The following presentation was made August 3rd, 1993 at the annual Stanford TCAD review.   Some of the problems indicated here have been corrected since then, but are still included as examples as to the kinds of problems you might encounter in simulation.

Some might argue that this type of negative publicity hurts TCAD.   I'll state that my ultimate goal is to improve the quality of simulation.   I hope to have success stories elsewhere at this site.   Think of this as a counter-balance to all those TCAD publications which show perfect agreement between simulation and measurements.

This presentation highlights the importance of boundary conditions, an aspect of simulation that is typically neglected.

April 17, 1996: update on segregation problem.

April 17, 1996: update on initial point defect concentration.

Purpose

• Raise awareness of TCAD weaknesses.
• Point out some representative problems.
• Make TCAD more useful.

Defaults

• Default coefficients adequate for qualitative simulation.
  • Change grid before changing coefficients.
  • Changing coefficients without understanding is risky.
• Default models often the simplest.
  • OED in SUPREM; mobility in PISCES.
• Effect of boundary conditions often overlooked.

Examples of Poor Default Coefficients

• N-type segregation is temperature independent.
• Segregation and transport (in general).
• Electron and hole lifetimes.
• OED parameters.
• RTA parameters.
• Mechanical properties - stress dependent oxidation.
• Polysilicon.

A pet peeve of mine is that fact that the segregation coefficient for N-type dopants is constant; independent of dopant species, time, temp, orientation, or oxidizing ambient.
 

Polysilicon Default Coefficients

• Poly coefficients often default to silicon values.
  • Mobility can be much lower [Kamins].
  • Diffusion 100x of silicon neutral values.
    (For high dopant concentrations, simulated diffusivity is higher in silicon - Dave Clark, TI)
  • Oxidation rate.
  • Work-function should be set explicitly [Lifschitz].
  • Polysilicon/silicon interface dopant pile-up.

The doubly negative intrinsic diffusivity is multiplied by (n/ni)^2. For high concentrations, this can be quite large. If your poly diffusion model assumes the intrinsic diffusivities for the charged vacancy states are zero, you can get the unusual situation that diffusion in Si is larger than in Poly.

The work-function must be set to get proper Vt results. Wf in n-type poly is typically 200 mV higher than for Si.
 

Poor Default Process Models

• Better models may be available, but must be requested.
• Clustering and activation (steady-state values).
• High concentration dopant diffusion.
• Angled ion implantation (angle independent channeling).
• No OED with diffusion model.
• No poly or sidewall oxidation with oxidation model.
• Damaged-enhanced diffusion/oxidation.

One of the most common problems in TCAD is the instantaneous de-activation of dopant caused by a final low temperature anneal in the simulation. Dopants don't really deactivate that fast at low temperature.

Some angled implant models simply tilt the incoming beam, and do not account for the different range due to the tilt angle (no channeling effects). Other models do properly include the effect of tilt.
 

Poor Default Device Models

• Better models may be available, but must be requested.
• Impact ionization model overpredicts substrate current.
• Field independent mobility overpredicts drain current.
• Auger recombination and bandgap narrowing reduce beta.

Default coefficients for drift-diffusion impact ionization typically overpredict the substrate current by factors of 10 or more.   I have not had much success using Energy Balance models.
 

Specific Problem Cases

• Diffusion through gate oxide.
• Dual Pearson implants.
• Capacitance of a metal line.
• Low temperature n-type oxidation.
• Setting initial point defect concentration.
• Stress dependent oxidation.

Diffusion Through Gate Oxide

• Frequent problem: phosphorus penetrating gate oxide.
• Cause: insufficient grid in oxide.
• Example: 500 A oxide with no grid versus 100 A grid.
• Recommendation:
  • Include several grid points in any thin oxide.
  • Check for dopant penetration.

