Characterization of DRIE silicon trenches

Deep silicon trenches come in many sizes and shapes. The best way of characterizing them is to cleave the wafer perpendicular to the trench and inspect the profile in an SEM or optical microscope. In the SEM the challenge is to get the best information possible about the profile with as little effort as possible. The information acquired must be simple and useful. Below is an example.

Input parameters

At the SEM

Many users make measurements using the annotations in the SEM. However, instead of adding a ton of measurements to each SEM image while at the SEM and hence spend an unreasonable amount of time there, one can postpone making the measurements till afterwards. The only requirement is that the pixel size of every SEM image is known - one can add it to the datazone: See any SEM manual for instructions - for instance HERE

Making measurements

Opening the SEM images with Irfanview (or any other image viewer with the same possibilities) and drawing squares (the pixel dimensions are shown in the top) as measurements. These squares are one pixel wide compared to the 2 (or even 3) which are default for the annotations in smartSEM.

Pixel Size (PS): Shown in the datazone or read from the tiff header.
Number of cycles (NC): In case of a Bosch process, the number of cycles may be used instead of the process time.
Etch Time (ET): The duration of the etch process expressed as a number (5.5 minutes rather than mm:ss 5:30).
Mask Thickness (MT): The thickness of the mask prior to etching.
Mask Remains (MR): The thickness of the mask after etching.
Mask Opening (MO): The width of the mask opening measured at the mask/substrate interface.
Top Width (TW): The narrowest part of the open feature near the mask/substrate interface.
Mid Width (MW): The width of the trench at half the distance to the bottom of the trench.
Bottom width (BW): The width of the trench at the bottom. As many trenches have more or less rounded corners at the bottom, this point defined to be where the slope passes 45 degrees to the surface as indicated in the SEM image above with black bars.
Bottom Height (BH): The height difference between the 'Bottom width' points and the center of the trench.
Etched Depth (ED): The distance from the top to the bottom of the trench..

Output parameters

Assuming that all measurements in the image are done in pixels (as described above) rather than in microns/nanometers:

Etched depth (nm or µm)

The etched depth (ED) is rather self explanatory: ED

\times

PS

Etch rate (nm or µm per min.)

Divide the etched depth (ED) by the etch time (ET) of the process:

{\tfrac {\mathrm {ED} \times \mathrm {PS} }{\mathrm {ET} }}

Sidewall bowing (%)

The sidewall bowing is a measure of how much the sidewall profile deviates from a straight line - regardless of what angle it is at:

\sin(\cos ^{-1}({\tfrac {\mathrm {TW-BW} }{2{\sqrt {\mathrm {ED} ^{2}+({\tfrac {\mathrm {TW} -\mathrm {BW} }{2}})^{2}}}}}))\times {\tfrac {\mathrm {MW} -{\tfrac {\mathrm {TW} +\mathrm {BW} }{2}}}{2{\sqrt {\mathrm {ED} ^{2}+({\tfrac {\mathrm {BW} -\mathrm {TW} }{2}})^{2}}}}}

or

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin(\cos^{-1}(\tfrac{ \alpha}{\sqrt{\mathrm{ED}^2+\alpha^2}})) \times \tfrac{\mathrm{MW} - \alpha}{2\sqrt{\mathrm{ED}^2+ \alpha^2}}} with