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.

Uploaded Profile
CSV US/UK (comma delimited) CSV Euro (semicolon delimited)
Depth (μm)	Dopant conc. (cm–3)
	Phosphorus Boron
→	→
The data can be directly modified in the text boxes. NB: This data is not saved onto the PV Lighthouse server.

Active doping limit
Apply to defined profile
Apply to uploaded profile
Miscellaneous
Mobility model	Klaassen1992 Arora1982 Dorkel1981
Units for temperature	Kelvin Celsius
Doping profile interval, Δz		μm
Doping profile minimum conc., Nmin		cm–3

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 doped region, 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 doped region at any temperature.

The sheet resistance ρ_sq at equilibrium is determined from the net ionised doping concentration N(z) and the mobility of the majority carriers μ_maj by the equation

where z_j 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) = |N_A(z) – N_D(z)|, where N_A and N_D 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, uniform 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 z_j is defined as follows: If there is no background, z_j equals the depth at which the minimum permissible dopant concentration N_min occurs, as defined on the ''Option'' page; if the background and dopant profile are of opposite types, z_j is the depth at which |N_A(z) – N_D(z)| equals zero; and if the background and dopant profiles are of the same type, z_j 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 N_p, the depth of the peak concentration z_p, and a depth factor z_f.

PC1D defines z_f such that the Gaussian and ERFC equations have the simplest form.

Uniform:	N(z) = Np for z ≤ zp and N(z) = 0 for z > zp
Exponential:	N(z) = Np ⋅ exp[–|z – zp| / zf]
Gaussian:	N(z) = Np ⋅ exp[–(z – zp)2 / zf2 ]
ERFC:	N(z) = Np ⋅ {1 – erf[ (z – zp) / zf ] }

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 z_f as the standard deviation, in which case the profiles are defined as follows.

Uniform:	N(z) = Np for z ≤ zp and N(z) = 0 for z > zp
Exponential:	N(z) = Np ⋅ exp[–|z – zp| / zf]
Gaussian:	N(z) = Np ⋅ exp{–[ (z – zp) / (zf ⋅ √2) ]2} / [zf ⋅ √(2π)]
ERFC:	N(z) = Np ⋅ {1 – erf[ (z – zp) / (zf ⋅ √2) ] }

The selection of either the PC1D definition or the traditional definition of z_f is now available on the ''Calculator'' page. Given the widespread use of PC1D in the field of photovoltaics, the default definition of z_f 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 [3] or Dorkel and Leturcq [4].

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.

[1]	D.B.M. Klaassen, "A unified mobility model for device simulation—I. Model equations and concentration dependence," Solid-State Electronics, 35 (7), pp. 953–959, 1992.
[2]	D.B.M. Klaassen, "A unified mobility model for device simulation—II. Temperature dependence of carrier mobility and lifetime," Solid-State Electronics, 35 (7), pp. 961–967, 1992.
[3]	N.D. Arora, J.R. Hauser and D.J. Roulston, "Electron and hole mobilities in silicon as a function of concentration and temperature," IEEE Transactions on Electron Devicies, ED-29 (2), pp. 292–295, 1982.
[4]	J.M. Dorkel and PH. Leturcq, "Carrier mobilities in silicon semi-empirically related to temperature, doping and injection level," Solid-State Electronics, 24 (9), pp. 821–825, 1981.

Please email corrections, comments or suggestions to support@pvlighthouse.com.au.