A REVIEW OF DIODE AND SOLAR CELL EQUIVALENT CIRCUIT MODEL LUMPED PARAMETER EXTRACTION PROCEDURES
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paper_title: Experimental determination of series resistance of p-n junction diodes and solar cells

paper_content:

Various methods for determining the series resistance of p-n junction diodes and solar cells are described and compared. New methods involving the measurement of the ac admittance are shown to have certain advantages over methods proposed earlier.
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paper_title: A comparative study of extraction methods for solar cell model parameters

paper_content:

Abstract A comparative study of three methods for extracting solar cell parameters of the single-diode lumped-circuit model is presented. The methods compared are the curve-fitting method, an iterative 5-point method and a recently proposed analytical 5-point method. Parameter values were extracted using these three methods from experimental characteristics collected from two silicon cells over a range of illuminations and temperatures. The results show that the curve-fitting method can often give erroneous parameter values and the reasons for the errors are discussed. The 5-point methods are found to be reliable and accurate in situations where the model is a good approximation of cell performance. The analytical 5-point method, however, has the added advantage of simplicity. It is also found that for the cell measured, the single diode model is valid at illuminations above one-half AM1 but gives non-physical parameter values at lower illumination.
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paper_title: Comparison of different metaheuristic algorithms for parameter identification of photovoltaic cell/module

paper_content:

The estimation of the photovoltaic (PV) cell/module model parameters could lead to accomplish a diagnostic tool and to estimate several factors which affect the health state of a PV generator. In this context, it is crucial to look for an extraction technique which performs this evaluation precisely and quickly. Due to the nonlinear and implicit nature of the PV cell/module, significant computational effort is required to obtain all the parameters; therefore, in this context different metaheuristic algorithms are proposed. For the identification of the meaningful parameters of PV cell/module models, illuminated current-voltage (I–V) curves, under real conditions of PV cells temperature and incident irradiance, are employed. Considering several PV cell/module models, the goodness of the proposed algorithms is analyzed by means of statistical errors, convergence speed, and unknown parameters precision. Then these algorithms are tested and validated using a daily set of measured I–V curves, specifically for ...
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paper_title: The theory of p-n junctions in semiconductors and p-n junction transistors

paper_content:

In a single crystal of semiconductor the impurity concentration may vary from p-type to n-type producing a mechanically continuous rectifying junction. The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium. The currents across the junction are carried by the diffusion of holes in n-type material and electrons in p-type material, resulting in an admittance for a simple case varying as (1 + iωτ p )1/2 where τ p is the lifetime of a hole in the n-region. Contact potentials across p-n junctions, carrying no current, may develop when hole or electron injection occurs. The principles and theory of a p-n-p transistor are described.
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paper_title: History of Semiconductor Research

paper_content:

This paper presents a running story of semiconductor research from its earliest beginnings up to the present day, with special emphasis on the inception of new ideas and the resolution of older discrepancies. At several points in the story; short interludes are taken to fill in the status as of that time. Semiconductor research began quite inconspicuously about 120 years ago with some observations on the electrical properties of silver suphide. Progress was very slow for the next 50 years and then, about 1885, a mild interest developed with the discovery of point contact rectifiers. These devices were used as detectors until displaced by the vacuum tube around 1915. Development of selenium and cuprous oxide rectifiers about 1930 revived interest and the publication of a good theory of semiconductors in 1931 added still more momentum. The next period of active interest came around World War II when the catwhisker diode was revived and developed into an excellent radar detector. The announcement of the transistor in 1948 gave this field of research such a boost that it has become a real giant in the last few years and semiconductor electronics now rates as a major field of endeavor.
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paper_title: The origins of the pn junction

paper_content:

The excerpts presented, from the authors' book Crystal Fire, track the work of an unsung hero of semiconductor history: Russell Ohl, the inventor of the pn junction.
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paper_title: Direct extraction of semiconductor device parameters using lateral optimization method

paper_content:

Direct extraction of semiconductor device parameters using lateral optimization method A. Ortiz-Conde, Yuansheng Ma, J. Thomson, E. Santos, J.J. Liou*, F.J. GarcoÂ a SaÂ nchez, M. Lei, J. Finol, P. Layman Departamento de ElectroÂnica, Universidad SimoÂn BoloÂvar, Apartado 89000, Caracas, 1080-A, Venezuela Department of ECE, University of Central Florida, Orlando, FL 32816-2450, USA Modeling and Simulation Group, Lucent Technologies, Orlando, FL, USA Motorola, 3102 North 56th Street, Phoenix, Arizona 85018, USA
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paper_title: Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics

paper_content:

For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.
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paper_title: Parameters extraction of solar cells – A comparative examination of three methods

paper_content:

Abstract This paper deals with the extraction of the parameters of the single-diode solar cell model from experimental I–V characteristics of Si and Multi-junction solar cells. The extraction is carried out by three different optimization methods in an attempt to judge which method surpasses the others in terms of data-to-model fitting. The first and the second methods are a variation of the Newton-Raphson method and the Levenberg–Marquardt algorithm, respectively. Both methods are based on the gradient descent approach. The third method is a global-search method based on a Genetic-Algorithm. The extraction of the parameters was done in two stages. On the first stage, empirical I–V characteristics of solar cells that contained measurement errors were used, whereas on the second stage the parameters were re-extracted using a smooth synthetic I–V data. In the absence of true measured parameter values of the cells, it was left to rate the performance of the three optimization methods by the extraction error alone. Although no definitive conclusions could be drawn from the results of the noisy data, results of the smooth data are far more pronounced in terms of the extraction error, and tend to favor the Newton-Raphson method.
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paper_title: The diode quality factor of solar cells under illumination

paper_content:

A review of the methods of determination of solar cell quality factors is discussed from a theoretical point of view; experimental results are compared. Temperature effects, light and bias dependencies of the parameters and the models are considered in order to specify the limits of application of each method.
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paper_title: Methods to determine the dc parameters of solar cells: A critical review

paper_content:

