Hall Coefficient for Both Electrons and Holes

The determination of the Hall coefficient in the presence of multiple carriers is a little more involved than the derivation in Chapter 19. The current density is given by 

The velocities of the electrons are Vjxx= —p-n x and the holes are Vpx = iXpEx. Putting these into Equation 20.29, 

One can easily see that if n p, Eh reduces to -1/ne. Hall measurements are easiest to interpret in doped materials when either n 3 p orn p. Otherwise one is faced with four unknowns, which require other measurements to resolve. For example, except for the difference between electron and hole mobilities, the Hall effect would be zero for intrinsic materials. One can also see that doing Hall measurements as a fimction of temperature offers a means of determining the occupancy number and energy levels of the various impurity states in the freeze-out region through Equation 20.22. 

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