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Physics of solar cells

This part focuses on the classical Si-based PV solar cells, with a p-n junction created by the association of both p- and n-type crystalline Si materials (homo-junction solar cells).

Doping of silicon, the p-n junction

Doping is a defect-engineering technique used to vary the density of electrons and holes in semiconductors. Doping creates n- (electron rich) or p-type (hole rich) materials and is therefore essential to form the p-n junction of solar cells. For the doping procedure, impurity atoms are introduced into an otherwise intrinsic semiconductor. These impurity atoms are classified as donor or acceptor elements.
Regarding Si, donor elements have more valence electrons than the substitutional Si atom they replace (Figure 1.1). Donor elements offer their extra valence electrons to the conduction band, making it n-type.
Acceptor elements have fewer valence electrons than the substitutional Si atom they replace (Figure 1.1). They provide excess holes that increase the hole carrier density of the semiconductor, making it p-type.
Si (element from the group IV of the periodic table) uses group V atoms as donors and group III atoms as acceptors. The Si wafers used by the PV industry are usually p-type, boron (B)-doped. The n-type region is usually created by the high T diffusion of phosphorus (P) atoms.
Figure 1.1 – Schematic of a silicon crystal lattice doped with P and B impurities to produce n-type (left) and p-type (right) semiconductor materials.
Figure 1.2 – Schematic variations of the charge density and the electric field across a p-n junction. A p-n junction diode is formed by joining n-type and p-type semiconductor materials (Figure 1.2). When n- and p-type materials are set into contact, the electrons and holes move to the other side of the junction, leaving behind charges on dopant atom sites, which are fixed in the crystal lattice. Therefore, an electric field Ē is created by these fixed charges (positive ions in the n-type material and negative ions in the p-type material). This region is called the « space charge region » (scr).

Light absorption, carrier photogeneration and collection

A simple conventional solar cell structure is depicted in Figure 1.3. Sunlight is incident from the top, on the front of the solar cell. A metallic grid forms one of the electrical contacts of the diode and allows light to penetrate the semiconductor between the grid lines and thus be absorbed and converted into electrical energy. An antireflective layer between the grid lines increases the amount of light transmitted to the semiconductor. The diode’s other electrical contact is formed by a metallic layer on the back of the solar cell [1].
All electromagnetic radiations, including sunlight, can be viewed as being composed of particles called photons which carry specific amounts of energy determined by the spectral properties of their source. Photons also exhibit a wavelike character with the wavelength (λ), being related to the photon energy (E(λ)) by E(λ) = hc (1.1) where h is Plank’s constant and c is the speed of light.
If the photon is absorbed within the Si material, it has the possibility of exciting an electron from the valence band to the conduction band. A key factor in determining if a photon is absorbed or transmitted is the energy of the photon. Photons entering a semiconductor material can be divided into three groups based on their energy (Eph) compared to that of the semiconductor band gap (EG) [2]:
• Eph < EG Such photons interact only weakly with the semiconductor, passing through it as if it were transparent.
• Eph >≈ EG Such photons have enough energy to create an electron-hole pair and are efficiently absorbed.
• Eph >> EG Such photons are strongly absorbed. However, for photovoltaic applications, the photon energy higher than the band gap is wasted as electrons quickly thermalize back down to the conduction band edges.
In Si, at room temperature, thermal energy is sufficient to instantaneously dissociate the photogenerated electron-hole pair (exciton). If the photon is absorbed within the p-type region of the cell, an excess minority carrier (electron) is created. This electron diffuses within the semiconductor material. If the electron reaches the p-n junction, the carrier is accelerated by the permanent electric field within the space charge region, and is collected by the metal electrodes. However, a number of pitfalls (e.g. recombination on impurity or structural defects) may prevent the photogenerated electron to reach the electrode, thus reducing the efficiency of the conversion process.

Charge carrier diffusion length, lifetime and mobility.

