Specific Process Knowledge/Etch/DRIE-Pegasus/TrenchCharacterisation

Quantify profiles

The challenge is here to get the best information possible about the profile with as little effort as possible. The information acquired must be simple and useful.

Input parameters

The trenches are cleaved and their profiles inspected in a SEM. Instead of adding a ton of measurements to each SEM image while at the SEM and hence spend an unreasonable amount of time there, I prefer to do the measurements afterwards: Opening the 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)

...self explanatory.

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.

Top Width (TW)

The narrowest part of the open feature near the surface.

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..

Mask Remains (MR)

The thickness of the mask that remains.

Output parameters

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

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

Mask etch rate (nm per min.)

${\tfrac {(\mathrm {MT-MR} )\times \mathrm {PS} }{\mathrm {ET} }}$

CD loss (nm per edge)

${\tfrac {(\mathrm {MO-TW} )}{2}}$

Sidewall angle (degrees)

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

or

$\cos ^{-1}({\tfrac {\alpha }{\sqrt {\mathrm {ED} ^{2}+\alpha ^{2}}}})$ with $\alpha ={\tfrac {\mathrm {TW} -\mathrm {BW} }{2}}$

Parameters

	In the image the following parameters are shown: Top Width (TW) Depth (D) Bottom Width (BW) Mid Width (MW) To speed up the characterisation post-SEM the parameter 'Pixel Size' (PS) is added to the SEM databar (the blue circle).
	Depth	D*PS
	Bowing	$2{\frac {MW-{\frac {TW+BW}{2}}}{(TW+BW)}}$
	Sidewall angle	$acos({\frac {TW-BW}{2{\sqrt {D^{2}+{\frac {1}{4}}(TW^{2}-BW^{2})}}}})$

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