3 Solar Cells: Basics
51
Fig. 3.13 One strives, in all practical situations, to harvest a maximum amount of sunrays. Courtesy
Dji-illustrations, Neuchâtel
Equation (3.6) is the basic diode equation; it can, for the case n= 1, be more
or less rigorously derived from basic semiconductor device theory, i.e. from the
drift-diffusion equation and from Poisson’s equation, albeit in a somewhat “roundabout” way, with many assumptions and approximations (see [4], or any textbook
on semiconductor device physics) (Fig. 3.14).
The case n = 1 is based on a very crass approximation, whereby two exponential
functions, each with a different argument are combined into a single exponential
function with its argument lying somewhere between the first two ones.
Equation (3.8) follows from (3.6) by using the so-called “superposition principle”,
i.e. by postulating that under illumination, the total solar cell current J illim is simply given as superposition (addition) of the diode dark current J dark and the photogenerated current J ph . This is not at all obvious, if one looks in detail at the applicable
semiconductor device equations within the solar cell. In fact, the addition of light, i.e.
of photo-generated electron-hole pairs, completely changes the entire profiles n(x)
and p(x) of electrons and holes within the photo-absorbing layers of the solar cell.
However, as the equations used to derive the diode characteristics are all linear, the
superposition principle can be intuitively justified, but only for pn-type solar cells
and under restrictive assumptions (see [12, 13]).
51
Fig. 3.13 One strives, in all practical situations, to harvest a maximum amount of sunrays. Courtesy
Dji-illustrations, Neuchâtel
Equation (3.6) is the basic diode equation; it can, for the case n= 1, be more
or less rigorously derived from basic semiconductor device theory, i.e. from the
drift-diffusion equation and from Poisson’s equation, albeit in a somewhat “roundabout” way, with many assumptions and approximations (see [4], or any textbook
on semiconductor device physics) (Fig. 3.14).
The case n = 1 is based on a very crass approximation, whereby two exponential
functions, each with a different argument are combined into a single exponential
function with its argument lying somewhere between the first two ones.
Equation (3.8) follows from (3.6) by using the so-called “superposition principle”,
i.e. by postulating that under illumination, the total solar cell current J illim is simply given as superposition (addition) of the diode dark current J dark and the photogenerated current J ph . This is not at all obvious, if one looks in detail at the applicable
semiconductor device equations within the solar cell. In fact, the addition of light, i.e.
of photo-generated electron-hole pairs, completely changes the entire profiles n(x)
and p(x) of electrons and holes within the photo-absorbing layers of the solar cell.
However, as the equations used to derive the diode characteristics are all linear, the
superposition principle can be intuitively justified, but only for pn-type solar cells
and under restrictive assumptions (see [12, 13]).