This review article critically outlines and discusses the main issues of 34 methods which have been developed and validated over the past 35 years in order to determine with an acceptable accuracy and reliability fundamental parameters of solar cells. This review covers methodologies which deal with current–voltage characteristic (I–V) analysis either theoretically through elaborated models and/or treated graphically. Methodologies based on the theoretical analysis of the I–V characteristics using the one or two diode model are discussed. The investigation on the I–V characteristics is processed via statistical functions, non-linear regression and stochastic models. A second family of methods to determine the solar cell electric parameters comprises the ones which deal with the graphical treatment and analysis of the I–V characteristics which are measured at different environmental conditions. To the third family belong the methods which use a mix approach of theoretical analysis of the I–V characteristics through modeling on one hand and the graphical analysis of their experimental configuration, on the other. The paper comments on each of the 34 methods and provides pros and cons for the determination of the fundamental electric parameters of solar cells.
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paper_title: New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics

paper_content:

We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current–voltage (I–V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I–V characteristics and an analysis of the errors is presented.
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paper_title: An improved model and parameters extraction for photovoltaic cells using only three state points at standard test condition

paper_content:

Abstract In this paper, a comprehensive modeling and parameters extraction method is proposed to describe the current–voltage and power–voltage characteristic of photovoltaic cells. This method is based on data commonly issued by commercial photovoltaic data sheet. By using Lambert W function, the improved model of solar cells is given. Meanwhile, the current–voltage and power–voltage curves of photovoltaic cells are calculated. To extract the model parameters from only three state points at standard test conditions, an optimized approach using iterative method and approximate method is presented. Compared to the popular R p model and experimental data, the proposed method shows excellent agreement between the current–voltages points. It is found that the proposed modeling and parameters extraction method has less error at the maximum power point state. Moreover, the proposed model is more realistic when subjected to ideality factors variations.
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paper_title: Eliminating parasitic resistances in parameter extraction of semiconductor device models

paper_content:

A network theorem based on potential functions is used for the purpose of cancelling the detrimental effect that the presence of parasitic linear elements has on procedures used for extracting the intrinsic-model parameters of semiconductor devices. The method is based on the use of an auxiliary function: the difference between the content and the co-content functions of the device. The theorem states that, for any arbitrarily connected network of linear and nonlinear branch elements, the summation of the difference functions of each of the branches is zero, and that this difference function is zero at any branch represented by a linear I-V characteristic. In establishing this theorem we also show that: (a) the summation of the contents, over all the branches, is zero; and (b) the summation of the co-contents, over all the branches, is zero. To illustrate the procedure the intrinsic model parameters of a real p-n junction are extracted using this idea.
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paper_title: Silicon Solar Energy Converters

paper_content:

Theory is given for the design of silicon solar energy converters commonly known as the Bell Solar Battery. Values are given for the various parameters in the design theory. Experimental data are presented and compared with the theoretical relations based on a simple model.It is found that with present techniques, units can be made with up to 6 percent efficiency in the conversion of solar radiant energy to electrical energy. An important factor in obtaining such high efficiencies is the reduction of the series resistance of the cell to as low a value as possible.
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paper_title: The theory of p-n junctions in semiconductors and p-n junction transistors

paper_content:

In a single crystal of semiconductor the impurity concentration may vary from p-type to n-type producing a mechanically continuous rectifying junction. The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium. The currents across the junction are carried by the diffusion of holes in n-type material and electrons in p-type material, resulting in an admittance for a simple case varying as (1 + iωτ p )1/2 where τ p is the lifetime of a hole in the n-region. Contact potentials across p-n junctions, carrying no current, may develop when hole or electron injection occurs. The principles and theory of a p-n-p transistor are described.
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paper_title: Bipolar transistor circuit analysis using the Lambert W-function

paper_content:

The generalized diode equation describes conduction in a diode with series resistance. An analytical solution for the generalized diode equation has been elusive; however, one was found based on the transcendental equation w=ln(x/w). The solution of this equation; w=W(x), is traditionally referred to as the Lambert W-function. This function provides a long sought after natural continuity between exponential diode and linear resistor behavior. The W-function also describes more general circuits consisting of a diode or bipolar transistor with local linear negative or positive feedback. The properties of W(x) are reviewed and several iterative methods for its calculation are compared. Three approximations for the W function are derived which can simplify bipolar circuit analysis and design. The practical utility of the proposed solutions are demonstrated in four circuits along with experimental confirmation: a common emitter amplifier with an emitter or collector feedback resistor, Schmitt trigger threshold temperature compensation, bandgap stabilized current source, and a novel current-efficient laser driver.
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paper_title: Semiconductor Device Modeling for VLSI

paper_content:

The invention discloses a dielectric window serving as an interface between different atmospheric media and/or propagating structures incorporating means for detuning ghost-modes to frequencies outside of a desired tuning range. The window is provided with a thicker cross-sectional interface of a compatible dielectric material principally disposed in the diametrically spaced regions of zero electric field intensity of the normal resonant frequency resonant mode. Crossed field devices having tunable coaxial cavity resonators employ the applicable structures in the output energy coupling section. Dielectric materials such as alumina ceramic or beryllium oxide provide high peak power handling capability for devices employing the disclosed window.
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paper_title: Exact analytical solution for current flow through diode with series resistance

paper_content:

A simple analytical expression is presented for the current flow in a diode driven by a voltage source through a series resistance. The proposed solution is based on the Lambert W-function. The new expression leads to an efficient method for extracting series resistance from measured current-voltage data. Experimental results are presented which validate the proposed solution and extraction method.
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paper_title: Exact analytical solution of channel surface potential as an explicit function of gate voltage in undoped-body MOSFETs using the Lambert W function and a threshold voltage definition therefrom

paper_content:

Two useful applications of the Lambert W function to undoped-body MOSFET modeling are presented. Firstly, it is applied to the problem of inverting the gate voltage versus channel surface potential equation. The result is an exact analytical solution of the channel surface potential as an explicit function of the gate voltage for either n or p channel operation. Additionally an approximate but highly accurate analytical solution is presented which is continuously valid for all regions of operation. Secondly, we propose a new unambiguous analytical definition for the threshold voltage of these undoped-body devices. This definition overcomes the impossibility of using the traditional definition based on the bulk Fermi potential, and the ambiguities introduced by other definitions. The threshold voltage is mathematically described also using the Lambert W function at the transition point from subthreshold to superthreshold behavior. An approximation for the )1 branch of the Lambert W function is proposed to express the threshold voltage approximately using elementary logarithmic functions. These new descriptions are then verified against two-dimensional numerical device simulations. 2003 Elsevier Ltd. All rights reserved.
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paper_title: Direct extraction of semiconductor device parameters using lateral optimization method

paper_content:

