ABSTRACT
Section 1.10 discussed the basics of carrier (electron or hole) transport and mobility. It is straightforward to relate mobility to electrical conductivity. The current that flows through a crosssectional area A is
(9.1)
I Q dt
=
where Q is the amount of charge (Coulombs) that flows through the area in a time dt (Figure 9.1). The charge Q is given by the charge density times the volume of the cylinder that passed through the area:
(9.2)Q ne Av dtd= ( )( )
where n is the free-carrier concentration, e is the charge (±1.6 × 10−19 C), and vd is the drift velocity. Plugging Equation 9.2 into Equation 9.1 yields
(9.3)I nAv ed= The current density is given by
(9.4)j I A nv ed= =/
Because vd = µE (Equation 1.34), the current density can be expressed as (9.5)j E E= ≡( )neµ σ where σ is the electrical conductivity: (9.6)σ µ=ne
The resistivity ρ is defined as the inverse of the conductivity:
(9.7)
ρ σ µ
≡ = 1 1
ne
From Ohm’s law, V = IR, the resistance R of a sample is given by
(9.8)R l A=ρ / where l is the length and A is the area through which the current flows.
