
The objective of a solar cell is to absorb as many photons from the incoming solar power as possible, and to allow the collection of the maximum amount of photo-generated electron-hole pairs at each of its terminals. The maximum theoretical efficiency for a single junction solar cell based on a semiconductor absorber material of bandgap energy is mainly limited by photons of too low energy to be absorbed (ℎ < ) and thermalization of photons with too high energy (ℎ > ). Advanced concepts  are needed to tackle those limitations, and the maximum theoretical efficiency has been estimated to be 29.43% for conventional silicon solar cells .
The remaining “non-ideal” losses ruling the efficiency of a solar cell include electrical losses (recombination, shunt and series resistances), and optical losses (parasitic absorption or unabsorbed photons due to transmission or reflection).
The higher the excess density of charge, the stronger the separation of the quasi-Fermi energy levels (QFL) will be. The voltage resulting from the QFL splitting is referred to as the implied-voltage
When charge collection is ideal, the implied voltage is the external voltage. However, when non-ideal charge collection occurs at the electron or hole contacts, i.e. when contacts are highly recombining or resistive, the QFL splitting is reduced near the contacts, and from Eq. 6 the external voltage diminishes .
• In open circuit conditions, considering perfect charge collection, the open-circuit implied-Voltage corresponds to . Therefore the main limiting factor of in solar cells is recombination.
• In short circuit conditions, for high to moderate cell efficiencies where = , the current is not affected by resistive effects nor recombination. is then only limited by optical effects.
• At maximum power point, both effective lifetime and charge collection are of importance, so resistive effects will intervene. is affected by series resistance, shunt resistance, and recombination losses.
Generation and recombination refer to the processes in which free electron-hole pairs are created and annihilated: respectively, an electron in the valence band is either excited to the conduction band, or transfers back energy to transition back to the valence band. This can happen through different channels, through the absorption and emission of phonons and photons.
At thermal equilibrium the generation rate ( 0) is equal to the recombination rate ( 0), leading to constant charge density of holes and electrons. Once excited, an electron is in an unstable state, where it will rapidly transfer back its energy through the emission of other particles. This happens through two channels:
1- Thermalization: Intra-band multiple emissions of low-energy phonons. This is the fastest process, occurring in time scales of the order of 10−12 seconds .
2- Recombination. This is a much slower process, occurring in time scales of the order of several milliseconds in high quality crystalline silicon.
In metals, where the energy states form a continuum, the excess energy of an excited electron is predominantly transferred through thermalization, leading to the quick de-excitation of said electron and production of heat, whereas in semi-conductors, both processes are of importance. When a photon of energy higher than is absorbed, thermalization will occur first, decreasing the electron energy to the bottom of : as thermalization can only induce low energy steps, it cannot overcome . In a second time, recombination takes place and the electron is de-excited to the valence band. There are several mechanisms that lead to the recombination of charge carriers. Among them, we can distinguish between intrinsic and extrinsic recombination. Intrinsic recombination is related to inherent bulk material properties, meaning it cannot be avoided whatever the optimization, whereas extrinsic recombination is related to the impact of defects. When several recombination processes are in competition, the effective lifetime is the reciprocal sum of all given phenomena limited lifetimes: 1 = ∑ 1 Eq. 16
In principle, any extrinsic recombination is avoidable and can be tackled either by removing defects or by passivating them. Passivation is the process of reducing recombination through the reduction of the activity of these defects. The most common example is the hydrogenation of surface defects, where through the incorporation of hydrogen, dangling bonds will form links with hydrogen, strongly reducing their recombination rate. Passivation can be applied to the bulk of a material, notably through hydrogenation, but most processes involve high temperatures usually not compatible with low-temperature processed cells, such as SHJ cells .
Radiative recombination is the direct recombination of an electron-hole pair through the emission of a photon. In indirect semi-conductors such as silicon, radiative recombination is mediated by phonons, which makes it fare less likely to happen. The conduction band electron transits to the valence band by emitting a photon of energy very close to .
The radiative-limited lifetime ( ) only varies as a function of carrier density and can be expressed such as : = 1 Eq. 17 ( 0 + 0) + ∆ Where is a constant, which depends on the band structure of the material. For silicon = 4.73 ∗ 10−15 3/ at room temperature .