Direct extraction of semiconductor device parameters using lateral optimization method A. Ortiz-Conde, Yuansheng Ma, J. Thomson, E. Santos, J.J. Liou*, F.J. GarcoÂ a SaÂ nchez, M. Lei, J. Finol, P. Layman Departamento de ElectroÂnica, Universidad SimoÂn BoloÂvar, Apartado 89000, Caracas, 1080-A, Venezuela Department of ECE, University of Central Florida, Orlando, FL 32816-2450, USA Modeling and Simulation Group, Lucent Technologies, Orlando, FL, USA Motorola, 3102 North 56th Street, Phoenix, Arizona 85018, USA
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paper_title: New method of parameters extraction from dark I-V curve

paper_content:

It is very necessary, for solar cells, to obtain a low series resistance and to be able to determine it with accuracy because it is an important parameter of fill factor and efficiency improvement. In the case of low series resistance, we have developed a new method of parameters extraction from only one dark I-V characteristic. We have also improved another technique (the integral) of series resistance extraction. We have compared these two methods to two other ones (the derivative and the Lee et al. method). Our method gives very good results. Moreover it is very simple to use and presents the advantage of being independent of the voltage step in contrary to the derivative and to the integral. We have then applied our technique to a whole solar cell I-V curve and the results are very good.
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paper_title: A new method for experimental determination of the series resistance of a solar cell

paper_content:

A new method for determining the series resistance of a solar cell from illuminated I-V measurements is presented. The method, based on the computation of the area A , under the I-V curve, evaluates R s using the equation R_{s} = 2[V_{oc}/I_{sc} - A/_sc^2 - (mkT/q) (1/I_{sc})] This technique takes advantage of the special feature of integration as a procedure to smooth data errors. The R s obtained represents the resistive effects globally.
---
paper_title: Eliminating parasitic resistances in parameter extraction of semiconductor device models

paper_content:

A network theorem based on potential functions is used for the purpose of cancelling the detrimental effect that the presence of parasitic linear elements has on procedures used for extracting the intrinsic-model parameters of semiconductor devices. The method is based on the use of an auxiliary function: the difference between the content and the co-content functions of the device. The theorem states that, for any arbitrarily connected network of linear and nonlinear branch elements, the summation of the difference functions of each of the branches is zero, and that this difference function is zero at any branch represented by a linear I-V characteristic. In establishing this theorem we also show that: (a) the summation of the contents, over all the branches, is zero; and (b) the summation of the co-contents, over all the branches, is zero. To illustrate the procedure the intrinsic model parameters of a real p-n junction are extracted using this idea.
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paper_title: Evaluating MOSFET harmonic distortion by successive integration of the I–V characteristics

paper_content:

A new method, which we have named “Full Successive Integrals Method” (FSIM), is presented for evaluating harmonic distortion of semiconductor devices from their static I–V characteristics. To assess the method’s applicability, it is used to calculate the harmonic distortion components (Hn) from the measured output characteristics of several experimental n-MOSFETs with various channel lengths. The resulting values of the harmonic components are compared to, and match very well, those obtained through conventional Fourier analysis techniques. The proposed method’s main appeal is that its implementation is fast and straight forward, and inherently filters out measurement noise. It can be used to calculate distortion harmonics for any desired input level, without having to deal with AC signals or having to perform lengthy Fourier type analysis.
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paper_title: New method for determination of harmonic distortion in SOI FD transistors

paper_content:

We present a new method for calculating the total harmonic distortion (THID) and the third harmonic distortion (HD3) of the output current-voltage characteristics of a semiconductor device. The method is based on the calculation of two functions which we call D and D3 and are based on a specific integration of the DC current-voltage characteristic of the device. In this paper we demonstrate that function D can be correlated with the THD and function D3 with the HD3, so that they can be determined in a much simpler way, with no need to use derivatives, Fourier coefficients or fast Fourier transforms. The new method is applied to calculate the harmonic distortion of a silicon-on-insulator (Sol) fully depleted (FD) MOS transistor in the triode regime to be used as an active resistor at the input of an operational amplifier in a MOSFET-C filter configuration. It is also demonstrated that the transistor I-DS-V-DS characteristics used in these calculations can be obtained from either measurements, analytical models or numerical simulations. (C) 2002 Elsevier Science Ltd. All rights reserved.
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paper_title: Parasitic series resistance-independent method for device-model parameter extraction

paper_content:

A new method is presented that permits the extraction of a semiconductor device's intrinsic model parameters from its experimental extrinsic forward I-V characteristics, independently of the parasitic resistance that might be present in series within the real device. The extraction is performed from an auxiliary function which contains the integral of the experimentally measured data. Integrating the data also serves as a smoothing procedure. The diode quality factor, reverse current and series resistance parameters of a single exponential diode model are extracted from a real p-n junction diode in order to illustrate the method.
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paper_title: An improved forward I-V method for nonideal Schottky diodes with high series resistance

paper_content:

Two methods are described to obtain the value of the series resistance (R) of a Schottky diode from its forward I-V characteristic. The value of R is then used to plot the curve ln ( I ) versus V_{D} (= V - IR) which becomes a straight line even if ln (I) versus V does not. The ideality factor n and the Schottky-barrier height \Phi_{B0} of the diode then follow from the standard procedure. The main advantages of the methods are: 1) a linear regression can be used to calculate the value of R , 2) many data points are used over the whole data range which raises the accuracy of the results, and 3) the validity of constant R assumption can be checked by the linearity of the ln (I) versus V D curve. The methods are illustrated on the experimental data of a real diode.
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paper_title: Direct extraction of semiconductor device parameters using lateral optimization method

paper_content:

