# 2. Illuminated Characteristics

The **illuminated characteristics** of a diode are similar to the dark characteristics, except that now a light-induced current ("photocurrent") is flowing in the device. This section looks at the effect of incident light on a diode.

### Ideal diode under illumination

When an ideal diode is illuminated, the incident light knocks electrons out of their bonds and creates electron-hole pairs. Due to the internal electrical field in the diode, caused by the space charge region, the electrons and holes are forced in opposite directions; this creates a coherent current, called a "photocurrent", because it is driven by light. Because electrons are forced towards the *n*-type material, and holes forced towards the *p*-type material, the resulting photocurrent *i _{P}* runs from

*n*-type to

*p*-type.

Once an incident photon creates an electron-hole pair, the built-in electrical field pushes them in opposite directions. The hole, being positively charged, feels an electrostatic force *F _{p}* to the left; the negatively-charged electron feels an electrostatic force

*F*to the right.

_{n}

As many electron-hole pairs are created, a substantial current is created. The photocurrent flows

in the direction of the electic field vector: from *n*-type to *p*-type.

If the diode is then attached to a load of resistance *R*, a voltage of *v* = *i _{P}R* will develop across the diode.

When the photocurrent is wired to a load resistance *R*, a voltage *v* = *i _{P}R* develops across the load -- and across the diode.

Recall that a voltage drop from *p*-type to *n*-type* *is a forward bias. Therefore, the presence of the photocurrent *i _{P}* induces a voltage that forward biases the diode. As can be seen from the ideal diode equation, a forward bias causes current to flow "forward" as well -- that is, from

*p*-type to

*n*-type. This means that a second current will flow against the photocurrent. This second current is referred to as the

**dark current**, since it is equivalent to the current that flows through a diode in the dark (when it is biased).

To find the resulting current through an illuminated diode, *i _{tot}*, we assume that the total current is simply a superposition of the two opposing currents. Now changing the convention to define the direction of the photocurrent as the positive direction, we can write:

*i _{tot}* =

*i*.

_{P}- i_{dark}Assuming that the dark current is described by the ideal diode equation, we can substitute it for *i _{dark}*:

*i _{tot} *=

*i*-

_{P}*I*[exp(

_{S}*v*/ η

*V*) - 1].

_{T}

The photocurrent is a function of the incident light spectrum and the material properties of the diode. The incident spectrum can be defined by the function *b*(*E*), the incident photon flux density, which gives the number of incident photons of energy *E* per area per time. The photovoltaic properties of the material can be summed up by its quantum efficiency, *e _{quantum}*(

*E*), which is the probability that one incident photon of energy

*E*will contribute one electron to the photocurrent. When the product of

*b*(

*E*) and

*e*(

_{quantum}*E*) -- which gives the number of electrons contributed to the photocurrent due to photons of energy

*E*, per unit area -- is integrated over all values of

*E*, and multiplied by the diode's area,

*A*, an expression for the total number of electrons in the photocurrent is found. Multiplying this by the elementary charge

*e*gives the total photocurrent:

Therefore, the total *i*-*v* characteristic of an illuminated diode is given by:

More on quantum efficiency can be found at PVEducation.org, here.

### References

"Chapter 6: Diodes." *Fundamentals of Electrical Engineering*. 2nd ed. New York, New York: Oxford UP, 1996. 363-74. Print.

- Nelson, Jenny. "Chapter 1: Introduction."
*The Physics of Solar Cells*. London: Imperial College, 2003. 9-10. Print.