Figure 1. Control factor distribution
| CONTROL FACTOR | SETTING |
| LDD Implant Dose | 10E14atoms cm-2 |
| LDD Implant Energy | 60 keV |
| Sidewall Slope | 90° |
Table 1: Nominal Control factor settings for the distributions shown in figure 1 and 2.
Since we have a response surface that is a function of the control factor settings we can use this to calculate process distributions. Each individual control factor will have a distribution about its setpoint - e.g. a nominal 90° slope will have a wafer-to-wafer variation of a few degrees. We would expect the distribution to be Gaussian. Figure 1 shows sample distributions for each of the control factors.
Figure 1. Control factor distribution
Each of the 4 responses is a function of all of the control factors. If we choose one point within each control factor distribution we can calculate a corresponding value for each of the four responses. If this process is repeated many times and each control factor point is chosen at random with respect to the other two, the corresponding responses will show a distribution profile as shown in figure 2.
Figure 2. Response distributions for the control factor variation of figure 1
An RPL (RS/1 Programming Language) procedure has been written to select points within each control factor distribution. Each control factor point is chosen at random with respect to the other two control factor points. The corresponding responses are calculated using the response surfaces you calculated in exercise 3. This allows the response distributions to be calculated as seen in figure 2.
Before this procedure can be run, the file EX4_START.ARX must be downloaded into your home directory and then dearchived to be used within RS1. It is also recommended that you print this webpage before continuing so that the results can be recorded.
Open EX4_START for editing by selecting file->edit in the browser window, and view the worksheet by selecting option 2 (ENTER) and using both default values. It can be seen in rows 7 and 12 that there
are empty cells. Note the values of Slope, Dose, and Energy of these rows.
Row 7:
Slope = ____________
Dose = _____________
Energy
= ____________
Row 12:
Slope = ____________
Dose = _____________
Energy
= ____________
To find the missing response values of V_PT_MIN in row 7 and R_SD_MAX in row 12, exit the table (/exit) and then type the following to initiate the RS1 procedure:
!call #distrib
The experiment name is EX4_START. Re-use the StDev values, do not include the 1.5 sigma drift and do not use the previous factor settings. See the screen shot.
Enter control factor values which you should have noted down when prompted and use default number of random samples. Record the results generated in
the space provided below. Some of the results can be obtained by plotting the graphs, however for a complete table of results, select no when prompted
to plot distributions. Repeat this using the second set of values noted.
V_PT_MIN = _______________________(row 7)
R_SD_MAX = _______________________(row 12)
It is now possible to go back to the worksheet and enter the results. To do this, move to the empty cells using the cursor keys, enter the new value, and then answer yes. This will enable curves to be fitted to the responses. If you are having problems at this stage, you may download the archive file called EX4_TABLE.ARX (shift-click to download). Copy this experiment into your own directory then dearchive it within RS1.
Once this has been done it is possible to optimise the fit of the models used. In order to do this you must first leave the table by typing: /exit
To do this use the following command sequence:
4. ANALYZE 4. FIT Models, At this point you will be asked which model you want to fit to, type: DESIGN and press RETURN *** 8. RESPONSE/MODEL At this point you will be asked to select a response : you need to complete the following steps for both the V_PT_MIN and R_SD_MAX responses. 5. REFINE Model 1. STEP Enter term(s) to move in and out,AUTO, MOVETO, or STOP: This stage is optimising the model for representing the response, terms that have little relevance are removed. The program will either suggest a variable to remove from the expression or will suggest stopping (Variables will move from the P-Remove column to the P-Enter column in the table as they are removed) it is suggested that the default values in sqaure brackets are used. 11. NEXT 6. CHECK Fit 1 CHECK Y TRANSFORM As it is possible that the best can representation be achieved using LOG(Y) = expression or 1/Y = expression - this checks various transforms and plots the results. The lowest value indicates the most appropriate transform, the program will pick this up and complete the conversion. select continue 3 CHECK ROBUST This will attempt to optimise the fit by applying a weighting to each of the values with lower weighting being associated witht hose points that are far from the line and a high weighting for those close. Various approximations are tried and a curve for the weightings is selected select continue 8. NEXT 7. ACCEPT Model You will be asked to store a temporary model - select Yes Then you will be asked for a name for the model - pick one or go with the default, it is up to you ACCEPT which model? DESIGN Choose one response to accept model DESIGN: this will be either V_PT_MIN or R_SD_MAX depending on which you have optimisedAt this point you should go back and to the point above, marked *** in the left hand margin and complete the steps for the other response.
The generation of all models within the experiment can be a lengthy process.In order to keep every one consistent download the file if you have any problems EX4_AF_COMPLETE.ARX which provides a completed table with the correct models present.
Once you have fitted all the responses (loaded the file) you can now contour plot the desired values.
To do this use the following command sequence:
5. INTERPRET
5. VISUALIZE,
2. CONTOUR/3D
3. MAKE Spec
- give the spec a name (eg newspec)
4. MODIFY Spec
6. SURFACES - You are then asked for the selected surface variable. We want to
only display the following:
V_PT_MIN
E_PEAK_MAX
GM_MIN
R_SD_MAX
You therefore want
to HIDE the response surfaces for:
E_PEAK
E_PEAK_MIN
E_PEAK_SNR
and PLOT the ones for
V_PT_MIN
GM_MIN
R_SD_MAX
(using the default level
values).- Type <RETURN> with no input to get back to:
INTERPRET.VISULIZE.CONTOUR/3D.MODIFY>
11. NEXT
6. PRODUCE GRAPHS,
- use the default settings to view the contour plot.
The final contour plot should now be displayed.
Last Update: 6th May, 2004