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CHAPTER 2 Theory of Solids Because of the difference in motion of the marble in these two cases, the mass of the particle would appear to be different in water than in oil. (As with many analogies, we must be careful not to betoo literal.) If we consider the movement of an electron in the top of the valence band,we find that the effective mass is negative. An electron moving near the top of an allowed band behaves as if it has a negative mass. We must keep in mind that the effective mass parameter is used to relate quantum mechanics and classical mechanics. The attempt to relate these two theories leads to this strange result of a negative effective mass. However, solutions to Schrodingers wave equation also lead to results that contradict classical mechanics (see results from Appendix E). The negative effective mass is another such example. In discussing the concept of effective mass in this section, we used an analogyof marbles moving through two liquids. Now consider placing an ice cube in the center of a container filled with water: the ice cube will move upward toward the surface in a direction opposite to the gravitational force. The ice cube appears to have a negative effective mass since its acceleration is opposite to the external force. The effective mass parameter takes into account all internal forces acting on the particle. If we again consider an electron near the top of an allowed energy band and use Newtons force equation with an applied electric field, we will have However, m* is now a negative quantity, so we can write An electron moving near the top of an allowed energy band moves in the same direction as the applied electric field. The hole, then, has a positive effective mass denoted by m; and a positive electronic charge so that it will move in the same direction as an applied electric field. The effective mass just discussed is referred to as the density of states effective mass. These parameters for various semico