Substrate manufacturers usually mention the roughness of the substrates that they sell. However, they do not say over what area the roughness was measured. If Dupont are selling plastic films with roughness of 0.7 nm, does this mean that this roughness is the average roughness of the whole substrate? (it is an A4 sheet in this case.)
In the case of GaAs wafer you find a declaration of the parameter here:
http://www.freiberger.com/en/products/gaas-wafers/standard-definitions.html
So they measure substrate roughness for the whole substrate, i.e. on a mm to cm scale right?
That is right, but the edge exclusion is 3 mm. The wafer diameter you find here:
http://www.freiberger.com/produkte/gaas-wafer/spezifikationen.html
sorry, in English:
http://www.freiberger.com/en/products/gaas-wafers/specifications.html
Surface roughness is well described by a scaling theory for self-affine fractal surfaces (for details see works G. Palasantzas, J. Krim, Phys. Rev. B48 (1993) 2873 and G. Palasantzas, Phys. Rev. B48 (1993) 14472). Generally speaking below a certain correlation length the roughness parameter scales with a linear dimension of the analyzed area (e.g. by AFM). Above this correlation length this function saturates and the saturation value is assumed as a roughness parameter.
Roughness is descriptive number of the surface. Then it depends on the scale you need to work. For example, in micro-nano scale and studying roughness by AFM, you need to take a series of the most representative regions, images big enough to get as many observable features as posible but small enough to keep the feature resolution. Also avoid regions with defects and non typical features such as imerfections or contaminants.
@ F. Caballero-Briones: Your advice is not meant as serious for a comercial substrate manufacturer?! ;-)
You,re right Volker, I tried to describe a local measure for surface quality sucha as Andrejz did. Commercial mueasurements are as you mention :) cheers
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