MSE 460: Electronic Materials and Processing I

Problem set #4; assigned February 16

1. Show that that the matrix element that connects the different sp3 hybrids on the same atom is given by (E_s-E_p)/4.
2. What are the values of the Bloch sum g₀ (AR Eq. 5.13) at the G, X, and L points of the Brillouin zone? (Do not calculate the other sums such as g₁.)
3. Using the expression for the energies at the G point (AR Eq. 5.15), what does the LCAO model predict for the bandgap of GaAs using the parameters listed in Tables 5.1 and 5.2 and the values of the matrix elements given in Problem 5.11 of AR? Check your answer using this Java program. Note that there is a sign error in Table 5.1: the energies of the s and p states in this table should be negative. Also, there are two mistakes in Problem 5.11 of AR. The value of (^h/_2p)² /m is incorrect and the expression for the bond length is incorrect.

---

File translated from T_EX by T_TH, version 3.74.
On 17 Feb 2009, 12:15.