The minority carrier diffusion length (L) is the average distance a carrier can move from the point of generation until it recombines. Thus, L is a key parameter, which strongly governs the PV performances: the higher the L, the higher the PV conversion efficiency (η). L is defined by the following expression: L = Dτ (1.2) where τ is the charge carrier lifetime, which can be seen as the time interval between the photogeneration of a charge carrier, and its recombination. As evoked later in the manuscript (section 1.2.2), τ is a key parameter, which is usually strongly affected by the presence of impurities.
Diffusion coefficient or diffusivity (D) is related to the carrier mobility (µ) via the Einstein relation: D = kT µ (1.3) q where kT/q the thermal voltage (k is the Boltzmann constant, T the temperature and q the elementary charge).
In standard Si materials, µ is mainly governed by the phonons and the substitutional dopants, structural defects are expected to play a minor role.

Forward I-V characteristics under illumination

The illuminated current-voltage (I-V) characteristic of a solar cell is given by the superposition of the dark I-V curve of the solar cell diode with the light-generated current. An example of illuminated I-V curve is shown in Figure 1.4, with the key PV parameters represented.
The short circuit current (Isc) is the current delivered by the cell when the potential difference across the cell is zero. The Isc depends on various factors which are described below:
• the area of the solar cell. In order to compare the performances of solar cells with difference areas, the short-circuit current density (Jsc in A/cm2) is commonly presented, rather than the Isc;
• the number of incident photons (i.e., the power of the incident light source);
• the spectrum of the incident light. For most solar cell measurements, use is made of the standardized to the AM1.5 spectrum;
• the optical properties (absorption and reflection) of the solar cell;
• and last but not least, the collection probability of the solar cell, which depends chiefly on the surface passivation and the carrier lifetime or minority carrier diffusion length in the base (p-type region in Fig. 1.3) and the emitter (n-type region in Fig. 1.3). Therefore as τ and L are usually affected by the presence of metal impurities, high metal impurity contents are generally responsible for low Isc.
The open-circuit voltage (Voc) is the maximum voltage delivered by corresponding to a zero current. The Voc can be estimated by the following equation: nkT IL Voc = ln +1 q I0 the cell, (1.4)
The above equation shows that Voc depends on the saturation current (I0) of the solar cell and the light-generated current (IL). I0 is a parameter varying on orders of magnitude from one PV device to another. I0 depends on carrier recombination in the solar cell (bulk and surface recombinations). Particularly, the lower the L, the higher the I0. Therefore, Voc can significantly be affected by large amounts of metal impurities.
The Isc and the Voc are the maximum current and voltage that a solar cell can deliver. However, at both of these operating points, the electric power from the solar cell is zero. The fill factor (FF) is a parameter which, in conjunction with Voc and Isc, determines the maximum electric power (Pmax) that can be delivered by a solar cell. The FF is defined as the ratio of Pmax to the Voc×Isc product: FF = P = Vmp Imp (1.5) where Vmp and Imp are the voltage and current respectively, associated with the point of maximum power.
FF is influenced by several mechanisms. Firstly the parasitic resistive losses and the shunt issues strongly affect FF. The shunt issues can be due to non-optimized metallization processes, but also to the presence of conductive precipitates (e.g. metal silicides) crossing the p-n junction. FF also depends on carrier recombination within the space charge region. Therefore the presence of high amounts of metal impurities within the space charge region can detrimentally affect the FF. Also high increases of the charge carrier lifetime with the excess carrier density can significantly decrease FF, as explained in [4]. Indeed, according to Macdonald et al. [4], the FF reveals how the voltage changes from open-circuit to maximum power in comparison to the ‘ideal’ case. In this ideal case the lifetime is assumed constant at all voltages, or in other words, injection-level independent. If the lifetime changes with injection-level, an altered fill factor will result.
Figure 1.5 – Solar cell output current (red line) and power (blue line) versus the applied voltage. This figure presents also the key PV parameters: the Voc and Isc points, as well as the maximum power point (Vmp, Imp).
The conversion efficiency (η) is the most commonly used parameter to compare the performances of different solar cells. η is determined as the fraction of incident power (Pin) which is converted to electricity and is defined by: η = Pmax = Voc I sc FF (1.6) Pin Pin η depends on the spectrum and intensity of the incident sunlight and the temperature of the solar cell. Therefore, conditions under which η is measured must be carefully controlled in order to compare the performance of one device to another. Terrestrial solar cells are measured under AM1.5 conditions and at a temperature of 25 °C.