Auger recombination is based on a three-particle interaction: the energy from an electron-hole pair recombining is transferred to another free charge carrier through collision; or additionally through Coulomb interaction of free charge carriers in said Coulomb-enhanced Auger recombination. The process either involves two electrons and a hole (eeh process) or two holes and an electron (ehh process).
Richter et al. proposed a general parametrization of intrinsic recombination (Auger and radiative) of both n and p-type c-Si in 2012 . Recently a more accurate model for n-type c-Si was proposed by Veith-Wolf et al. , while for p-type Richter’s model is still considered as the state-of-the-art.
Defects introduced in a semi-conductor lattice, such as metallic impurities or crystallographic defects, induce parasitic energy states in the band structure. Electrons and holes can transit to these energy levels, and recombine or be generated in them. The formalism proposed by Shockley, Read and Hall ,  to describe this phenomenon is referred to as SRH recombination. In usual cases of no trapping (∆ = ∆ ) and single defect level, the SRH-limited lifetime reads
In the energy range where photons can be absorbed by the absorber, i.e. when their energy is higher than the bandgap energy of the absorber material, there is still some non-ideal optical losses that affect efficiency, mostly through a diminution. Mechanisms for optical losses are (see Figure 10):
(a) Reflected light at the front electrodes, at the front surface or at interfaces
(b) Un-absorbed photons due to the finite absorbance and thickness of the absorber material, which lead to non-ideal optical confinement.
(c) Parasitic absorption, or absorption that does not participate to the current flow, such as free carrier absorption where photons are absorbed by already excited electrons, or generation of electron-hole pairs in locations where they very quickly recombine (e.g. antireflective coatings).
From their generation in the absorber to their collection in the external circuit, charge carriers experience resistive effects as they cross materials with finite resistivity, interfaces and contacts. Indeed, this generates power losses due to Joule effect. Figure 11 illustrates the path of an electron hole pair across the cell.
In the frame of the diode(s) model, the series resistance, denoted as represents the lumped effect of all resistive effects through the cell, i.e. the conduction through all layers, interfaces, contacts and metallizations typically has a very low impact on for solar cells of decent efficiencies, but can have a significant effect on FF.
A single value of would only exist if the cell was homogeneous, however due to spatial heterogeneity, is a function of the voltage . For this reason is mostly reported at maximum power point to be representative of the functioning point of the cell.
Shunt resistance stems from photo-generated current flowing through an alternate path than the external load, lowering the built-in potential through the device. For example, shunts can arise from edge leakage current if no proper edge isolation is carried out .
Shunt resistance is usually high (i.e. low current flow through the shunt paths) in high efficiency silicon solar cells  and we will mostly overlook it in this work.
Photovoltaic solar cell technologies
Mainstream silicon PV cells
The vast majority of the solar cells produced up to 2020 are based on silicon material . Among the silicon cells, two technologies form the mainstream with more than 95% combined market share as of 2018 , the Aluminum-Back Surface Field (Al-BSF) and Passivated Emitter Rear Contact (PERC) cells.
The Al-BSF structure (see Figure 12) is the most-simple one, based on a P-type absorber. The front surface consists of a highly n-doped emitter, formed using phosphorous diffusion on the front side with an upper layer of anti-reflection coating, and fire-through metallization. The rear side features a full area aluminum contact, which upon annealing at high temperatures, enables the formation of an AlSi alloy which acts as back surface field (BSF). It allows efficiencies of 19-20 % in production as of 2018 .
The more limiting factor of the structure is its back contact, which is, despite the BSF, the major source of losses due to recombination. The PERC structure (see Figure 13) proposed in 1989 41] is an evolution of the Al-BSF, which features the same front side, but a more complex rear side. To decrease recombination at the rear, a passivation stack is deposited on the c-Si at the rear contact, typically aluminum oxide and silicon nitride. However theses stacks cannot be directly used as contacts as they are insulating materials, so the contact is made through the passivation oxides, and there is still a direct c-Si(p+)/Al direct local contact. This structure enables higher efficiencies than the Al-BSF, at 20-22% in production lines .