Direct extraction of semiconductor device parameters using lateral optimization method A. Ortiz-Conde, Yuansheng Ma, J. Thomson, E. Santos, J.J. Liou*, F.J. GarcoÂ a SaÂ nchez, M. Lei, J. Finol, P. Layman Departamento de ElectroÂnica, Universidad SimoÂn BoloÂvar, Apartado 89000, Caracas, 1080-A, Venezuela Department of ECE, University of Central Florida, Orlando, FL 32816-2450, USA Modeling and Simulation Group, Lucent Technologies, Orlando, FL, USA Motorola, 3102 North 56th Street, Phoenix, Arizona 85018, USA
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paper_title: Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics

paper_content:

For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.
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paper_title: A modified forward I‐V plot for Schottky diodes with high series resistance

paper_content:

It is shown that by plotting the function F (V) =V/2−(kT/q) ln(I/AA**T2) a reliable value of the barrier height can be obtained even if there is a series resistance which would hamper the evaluation of the standard lnI‐vs‐V plot. A theoretical examination of F (V) is followed by experimental plots for some common Schottky‐barrier diodes.
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paper_title: Generalized Norde plot including determination of the ideality factor

paper_content:

An extended Norde plot is described which makes it possible to determine the series resistance, barrier height, and ideality factor from one I‐V measurement of a Schottky barrier diode. A theoretical derivation is performed followed with experimental data, which demonstrates the feasibility of the method.
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paper_title: Extraction of Schottky diode parameters from forward current‐voltage characteristics

paper_content:

It is shown that by using the forward current density‐voltage (J‐V) characteristics of a Schottky diode, a plot of d(V)/d(ln J) vs J and a plot of the function H(J) vs J, where H(J)≡V−n(kT/q)ln(J/A**T2), will each give a straight line. The ideality factor n, the barrier height φB, and the series resistance R of the Schottky diode can be determined with one single I‐V measurement. This procedure has been used successfully to study thermal annealing effects of W/GaAs Schottky contacts.It is shown that by using the forward current density‐voltage (J‐V) characteristics of a Schottky diode, a plot of d(V)/d(ln J) vs J and a plot of the function H(J) vs J, where H(J)≡V−n(kT/q)ln(J/A**T2), will each give a straight line. The ideality factor n, the barrier height φB, and the series resistance R of the Schottky diode can be determined with one single I‐V measurement. This procedure has been used successfully to study thermal annealing effects of W/GaAs Schottky contacts.
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paper_title: Bipolar transistor circuit analysis using the Lambert W-function

paper_content:

The generalized diode equation describes conduction in a diode with series resistance. An analytical solution for the generalized diode equation has been elusive; however, one was found based on the transcendental equation w=ln(x/w). The solution of this equation; w=W(x), is traditionally referred to as the Lambert W-function. This function provides a long sought after natural continuity between exponential diode and linear resistor behavior. The W-function also describes more general circuits consisting of a diode or bipolar transistor with local linear negative or positive feedback. The properties of W(x) are reviewed and several iterative methods for its calculation are compared. Three approximations for the W function are derived which can simplify bipolar circuit analysis and design. The practical utility of the proposed solutions are demonstrated in four circuits along with experimental confirmation: a common emitter amplifier with an emitter or collector feedback resistor, Schmitt trigger threshold temperature compensation, bandgap stabilized current source, and a novel current-efficient laser driver.
---
paper_title: Extraction of Schottky diode parameters from forward current‐voltage characteristics

paper_content:

It is shown that by using the forward current density‐voltage (J‐V) characteristics of a Schottky diode, a plot of d(V)/d(ln J) vs J and a plot of the function H(J) vs J, where H(J)≡V−n(kT/q)ln(J/A**T2), will each give a straight line. The ideality factor n, the barrier height φB, and the series resistance R of the Schottky diode can be determined with one single I‐V measurement. This procedure has been used successfully to study thermal annealing effects of W/GaAs Schottky contacts.It is shown that by using the forward current density‐voltage (J‐V) characteristics of a Schottky diode, a plot of d(V)/d(ln J) vs J and a plot of the function H(J) vs J, where H(J)≡V−n(kT/q)ln(J/A**T2), will each give a straight line. The ideality factor n, the barrier height φB, and the series resistance R of the Schottky diode can be determined with one single I‐V measurement. This procedure has been used successfully to study thermal annealing effects of W/GaAs Schottky contacts.
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paper_title: Extraction of non-ideal junction model parameters from the explicit analytic solutions of its I-V characteristics

paper_content:

In modeling semiconductor junctions the extraction of the models parameters is often hindered by the presence of parasitic series resistance and shunt conductance. We propose a method to extract the intrinsic and extrinsic model parameters using the exact explicit analytic solutions for current and voltage of the junctions I–V characteristics, which are expressed in terms of Lambert W functions. However, direct numerical fitting of these solutions to extract the models parameters would be an unwieldy and computationally inefficient task. To circumvent this difficulty, the proposed method is based on first calculating the Integral Difference Function, D, from the explicit analytic solutions for I and V. This produces a purely algebraic equation in I and V whose coefficients contain the models parameters. The coefficients of this auxiliary equation can be quickly determined by direct numerical fitting. From them, all the intrinsic and extrinsic model parameters are then readily obtained at once. The method is tested on representative synthetic I–V characteristics to illustrate the computation process. 2004 Elsevier Ltd. All rights reserved.
---
paper_title: A new method for experimental determination of the series resistance of a solar cell

paper_content:

A new method for determining the series resistance of a solar cell from illuminated I-V measurements is presented. The method, based on the computation of the area A , under the I-V curve, evaluates R s using the equation R_{s} = 2[V_{oc}/I_{sc} - A/_sc^2 - (mkT/q) (1/I_{sc})] This technique takes advantage of the special feature of integration as a procedure to smooth data errors. The R s obtained represents the resistive effects globally.
---
paper_title: Extraction of non-ideal junction model parameters from the explicit analytic solutions of its I-V characteristics

paper_content:

