Scattering from rough surfaces

Surface roughness scattering or interface roughness scattering is the elastic scattering of a charged particle by an imperfect interface between two different materials. It is an important effect in electronic devices which contain narrow layers, such as field effect transistors and quantum cascade lasers. [citation
last1=Valavanis
first1=A
last2=Ikonić
first2=Z
last3=Kelsall
first3=R. W.
date=2008-02-11
title=Intersubband carrier scattering in "n"- and "p"-Si/SiGe quantum wells with diffuse interfaces
journal=Phys. Rev. B
publisher=American Physical Society
volume = 77
issue = 7
pages = 075312
url = http://link.aps.org/abstract/PRB/v77/e075312
doi = 10.1103/PhysRevB.77.075312
accessdate = 2008-03-21]

Description

Interface roughness scattering is most noticeable in confined systems, in which the energies for charge carriers are determined by the locations of interfaces. An example of such a system is a quantum well, which may be constructed from a sandwich of different layers of semiconductor. Variations in the thickness of these layers therefore causes the energy of particles to be dependent on their in-plane location in the layer. [citation
last1 = Prange
first1 = R. E.
last2 = Nee
first2 = Tsu-Wei
title = Quantum Spectroscopy of the Low-Field Oscillations in the Surface Impedance
journal = Phys. Rev.
volume = 168,
issue = 3
pages = 779-786
year = 1968
month = April
doi = 10.1103/PhysRev.168.779
publisher = American Physical Society
accessdate= 2008-03-21] Although the roughness $Delta\_z(mathbf\{r\})$ varies in a complicated way on a microscopic scale, it can be considered to exhibit a Gaussian distribution [citation
first1 = H.
last1 = Sakaki
first2 = T.
last2 = Noda
first3 = K.
last3 = Hirakawa
first4 = M.
last4 = Tanaka
first5 = T.
last5 = Matsusue
title = Interface roughness scattering in GaAs/AlAs quantum wells
publisher = AIP
year = 1987
journal = Appl. Phys. Lett.
volume = 51
issue = 23
pages = 1934-1936
url = http://link.aip.org/link/?APL/51/1934/1
doi = 10.1063/1.98305
accessdate = 2008-03-21] characterised by a height $Delta$ and a correlation length $Lambda$ such that:$langleDelta\_z(mathbf\{r\})Delta\_z(mathbf\{r\text{'}\})\; angle\; =\; Delta^2expleft(-frac\{|mathbf\{r\}-mathbf\{r\text{'}\}|^2\}\{Lambda^2\}\; ight)$

Notes