2.3.2 Odd Moments: Mobilities

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2.3.2 Odd Moments: Mobilities

As the odd equilibrium values vanish, the macroscopic relaxation time approximation simplifies. To approximate the odd scattering terms we introduce the mobilities [GJK⁺04] in the odd equations. By setting

$\displaystyle \tau \hat{=} \frac{m^* \mu}{q}$

(2.56)

we get a formal correspondence between relaxation times and mobilities for parabolic bands. If $\mu$ and

have the same sign, then $\tau$ is positive.

With this correspondence we get:

$\displaystyle \langle O_{2i+1}\rangle = - \frac{\mu_{2i+1} m^{*}}{q} \bigg( \fr... ...3} \bigg( \bigg(1 + \frac{2i}{3}\bigg)M_{2i}\bigg) \bigg) \quad (i=0,1,2)$

(2.57)

One possibility to model $\mu$ is as a function depending on the the local temperature

. Hence the equations depend in a nonlinear way on

and

. Information about the scattering term can be encoded into a fitting ansatz for the mobilities, for example in the form $\mu_{\phi} (T) = a_{\phi} T^{b_{\phi}}$ with fitting parameters $a_{\phi},b_{\phi}$ .

Alternatively, we can approximate the mobilities as functions of temperature and doping using results from bulk Monte Carlo simulations, see Section 2.3.4.

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