Determine size of mask opening for membrane etch using KOH

twfr        thickness of wafer in m
tmem     thickness of membrane in m
size        size of one side of membrane in m
sel          mask size


Aqueous solution of KOH or pottasium hydroxide is widely used in MEMS to define deep cavities with slanted walls like that of the pressure sensor cavity. KOH based anisotropic etching gives good accuracy and control over the etch profile with very limited lateral etching. Thermal oxide is often used to selectively mask the substrate during KOH etch due to the low etch rate of oxide in KOH.

Etching of a <100> silicon substrate using KOH will produce well defined slanted walls formed by <111> plane at angles of 54.74 to the <100> plane. If the opening of the etch mask is wide enough these slanted walls will form a similar shaped feature at the bottom of the etch pit. If the size of final feature (membrane) is known along with how deep it was etched to reach that pattern, the initial size of the mask opening can be calculated. A square membrane is considered, but for a rectangular membrane, the length of each side of the mask can be found separately using the same interface.

The plot shows the the mask opening required to create membranes of various thickness of the given size for a given wafer thickness. Using the crosshair, the mask size can be directly read off for any membrane thickness.


-The base wafer is assumed to be <100> oriented silicon surface.
-The undercutting of the mask due to etching of <111> planes is assumed to be very small and hence not considered.
-The undercutting of the mask may vary based on doping concentration of the base wafer.
-The temperature and concentration of the etchant remains constant.
-The influence of misalignment of the mask is not considered..
-The thermal oxide mask is assumed to be free of pin holes and defects.
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