![]() In reality, there are different types of electrons and holes in a semiconductor (belonging to different valleys and subbands), and each type of the carriers (electrons or holes) may have complicated shapes of isoenergetic surfaces - ellipsoids (e.g., electrons in Si and Ge) that are characterized by two parameters - longitudinal and transverse effective mass (ml and mt), or warped surfaces (e.g., heavy holes in Si), etc. In general, the behavior of electrons and holes is determined by dispersion relation - dependence of energy on the wavevector k, and only in a simple model of effective mass this dependence looks similar to free electron dispersion relation: E=mp^2/2 = m(hk)^2/2. The concept of effective mass in semiconductors is an oversimplification of the real physical situation. ![]() In silicon, GaAs, and other materials hole effective mass is larger than electron effective mass, but in Germanium, for example, the opposite is true (m_h < m_e). In general, hole effective mass can be either larger or smaller than the electron effective mass - that depends on semiconductor material. The effective mass of a hole in semiconductors is positive (I should say - mostly positive, because warping of isoenergetic surfaces for holes in k-space (k is a wavevector) in some semiconductors - for example, in silicon - may lead to negative effective mass in certain domains of k-space).
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