Experimental data fit of the VA characteristics is based on 4 parameter $a=(a_1,a_2,a_3,a_4)$ formula (see \href{http://scitation.aip.org/content/aip/journal/rsi/79/10/10.1063/1.2976755}{Aazoz@AIP, 2009}):

$$I(a,V_{bias})=\exp[a_1 \tanh{(V_{bias}+a_2)/a_3}]+a_4 $$

where $I$ is the probe current measured on the resistor $R$ and 
performed via function \href{http://www.mathworks.com/help/stats/nlinfit.html}{matlab function nlinfit}, see \href{http://golem.fjfi.cvut.cz/wiki/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/Analysis/EEDF/Analyze_LangmuirWOgraphics.m}{code, part "Perform fit"} originally created by \href{http://www.mathworks.com/matlabcentral/fileexchange/19312-langmuir-probe-data-analysis-code}{Aazoz@matlab, 2008}



and output parameters are calculated as follows (see \href{http://golem.fjfi.cvut.cz/wiki/Experiments/EdgePlasmaPhysics/ParticleFlux/RakeProbe/1114ShotToShotMeasurement/Sessions/1114Intro/Analysis/EEDF/Analyze_LangmuirWOgraphics.m}{code} and \href{http://www-pub.iaea.org/MTCD/publications/PDF/P1256-cd/papers/crowley.pdf}{Crowley et al@IAEA TM, 2005}):

\begin{itemize}
\item Ion saturation current: $I_{is}=I(a,2*min(V_{bias}))$
\item Electron saturation current: $I_{es}=I(a,3*max(V_{bias}))$ 
\item Plasma potential: $V_p=a_3*\text{atanh}(((\sqrt{1+a_1^2})-1)/a_1)-a_2$;
\item Floating potential $V_{fl}$ from the condition $I(a, V_{fl})=0$
\item Electron energy distribution function (EEDF): $N(\epsilon)=\frac{2}{Ae}\sqrt{\frac{2m\epsilon}{e}}\frac{d^2I}{dV^2}$
\item Electron energy distribution function (EEPF): $P(\epsilon)=\frac{2}{Ae}\sqrt{\frac{2m}{e}}\frac{d^2I}{dV^2}$
\item Electron density $$n_e=\int_0^\infty{P(\epsilon)d\epsilon}$$
\item Ion density $n_i=\frac{|I_{is}|}{0.52*A*e^{2/3}}\sqrt{\frac{M_i}{T_e}}$
\item Electron temperature $$T_e=\frac{2}{3}<\epsilon>=\frac{2}{3n_e}\int_0^\infty{\epsilon P(\epsilon)d\epsilon}$$
\end{itemize}

where $M_i$ is ion mass, $A$ is probe effective area, $e$ and $m$ are the electron charge and mass.