3.2 Loss Mechanisms of Solar Cells
3.2.1 Series Resistance Losses
The series resistance losses,RS[Ωcm2] can be dominant for the reduced solar cell performance by limiting the output power of the solar cell device. The totalRS is given by all parasitic ohmic losses as found throughout the solar device, which increase the resistance of the current transport, as shown in Figure 3.1 [63]. Its value is given by:
whereRi represents each component of resistance.R1is the contact resistance between the fully covered Al rear layer and thep-Si bulk. Due to the high series resistance of the bulk material and the large covered area, its value has a non-measurable influence on the total current-voltage characteristic and is generally
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negligible [64]. R2 is given by the doping of the bulk material. R3, one of the main contributors toRS, is the sheet resistance of the emitter and depends on the emitter profile characteristics (i.e. doping concentration, thickness).R4is given by the contact resistivity. R5andR6represent the resistance of the silver finger grid contacts and busbars, and their values depend on many factors as the paste properties (glass and silver composition) and deposition method (firing profile and geometry).
High series resistance mostly affects the FF of the solar cell. The maximum is reached when RS→ 0 (ideal case), and decreases with increasing series resistance. JSC is also affected byRS, decreasing its value more than 8 mA/cm2 whenRSincreases to values up to 20Ωcm2[65].RSvalues of standard industrial solar cells are in the range of 0.5-1Ωcm2.
Shunt Resistance
The shunt resistance losses are caused by short-circuits in solar cell devices.
The shunt resistance, also called parallel resistance (RP), is measured inΩcm2. The most affected variable is the FF of the solar cell which achieves its maximum whenRP→ ∞, and decreases with decreasing shunt resistance. The open-circuit voltage is also affected, reducing its value by more than 300 mV withRP values as low as 10Ωcm2 [65]. Thus, for good solar cell performance,RP needs to be maximized (values in the range of 104Ωcm2are required).
Bulk Resistivity
The conductivity, σ, of a semiconductor with electrons and holes as charge carriers, is represented by the sum of the product of the carrier concentrations (n,
Figure 3.1: Different contributions to total series resistance loss in a solar cell device, after reference [63].
3.2. Loss Mechanisms of Solar Cells 27
p) with their mobilities (µn,µp), and is given by:
σ=q(µnn+µpp)=1
ρ (3.10)
Its value increases by several orders of magnitude when the doping concentra-tion in the bulk material is increased, and under illuminaconcentra-tion due to the increase of free net charge carriers [52]. ρ [Ω-cm] is the resistivity of the material. The mobility of charge carriers is variable and depends on the diffusion coefficient in presence of a concentration gradient of defects [52, 66])||, and can therefore also affect the material resistivity.
Ohmic Contact
Contact losses are supposed to only faintly disturb the device performance.
Therefore, in order to transport the photocurrent out of the semiconductor with minimal losses, a negligible metal-semiconductor contact resistance, which shows ohmic behavior, is required [64, 67]. Ohmic contacts obey the fundamental requirements of Ohm’s law within a large voltage range [64].
Ohmic contacts are achieved by high doping concentrations of the silicon and, according to the Schottky theory (see reference [68]), by low barrier heights or small barrier widths to the metal. In a solar cell device this is an important topic since two metal-semiconductor junctions are found in direct contact to the cell structure: at the front, crystalline silver particles contact the emitter, and at the rear, an aluminum-silicon (Al-Si) eutectic is found. Therefore the most practical technique in photovoltaics to achieve high performance contacts is to deposit the metal onto a highly doped semiconductor, as already shown by Cabreraet al.[69].
Low-resistance ohmic contacts at the rear side of industrial solar cell structures are a result of the interdiffusion between Al and Si, which takes place at the local contact interface [70]. However, the interaction between Al and Si (their interdiffusion), is not homogeneously distributed at the interface over the contact area [71]. This phenomenon will be discussed in more details in chapter 6.
