Question

Which of following is true :
(1) Hole is missing electron in valence band
(2) Effective mass of hole is greater than that of electron
(3) Mobility of electrons is greater than that of holes
(4) All of the above​

Answer 1

Explanation:

The concept of effective mass follows from physicists' love for simple relations such as Ohm's law (current density = conductivity x electric field intensity) or Newton's second law of motion (acceleration = force / mass). For a free electron, the mass in the latter is just the electron mass. But, if one wants to write a similar relation for a charge carrier in a crystal lattice, the situation changes. Going through the math (see any solid state physics textbook) allows you to write F = m x a, where the force is charge x electric field, but the mass is no longer the mass of the electron, but reflects the curvature of the conduction band bottom (for electrons) or valence band top (for holes), as it is inversely proportional to the second derivative of the energy as a function of k. This is the so-called effective mass. Again, physicists like simple things, so one often expresses the effective mass as a constant x electron mass, although this has very little (or nothing) to do with the actual physics of the situation. Hence: it is just a practical mathematical construction aimed at simplifying equations (in a similar manner as the reciprocal lattice, for example). The hole itself is also a mathematical construction helping us to avoid using negative values for mass in the simple equations (the effective mass for conduction occurring through the unoccupied electron states in the valence band would be negative, if we didn't invert the charge).

In the majority of cases, the top of the valence band is clearly "flatter" than the bottom of the conduction band. From this follows that the hole effective mass is often larger than the electron effective mass. The top of the valence band tends to be flatter due to the asymmetry of the situation: you are talking about the highest occupied states for electrons. The bottom of the conduction band is formed by the lowest unoccupied states.