In modeling semiconductor junctions the extraction of the models parameters is often hindered by the presence of parasitic series resistance and shunt conductance. We propose a method to extract the intrinsic and extrinsic model parameters using the exact explicit analytic solutions for current and voltage of the junctions I–V characteristics, which are expressed in terms of Lambert W functions. However, direct numerical fitting of these solutions to extract the models parameters would be an unwieldy and computationally inefficient task. To circumvent this difficulty, the proposed method is based on first calculating the Integral Difference Function, D, from the explicit analytic solutions for I and V. This produces a purely algebraic equation in I and V whose coefficients contain the models parameters. The coefficients of this auxiliary equation can be quickly determined by direct numerical fitting. From them, all the intrinsic and extrinsic model parameters are then readily obtained at once. The method is tested on representative synthetic I–V characteristics to illustrate the computation process. 2004 Elsevier Ltd. All rights reserved.
---
paper_title: Evaluating MOSFET harmonic distortion by successive integration of the I–V characteristics

paper_content:

A new method, which we have named “Full Successive Integrals Method” (FSIM), is presented for evaluating harmonic distortion of semiconductor devices from their static I–V characteristics. To assess the method’s applicability, it is used to calculate the harmonic distortion components (Hn) from the measured output characteristics of several experimental n-MOSFETs with various channel lengths. The resulting values of the harmonic components are compared to, and match very well, those obtained through conventional Fourier analysis techniques. The proposed method’s main appeal is that its implementation is fast and straight forward, and inherently filters out measurement noise. It can be used to calculate distortion harmonics for any desired input level, without having to deal with AC signals or having to perform lengthy Fourier type analysis.
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paper_title: A new method to extract diode parameters under the presence of parasitic series and shunt resistance

paper_content:

Abstract A simple method is presented for extracting the diode ideality factor and saturation current in the presence of significant series and parallel parasitic resistances. Additionally, the values of both resistances can be determined. The method is compared to conventional direct optimization, which fails when both resistances are simultaneously significant.
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paper_title: A new method to extract diode parameters under the presence of parasitic series and shunt resistance

paper_content:

Abstract A simple method is presented for extracting the diode ideality factor and saturation current in the presence of significant series and parallel parasitic resistances. Additionally, the values of both resistances can be determined. The method is compared to conventional direct optimization, which fails when both resistances are simultaneously significant.
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paper_title: The theory of p-n junctions in semiconductors and p-n junction transistors

paper_content:

In a single crystal of semiconductor the impurity concentration may vary from p-type to n-type producing a mechanically continuous rectifying junction. The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium. The currents across the junction are carried by the diffusion of holes in n-type material and electrons in p-type material, resulting in an admittance for a simple case varying as (1 + iωτ p )1/2 where τ p is the lifetime of a hole in the n-region. Contact potentials across p-n junctions, carrying no current, may develop when hole or electron injection occurs. The principles and theory of a p-n-p transistor are described.
---
paper_title: Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics

paper_content:

For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.
---
paper_title: New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics

paper_content:

We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current–voltage (I–V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I–V characteristics and an analysis of the errors is presented.
---
paper_title: Parameter Extraction in Quadratic Exponential Junction Model with Series Resistance using Global Lateral Fitting

paper_content:

A global lateral fitting procedure is proposed to extract the parameters of quadratic double exponential junction models in the presence of parasitic series resistance. Error analysis of the extracted parameters values within a large representative family of synthetic data indicate excellent match between the extracted values and a wide range of the original given model parameters. The procedure was also tested on real data to extract the model parameters of an experimental Silicon PIN diode measured at cryogenic temperature.
---
paper_title: Parasitic series resistance-independent method for device-model parameter extraction

paper_content:

A new method is presented that permits the extraction of a semiconductor device's intrinsic model parameters from its experimental extrinsic forward I-V characteristics, independently of the parasitic resistance that might be present in series within the real device. The extraction is performed from an auxiliary function which contains the integral of the experimentally measured data. Integrating the data also serves as a smoothing procedure. The diode quality factor, reverse current and series resistance parameters of a single exponential diode model are extracted from a real p-n junction diode in order to illustrate the method.
---
paper_title: New method of parameters extraction from dark I-V curve

paper_content:

It is very necessary, for solar cells, to obtain a low series resistance and to be able to determine it with accuracy because it is an important parameter of fill factor and efficiency improvement. In the case of low series resistance, we have developed a new method of parameters extraction from only one dark I-V characteristic. We have also improved another technique (the integral) of series resistance extraction. We have compared these two methods to two other ones (the derivative and the Lee et al. method). Our method gives very good results. Moreover it is very simple to use and presents the advantage of being independent of the voltage step in contrary to the derivative and to the integral. We have then applied our technique to a whole solar cell I-V curve and the results are very good.
---
paper_title: Diode I-U Curve Fitting with Lambert W Function

paper_content:

Application of the Lambert W function in diode forward i-u curve fitting for the purpose of diode parameters determination is described. CFTOOL of Matlab7 is utilized. Fitting and its results are discussed. Semiconductor PN junction solar cells are used as the diode samples. Brief Lambert W function appendix is attached
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paper_title: Approximate analytical expression for the tersminal voltage in multi-exponential diode models

paper_content:

We propose a simple approximate solution for the terminal voltage as an explicit function of the terminal current for diodes which need to be modeled by two or more ideal diodes in parallel. As a result, this solution is better suited for repetitive simulation applications than conventional implicit equations because of its inherently higher computational efficiency. Its explicit nature also makes direct analytic differentiation and integration possible. The approximate solution’s applicability has been assessed by parameter extraction and subsequent playback using measured I–V characteristics of lateral thin-film SOI PIN diodes and also using synthetic I–V characteristics of a solar cell.
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paper_title: A new method for experimental determination of the series resistance of a solar cell

paper_content:

A new method for determining the series resistance of a solar cell from illuminated I-V measurements is presented. The method, based on the computation of the area A , under the I-V curve, evaluates R s using the equation R_{s} = 2[V_{oc}/I_{sc} - A/_sc^2 - (mkT/q) (1/I_{sc})] This technique takes advantage of the special feature of integration as a procedure to smooth data errors. The R s obtained represents the resistive effects globally.
---
paper_title: Exact analytical solutions of the parameters of real solar cells using Lambert W-function

paper_content:

