Conduction in Solids I have some text:

I could understand it partially.
My doubts are:


*

*What is effective mass $m^*$ (real meaning apart from explained in this text) and how can we calculate it/or what is it's value? and why?

*In actual situation $\lambda$ would not be $\infty$. yes? and if yes then how can we make it very large by changing temperature and frequency, i.e. which range  of these parameters (high or low) is suitable?

 A: In a crystal, each electron polarizes its vicinity, meaning positive charges prefer to stay nearer to the electron while negative charges move away from it. As the electron traverses through the crystal, it has to drag the polarization cloud with it, which can effectively increase or decrease its mass. Actually, the system "electron+polarization cloud" can be considered as a quasiparticle and it is the mass of this quasiparticle that we usually refer to as the effective mass of the electron (or hole). There are many ways to determine $m^*$, but perhaps the simplest is to do a band structure calculation and find the second derivative of the conduction band minimum at the $\Gamma$ point, i.e. $1/m^* = \hbar^{-2} \frac{\partial^2 E}{\partial q^2}$. Alternatively, in a cyclotron resonance experiment, $m^*$ is determined from $\omega = eB/m^*$. The effective masses generally range from the order of a 100th of the free electron mass to almost infinity. The latter can refer to the case of self-trapping, where the electron or hole remains immobile regardless of the force applied.
In an ideal crystal without lattice vibrations, the mean free path would be infinite. In a real crystal there is always some scattering off defects, which include structural defects, impurities, and phonons. By lowering the temperature, $\lambda$ can be increased, but not to infinity. Also, even if you produce a perfectly pure sample, there will always be some contribution from the phonon zero-point motion, which leads to some scattering and hence a finite $\lambda$.
A: As far as I understand. The effective mass is given by a lattice. There is a periodic field that makes electrons move differently in comparison to free electrons.
