Download thin films2

Thin films II
Kinematic theory - works OK for mosaic crystals
& other imperfect matls
Doesn't work for many, more complicated films
Thin films II
(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
Thin films II
(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
!!!
Thin films II
(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
The Borrmann effect
Thin films II
(see Batterman & Cole, Dynamical Diffraction of X-rays by Perfect
Crystals. Rev. Mod. Phys. 36, p 681 (1964))
Past discussions of diffraction – 2 beams, in & out
("kinematic theory")
But these beams coherently coupled – energy swapped back
forth betwn them
&
Thin films II
Past discussions of diffraction – 2 beams, in & out
("kinematic theory")
But these beams coherently coupled – energy swapped back
forth betwn them
Must consider all of field as a unit
("dynamical theory")
&
Thin films II
For Borrmann effect, dynamical theory
predicts standing wave in diffracting
medium
Two solutions – one for no absorption,
one for enhanced absorption
Thin films II
Dynamical theory changes
Ewald construction
In dynamical theory, more than
one sphere
Thin films II
Dynamical theory changes
Ewald construction
In dynamical theory, more than
one sphere
Determine loci of permitted
Ewald spheres – the "dispersion
surface". Drawing vectors from
points on this surface to reciprocal
lattice points gives allowed waves
Thin films II
Main problem – solve Maxwell's eqns. for medium with periodic,
anisotropic, complex dielectric constant
assume solutions consistent with Braggs' law
obtain solns of waves w/ permitted wave vectors
tips of these vectors form dispersion surface
dispersion surface used to generate all diffraction effects
Thin films II
Correct for index of refraction in medium
Thin films II
Correct for index of refraction in medium
Nature of dispersion surfaces
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Each lattice point occupied by a dipole set into oscillation by
radiation field of electromagnetic wave passing thru crystal
Oscillation of dipoles produces radiation and create radiation field
Oscillation is itself a plane
wave advancing thru lattice
normal to lattice planes
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Each lattice point occupied by a dipole set into oscillation by
radiation field of electromagnetic wave passing thru crystal
Oscillation of dipoles produces radiation and create radiation field
Oscillation is itself a plane
wave advancing thru lattice
normal to lattice planes
Dipoles in lattice plane
oscillate in phase
Two waves result, one going up, other down
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Think now of two waves:
scattered wave shown in diagram, wave vector k,
velocity = c
dipole wave, wave vector K, velocity = nearly c
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Think now of two waves:
scattered wave shown in diagram, wave vector k,
velocity = c
dipole wave, wave vector K, velocity = nearly c
Can be shown that:
K = k(1+ ),  small
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Actually, K is an infinite set of vectors
In reciprocal space
Thin films II
(see James, Optical Principles of the Diffraction of X-rays,(1962))
Actually, K is an infinite set of vectors
In reciprocal space
In real space
Thin films II
(see Bowen and Tanner)
K slightly smaller than k
Interaction of incident and diffracted beams takes place at
and/or near
H
O
Thin films II
(see Bowen and Tanner)
Deviations in dynamical theory are extremely small
Highly magnified view req'd
Thin films II
(see Bowen and Tanner)
Deviations in dynamical theory are extremely small
Highly magnified view req'd
Interaction takes place
on hyperbolic surfaces
near L
Thin films II
(see Bowen and Tanner)
Unfortunately, cannot use dynamical theory to extract structure
directly from rocking curves
But, can use it to simulate rocking curves
These then compared to experimental curves and refined
Thin films II
MnxHg1-xTe on CdTe on GaAs substrate
Thin films II
Graded layers
Simulated rocking curves for
InxGa1-xAs on InP &
AlxGa1-xAs on GaAs