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Reverse I-V characteristics, junction hard breakdown voltage

Another important parameter for solar cells is the absolute value of the junction hard breakdown voltage (Vbd). The junction hard breakdown is related to the part of the reverse I–V curve where the current suddenly sharply increases upon lowering the reverse bias. This breakdown type governs the global I–V curve at high reverse bias (in absolute values). Vbd is a crucial parameter since it governs the long-term performances of a solar module. Indeed when a cell within the module is shaded, it can be reversely biased and act as a receptor, inducing a loss of the global power of the panel. If the reverse bias is close to Vbd, large currents can locally flow through the cell leading to thermal damages. These issues can be mitigated by the presence of protection diodes [5]. However they are only efficient in standard modules (60 cells) provided that Vbd is higher than about 12 V. For the base doping levels usually used for the solar cell fabrication (lower than 1017 cm-3), the junction hard breakdown is usually governed by the avalanche effect (impact ionization) [6]. Figure 1.6 presents the mechanism which leads to avalanche breakdown. In reversely-biased p-n junctions, large electric fields accelerate free carriers in the space charge region. When the electric field is sufficiently strong (of the order of 105, the kinetic energy gained by the carriers is high enough to knock valence electrons out of their state and lift them to the conduction band (impact ionization) when in turn they may be accelerated and participate in the multiplication process. When the breakdown is governed by the avalanche effect, the Vbd values increase as the T increases (for high T the accelerated free carriers within the scr lose part of their energy to optical phonons).
Figure 1.6 – Schematics of the avalanche breakdown process. Electrons in the conduction band are accelerated by the large electric field in the reversely-biased p-n junction. If the carrier kinetic energy is high enough, valence electrons can be transferred to the conduction band, taking part in the electron multiplication process.
An approximate empirical universal expression for Vbd calculation (in volts) can be given as follows, for abrupt junction [6]: ≅ 60� /1.1�3/2( /1016)−3/4 (1.7) where Eg is the band gap (eV), and NB is the background doping density (cm-3).

Charge carrier transport properties, recombination and trapping

Charge carrier mobility, silicon resistivity

µ determines the manner charge carriers move through a semiconductor under an external electric field (E). In a semiconductor, µ can be expressed as [7]: µ = ν d (1.8) E where νd is the drift velocity of the charge carrier (i.e., the average velocity increase of the carrier between two consecutive collisions caused by the electric field).
Electrons and holes in a semiconductor behave much like free particles of the same electronic charge with effective masses. Thus, they are subject to the classical processes of drift and diffusion. Drift is a charged particle’s response to an applied electric field.
Different carrier scattering mechanisms influence µ in Si materials, e.g. lattice (phonon) scattering, defect scattering (extended crystal defects, ionized or neutral impurities), and carrier-carrier scattering. The overall carrier mobility (µtot) that takes into account all these different mechanisms can be approximated through Matthiessen’s rule: 1 n 1 = ∑ (1.9) µtot µi i−1 where µi is the mobility related to the i-th scattering mechanism. The balance between these mechanisms varies with temperature, and it has been shown that the dominant scattering mechanisms in a non-compensated Si material at room temperature are ionized impurity scattering and lattice scattering. The scattering of charge carriers by phonons and ionized impurities is in principle well covered in classical µ models [8].
The bulk resistivity (ρ) of the Si wafers has strong influences on the performances of the PV device. For crystalline Si, the optimum bulk ρ has been empirically determined to be approximately 1 Ω.cm, a value which balances the requirements for carrier recombination, operating voltage of the solar cell and surface passivation [9]. The resistivity (ρ) is defined as the proportionality constant between the electric field and the current density.
For semiconductors with both electrons and holes as carriers, we obtain: = 1 = 1 (1.10) where σ is the material conductivity, µn and µp the electron and hole µ; and n and p the electron and hole densities, respectively.
Consequently for n-type Si: 1 and for p-type Si: 1 ρ ≅ ρ ≅ (1.11) qµn n qµ p p
Notice that in a B-doped material, with a standard ρ equal to 1 Ω.cm, p is approximately equal to the B concentration ([B]). Consequently, from the ρ (usually determined by the four point probe method), the dopant density can be computed.