Abstract Exact closed-form solution based on Lambert W -function are presented to express the transcendental current–voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. The W -function expressions are derived using Maple software. Different parameters of solar cell are calculated using W -function method and compared with experimental data of Charles et al. for two solar cells (blue and grey). Percentage accuracy of W -function method is also calculated to prove the significance of the method.
---
paper_title: Extraction of circuital parameters of organic solar cells using the exact solution based on Lambert W-function

paper_content:

The electrical behavior of organic solar cell (OSC) has been analyzed using a simple circuital model consisting on an ::: ideal diode together with a series and parallel resistances (R S and R P respectively). Applying Kirchhoff's Laws to the ::: circuit leads to a transcendental equation that can be solved numerically without approximations using the Lambert W ::: function. Theoretical expression has been fitted to experimental current-voltage (I-V) curves under forward bias, ::: obtaining fairly accurate values for the electrical parameters. This model has been validated comparing the extracted ::: parameters for dark and illumination conditions of different devices. Results show good agreement for R S , and ideality ::: factor (η). ::: Electrical parameters obtained in this work are also compared to those ones extracted using an approximated method ::: often employed by other authors 1 . We conclude that approximated method leads to reasonable good values for R S , R P ::: and η. However, in the case of R p the voltage range chosen to fit the data with the exact method must be constrained to ::: the fourth quadrant, where the role of parallel resistance is more critical. ::: To validate the model, a bunch of organic solar cells with structure ITO/ poly(3,4-ethylenedioxythiophene)-poly ::: (4-styrene sulfonate (PEDOT:PSS)/ poly(3-hexylthiophene) (P3HT): ::: 1-(3-methoxycarbonyl)-propyl-1-1-phenyl-(6,6)C61 ::: (PCBM)/Al has been fabricated in inert atmosphere. Different active layers were deposited varying the P3HT:PCBM ::: ratio (1:0.64, 1:1, 1:1.55) and the active layer thickness (ranging from 100 to 280 nm). Devices are encapsulated inside ::: the glove-box prior its characterization outside the glove-box. Electro optical characterization has been performed with a ::: halogen lamp. ::: Values extracted for RS range from 142 Ω to 273 Ω, values for RP range from 25 kΩ to 331 kΩ. Ideality factor ranges ::: from 5 to 17.
---
paper_title: Diode I-U Curve Fitting with Lambert W Function

paper_content:

Application of the Lambert W function in diode forward i-u curve fitting for the purpose of diode parameters determination is described. CFTOOL of Matlab7 is utilized. Fitting and its results are discussed. Semiconductor PN junction solar cells are used as the diode samples. Brief Lambert W function appendix is attached
---
paper_title: Patterns of efficiency and degradation of composite polymer solar cells

paper_content:

Bulk-heterojunction plastic solar cells (PSC) produced from a conjugated polymer, poly(2-methoxy-5-(3′,7′-dimethyloctyl-oxy)-1,4-phenylenevinylene) (MDMO-PPV), and a methanofullerene [6,6]-phenyl C61-butyric acid methyl ester (PCBM) were investigated using photocurrent imaging techniques to determine characteristic patterns of efficiency and degradation. The solar cells with power efficiencies of up to 2.6% showed significant inhomogeneities and variations depending on the preparation steps (e.g. aluminum deposition), suggesting there is still room for improvements. A characteristic feature of the well-known photoinduced and dark cell degradation is the formation of islands of higher efficiency. Degradation mechanisms appear to have a morphological component. The imaging technique will open opportunities for combinatorial plastic solar cell research.
---
paper_title: New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics

paper_content:

We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current–voltage (I–V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I–V characteristics and an analysis of the errors is presented.
---
paper_title: Evaluating MOSFET harmonic distortion by successive integration of the I–V characteristics

paper_content:

A new method, which we have named “Full Successive Integrals Method” (FSIM), is presented for evaluating harmonic distortion of semiconductor devices from their static I–V characteristics. To assess the method’s applicability, it is used to calculate the harmonic distortion components (Hn) from the measured output characteristics of several experimental n-MOSFETs with various channel lengths. The resulting values of the harmonic components are compared to, and match very well, those obtained through conventional Fourier analysis techniques. The proposed method’s main appeal is that its implementation is fast and straight forward, and inherently filters out measurement noise. It can be used to calculate distortion harmonics for any desired input level, without having to deal with AC signals or having to perform lengthy Fourier type analysis.
---
paper_title: Parasitic series resistance-independent method for device-model parameter extraction

paper_content:

A new method is presented that permits the extraction of a semiconductor device's intrinsic model parameters from its experimental extrinsic forward I-V characteristics, independently of the parasitic resistance that might be present in series within the real device. The extraction is performed from an auxiliary function which contains the integral of the experimentally measured data. Integrating the data also serves as a smoothing procedure. The diode quality factor, reverse current and series resistance parameters of a single exponential diode model are extracted from a real p-n junction diode in order to illustrate the method.
---
paper_title: A new method for determining the characteristics of solar cells

paper_content:

Abstract A new method is proposed to describe the characteristics of solar cell and module in this article. By using the exact explicit analytical solutions, the current–voltage and power–voltage curves of the corresponding modules are calculated and simulated. In order to extract the parameters of the solar cells, an optimized technique is presented by using Lambert W function and polynomial curve fitting. The accuracy of the model is compared with previous methods in other work. Results have the good agreement between the fitted current–voltage curves and the experimental data. Moreover, error and statistical analyses are carried out to illustrate the accuracy of the estimated parameters and procedure suitability.
---
paper_title: New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics

paper_content:

We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current–voltage (I–V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I–V characteristics and an analysis of the errors is presented.
---
paper_title: Estimation of parameters for single diode models using measured IV curves

paper_content:

Many popular models for photovoltaic system performance (e.g., [1], [2]) employ a single diode model (e.g., [3]) to compute the IV curve for a module or string of modules for given irradiance and temperature conditions. Most commonly (e.g., [4]), parameters are determined using only current and voltage at short circuit, open circuit and maximum power from a single IV curve at standard test conditions, along with reported temperature coefficients. In contrast, module testing frequently records IV curves at a wide range of irradiance and temperature conditions, such as those specified in IEC 61853-1 [5], which, when available, should also be used to parameterize the performance model. We propose a parameter estimation method that makes use of the full range of available IV curves, and demonstrate the accuracy of the resulting performance model.
---
paper_title: Solar cells parameters evaluation considering the series and shunt resistance

paper_content:

