IMG29smallhw1.jpg - 3.5 The E-k relationship characterizing an electron confined to a two-dimensional surface layer is of the form hzki hzké E — E

IMG29smallhw1.jpg - 3.5 The E-k relationship characterizing...

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Unformatted text preview: 3.5 The E-k relationship characterizing an electron confined to a two-dimensional surface layer is of the form hzki hzké _ + ' E — E — C 2m1 2m2 ...m]¢m2 An electric field is applied in the x—y plane at a 45 degree angle to the x—axis. Taking the electron to be initially at rest, determine its direction of motion in the x—y plane. 3.6 Consider the detailed E-k diagram for GaAs reproduced in text Fig. 3.13(d). (a) How does one deduce the 300 K value of EC from the diagram. Is the value of EG(3()0 K) deduced from the diagram consistent with that quoted in the Fig. 3.17 in— sert? (b) How does one deduce that GaAs is a direct semiconductor from the given E-k dia- gram? (c) As best as can be determined from Fig. 3.13(d), is the pictured E—k diagra’m consistent with the effective masses for GaAs quoted in Table 3.1? Explain. 3.7 (a) The E-k relationship about the GaAs conduction—band minimum becomes non—para- bolic at energies only slightly removed from EC and is more accurately described by E—Ec=ak2—bk4 (a>0,b>0) What effect will the cited fact have on the effective mass of electrons in the GaAs con— duction band? Substantiate your conclusion. (Is your answer here in agreement with the Table 3.1 footnote?) (b) Electrons in GaAs can transfer from the F minimum to the L minima at sufficiently high electric fields. If electrons were to transfer from the T minimum to the L minimum shown in Fig. 3.13(d), 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.) 3.8 Like GaAs, GaP crystallizes in the zincblende lattice and the valence band maxima occur at the T-point in the first Brillouin zone. Unlike GaAs, the conduction band minima in GaP occur at the X-points in the Brillouin zone. (a) Where are the X—points located in k—space? (b) Is GaP a direct or indirect material? Explain. (c) Given that the constant energy surfaces at the X-points are ellipsoidal with mi/mo = 1.12 and mt/mo = 0.22, what is the ratio of the longitudinal length to the max— imum transverse width of the surfaces? (d) Picturing only that portion of the constant energy surfaces within the first Brillouin zone, construct a constant-energy surface diagram characterizing the conduction-band structure in GaP. ...
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