# 2. Illuminated Characteristics

- Page ID
- 5971

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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.