In a solid, like \(\mathrm{Si}\), the mobile charge carriers are in constant motion due to their thermal energy. This energy, a classic kinetic energy, is \(3 k_{b} T / 2\).

a. What is the thermal velocity, \(v_{t h}\), of the charge carriers at room temperature, \(300 \mathrm{~K}\) ? Use the effective mass given in Table 3.14.

b. What is the drift velocity of those carriers, \(v_{d}\), if their mobility, \(\mu_{e}\), is \(1000 \mathrm{~cm}^{2} / \mathrm{Vs}\) and the applied electric field, \(\mathcal{E}\), is \(1000 \mathrm{~V} / \mathrm{cm}\) ?

c. Compare the results of parts(a) and (b). Can we cause gas molecules to move faster than their thermal velocity using a pressure gradient? Can we get the charges to move faster than their thermal velocity?

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TABLE 3.14 Effective Masses of Charge Carriers in Semiconducting Materials Effective Mass of an Effective Mass of a Hole Material Electron meff (me) mheff (me) Si 0.26 0.38 Ge 0.35 0.56 GaAs 0.068 0.50 Source: Data obtained from Sze [40].