Due to manufacturing costs reduction , and monocrystalline wafer price drop , the total cost of PV systems has dropped over the last decade (~-66% in 6 years ). This makes high-efficiency devices more and more cost-efficient. For these reasons, forecasts predict that the less efficient solar cell concepts such as the Al-BSF technology may soon disappear for the profit of PERC and more evolved efficient architectures.
High efficiency silicon solar cells
The main problem with standard PV cell technology is their highly recombinative metal contact , thus new approaches to increase the efficiency of single junction silicon cells rely on so-called “passivating contacts”. Passivating contact solar cells employ thin passivating layers in between the c-Si absorber and the metal contacts to play simultaneously contacting and passivating roles. The two predominant technologies for passivating contacts are the poly-silicon based approaches (e.g. TOPCon , POLO ) and the silicon heterojunction solar cell (SHJ).
The TOPCon structure employs a diffused emitter at the front surface, and a very thin (<20 Å) tunnel oxide combined with a poly-Si layer at the rear surface  (see Figure 15). The tunnel oxide passivates very effectively dangling bonds at the c-Si surface, and if thin enough, allows for efficient transport (either by tunneling or through “pinholes” conduction ) and therefore generates no important transport losses. The poly-Si, which is typically highly doped, is a very good selective contact thanks to its high conductivity and to the band bending it induces in the absorber. It however leads to substantial free carrier absorption, reason why it is usually put at the rear surface, and complicates its integration in both side poly-Si based contacts devices .
Historically, the first passivating contact structure that reached high efficiencies was the SHJ cell, but we will discuss it in the next chapter.
Additionally, both the TOPCon and the SHJ concepts have been derived in back-contact architectures, which enables better due to the absence of shading at the front surface and have reached very high efficiencies , .
To achieve even higher efficiencies in the near-future, beyond that of the theoretical limit of single-junction c-Si cells, silicon-based tandem solar cells are a very promising approach which still needs to be demonstrated at the production scale .
Objectives of this work
In this chapter, we have seen that PV energy is forecasted to be a very important source of electricity at the global scale in the near future as it provides low-carbon non-fossil energy. We have then discussed the working principles of solar cells, their main figures of merit, and the main factors limiting the efficiency of solar cells. Finally, we have discussed the main PV cell technologies in the market today, and the emerging trend for passivating contact designs enabling to reach high efficiencies that are expected to dominate the market in the near future.
This work addresses the resistive losses in silicon heterojunction solar cells. In particular, it focuses on current transport through the interfaces and contacts of the SHJ cell and how we can characterize, model, and improve it.
In Chapter 2, State-of-the-art, we will review the literature on resistive losses in silicon heterojunction solar cells. First, we will discuss the SHJ device and its pros and cons. Then we will address the measurement methods for series and contact resistances. Subsequently, we will break down the different contributions of the series resistance and see how it can be calculated from these various inputs. Finally, we will examine charge transport in SHJ cells.
In Chapter 3, Characterization & fabrication processes, we will describe the fabrication of various samples and the main characterization methods employed during this work. We will also discuss the details of our numerical simulations.
In Chapter 4, Development of methods to measure contact resistance in SHJ cells, we will discuss our approach for the fabrication of samples to measure accurately the contact resistance of the Ag/ITO contact and the electron and hole contact stacks.
In Chapter 5, Impact of varying the fabrication process on SHJ cells and on the electron contact, we will review the various studies that we conducted to understand the influence of fabrication settings on the series and contact resistances in the device.
In Chapter 6, Impact of varying measurement conditions on SHJ cells and contacts, we will discuss how temperature and illumination influence efficiency, series and contact resistances. We will also discuss what can be learned from those regarding the transport mechanisms in SHJ cells.
In Chapter 7, Resistive power loss analysis for bifacial SHJ cells, we will derive a model to break down the series resistance of SHJ cells such as produced at CEA into different contributions, and identify the main resistive losses. We will then propose pathways for loss mitigation in such devices.
