Editing Electron mobility (section)

==Doping concentration dependence in heavily-doped silicon==
The [[charge carrier]]s in semiconductors are electrons and holes. Their numbers are controlled by the concentrations of impurity elements, i.e. doping concentration. Thus doping concentration has great influence on carrier mobility.

While there is considerable scatter in the [[experimental data]], for noncompensated material (no counter doping) for heavily doped substrates (i.e. <math>10^{18}\mathrm{cm}^{-3} </math> and up), the mobility in silicon is often characterized by the [[empirical relationship]]:<ref>B. L. Anderson and R. L. Anderson, "Fundamentals of Semiconductor Devices, " Mc Graw Hill, 2005</ref> 
<math display="block">\mu = \mu_o + \frac{\mu_1}{1 + \left(\frac{N}{N_\text{ref}}\right)^\alpha}</math>
where ''N'' is the doping concentration (either ''N<sub>D</sub>'' or ''N<sub>A</sub>''), and ''N''<sub>ref</sub> and α are fitting parameters. At [[room temperature]], the above equation becomes:

Majority carriers:<ref>{{cite journal|last1=Caughey|first1=D.M.|last2=Thomas|first2=R.E.|title=Carrier mobilities in silicon empirically related to doping and field|journal=Proceedings of the IEEE|volume=55|issue=12|pages=2192–2193 |year=1967 |doi=10.1109/PROC.1967.6123}}</ref> 
<math display="block">\mu_n(N_D) = 65 + \frac{1265}{1+ \left(\frac{N_D}{8.5\times10^{16}}\right)^{0.72}}</math>
<math display="block">\mu_p(N_A) = 48 + \frac{447}{1+ \left(\frac{N_A}{6.3\times10^{16}}\right)^{0.76}}</math>

Minority carriers:<ref>{{cite journal|last1=Del Alamo|first1=J|title=Measuring and modeling minority carrier transport in heavily doped silicon|journal=Solid-State Electronics|volume=28|issue=1|pages=47–54|year=1985|doi=10.1016/0038-1101(85)90209-6 |bibcode = 1985SSEle..28...47D }}</ref> 
<math display="block">\mu_n(N_A) = 232 + \frac{1180}{1+ \left(\frac{N_A}{8\times10^{16}}\right)^{0.9}}</math>
<math display="block">\mu_p(N_D) = 130 + \frac{370}{1+ \left(\frac{N_D}{8\times10^{17}}\right)^{1.25}}</math>

These equations apply only to silicon, and only under low field.