|Energy Bands and Charge Carriers in Semiconductors|
EXAMPLE 2.1: Find the dispersion relation for a free electron, and, thus, observe the relation between its rest mass and effective mass.
SOLUTION: For a free electron, the electron momentum is . Thus, . Therefore, the dispersion relation, i.e., the E-k relation is parabolic. Hence, . This is a very interesting relation, which states that for a free electron, the rest mass and the effective mass are one and the same, which is due to the parabolic band structure. Most materials have non-parabolic E-k relation, and, thus, they have quite different rest mass and effective mass for electrons.
Note: for severely non-parabolic band structures, the effective mass may become a function of energy, however, near the minima of the conduction band and towards the maxima of the valence band, the band structure can be taken to be parabolic, and, thus, an effective mass, which is independent of energy, may be obtained.
EXAMPLE 2.2: Calculate the approximate donor binding energy for Si ( r = 11.7, = 1.18).
SOLUTION: From Eq.(2.6), we have = 1.867 x J = 0.117 eV.
Note: The effective mass used here is an average of the effective mass in different crystallographic directions, and is called the "conductivity effective mass" with values of 1.28 (at 600 K), 1.18 (at 300 K), 1.08 (at 77 K), and 1.026 (at 4.2 K).
Fig.2.4 The density of states N(E), the Fermi-Dirac distribution function f(E), and the carrier concentration as functions of energy for (a) intrinsic, (b) n-type, and (c) p-type semiconductors at thermal equilibrium.
sábado, 20 de marzo de 2010
Publicado por Tecnología en Telecomunicaciones - conocimientos.com.ve en 11:24
Etiquetas: 3 Anderson J. Mariño O