欧洲电子显微镜介绍课件8_Lecture_V1

GaAs
InAs
GaAs y x
One Howie-Whelan computation is carried out for each column 1) g (x,y,z) = g (z) 2) g (z) >> Dg (z)
Z
Dg (z) is neglegiable
Sources for displacement of unit cells
Amplitude of diffracted beam depends on the spatial coordinate r
GaAs
InAs
GaAs

GaAs 002

InAs 002

GaAs 002
Column approximation
decomposition into columns
Displacement R of unit cells
crystal unit cell
one column for column approximation
when the electron travels through the column, it sees a shifted potential. The shift is equal to R.
Sources for displacement of unit cells
dislocations
perfect dislcocation (one lattice plane terminates at dislocation core
partial dilocations and a stacking fault
n
n1 n D z f ( n , z)

4-th order Runge Kutta method
f ( , z ) z z n nD z n1 n 1 6 ( k1 2k 2 2k3 k 4 ) k1 D z f ( n , zn ) 1 k2 D z f ( n 2 k1 , zn 1 2 D z) 1 k3 D z f ( n 1 k , z n 2 2 2 D z) k4 D z f ( n k3 , zn D z )
displacement vector
stacking fault
some strain
1 0 0 ... 0

at entrance, only undiffracted wave is excited
1 0 D z 0 D z f ( 0 , z ) z

Decomposition into slices for multi-slice algorithm
one slice
thickness of one slice is e (e.g. ¼ unit cell)
1 2 3
0 1 2 3
For improvement of accuracy
ቤተ መጻሕፍቲ ባይዱ
1 2
3
0 1 2 3
wave function must be propagated ½ e at the beginning, and - ½ e at the end.
strained layer multi layer systems: layer and substrate have different lattice parameter
lattice planes are strained close to the interlayer – „displacement“ of unit cells