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Page 2 of 3

2) A certain hypothetical material with cubic crystal symmetry is characterized by the E-k plot sketched in Fig. P3.4. a) Which set of holes, band A holes or band B

holes, will exhibit the greater [100]-direction (mxx) effective mass? Explain.

b) Sketch the expected form of the valence-band constant-energy surfaces for the represented cubic material. Assume that the E-k relationship is parabolic (i.e., an ellipsoid of revolution).

Page 3 of 3

3) The E-k relationship about the GaAs conduction-band minimum becomes non-parabolic at energies only slightly removed from Ec and is more accurately described by

( )2 4 0, 0cE E ak bk a b− = − > > (a) What effect will the cited fact have on the effective mass of electrons in the GaAs conduction

band? Substantiate your conclusion. (Is your answer here in agreement with the Table 3.1 footnote?)

(b) Electrons in GaAs can transfer from the Γ minimum to the L minima at sufficiently high electric fields. If electrons were to transfer from the Γ minimum to the L minimum shown in Fig. 3.13(d) of the notes/text, would their effective mass increase or decrease? Explain. (The constant-energy surfaces about the L minima are actually ellipsoidal, but for simplicity assume the surfaces to be spherical in answering this question.)