Editing Electron mobility (section)

===Field-effect mobility===
{{See also|MOSFET}}
{{Distinguish|Wien effect}}
The mobility can also be measured using a [[field-effect transistor]] (FET). The result of the measurement is called the "field-effect mobility" (meaning "mobility inferred from a field-effect measurement").

The measurement can work in two ways: From saturation-mode measurements, or linear-region measurements.<ref name=Rost>{{cite book |author=Constance Rost-Bietsch|title=Ambipolar and Light-Emitting Organic Field-Effect Transistors|url=https://books.google.com/books?id=Xxvt0CkVKaIC&pg=PA17|access-date=1 March 2011|date=August 2005|publisher=Cuvillier Verlag |isbn=978-3-86537-535-3 |pages=17–}}. This reference mistakenly leaves out a factor of 1/V<sub>DS</sub> in eqn (2.11). The correct version of that equation can be found, e.g., in {{cite journal|last1=Stassen|first1=A. F.|last2=De Boer|first2=R. W. I.|last3=Iosad|first3=N. N.|last4=Morpurgo|first4=A. F.|title=Influence of the gate dielectric on the mobility of rubrene single-crystal field-effect transistors|journal=Applied Physics Letters|volume=85|issue=17|pages=3899–3901|year=2004|doi=10.1063/1.1812368|arxiv = cond-mat/0407293 |bibcode = 2004ApPhL..85.3899S |s2cid=119532427|url=http://resolver.tudelft.nl/uuid:868f9c8e-b994-47e8-b2fd-69cca21b1415}}</ref> (See [[MOSFET]] for a description of the different modes or regions of operation.)

====Using saturation mode====
In this technique,<ref name=Rost/> for each fixed gate voltage V<sub>GS</sub>, the drain-source voltage V<sub>DS</sub> is increased until the current I<sub>D</sub> saturates. Next, the square root of this saturated current is plotted against the gate voltage, and the slope ''m''<sub>sat</sub> is measured. Then the mobility is:
<math display="block">\mu = m_\text{sat}^2 \frac{2L}{W} \frac{1}{C_i}</math>
where ''L'' and ''W'' are the length and width of the channel and ''C''<sub>''i''</sub> is the gate insulator capacitance per unit area. This equation comes from the approximate equation for a MOSFET in saturation mode:
<math display="block">I_D = \frac{\mu C_i}{2}\frac{W}{L}(V_{GS}-V_{th})^2.</math>
where ''V''<sub>th</sub> is the threshold voltage. This approximation ignores the [[Early effect]] (channel length modulation), among other things. In practice, this technique may underestimate the true mobility.<ref name=Rost2>{{cite book|author=Constance Rost-Bietsch|title=Ambipolar and Light-Emitting Organic Field-Effect Transistors|url=https://books.google.com/books?id=Xxvt0CkVKaIC&pg=PA19|access-date=20 April 2011|date=August 2005|publisher=Cuvillier Verlag|isbn=978-3-86537-535-3 |pages=19–}} "Extracting the field-effect mobility directly from the linear region of the output characteristic may yield larger values for the field-effect mobility than the actual one, since the drain current is linear only for very small VDS and large VG. In contrast, extracting the field-effect mobility from the saturated region might yield rather conservative values for the field-effect mobility, since the drain-current dependence from the gate-voltage becomes sub-quadratic for large VG as well as for small VDS."</ref>

====Using the linear region====
In this technique,<ref name=Rost/> the transistor is operated in the linear region (or "ohmic mode"), where V<sub>DS</sub> is small and <math>I_D \propto V_{GS}</math> with slope ''m''<sub>lin</sub>. Then the mobility is:
<math display="block">\mu = m_\text{lin} \frac{L}{W} \frac{1}{V_{DS}} \frac{1}{C_i}.</math>
This equation comes from the approximate equation for a MOSFET in the linear region:
<math display="block">I_D= \mu C_i \frac{W}{L} \left( (V_{GS}-V_{th})V_{DS}-\frac{V_{DS}^2}{2} \right)</math>
In practice, this technique may overestimate the true mobility, because if V<sub>DS</sub> is not small enough and V<sub>G</sub> is not large enough, the MOSFET may not stay in the linear region.<ref name=Rost2/>