Effective mass of electron (hole) I was reading about the concept of effective mass and came across the statement that the effective mass of a particle can be negative, zero and even infinite. When will the effective mass of an electron (hole) become zero and infinite?
 A: @freecharly has given an excellent answer! In human words it means that the effective mass is the curvature of the conduction/valence band near its minimum/maximum (respectively for electrons/holes).
It is worth adding that electrons and holes in a crystal lattice are not free particles, but excitation of a complex system. Effective mass is just a way of making them resemble free particles by expending their energy to the second order in quasi-momentum. In other words, physically it is not the same as the real mass.
A: For a given dispersion relation $\epsilon (\vec k)$ for electrons in a crystal , the tensor of the reciprocal effective mass is defined by $$ (1/m)_{ij}= \frac{1}{\hbar^2} \frac {\partial^2 \epsilon}{\partial k_i \partial k_j}$$ where $k_i$, $k_j$ are the components of the wave vector $\vec k$. When you chose the principal axes of this tensor for the $k_i$, you get an infinite mass $m_i \to \infty$ in a considered direction $k_i$ when $$\frac{1}{\hbar^2} \frac {\partial^2 \epsilon}{\partial k_i^2}=0$$ which happens at inflection points of the dispersion function in this direction,  and $m_i=0$ when $$\frac{1}{\hbar^2} \frac {\partial^2 \epsilon}{\partial k_i^2} \to \infty$$ 