Table of contents :
1 General introduction
1.1 Photovoltaics in the energy production
1.2 Photovoltaic solar cells
1.2.1 Photovoltaic cells’ working principle
1.2.2 Basics of PV solar cells
1.2.3 Efficiency limiting factors
1.2.4 Photovoltaic solar cell technologies
1.3 Objectives of this work
2.1 Silicon heterojunction solar cells
2.2 Measuring series resistance
2.3 Measuring contact resistance
2.3.1 The transfer length method (TLM)
2.3.2 Transfer length model for a two-layer system
2.4 Resistive power loss analysis
2.5 Charge transport in SHJ cells
2.5.1 TCO/Ag contact
2.5.2 Transport through the interfaces of SHJ cells
2.5.3 Lateral transport in SHJ cells
2.5.4 Cell inhomogeneity and impact on transport
2.6 Chapter outlook
3 Characterization & fabrication processes
3.1 Fabrication of SHJ cells at CEA industrial pilot line
3.2 Effective lifetime measurements
3.3 Luminescence techniques for imaging
3.5 I-V measurements
3.6 Review of the different 𝑅𝑆 measurement methods
3.7 Numerical simulation on Silvaco Atlas
3.7.1 Simulation parameters
3.7.2 Simulating solar cell performance
3.7.3 Simulating TLM samples
3.8 Contact resistance measurement
3.8.1 Improving the measurement precision of contact resistivity
3.8.2 Technical implementation of the TLM
3.9 Chapter outlook
4 Development of methods to measure contact resistance in SHJ cells
4.1 Measuring the ITO sheet resistance and ITO/Ag contact with high fidelity to SHJ structure
4.1.1 4-point probe measurement of ITO sheet resistance
4.1.2 Insulating the TCO layer from the c-Si to measure Ag/TCO contact resistance and sheet resistance of the TCO
4.1.3 Simulation of Ag/ITO TLM samples
4.2 Measuring the electron and hole contact layers in SHJ structures
4.2.1 Development of a process for the fabrication of structures for electron and hole contact resistivity measurement
4.2.2 Measurement of the electron and hole contact resistivities
4.2.3 Discussion of the approach
4.3 Chapter outlook
5 Impact of varying the fabrication process on SHJ cells and on the electron contact
5.1 Influence of the c-Si substrate doping
5.1.1 Influence of c-Si doping on J-V parameters
5.1.2 Influence of c-Si doping on effective lifetime
5.1.3 Influence of c-Si doping on the electron contact properties
5.1.4 Analysis of the 𝑅𝑆 variation with c-Si doping
5.2 Integrating alternative TCOs
5.3 Varying the thickness of the front stack layers
5.3.1 ITO thickness
5.3.2 Varying the a-Si:H(i) layer thickness
5.3.3 Varying the a-Si:H(n) layer thickness
5.3.4 Breakdown of the electron contact
5.4 Chapter outlook
6 Impact of varying measurement conditions on SHJ cells and contacts
6.1 Effect of measurement conditions on the determination of the Ag/ITO contact resistance
6.2 Effect of measurement conditions on electron and hole contact resistance
6.2.1 Dependence of c-Si resistivity versus temperature and illumination
6.2.2 Variation of the electron and hole contact resistance with temperature
6.2.3 Variation of the electron and hole contact resistance with illumination
6.3 Chapter outlook
7 Resistive power loss analysis for bifacial SHJ cells
7.1 Lateral transport in SHJ cells
7.1.1 Two-layer TLM with interface and contact resistances
7.1.2 Resistive power loss due to lateral transport
7.2 Comparison of the models with experimental data
7.3 Resistive loss breakdown for a standard CEA SHJ cell
7.4 Impact of the electron and hole contacts on 𝑅𝑆
7.5 Chapter outlook
General conclusion and perspectives
Appendix 1: Demonstration of the transmission line model of the standard TLM
Appendix 2: Demonstration of resistive power loss
Appendix 2 (a): Resistive losses from lateral current in the emitter
Appendix 2 (b): Resistive losses due to the contact:
Appendix 2 (c): Resistive losses from the fingers
Appendix 2 (d): Resistive losses due to busbars
Appendix 2 (e): Resistive losses from transverse current in the bulk c-Si
Appendix 2 (f): Note on the generation hypothesis
Appendix 3: Demonstration of measurement methods of 𝑅𝑆
Appendix 3 (a): Dual light method
Appendix 3 (b): Multi-light method
Appendix 3 (c): Dark-light method
Appendix 3(d): Comparison between Jsc-Voc & J-V curves
Appendix 4: Haschke et al.’s model for power loss analysis