Dual Pearson Implants

• Dual Pearson predicts dose dependent channeling tail.
• Does not account for rotation during implant.
  Problem pointed out by Peter Nunan, SEMATECH.
• Lateral coefficients are not dual Pearson.
  • Issue: Difficult to measure lateral profiles.

Peter used four 1/4 dose implants in his simulation, just as the fab did. I simply lumped them together into one implant. There was a significant difference between the two approaches, as the channeling tail was dose dependent, but there was no cumulative damage model. UT promptly corrected this when we pointed it out. Your version may not have this correction yet.
 

Boron concentration plots immediately after a 25 keV, 0 degree tilt, BF2 implant. There may be a sophisticated model for the channeling tail in the vertical direction, but not for the more important lateral profile. Of course, it is difficult to measure the lateral profile. UT is working on this problem using Monte Carlo simulations.
 

Capacitance and Boundary Conditions

• 1 um cylinder, 1 um above ground plane (nearest point).
• Analytic formula predicts 1.23E-16 F/um for oxide dielectric.
• Simulated capacitance depends on spacing to edges.
  • Boundary condition: normal component of E-field = 0.
  • "Adaptive boundary conditions" needed.

PISCES forces the potential countours to be perpendicular to the simulation structure edges. This can induce an artificial constraint on the problem if your structure is not wide enough.
 

Capacitance versus Spacing to Reflecting Edges

Spacing  Capacitance  Error
 (um)      (F/um)      (%)
   1      7.64E-17    -38
   2      9.76E-17    -21
   3      1.08E-16    -12.5
   4      1.13E-16    -8.3
   5      1.16E-16    -5.8
   6      1.18E-16    -4.3
   8      1.20E-16    -2.7
  10      1.21E-16    -1.8
  15      1.22E-16    -0.9
  20      1.22E-16    -0.6

This table shows the capacitance of 1 um cylinder that is 1 um above a ground plane versus the distance to the top, right and left of the simulation structure. Valery Axelrad pointed out that this is a worst case, and that you typically don't need structures 10x wider than the device. But sometimes you do.
 

Low Temperature N-type Oxidation

• Integrated dopant concentration increases during oxidation!
• 1E13/cm^2 arsenic, 50 keV; 800 C wet oxidation:

  Time   Tox    Dose (atoms/cm^2)
  (min)  (A)    Oxide    Silicon
   10     78   1.00e09   1.00e13
   20    135   4.92e09   1.00e13
   50    305   9.40e10   1.05e13
  100    588   1.07e12   1.12e13
  200   1258   1.21e13   2.20e13
  500   3191   5.56e13   2.07e13
  
  

Notice that the integrated dose is >> than the original implant dose. This problem is not as bad as it used to be. The worst case is slow diffusion and rapid oxidation.

Update: Andy Strachan said he couldn't reproduce this. Neither could I in recent versions of ATHENA or TSUPREM4. Looks like this is no longer a problem, although I still recommend checking integrated doses.
 

Low Temperature N-type Oxidation

• One solution: use finer grid.
• Recommendation (general):
  • Check integrated doping concentrations.
  • Check in more than one location.

Initial Point Defect Concentration

• Initial anneals affect subsequent diffusion.
  • Order of anneals; length of anneals affect results.
  • Problem pointed out by Dave Clark, TI.
• Process Description:
  • 1E16/cm^3 boron substrate
  • Pre-anneals (inert)
  • Implant arsenic, 1E16/cm^2, 50 keV
  • 900 C, 30 minute, dry oxidation
  • Measure junction depth

Junction Depths versus Pre-anneals

• Simulation uses TWO.DIM model
• Anneals are inert, and before arsenic implant!

