Editing Electromotive force (section)

===Solar cell===
{{Main|Theory of solar cells}}

[[Image:Solar cell equivalent circuit.svg|thumb|250px |The [[Theory of solar cells#Equivalent circuit of a solar cell|equivalent circuit of a solar cell]], ignoring parasitic resistances.]]

Operation of a [[solar cell]] can be understood from [[Theory of solar cells#Equivalent circuit of a solar cell|its equivalent circuit]]. [[Photon]]s with energy greater than the [[bandgap]] of the [[semiconductor]] create mobile [[electron–hole pair]]s. Charge separation occurs because of a pre-existing electric field associated with the [[p-n junction]]. This electric field is created from a [[p–n junction#Equilibrium (zero bias)|built-in potential]], which arises from the [[Volta potential|contact potential]] between the two different materials in the junction. The charge separation between positive [[Electron hole|hole]]s and negative [[electron]]s across the [[p–n diode]] yields a ''[[forward voltage]]'', the ''photo voltage'', between the illuminated diode terminals,<ref name="Dhir">{{cite book |first=S. M. |last=Dhir |title=Electronic Components and Materials: Principles, Manufacture & Maintenance |date=2000 |orig-year=1999 |publisher=[[Tata McGraw-Hill Publishing Company Limited]] |location=India |edition=2007 fifth reprint |isbn=0-07-463082-2 |page=283 |chapter=§3.1 Solar cells |url=https://books.google.com/books?id=sGbwj4J76tEC |chapter-url=https://books.google.com/books?id=sGbwj4J76tEC&pg=PA283}}</ref> which drives current through any attached load. ''Photo voltage'' is sometimes referred to as the ''photo emf'', distinguishing between the effect and the cause.

==== Solar cell current–voltage relationship ====
Two internal current losses <math>I_{SH} + I_D</math> limit the total current <math>I</math> available to the external circuit. The light-induced charge separation eventually creates a forward current <math> I_{SH}</math> through the cell's internal resistance <math>R_{SH}</math> in the direction opposite the light-induced current <math>I_L</math>. In addition, the induced voltage tends to [[p-n junction#Forward bias|forward bias]] the junction, which at high enough voltages will cause a recombination current <math> I_{D}</math> in the diode opposite the light-induced current.

When the output is short-circuited, the output voltage is zeroed, and so the voltage across the diode is smallest. Thus, short-circuiting results in the smallest <math>I_{SH} + I_D</math> losses and consequently the maximum output current, which for a high-quality solar cell is approximately equal to the light-induced current <math> I_{L}</math>.<ref name="Lorenzo">{{cite book
 |title=Solar Electricity: Engineering of photovoltaic systems
 |editor=Eduardo Lorenzo
 |first= Gerardo L.|last=Araújo
 |chapter-url=https://books.google.com/books?id=lYc53xZyxZQC&pg=PA74
 |chapter=§2.5.1 Short-circuit current and open-circuit voltage
 |isbn=978-84-86505-55-4
 |year=1994
 |page=74
 |publisher=Progenza for Universidad Politechnica Madrid
 }}</ref> Approximately this same current is obtained for forward voltages up to the point where the diode conduction becomes significant.

The current delivered by the illuminated diode to the external circuit can be simplified (based on certain assumptions) to:

:<math>I = I_L -I_0 \left( e^{\frac{V}{m\ V_\mathrm{T}}} - 1 \right) \ . </math>

<math>I_0</math> is the [[reverse saturation current]]. Two parameters that depend on the solar cell construction and to some degree upon the voltage itself are the [[ideality factor]] ''m'' and the [[thermal voltage]] <math>V_\mathrm{T} = \tfrac{k T}{q} </math>, which is about 26 millivolts at [[room temperature]].<ref name= Lorenzo/>

==== Solar cell photo emf ====

[[File:Solar cell characterisitcs.JPG|thumb|250px |Solar cell output voltage for two light-induced currents ''I''<sub>L</sub> expressed as a ratio to the reverse saturation current ''I''<sub>0</sub><ref>{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=8}}</ref> and using a fixed ideality factor ''m'' of 2.<ref name="params">In practice, at low voltages ''m''&nbsp;→ 2, whereas at high voltages ''m''&nbsp;→ 1. See Araújo, ''op. cit.'' {{ISBN|84-86505-55-0}}. [https://books.google.com/books?id=lYc53xZyxZQC&pg=PA72 page 72]</ref> Their emf is the voltage at their y-axis intercept.]]

Solving the illuminated diode's above simplified [[Current-voltage relationship|current–voltage relationship]] for output voltage yields:

:<math>V = m\ V_\mathrm{T} \ln \left( \frac{I_\text{L} - I}{I_0}+1 \right) \ , </math>
which is plotted against <math>I / I_0 </math> in the figure.

The solar cell's ''photo emf'' <math>\mathcal{E}_\mathrm{photo}</math> has the same value as the open-circuit voltage <math>V_{oc}</math>, which is determined by zeroing the output current <math>I</math>:

:<math>\mathcal{E}_\mathrm{photo} = V_\text{oc} = m\ V_\mathrm{T} \ln \left( \frac{I_\text{L}}{I_0}+1 \right) \ . </math>

It has a [[logarithm]]ic dependence on the light-induced current <math>I_L</math> and is where the junction's forward bias voltage is just enough that the forward current completely balances the light-induced current. For silicon junctions, it is typically not much more than 0.5 volts.<ref name="Northrop">{{cite book
 | title=Introduction to Instrumentation and Measurements
 | first=Robert B.|last=Northrop
 | page=176
 | chapter=§6.3.2 Photovoltaic Cells
 | chapter-url= https://books.google.com/books?id=mcpcfpQfxB4C&pg=PA176
 | isbn=978-0-8493-7898-0 |year=2005 |publisher=CRC Press
 }}</ref> While for high-quality silicon panels it can exceed 0.7 volts in direct sunlight.<ref>{{cite web| url = https://www.pveducation.org/pvcdrom/solar-cell-operation/open-circuit-voltage#:~:text=Silicon%20solar%20cells%20on%20high,circuit%20voltages%20around%20690%20mV. | title = Open-Circuit Voltage}}</ref>

When driving a resistive load, the output voltage can be determined using [[Ohm's law]] and will lie between the short-circuit value of zero volts and the open-circuit voltage <math>V_{oc}</math>.<ref>{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=6}}</ref> When that resistance is small enough such that <math>I \approx I_L</math> (the near-vertical part of the two illustrated curves), the solar cell acts more like a ''current generator'' rather than a voltage generator,<ref name="Nelson_page7">
{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=7}}</ref> since the current drawn is nearly fixed over a range of output voltages. This contrasts with batteries, which act more like voltage generators.