William Angerer - Department of Physics and Astronomy - University ...

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of this second order susceptibility element. We express the influence of the interface
states on X~~)=
as
(6.39 )
where X~~);bulk
is the second-order susceptibility element due to the bulk band structure
and x~~;interface
is the second-order susceptibility element due to interface states.
vVe calculated the minimum magnitude of X~;~interface
that is observable by SHG
spectroscopy using our theory of SHG from GaN in the p-in/p-out geometry (equation
(6.30)). Our calculation assumed an angle of incidence of 88° to ma.'{imize coupling
of the fields to X~;)=.
The interface states are said to be observable if they
influence the magnitude of the SHG signal by at least 10%. Our calculation determined
the minimum observable X~~);interface
in terms of the the bulk second-order
susceptibility as X~;);interface = 0.35X~~);bulk. If we assume IX~;~bulkl ~ -t.8 x 10- 8 esu
and an interface defect volume density, N i , of 10 15 em -3, then the minimum observable
interface defect hyperpolarizability is a~~t:rface
~ 1.7 X 10- 23 esu. This is a
nonphysical (too large) second-order hyperpolarizability, and illustrates that interface
defect states associated with X~;)z
are not observable. Note that this analysis is not
limited to GaN [0001]. The observation of X~;);interface
is inhibited by the large index of
refraction of GaN, which refracts the field polarization away from the z direction. and
the other nonzero susceptibility elements, which provide a large signal background.
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