This paper presents a new technique for the evaluation of the parameters of illuminated solar cell with a single diode lumped circuit model and considering the series and shunt resistances. This method includes the presentation of the standard I=f(V) function as V=f(I) and the determination of the factors C0, C1, C2 of this function that provide the calculation of the illuminated solar cell parameters. These parameters are usually the saturation current (Is), the series resistance (Rs), the ideality factor (n), the shunt conductance (Gsh=1/Rsh) and the photocurrent (Iph). ::: ::: Parameter values were extracted using the present method from experimental I–V characteristics of commercial solar cells and modules. The method proposed below appears to be accurate even in the presence of noise and/or random errors during measurement and it needs no a prior knowledge of the parameters compared to other methods.
---
paper_title: Extraction and analysis of solar cell parameters from the illuminated current–voltage curve

paper_content:

Abstract In this work we describe, apply and analyze a procedure to extract the physical parameters of a solar cell from its I–V curve under illumination. We compare it with other procedures and assess the statistical significance of the parameters. Our method, called APTIV, uses separate fitting in two different zones in the I – V curve. In the first one, near short circuit, current fitting is used because the error in current dominates. In the second one, near open circuit, voltage fitting is used because this is the dominant error. The method overcomes some drawbacks of common procedures: voltage errors are properly managed and no accurate initial guesses for the parameters are needed. In addition, the numerical implementation is very simple.
---
paper_title: Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics

paper_content:

For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.
---
paper_title: Current―voltage analysis of the record-efficiency CuGaSe2 solar cell: Application of the current separation method and the interface recombination model

paper_content:

Abstract Current–voltage ( j–V ) characteristics of the record-efficiency CuGaSe 2 solar cell measured under several illumination levels are analyzed using a two-diode equation for a more accurate description of cell behavior. The contribution of each diode to the total cell j–V characteristic under illumination was estimated using the current separation method presented recently [1] . This is performed in an effort to identify the distinctive features of this record-efficiency cell, which have led to the up-to-date highest open circuit voltage of V oc =946 mV and fill factor of FF =66.5% for CuGaSe 2 solar cells. Furthermore, the interface recombination component of the cell current under illumination is quantitatively discussed applying the interface recombination model presented earlier [2] .
---
paper_title: Lumped Parameter Modeling of Organic Solar Cells’ S-Shaped I–V Characteristics

paper_content:

This paper addresses lumped parameter equivalent circuit modeling of the S-shape anomaly observed in many experimental organic solar cells' I-V characteristics measured under illumination. It presents a convenient exact analytic expression for the cell's terminal voltage as an explicit function of its terminal current according to a model previously proposed by other authors. A new model is also recommended here in order to improve the previous model so that it may also describe the exponential-like upward bend observed at large forward voltages in the first quadrant of the I-V characteristics beyond the S-shape kink. The explicit nature of the proposed equations avoids numerical iteration and eases fitting to experimental data when extracting the cell's model parameters. It also facilitates the derivation of other analytic expressions, such as the temperature dependence of the open-circuit voltage.
---
paper_title: Current―voltage analysis of the record-efficiency CuGaSe2 solar cell: Application of the current separation method and the interface recombination model

paper_content:

Abstract Current–voltage ( j–V ) characteristics of the record-efficiency CuGaSe 2 solar cell measured under several illumination levels are analyzed using a two-diode equation for a more accurate description of cell behavior. The contribution of each diode to the total cell j–V characteristic under illumination was estimated using the current separation method presented recently [1] . This is performed in an effort to identify the distinctive features of this record-efficiency cell, which have led to the up-to-date highest open circuit voltage of V oc =946 mV and fill factor of FF =66.5% for CuGaSe 2 solar cells. Furthermore, the interface recombination component of the cell current under illumination is quantitatively discussed applying the interface recombination model presented earlier [2] .
---
paper_title: New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics

paper_content:

We present a new method to extract the intrinsic and extrinsic model parameters of illuminated solar cells containing parasitic series resistance and shunt conductance. The method is based on calculating the Co-content function (CC) from the exact explicit analytical solutions of the illuminated current–voltage (I–V) characteristics. The resulting CC is expressed as a purely algebraic function of current and voltage from whose coefficients the intrinsic and extrinsic model parameters are then readily determined by bidimensional fitting. The procedure is illustrated by applying it to experimental and synthetic I–V characteristics and an analysis of the errors is presented.
---
paper_title: An Explicit Multiexponential Model as an Alternative to Traditional Solar Cell Models With Series and Shunt Resistances

paper_content:

Classical analyses of various conventional solar cell models are examined. They are unified through the separation of their linear and nonlinear components and the application of Thevenin's theorem to the linear terms. An explicit multiexponential model with series and shunt resistances is proposed as an alternative to conventional implicit multiexponential models commonly used to describe significant parallel conduction mechanisms in real solar cells. The proposed model is better suited than conventional models for repetitive simulation applications because of its inherently higher computational efficiency. Its explicit nature is a very useful feature for direct analytic differentiation and integration. The model's applicability has been assessed by parameter extraction and subsequent playback using synthetic I–V characteristics of a hypothetical solar cell at various illumination levels chosen purely for illustrative purposes.
---
paper_title: Parameter Extraction in Quadratic Exponential Junction Model with Series Resistance using Global Lateral Fitting

paper_content:

A global lateral fitting procedure is proposed to extract the parameters of quadratic double exponential junction models in the presence of parasitic series resistance. Error analysis of the extracted parameters values within a large representative family of synthetic data indicate excellent match between the extracted values and a wide range of the original given model parameters. The procedure was also tested on real data to extract the model parameters of an experimental Silicon PIN diode measured at cryogenic temperature.
---
paper_title: Exact analytical solutions of the parameters of real solar cells using Lambert W-function

paper_content:

