MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE
MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE
MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE
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32 Chapter 3<br />
overcome the barrier and therefore an increase in temperature increases the<br />
conductivity.<br />
3.1.3.2.1 Band insulators/semiconductors<br />
The electron transport in a semiconductor with an energy gap E g between<br />
the conduction and valence bands is limited by the number of excited carriers.<br />
In the intrinsic regime (low doping concentrations and high temperatures),<br />
the chemical potential lies in the middle of the gap so that the thermal energy<br />
required to excite a carrier is E g /2. The carrier concentration n thus increases<br />
exponentially with temperature n ≈ exp(E g /2k B T). The drift mobility μ = v/E<br />
defined by the drift velocity v in an electric field E in a semiconductor can be<br />
complicated and depends on the doping [55]. At low temperatures, impurity<br />
scattering is expected to dominate giving μ ∝ T 3/2 . Above about 100K lattice<br />
scattering will dominate with an approximate temperature dependence<br />
μ ∝ T -3/2 . Thus the conductivity of an intrinsic semiconductor is σ = neμ ≈<br />
T ν exp(E g /2k B T). For elemental semiconductors, the experimentally observed<br />
mobilities have an exponent ν = -1.5 or larger (more negative) [55]. The Hall<br />
effect is more complicated to determine a priori for an intrinsic<br />
semiconductor since the concentration of electron and hole carriers are the<br />
same.<br />
In the extrinsic regime (doped semiconductors at lower temperatures) the<br />
carrier concentration is determined by the thermal excitation of carriers from<br />
donor or acceptor impurities. The carrier concentration retains the form<br />
n ≈ exp(ΔE/k B T) where ΔE is determined by the difference in energy between<br />
the donor and band energies and the temperature regime of interest [56]. For<br />
example, ΔE is one half the band gap (E g /2) for an intrinsic semiconductor or<br />
ΔE = E g - E d ≈ E g for an extrinsic semiconductor with donor (or acceptor)<br />
energy levels E d from the band edge. Since usually one type of carrier (hole or<br />
electron) is dominant, the Hall effect R H = 1/nec is quite large since n is small,
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