Semiconductors

Abstract

Starting with the development of the transistor by Bardeen, Brattain, and Shockley in 1947, the technology of semiconductors has exploded.

Problems

• 6.1. For the nondegenerate case where $E - \mu \gg kT$, calculate the number of electrons per unit volume in the conduction band from the integral

  $$ n = \int\limits_{{E_{c} }}^{\infty } {D\left( E \right)f\left( E \right){\text{d}}E.} $$

  D(E) is the density of states, f(E) is the Fermi function.

• 6.2. Given the neutrality condition

  $$ N_{c} \exp \left[ { - \beta \left( {E_{c} - \mu } \right)} \right] + \frac{{N_{d} }}{{1 + a\,\exp \left[ {\beta \left( {E_{d} - \mu } \right)} \right]}} = N_{d} , $$

  and the definition $x = { \exp }(\beta \mu )$, solve the condition for x. Then solve for n in the region kT ≪ E_c −E_d, where $n = N_{c} { \exp }[{-}\beta (E_{c} {-}\mu )]$.

• 6.3. Derive (6.45). Hint—look at Sect. 8.8 and Appendix 1 of Smith [6.38].

• 6.4. Discuss in some detail the variation with temperature of the position of the Fermi energy in a fairly highly donor doped n-type semiconductor.

• 6.5. Explain how the junction between two dissimilar metals can act as a rectifier.

• 6.6 Discuss the mobility due to the lattice scattering of electrons in silicon or germanium. See, for example, Seitz [6.35].

• 6.7 Discuss the scattering of charge carriers in a semiconductor by ionized donors or acceptors. See, for example, Conwell and Weisskopf [6.9].

• 6.8 A sample of Si contains 10⁻⁴ atomic per cent of phosphorous donors that are all singly ionized at room temperature. The electron mobility is 0.15 m² V⁻¹ s⁻¹. Calculate the extrinsic resistivity of the sample (for Si, atomic weight = 28, density = 2300 kg/m³).

• 6.9 Derive (6.163) by use of the spatial constancy of the chemical potential.

• 6.10 Describe how crystal radios work.