SCORPION Solar Cell: Series Reisitance &Shunt Resistance

1.1.1.1 Extracting parameters

As discussed above, the equivalent circuit and corresponding equations are used to evaluate or predict the performance of solar device. However, there are still several unknown parameters waiting for acquisition prior to use, such as serial resistance Rs, parallel resistance Rp, ideal factor n_D, and saturation current I₀. Usually, they are extracted from current-voltage (IV) curve. Figure 1 is an example of IV curve of the architecture ITO/PEDOT/P3HT:PCBM/Al. Several extraction methods are introduced below to discuss their feature and problems.

Figure 1 Current-voltage curve of solar cell with the architecture ITO/PEDOT/P3HT:PCBM/Al

Its J-V characteristics could be expressed by the generalized Shockley equation[31]

(1)

1.1.1.1.1 Reciprocals of slope at two point ^{1, 2}

The fastest estimation method to series resistance and parallel resistance is to use the reciprocals of slope of the output curve under dark conditions at V=0 Volt and V=2 Volt to find the shunt and series resistances respectively as shown in Eqn. (2) and (3). (Sometimes, we use 2 times of V_oc as the shunt resistance point instead of 2 Volt.) It is based on the assumption that the series resistance is small and the shunt resistance is large, i.e. the solar cell has reasonably good properties. Furthermore, the calculation for Rs is only valid if a ‘good’ voltage point is chosen for the slope calculation. In the study of organic solar cells, especially with new materials and varying solar cell architectures, the assumptions of low Rs and high Rp are not strictly valid.³

	(2)
	(3)

1.1.1.1.2 An extensively valid and stable method ⁴

This method has a stable solution and a rapid convergence property. It connects R_s and n_D with all other parameters, and Rs and n_D are found by fitting the data in terms of Eqn. (4). However, since the Eqn. (4) includes an item dV/dI, the current in data cannot be same at any two neighboring points, such that this method does not suit for some IV with very high FF. In addition, some bad data with high s curve (namely low FF) is hard to be convergent to find a stable solution.

(4)

1.1.1.1.3 Lambert W-function ⁵^,⁶

Another simply manner to extract these parameters is through the use of a nonlinear least squared error fit where Eqn. (1). Unfortunately, since equation (1) is a transcendental equation, it is very difficult to find the numerical solutions. In order to circumvent this problem, it is convenient to use the Lambert W function described in Ref. ^{5, 6}. Eqn. (1) is then written as below

(5)

Where, Lambert W function assumes I_ph is approximately equal to short current I_sc; Vth=k_BT/q is the thermal voltage. Based on Eqn. (5), A simple and accurate (without approximations) method⁵ using Lambert W function is introduced by Amit Jain. It still assumes Rp as the slope in Eqn. (2) The unknown parameter Rs, n and I₀ are found by a iterative searching method as shown below.

Figure 2 Flow diagram of the simulation program

Unfortunately, this method is computationally intensive and susceptible to divergence problems as well as local minima convergence issues. Furthermore, the requirement of initial guesses infers that the researcher has some knowledge regarding the device characteristics prior to analysis, which may not always be true.³

1.1.1.1.4 Bouzidi-Chegaar method ⁷

Bouzidi and Chegaar reported a fast method by collecting the non-exponential current terms. It can suit for some bad data with electrical noise or random errors. The Eqn. (1) was rewritten with the voltage as the dependent term and the current as the independent term in Eqn. (6),

(6)

Where,

(7)

The Eqn. (6) can be expressed in the common below, it is simple to perform a simple least squares method to determine the relevant solar cell parameters. (details see Ref. ⁷)