Radius Of Curvature Formula – Radius Of Curvature Equation

What is Radius Of Curvature?

In the case of differential geometry, the radius of curvature or R is the reciprocal of the curvature. For a given curve, it is equal to the radius of circular arc that perfectly approximates the curve at a particular point.

For surfaces, the radius of curvature is given as radius of circle that best fits the normal section or combination thereof. The major applications of the concept can be seen in differential geometry, to measure the radius of curvature of earth or bending of beams in a three-part equation. It is also used in optics as well.

The concept can be understood better by studying stress in semiconductor structures that usually involves the evaporation of thin films results from thermal expansion. This stress happens because film depositions are usually made up of the room temperature. When temperature is cool down to the room temperature then the difference in thermal expansion coefficients of substances will cause the stress.

Radius Of Curvature Formula

The intrinsic stress results due to microstructure created in films as atoms and deposited on substrate. The same stress in thin films semiconductor is the reason of buckling in wafers. Here, the radius of curvature of stressed structure can be described by modified Stoney formula.

\[\large R=\frac{(1+(\frac{dy}{dx})^{2})^{3}}{|\frac{d^{2}y}{dx}|}\]

Also, the radii of curvature can be measured through the optical scanner methods. There are modern scanner tools as well that are used to measure the full topography of substrate and to measure the principal radii of curvature too. It can give accuracy of the order of 0.1% for radii of curvature of 90 meters and more.