SHEET RESISTANCE CALCULATOR
User defined limit
The calculated sheet resistance simualtes an ideal four-point-probe measurement. (See the 'About' tab).
Computation time: 0.015 s.
Experimental data can be uploaded onto the doping profile plots.
To do so, either (i) paste your data into the text boxes below, or (ii) select a file on your local computer and press upload.
Each row of the uploaded file must contain two values: (i) the depth in µm, and (ii) the ionised dopant concentration in cm-3.
CSV US/UK (comma delimited)
CSV Euro (semicolon delimited)
The data can be directly modified in the text boxes.
NB: This data is not saved onto the PV Lighthouse server.
This calculator determines the sheet resistance of an arbitrarily doped semiconductor at equilibrium (i.e., in the dark and with no applied voltage).
The calculator simulates a four-point probe measurement of a surface diffusion, such as the emitter or the back-surface field of a photovoltaic solar cell. The user can either generate a dopant profile, or upload a profile from a SIMS, ECV, or spreading-resistance measurement. The calculator then determines the sheet resistance and the junction depth of the surface diffusion at any temperature.
The sheet resistance ρsq at equilibrium is determined from the net ionised doping concentration N(z) and the mobility of the majority carriers μmaj by the equation
where zj is the junction depth and q is the charge of an electron. The sheet resistance has the dimensions Ω/sq.
The net ionised doping concentration is defined as N(z) = |NA(z) – ND(z)|, where NA and ND are the ionised concentration of acceptor and donor atoms. In the case of a silicon semiconductor, boron atoms are acceptors and phosphorus atoms are donors.
A doping profile can be uploaded from a CSV file or generated as an exponential, Gaussian or inverse error function (ERFC). The equations for these functions are shown below. The doping profile represents a surface diffusion, such as an emitter or a back-surface field. These are usually created by diffusing dopant atoms into the semiconductor at high temperatures, but can also be created by implanting dopant atoms at high energies. A background concentration can be included in the analysis, which is necessarily a uniform doping profile.
The junction depth zj is defined as follows: If there is no background, zj equals the depth at which the minimum permissible dopant concentration Nmin occurs, as defined on the 'Option' page; if the background and dopant profile are of opposite types, zj is the depth at which |NA(z) – ND(z)| equals zero; and if the background and dopant profiles are of the same type, zj equals the background thickness. The latter two definitions were chosen so that the simulator returns the sheet resistance that would be measured by an ideal four-point probe measurement.
The user has the option of several mobility models, which are described on the About page of the mobility calculator
Warning: The input profile is the ionised dopant profile. It should not include inactive dopant atoms, like interstitial atoms, or non-ionised substitutional atoms, which can occur when the dopant concentration is high or the temperature low.
Like PC1D, the user can select from four equations where all are defined by a peak concentration Np, the depth of the peak concentration zp, and a depth factor zf.
PC1D defines zf such that the Gaussian and ERFC equations have the simplest form.
The traditional approach to employing Gaussian and ERFC equations is to set the standard deviation as the third input parameter. In this calculator, the user can select to define zf as the standard deviation, in which case the profiles are defined as follows.
The selection of either the PC1D definition or the traditional definition of zf is now available on the 'Calculator' page. Given the widespread use of PC1D in the field of photovoltaics, the default definition of zf follows the PC1D definition.
A maximum limit to the electrically active dopant concentration can be assigned. This maximum limit can be used to represent the solid solubility limit of the dopant species at a particular process temperature.
A future update of this calculator will include the solid solubility models from the literature.
For c-Si, the user may choose from the mobility models of Klaassen [1,2], Arora  or Dorkel and Leturcq .
For more information on the use of these models we suggest you visit either the Mobility Calculator or the Resistivity Calculator.
We thank Fa-Jun Ma (SERIS) for finding a bug that caused an underestimation of the sheet resistance for B diffusions in versions preceding 1.4 (12-Apr-2013); and Kean Fong (ANU) for finding a bug that caused an overestimation of the sheet resistance for 'traditional' Gaussian profiles in versions preceding 1.6 (4-Dec-2013). We also thank Dongchul Suh (ANU) and Yimao Wan (ANU), for the Korean and Chinese translations.
Please email corrections, comments or suggestions to firstname.lastname@example.org.
Comments? Bugs? Errors? Compliments?
Welcome to the sheet resistance calculator
This calculator determines the sheet resistance of an arbitrarily doped semiconductor at equilibrium.
The calculator simulates a four-point probe measurement of a surface diffusion, such as an emitter, a back-surface field or a front-surface field of a photovoltaic (PV) solar cell. The user can either generate a dopant profile, or upload a profile from a SIMS, ECV, or spreading-resistance measurement. The calculator then determines the sheet resistance and the junction depth at any temperature.
The assumptions used in the calculations are described on the 'About' page.
Neither PV Lighthouse nor any person related to the compilation of this calculator make any warranty, expressed or implied, or assume any legal liability or responsibility for the accuracy, completeness or usefulness of any information disclosed or rendered by this calculator.
New in this version:
Import PVL File