Editing Electron mobility (section)

===Matthiessen's rule===
Normally, more than one source of scattering is present, for example both impurities and lattice phonons. It is normally a very good approximation to combine their influences using "Matthiessen's Rule" (developed from work by [[Augustus Matthiessen]] in 1864):

<math display="block">\frac{1}{\mu} = \frac{1}{\mu_{\rm impurities}} + \frac{1}{\mu_{\rm lattice}}.</math>
where ''μ'' is the actual mobility, <math>\mu_{\rm impurities}</math> is the mobility that the material would have if there was impurity scattering but no other source of scattering, and <math>\mu_{\rm lattice}</math> is the mobility that the material would have if there was lattice phonon scattering but no other source of scattering. Other terms may be added for other scattering sources, for example
<math display="block">\frac{1}{\mu} = \frac{1}{\mu_{\rm impurities}} + \frac{1}{\mu_{\rm lattice}} + \frac{1}{\mu_{\rm defects}} + \cdots.</math>
Matthiessen's rule can also be stated in terms of the scattering time:
<math display="block">\frac{1}{\tau} = \frac{1}{\tau_{\rm impurities}} + \frac{1}{\tau_{\rm lattice}} + \frac{1}{\tau_{\rm defects}} + \cdots .</math>
where ''τ'' is the true average scattering time and τ<sub>impurities</sub> is the scattering time if there was impurity scattering but no other source of scattering, etc.

Matthiessen's rule is an approximation and is not universally valid. This rule is not valid if the factors affecting the mobility depend on each other, because individual scattering probabilities cannot be summed unless they are independent of each other.<ref name=Takeda/>  The average free time of flight of a carrier and therefore the relaxation time is inversely proportional to the scattering probability.<ref name=sct /><ref name=ssp /><ref name=pallab /> For example, lattice scattering alters the average electron velocity (in the electric-field direction), which in turn alters the tendency to scatter off impurities. There are more complicated formulas that attempt to take these effects into account.<ref>{{cite book|author1=Antonio Luque|author2=Steven Hegedus|title=Handbook of photovoltaic science and engineering|url=https://books.google.com/books?id=u-bCMhl_JjQC|access-date=2 March 2011|date=9 June 2003|publisher=John Wiley and Sons|isbn=978-0-471-49196-5|page=79, eq. 3.58}} [http://www.knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_bookid=1081 weblink (subscription only)]</ref>