MAGNETISM ELECTRON TRANSPORT MAGNETORESISTIVE LANTHANUM CALCIUM MANGANITE

Electronic and Magnetic Measurements 31
grain boundary is a plane of defects, grain boundary resistance is similarly
temperature independent and often quite large.
3.1.3.1.2 Electron-electron scattering
The strong Coulomb interaction between electrons provides a mechanism
for electron-electron scattering. The exclusion principle limits the scattering
to electrons in partially occupied levels near the Fermi surface. For two
electrons to scatter, both must be in this shell of partially occupied levels with
width k B T about the Fermi level. This leads to a scattering rate and therefore
resistivity proportional to (k B T) 2 .
3.1.3.1.3 Electron-phonon scattering
Other than impurities, lattice vibrations or phonons can disrupt the
periodic structure of the lattice. This will scatter the electrons and lead to an
intrinsic source of resistivity present even in a sample free of crystal
imperfections. The most widely employed expression for this resistivity is
the Bloch-GrŸneisen formula [54]: ρ =
− − − ∫
5
5
KT z dz
6 z z
Θ ( e 1)( 1 e )
D
Θ D
T
0
where K is a
constant characteristic of the metal, and Θ D is the Debye temperature (see
section 3.3.2.2).
At high temperatures T/Θ D > 0.5, this gives a resistivity proportional to T:
2
ρ ≈ KT/4ΘD . At low temperatures T/ΘD < 0.1 the resistivity follows the Bloch
T 5 law: ρ ≈ 124.4 KT 5 6
/ΘD .
3.1.3.2 insulators/semiconductors
A material is insulating or semiconducting when dρ/dT < 0. The
mechanisms described below predict this behavior because the conduction
must be thermally activated. The conducting species must overcome some
energy barrier for conduction. Thermal energy supplies the energy to