Carrier recombination and trapping

There are three fundamental recombination mechanisms in semiconductors which are necessarily present to some extent in any sample: radiative, Auger and multi-phonon recombination (known as Shockley-Read-Hall (SRH)), illustrated on Figure 1.7 [4, 6]. These mechanisms differ in the way the excess carrier energy is dispersed throughout the recombination process, being mediated by photons, carriers and phonons respectively.
Radiative recombination is simply the process of optical absorption occurring in reverse. Consequently, in radiative recombination, the excess energy is emitted as a photon as illustrated in Figure 1.7. The radiative recombination rate (Urad) depends jointly on both the electron and hole concentrations, since one of each is required for the process to occur [7].

Table of contents :

Introduction – Bibliography
1.1 Physics of solar cells
1.1.1. Doping of silicon, the p-n junction
1.1.2. Light absorption, carrier photogeneration and collection
1.1.3. Charge carrier diffusion length, lifetime and mobility.
1.1.4. Forward I-V characteristics under illumination
1.1.5. Reverse I-V characteristics, junction hard breakdown voltage
1.2 Charge carrier transport properties, recombination and trapping
1.2.1 Charge carrier mobility, silicon resistivity
1.2.2 Carrier recombination and trapping
1.3 Si production: from silica to virtually pure Si
1.3.1 Carbothermic reduction
1.3.2 Purification by chemical routes, the Siemens process
1.3.3 Purification by metallurgical routes: focus on the PHOTOSIL process
1.4 Crystallization of Silicon
1.4.1 Czochralski growth
1.4.2 Multicrystalline ingot casting
1.4.3 Segregation of impurities
1.5 Main crystal defects – Impact on the PV performances
1.5.1 Grain boundaries and dislocations
1.5.2 Light elements: C, N and O
1.5.3 Metal impurities in Si
1.6 Solar cell fabrication
1.7 External Gettering effect
1.8 Bulk Hydrogenation effects
Chapter 1 – Bibliography
2.1 Solubility and diffusivity
2.1.1 Solubility
2.1.2 Diffusivity
2.1.3 Precipitation mechanisms
2.2 Effect on the carrier lifetime
2.1.1 Interstitial Ti
2.1.2 Interstitial Cu
2.1.3 Copper pairs
2.1.4 Copper precipitates
2.1.5 Interactions with hydrogen
2.3 Effect on the PV performances
2.4 Cu-related LID
Chapter 2 – Bibliography
3.1 Description of the studied ingots
3.1.1 Czochralski ingots
3.1.2 Multicrystalline Si ingots
3.2 Techniques for the evaluation of the compositional properties
3.2.1 Fourier-transform infrared spectroscopy (FTIR)
3.2.3 DLTS
3.3 Techniques for evaluating the electrical properties
3.3.1 Four-point probe technique for resistivity measurements
3.3.2 Carrier lifetime measurement techniques (μW-PCD and QssPC)
3.4 Techniques for the characterizations of the photovoltaic properties of the solar cells
3.4.1 I-V characteristics
3.4.2 LBIC analyses: determination of the minority carrier diffusion length
3.4.3 Electroluminescence
3.4.4 Aging tests
Chapter 3 – Bibliography
4.1 Compositional properties of the studied wafers
4.2 Resistivity
4.3 Effect of the contaminations on the effective carrier lifetime – Influence of the P-dif step
4.4 Effect of the Si hydrogenation on the electron diffusion length
4.5 Illuminated forward I-V characteristics
4.6 Dark reverse J-V characteristics
4.7 Evolution of the photovoltaic performances under illumination
Chapter 4 – Bibliography
5.1 Compositional properties of the studied wafers
5.2 Resistivity
5.3 Effect of the contaminations on the effective carrier lifetime – Influence of the P-dif step
5.4 Effect of the Si hydrogenation on the electron diffusion length
5.5 Illuminated forward I-V characteristics
5.6 Dark reverse J-V characteristics
5.7 Evolution of the photovoltaic performances under illumination
Chapter 5 – Bibliography
6.1 Experimental details
6.2 Influences of phosphorus-rich layer during rapid annealing step on carrier recombination in mc-Cu
6.3 Influences of phosphorus-rich layer during RTP on carrier trapping in mc-Cu
6.4 Influences of phosphorus-rich layer during rapid annealing step on the stability of carrier lifetime under illumination in mc-Cu
6.5 On the role of Si self-interstitials on the limitation of the metal precipitates dissolution
Chapter 6 – Bibliography


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