Using the result of Prob. 3.15 we will assume that the non-zero and
linearly independent elements of the electromechanical tensor em
in wurtzite crystals have the contracted form:
In the contracted notation the strain tensor e corresponding to a phonon with displacement vector u and wavevector q is given by:
Once the strain tensor and the electromechanical tensor are known the
polarization P induced by the strain can be calculated from the
definition: Pi=(e)ijej while the
electric field E is related to P by: 
, 
being the dielectric constant.
To simply the notation without loss of generality we can assume that
the z-axis is parallel to the c-axis of the wurtzite structure and the
y-axis lies in the z-q plane so that 
. With
this notation we obtain:
From this strain tensor we obtain the polarization:
and the electric field. In particular we are interested in the longitudinal component of this piezoelectric field since this will couple most strongly to an electron. The longitudinal electric field El is given by the projection of E along q:
From this longitudinal field we can define a scalar potential V such
that
Note that a factor of 
is missing in
the book.
Copyrighted by Peter Y. Yu, 1997. You are allowed to download this material for your personal use. Reproduction for commercial sale prohibited.