Abstract Exact closed-form solution based on Lambert W -function are presented to express the transcendental current–voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. The W -function expressions are derived using Maple software. Different parameters of solar cell are calculated using W -function method and compared with experimental data of Charles et al. for two solar cells (blue and grey). Percentage accuracy of W -function method is also calculated to prove the significance of the method.
---
paper_title: Current―voltage analysis of the record-efficiency CuGaSe2 solar cell: Application of the current separation method and the interface recombination model

paper_content:

Abstract Current–voltage ( j–V ) characteristics of the record-efficiency CuGaSe 2 solar cell measured under several illumination levels are analyzed using a two-diode equation for a more accurate description of cell behavior. The contribution of each diode to the total cell j–V characteristic under illumination was estimated using the current separation method presented recently [1] . This is performed in an effort to identify the distinctive features of this record-efficiency cell, which have led to the up-to-date highest open circuit voltage of V oc =946 mV and fill factor of FF =66.5% for CuGaSe 2 solar cells. Furthermore, the interface recombination component of the cell current under illumination is quantitatively discussed applying the interface recombination model presented earlier [2] .
---

Title: A REVIEW OF DIODE AND SOLAR CELL EQUIVALENT CIRCUIT MODEL LUMPED PARAMETER EXTRACTION PROCEDURES

Section 1: INTRODUCTION
Description 1: In this section, provide an overview of the recent advancements in photovoltaic energy conversion and the significance of solar cells. Discuss the importance of lumped models and efficient parameter extraction methods for practical applications. Review historical developments in solar cell research and introduce the organization of subsequent sections.

Section 2: Single-exponential diode model without any resistance
Description 2: This section should describe the equivalent circuit model for an idealized diode without resistance. Include mathematical representations and illustrative figures to explain the terminal current and voltage relationships.

Section 3: Single-exponential diode model with series resistance
Description 3: Discuss the effect of series resistance on the diode I-V characteristics. Introduce methods to extract parameters, such as the Lambert W function, vertical and lateral optimization, and integration methods.

Section 4: Vertical and lateral optimization methods
Description 4: Elaborate on the optimization techniques for fitting experimental data to diode models. Discuss vertical and lateral approaches, including computational conveniences and measurement examples.

Section 5: Integration method to extract series resistance and ideality factor
Description 5: Present the integration-based approach for parameter extraction, including step-by-step procedures and theoretical foundations.

Section 6: The integral difference function concept and the G method
Description 6: Introduce the Integral Difference Function (INLF) and G method for parameter extraction. Explain how these methods eliminate series resistance effects and provide illustrative examples.

Section 7: Norde's method
Description 7: Describe Norde's method for extracting diode parameters, including mathematical formulations and examples demonstrating its application.

Section 8: Cheung's method
Description 8: Discuss Cheung's method for extracting the ideality factor and series resistance. Provide mathematical details and example applications.

Section 9: Bidimensional fit of function D
Description 9: Explain the bidimensional fitting technique for extracting parameters. Include mathematical formulations and example applications for accuracy verification.

Section 10: Iterative G function method
Description 10: Present the iterative procedure for parameter extraction using the G function and provide illustrative examples.

Section 11: MULTIPLE-EXPONENTIAL DIODE MODEL
Description 11: Discuss the need for multi-exponential models to represent real junctions. Present examples and methods for parameter extraction.

Section 12: Double-exponential diode model with series resistance
Description 12: Describe the double-exponential model for diodes with series resistance. Include mathematical descriptions and fitting methods.

Section 13: Functions
Description 13: Elaborate on various functions used for parameter extraction in double-exponential models, including their definitions and applications.

Section 14: Regional approach for a double diode with series and parallel resistance
Description 14: Present the approach of using voltage regions to extract parameters for double diodes with resistances. Include theoretical explanations and example applications.

Section 15: Alternative multi-exponential model with parasitic resistances
Description 15: Discuss alternative models that incorporate multiple exponential terms with parasitic resistances. Provide mathematical descriptions and fitting techniques.

Section 16: Single-exponential model without any resistance
Description 16: Discuss the single-exponential solar cell model without any resistances. Present mathematical formulations and parameter extraction methods.

Section 17: Single-exponential model with series resistance
Description 17: Describe the single-exponential solar cell model with series resistance. Include methods for parameter extraction and examples.

Section 18: First integration method to extract the series resistance of solar cells
Description 18: Present the integration method developed for solar cells to extract series resistance. Provide theoretical background and application examples.

Section 19: Single-exponential model with parallel resistance
Description 19: Describe the single-exponential solar cell model with parallel resistance. Discuss parameter extraction methods and illustrative examples.

Section 20: Single-exponential model with series and parallel resistances
Description 20: Discuss the combined model with both series and parallel resistances. Present fitting procedures, optimization techniques, and integration approaches.

Section 21: Extraction from the Co-Content function
Description 21: Explain methods for parameter extraction using the integral of the I-V characteristics, known as the Co-Content function. Include mathematical procedures and application examples.

Section 22: Extraction from the Content function
Description 22: Discuss parameter extraction using the integral of voltage with respect to current, known as the Content function. Provide theoretical and application details.

Section 23: Sandia's sequential approach
Description 23: Present the sequential approach developed by Sandia National Laboratories for solar cell parameter extraction. Include steps and examples.

Section 24: Regional optimization
Description 24: Discuss the method of fitting low and high voltage regions separately for parameter extraction. Provide mathematical details and application examples.

Section 25: Lateral and vertical optimization
Description 25: Elaborate on using different fitting criteria for various voltage ranges to improve parameter extraction accuracy. Discuss numerical algorithms and examples.

Section 26: MULTIPLE-EXPONENTIAL SOLAR CELL MODEL
Description 26: Present the need for multi-exponential models for solar cells. Discuss parameter extraction methods and provide examples.

Section 27: Alternative multi-exponential model for solar cells with resistances
Description 27: Discuss alternative multi-exponential models for solar cells incorporating resistances. Provide theoretical explanations and parameter extraction techniques.

Section 28: Approximate lateral optimization
Description 28: Explain the approximate solution for the terminal voltage in multi-exponential models. Include example applications and extracted parameters.