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)
(μm)	Dopant conc. (cm–3)
→	→
The data can be directly modified in the text boxes. NB: This data is not saved onto the PV Lighthouse server.

EDNA 2 calculates the recombination in a heavily doped region of silicon, such as an emitter or a back-surface field.

It determines the emitter saturation current density J_0E and the internal quantum efficiency for an arbitrary dopant profile. It can be used to determine an emitter's surface recombination velocity from an experimentally measured J_0E.

1. The simulation of heavily doped silicon is a contentious field. Models for Auger recombination, carrier mobility, and especially band-gap narrowing, have not been validated over a wide range of experimental dopant profiles, primarily because these fundamental properties are difficult to measure in heavily doped silicon. EDNA 2 permits the user to select various physical models even though some models yield significantly different outputs to others. Which models are best? The default models are recommended but they should not necessarily be trusted to give accurate results for all dopant profiles. More research is required in this field of photovoltaics.
2. EDNA 2 assumes that the heavily doped region is quasi-neutral; that is, that the concentrations of excess electrons and holes are equal. This assumption is justified over a variety of conditions [McI13], although more research is required to determine the conditions under which the quasi-neutral assumption breaks down.
3. A third warning relates to the boundary of a heavily doped silicon. What defines the boundary? Since in typical silicon solar cells, the dopant profile of the emitter (or back-surface field) decreases below the background dopant concentration, it might seem like its boundary could be defined as the location where the two concentrations are equal. This point is called the metallurgical junction. Yet at equilibrium, and many conditions besides, a depletion region exists at the metallurgical junction that cannot be considered a part of an emitter. (The quasi-neutral assumption does not hold in a depletion region.) As described below, EDNA 2 permits the user to define the boundary of the emitter. The boundary is only important when Shockley–Read–Hall (SRH) recombination in the emitter is significant.
4. It is tempting to adjust the SRH lifetimes in the heavily doped region (τ_n0 and τ_p0) until the simulated J_0E equals an experimentally measured J_0E. This may be instructive, but keep in mind that τ_n0 and τ_p0 are likely to vary strongly with depth. This scenario cannot be simulated with the current version of EDNA 2.
5. Since version 2.5 (14-Apr-2015), EDNA 2 has had the option to simulate a non-zero surface charge. The calculation of the surface recombination rate is solved by the approach of Girisch et al. [Gir88], which assumes that the quasi-Fermi levels are constant within the surface space-charge region. EDNA 2 also assumes that (i) the surface charge is fixed (i.e., it does not vary with surface potential), and (ii) that the effective intrinsic carrier concentration n_i eff is constant within the surface space-charge region. Assumption (i) can be poor when the interface defect concentration is high relative to the surface charge. Assumption (ii) can introduce significant error when surface charge is high. A future version will remove these assumptions.

Here, and on the Calculator tab, the heavily doped region is referred to as an 'emitter'. This term is a legacy of the semiconductor industry.

The general procedure is now described. A more detailed description of the assumptions, algorithms, and citations that underlie EDNA 2 is presented in [McI10]. Emitter simuation has a long an interesting history, and there are many other works on the subject. Some day, we'll review and cite them.

The EDNA 2 algorithm begins by loading the background and emitter dopant profiles and calculating the emitter's sheet resistance in equilibrium. An explanation of the functions used to generate the emitter profile, and the equations used to calculate the sheet resistance, are given by the sheet resistance calculator.

EDNA 2 then computes the intrinsic and equilibrium parameters of the silicon as a function of depth. These parameters include the ionised donor N_D⁺ and accetor N_A^– concentrations, the effective intrinsic carrier concentration n_{i eff}, the conduction band energy E_c, the valence band energy E_v, the electron Fermi energy E_Fn, and the hole Fermi energy E_Fp, following the procedure used in the band gap calculator.

Next, the excess carrier density is set at the surface Δn(0), providing the first of two boundary conditions. EDNA 2 then computes the surface recombination and applies the shooting method to determine the excess carriers as a function of depth within the emitter. This requires the computation of the recombination rate, as described on the About page of the recombination calculator. (Photon recyling is assumed negligible.)

Once the excess carrier density is known as a function of depth, the effective width of the emitter is determined from two (somewhat arbitrary) conditions specified in the Options. When SRH recombination in the emitter is small, the exact effective width is unimportant because little recombination occurs deep in the emitter (since in this case, the total recombination is dominanted by Auger recombination near the front surface). But when SRH recombination in the emitter is large, the definition of the emitter boundary is crucial and it causes the total recombination to depend on the conditions used to define the lower boundary. This problem arises whenever attributing recombination to an emitter: Where does the emitter end?

Having established the emitter's lower boundary, EDNA 2 calls this the 'junction'. A junction voltage V_j and a collection current J_j is then calculated from the carrier concentrations.

Finally, EDNA 2 iterates, varying Δn(0) and computing V_j and J_j, until one of four cases have been met (the second boundary condition). The first case is the dark case (when there is no generation) and when V_j equals the user-specified junction voltage. This gives a 'dark solution'. The other three cases relate to illuminated (or light) conditions, when a generation rate within the emitter is calculated from the generation inputs. EDNA 2 finds solutions for (i) the short-circuit case defined as V_j = 0, (ii) the open-circuit case defined as J_j = 0, and (iii) the case where V_j equals the specified junction voltage.

EDNA 2 does not recalculate the band gap energy or the dopant ionisation in steady state. It assumes that they vary negligibly from their equilibrium values.

EDNA was first created as an Excel spreadsheet. It can be downloaded from here. EDNA 2 is faster, contains more models, and permits sweeping of input parameters.

[Gir88]	R.B.M. Girisch, R.P. Mertens and R.F. De Keersmaecker, "Determination of Si-SiO2 interface recombination parameters using a gate-controlled point-junction diode under illumination," IEEE Transactions on Electron Devices 35, pp. 203–22, 1988.
[McI10]	K.R. McIntosh and P.P. Altermatt, "A freeware 1D emitter model for silicon solar cells," 35th IEEE Photovoltaic Specialists Conference, Honolulu, pp. 2188–2193, 2010.
[McI13]	K.R. McIntosh, P.P. Altermatt, T.J. Ratcliff, K.C. Fong, L.E. Black, S.C. Baker-Finch and M.D. Abbott, "An examination of three common assumptions used to simulate recombination in heavily doped silicon," Proc. 28th European Photovoltaic Science and Engineering Conference, Paris, pp. 1672–1679, 2013.

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

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.