Long-Range Interactions in Semiconductors

We derive an exponentially decaying interaction between atoms in semiconductors. The decay length is $\hslash {\left[2\right(m_1+m_2\left)E_g\right]}^{-\frac{1}{2}}$, where $m_1$ and $m_2$ are the valence-band and conduction-band effective masses and $E_g$ is the minimum energy gap. We show that Weber's bond-charge model of lattice vibrations leads to exponentially decaying interactions. Comparing the experimental vibration spectrum and the theoretical decay length suggests that the flattening of the TA mode is due to this long-range interaction.