The total contact resistance, RC, can be obtained by dividing the contact resistivity value,ρc, by the contact areaA. It has the unit Ohm (Ω) and is given by the following equation [52]:
RC=ρc
A (3.11)
||The mobility is proportional to the diffusivity,D, divided by the thermal voltage,kT/q(Einstein relationships).
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Contact Resistivity
As defined by Schroder [72], the specific contact resistance,ρc, is a theoretical quantity which refers to the metal-semiconductor interface only. It is defined as the reciprocal of the derivative of current density with respect to voltage (see equation 3.12). It has the unit mΩcm2, and characterizes the contact independent of its area [63]**. The solution of equation 3.12 is approximated by physical regimes, depending on doping and temperature, known as: thermionic emission (TE) for lowly doped bulk material, thermionic field/emission (TFE) for intermediate range, and tun-neling for higher doping concentrations. Due to these effects this parameter is actually not measurable [72].
For solar cells, this parameter is approximately determined by the Transmission Line Model (TLM, see next section). It is important to mention that the TLM method has been widely used for measuring the contact resistance of Ag lines alloyed on homogeneouslyn+-doped emitter layer (sheet resistance of the emitter constant).
Thus, there exists no generalization of the TLM method for measuring Al contact, where the sheet resistance is not constant due to the presence of the highly p+-doped layer (local BSF) underneath the Al lines. Nevertheless, results will be shown for the contact resistivity by TLM approach of aluminum lines on a dielectric layer and forming an ohmic contact to ap-type Si polished surface, assuming that the entire contact length contributes to current transfer [63].
For solar cell devices the interpretation ofρcis of strong importance to under-stand the performance of real contacts. It is very useful when comparing contacts of different sizes, to give information about the quality of the metal-semiconductor contact. Berger [73] and later also Schroder and Meier [63] have given useful definitions and explanations of many methods to determine the contact resistivity.
They have shown significant measurement techniques for contact resistivity of Al-Si contacts depending on surface doping concentration. Also a spatial variation of the contact resistivity was presented and explained by taking into account the inhomogeneity of the contacts. A variation of the contact resistivity was found from the middle to the edges of the contact area. This is also valid for the investigation presented in this thesis: it will be shown that the contact resistivity depends on the homogeneity of the Al-Si alloy formation.
**The contact resistance is normalized by the area.
3.2. Loss Mechanisms of Solar Cells 29
Transmission Line Model
One method to determine the contact resistivity and the sheet resistance of the semiconductor beneath the contact from the geometry of planar contacts, is called the Transmission Line Model (TLM). For deep details about the measuring method, examples and results, see for instance reference [63, 73, 74].
According to Schroder [63], the current transfer from semiconductor to metal takes place on the transfer length,LT. It is clear from the equation 3.13 thatLT
decreases with increasing sheet resistance (RSH) of the diffused layer, normally the phosphorous emitter. The two extremes are: (a) when ρc is too low, the current transfer will be located near the edge of the metal [63] (LT is small); and (b) whenρc is high orRSHlow (LT is large, but not larger than the contact width).
Nevertheless, it will be shown in this thesis that real contacts present uniformities on the metal-semiconductor interface, where the effective area may vary from the actual area [63].
Thin layers as the phosphorus-diffused emitter on the top of the solar cell, are characterized by their sheet resistanceRSH[Ω/]. Its value is normally charac-terized by the four-point-probe method that has been used since the 50’s [75].
Generally, the sheet resistance can be obtained by integrating the emitter profile of the phosphorous diffused layer. For a non-uniformly doped layer of thickness W, its value is given by:
RSH= 1 qRW
x
ρ(x)1 d x (3.14)
Equation 3.14 shows that the sheet resistance is actually determined by the resistivity profile of the diffused layer, moving along thex coordinate from the surface (at x = 0) into the thin layer, and can be characterized by removing thin layers one by one and measuring the resistivity of the bulk, ρ [72]. This measuring technique is based on the electrochemical capacitance-voltage (ECV) measurement, which allows the determination of the doping concentration peak close to the surface of the thin doped layer. The higher the concentrationNAof phosphorus (P) dopant atoms is, the lower will be the sheet resistance,RSH, of the P-diffused emitter.
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