# Flächen- und Volumendichten

Das ist ein kleiner Anhang aus dem Hyperscript "Semiconductors". Er enthält alles, was man zur Thematik wissen sollte

Changing from volume to surface concentrations might be a bit confusing, especially for mathematicians.
If you imagine a distribution of (mathematical) points in space with an average density of nv, and then ask how large is the density ns of points on an arbitrary (mathematical) plane stretching through the volume, the answer is ns = 0, because mathematical points are infinitely small and mathematical planes infinitely thin - you never will cut a point with a plane this way.
Our points, however, are atoms - they are not infinitely small. Our planes are not infinitely thin either, their minimal useful thickness corresponds to the size of an atom, or to a lattice constant.
So in computing a surface density of atoms, you can do two things:
1. You actually count the atoms lying on the chosen plane of the crystal (making sure you know if you want your density for a lattice plane or for crystallographically equivalent sheets of atoms in a crystal
This is not the same: the density of atoms on a {100} atomic layer of a fcc crystal is only 1/2 of that of a {100} lattice plane; if you don't see it, make a drawing!
2. You just take the atoms contained in a sheet with thickness a. For an area of S cm2 its volume thus is A · a . Since a volume of 1 cm3 contains nv particles, a volume of A · a contains nv · A · a particles; the surface density nS thus is

nS  =   nv · A · a
A
=  nv · a

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6.2.3 Difffusionskoeffizient und atomare Mechanismen

6.2.2 Die Fickschen Diffusionsgesetze

Lösung Übung 4.1-2

© H. Föll (MaWi 1 Skript)