   First Anneal   Second Anneal   Junctn Depth
       None             None        .4062
   900 C  1 min   1100 C  1 min     .5070
  1100 C  1 min    900 C  1 min     .5313
   900 C 10 min   1100 C 10 min     .5563
  1100 C 10 min    900 C 10 min     .4756
  
  

This was a disturbing problem. There was a large difference in the results depending on what you assumed for the initial point defect concentration. Typically, you do not specify the initial point defect profile, but they are created and annihilated starting with the first diffusion (even if it is non-oxidizing). When Dave reported this problem, he obtained deeper junctions when the first of the two inert pre-anneals was at the lower temperature. When making an example for this talk, I saw the opposite effect. Turns out the length of the pre-anneals has an effect as well.

Update: Andy Strachan also had trouble reproducing this problem. The pre-anneals appear to have no significant effect in current commercial versions of SUPREM4. However, the junction depth I get now is very different that the values above. This is with the original input file. This points out another issue - the evolution of default models and coefficients. It would be a good idea to keep a few simple examples laying around and re-run them whenever a new release comes out. If the results are different, you can then try to track down the reasons why. For example, the default implant range tables may be different. By placing "print interstitial" statements before and after the implant, I see where the default logical value for including implant damage has changed since the original problem was run. Hence, the same input file gives different results a few years later. It might be a good idea for industry to keep some generic files like this for comparing results when new versions arrive.

I asked Dave Clark for help with this one again. He was able to locate an old version of SUPREM4 which showed similar results to the above. That is, an anneal before the implant affected the final junction depth. This was always an unexpected result. I did not keep track of which version of the program I used to get the above results. In general, it would be a good idea to record the version used. I also received some good support from Don Ward in trying to understand what had changed over the years. More than one thing has changed, and I wasn't able to pin it down to a single cause. Let's just say the old version had a problem that is no longer there.

Again, the current commercial releases do not not show any dependence on the pre-anneals. However, the junction depth is now much shallower than the earlier release from the same vendor, even though DAMAGE is now defaulted to true. The reason for the shallower junction is unknown. The other major vendor predicts a junction depth that is even shallower (significantly). This is due to different implant tables being used (channeling not included).
 

Stress Dependent Oxidation

• Viscous oxidation of 45 degree silicon step predicts oxide bulge.
  • Problem pointed out by Steve McCormack, NCR.
• Less oxidation with stress dependent oxidation turned on.
• Accurate simulation of isolation oxidations require:
  • Changes to default material properties.
  • Stress dependent oxidation.
• But, coefficients are not well known.

There has been some more work on the coefficients since then. Look for references by Smeys or Rafferty. Note that stress-dependent oxidations can be extremely time consuming.
 

Oxidation Boundary Conditions

• Oxide is thinner on right side of simulation structure.
  • Worse for case with stress dependent oxidation.
• Even for 2 micron wide structure, 6% difference.
• Hydrostatic pressure is not symmetric.

A 45 degree step was etched in the silicon from (0.4,0) to (0.6,0.2). This was a quick approximation to what happens in a twin-well process. This was followed by a thick oxidation. The black line shows what happens with the default coefficients - an artificial bulge appears in the center of the structure. With stress dependent oxidation, a more realistic looking structure results (red).

Just a few days before the talk, I created the above overlay for the first time. That's when I noticed that the red lines are thicker than the black lines on the left of the structure, but thinner on the right. There is a 6% difference in the oxide thickness between the left and right edges with the stress dependent model. The next figure show why.
 

In the original simulation, the structure edge was almost 1.0 um away from the step in the silicon. This distance was 2.4x the thickness of the grown oxide, and seemed wide enough. The above figure shows the x-component of stress for the original structure and a wider one. The horizontal stress component is still quite high at the edge of the simulation structure for the narrow (top) case.
 

Final Remarks

• TCAD still only useable by experts.
• Know the range of validity of a model.
• Study default values.
  • Check reference dates.
  • Watch for simple coefficients ( 0 or 1 ).
• Assume there are bugs in the software.
• Test the sensitivity of results to model and grid changes!

If you haven't tested the sensitivity of your simulation to the grid, you haven't simulated anything at all!