After relaxation, we obtained central InP bond lengths of 2.480Å along the 111 axis parallel to the C3v axis, and 2.421Å otherwise (an error of 2.4% and 4.7% respectively, as the experimental bond length is 2.54 Å). The bond elongation in the (111) direction is due to the intrinsic dipole moment of a bond centred cluster. The nearest neighbour P-In-P bond angle was 111.5, and 107.3 when using the In-P bond parallel to the C3v axis; these are within 2 of the tetrahedral angle.
We next fitted the Musgrave Pople potential to the derivatives for the inner eight atoms (this is described further and the potential given in Section 2.8.2). The coefficients are shown in Table 4.1.
|L(,,)||LO||340 10||340.5||(5,6) 335.27|
|TO||317 5||315.5||(4) 314.03|
A supercell calculation of the full phonon dispersion curve was performed using the Musgrave-Pople interatomic potential. This is given in Figure 4.2 along with various experimental values. Selected values from this curve are given in Table 4.2. We do not obtain any LO-TO splitting because of an absence of long range electric field effects in the potential. The highest bulk phonon modes are 354.80 (351), 324.59 (328.5), and 335.27 cm-1 (340.5) at , X, and L respectively (the experimental modes are in brackets, at 20K), thus our frequency errors are 4 cm-1. The calculated band gap for InP was 0.84 eV, compared to an experimental value of 1.34 eV deduced from optical data, and is in good agreement with a previous LDF value of 0.8 eV (see Section 4.2 above). Our calculated band gap is underestimated, which is unusual for a cluster calculation.
We conclude that our method gives bond lengths and local vibrational modes within an acceptable error range.