Dislocation density

The dislocation density ρ is understood to mean the total length of all dislocation lines per unit volume in a crystalline solid . She has the unity ${\ displaystyle \ mathrm {{\ frac {m} {m ^ {3}}} = m ^ {- 2}}.}$

An increased dislocation density increases the strength in a metal (see work hardening ): ${\ displaystyle \ sigma}$

{\ displaystyle \ sigma \ propto {\ sqrt {\ rho}}}

and the deformability and electrical conductivity are reduced.

Example: The dislocation density in specially grown copper monocrystals is around 10 ⁸ m / m³ and can increase to around 10 ¹⁵ m / m³ in the event of strong deformation .

Measurement

Direct methods

Displacement rates / EPD determination

The oldest known way of making dislocations visible and determining their density is to etch the relevant crystals . At the same time, atoms are more easily removed from the stress field of near-surface dislocations. So-called etch pits are created , the density of which can be counted in a light microscope . The resulting etch pit density , engl. Etch pit density, EPD for short , is a measure of the quality of semiconductor wafers , especially in the semiconductor industry .

Silicon wafers for microelectronics or epitaxy usually have a relatively low etch pit density of <10 ³ cm ^−2, while GaAs wafers, for example, are in the order of 10 ⁵ cm ⁻² .

The determination of the etch pit density is regulated in DIN 50454-1 and ASTM F 1404.

TEM

The stress field around dislocations can also be made directly visible in the transmission electron microscope (TEM). This also enables the density of dislocations to be determined using image evaluation methods. However, since the volume that can be observed in an image is very small, there is a lot of effort involved.

Infrared light microscopy

In the case of semiconductors, the dislocation density can also be determined with special light microscopes that work with IR light . Many semiconductors are transparent in this spectral range - the dislocation lines become visible and can be counted.

Indirect methods

The dislocation density can also be determined using diffraction methods. The most frequently used method is the X-ray profile analysis , which measures the profile broadening of X-ray peaks as a result of the (integral) lattice distortion in the vicinity of the dislocations.

literature

Günter Gottstein: Physical basics of materials science. 2nd edition, Springer Verlag, Berlin Heidelberg 2001, ISBN 978-3-540-41961-7 .
B. Ilschner, Robert F. Singer: Materials science and manufacturing technology. 3rd edition, Springer Verlag, Berlin Heidelberg 2002, ISBN 978-3-540-67451-1 .
Günter Gottstein: Materials Science and Technology. 4th edition, Springer Verlag, Berlin Heidelberg 2014, ISBN 978-3-642-36602-4 .

Web links

Solidification mechanisms of metallic materials (accessed on November 10, 2016)
Modeling and simulation of crystal-plastic materials with the aid of dislocation densities (accessed on November 10, 2016)
Material Theory (accessed November 10, 2016)