View source for Specific Process Knowledge/Etch/DRIE-Pegasus/TrenchCharacterisation

<!-- Ok, jmli 20180629 -->
<!--Checked for updates on 5/10-2020 - ok/jmli -->
<!--Checked for updates on 15/8-2023 - ok/jmli -->
{{contentbydryetch}}  

'''Feedback to this page: 
[mailto:labadviser@nanolab.dtu.dk?Subject=Feed%20back%20from%20page%20http://labadviser.nanolab.dtu.dk/index.php/Specific_Process_Knowledge/Etch/DRIE-Pegasus/TrenchCharacterisaion click here]'''
[[Category: Equipment |Etch DRIE]]
[[Category: Etch (Dry) Equipment|DRIE]]


= Characterization of DRIE silicon trenches =
Dry etched silicon trenches come in many sizes and shapes. In most cases the best way of characterizing them is to cleave the wafer perpendicularly to the trench and inspect the profile in an SEM or optical microscope. The SEM provides by far the best information as there are no challenges with limited depth of focus or image resolution. To make a complete data set with, say, variations trench widths or etch loads 
the work of adding measurements to SEM images, collecting the data and making sure that it is complete is, however, tedious. 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 by using a Matlab script as the one described below.

== Using Matlab scripts ==

A Matlab script automating the measurements from SEM images on etched trenches has been developed in the Matlab AppDesigner. It follows the sequence:
# '''Input parameters''': The information about the etch process can be entered manually or read from a text file. 
## Date
## User
## Wafer info: Substrate size, material etched, etch load, mask material and thickness
## Chamber conditioning, steps before the actual etch
## Wafer ID, Labmanager process log
## Recipe, duration, number of cycles
## Comments
## Mask thickness before and after etch
# '''Input images''': A list of SEM images (only tiff format images from Carl Zeiss SEM's that have a correct header can be used) is entered and measurement points are added to every image one by one.
## The pixel size in the the SEM image is read from the tiff image header


'''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 <math>\times</math> PS

; Etch rate (expressed either as nm/min or µm/min  or as nm/cyc or µm/cyc)

: Divide the etched depth (ED) by the etch time (ET) or the number of Bosch cycles (NC) of the process:   

: <math> \tfrac{\mathrm{ED} \times \mathrm{PS}}{\mathrm{ET}}</math>  

: or

: <math> \tfrac{\mathrm{ED} \times \mathrm{PS}}{\mathrm{NC}}</math>  

; Sidewall bowing (%)

: The sidewall bowing is a measure of how much the sidewall profile at mid-depth deviates from a straight line drawn between the top width and bottom width points - regardless of what angle it is at:

: <math> \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}}</math>
: or 
 
: <math> \sin(\cos^{-1}(\tfrac{
\alpha}{\sqrt{\mathrm{ED}^2+\alpha^2}})) \times \tfrac{\mathrm{MW} - \alpha}{2\sqrt{\mathrm{ED}^2+
\alpha^2}}</math> with <math> \alpha = \tfrac{\mathrm{TW}-\mathrm{BW}}{2} </math>

; Mask etch rate (nm per min.)

: <math> \tfrac{(\mathrm{MT-MR}) \times \mathrm{PS}}{\mathrm{ET}} </math>

; Selectivity

: <math> \tfrac{\mathrm{ED}}{\mathrm{MT-MR}}  </math>
 
; CD loss (nm per edge)

: <math> \tfrac{(\mathrm{MO-TW})}{2 } </math>

; Sidewall angle (degrees)

: <math> \cos^{-1}(\tfrac{
\mathrm{TW-BW}}{2 \sqrt{\mathrm{ED}^2+(\tfrac{\mathrm{TW}-\mathrm{BW}}{2})^2}}) </math>

: or 
 
: <math> \cos^{-1}(\tfrac{
\alpha}{\sqrt{\mathrm{ED}^2+\alpha^2}}) </math> with <math> \alpha = \tfrac{\mathrm{TW}-\mathrm{BW}}{2} </math>

=== What the numbers fail to represent or ignore ===
The numbers and measurements above provide a reasonable good basis for comparing DRIE trenches. They do, however, not take the following aspects into account:

* '''Complex sidewall profiles''': The numbers give most sense if the profiles are almost straight. The more they deviate, the more nonsense...
** Excessive bowing
** Undercut features
* '''Aspect ratio dependent etching''': Trenches with high aspect ratios typically etch faster in the beginning of the etch process compared to the end because of aspect ratio dependent etching. The correct approach would be to establish an initial and a final etch rate but that requires more elaborate measurements. 
* '''Scallops''': The scallops from the Bosch process
*

=== Where have these numbers been used? ===

* [http://labadviser.danchip.dtu.dk/index.php/Specific_Process_Knowledge/Etch/DRIE-Pegasus/processA#Results:_Etched_depths_in_trenches_of_different_widths| Investigation of Process A performance on Pegasus 1]