For electron (or a hole) of a particular semiconductor (element or compound) how does the effective mass relate to the actual mass?
Usually the effective mass of an electron or a hole is given in units of the free electron mass, m0. For example, the effective mass of electron in Si is given here as 1.06m0, i.e, greater than m0:
http://en.wikipedia.org/wiki/Effective_mass_%28solid-state_physics%29
Thanks for your reply Gazi.
So can I say that the parameter that dictates whether the effective mass is greater or less than the free electron mass (or the actual mass) is dependent on the material or the solid that is considered ?
Shaumik, the effective mass is defined as the second derivative of the energy, therefore it depends also on the other parameters affecting the energy (band) structure of the material, for example, on stress applied to the material.
See e.g. this paper:
Quantum confinement effect on the effective mass in two-dimensional electron gas of AlGaN/GaN heterostructures J. Appl. Phys. 105, 073703 (2009); http://dx.doi.org/10.1063/1.3100206
I agree with those people commented on your question. You better start to understand the concept of effective mass from the definition which is given as the second derivative of the energy. Depending on the energy band structure of the material the effective mass will also differ from the free electron mass. I suggest you to read the text book by Charles KIttel."Introduction to Solid State Physics"
Yes, it can be. Think about some heavy fermions. In the composite fermion picture, the effective may diverge near the filling factor 1/2.
Understanding effective mass in terms of the second derivative of the energy band is the formally correct way, as mentioned in several posts above. On a more intuitive level, the classical mass of a particle relates its kinetic energy to its momentum. This relationship in free space is simple and is a fundamental property of the particle alone. In a solid, the particle is subjected to a strong crystal field that changes the energy / momentum relationship. Therefore, the free space mass is no longer the sole parameter that describes the particle motion. One can semi-classically recover the simple free space behavior, though, by defining the effective mass, which includes the influence of the crystal field. This brings you back the the second derivative of the energy band!
Thanks a lot to all for all your valuable suggestions and helping me out.
The effective mass has a mathematical definition - a mathematical convenience to get around having to include the internal forces acting on the electron in Newton's law of motion. It depends upon the band structure, i.e. the E(k) relation, and has nothing to do with the real mass of electron; so it can be greater or less than the physical mass of electron. When we write Newton's law of motion for the electron, we include only the external, i.e. the applied, force; the internal force is not included, but is represented by the mathematical entity of the effective mass.
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