Oxidation Thickness Calculator

This calculator determines the thickness of silicon dioxide (SiO₂) thermally grown on a pure Silicon wafer in an oxidizing ambient.
The model for thermal oxidation of silicon was pioneered by Deal and Grove in the 1960's. ^[1] Since that time, other researchers have honed the physics to account for different perturbations or regimes not originally considered by the Deal-Grove Model.
Today, thermal oxidation is perhaps the most important and contolled step in the manufacture of silicon integrated circuits, forming the gate oxide in a field effect transistor, and the tunnel oxide in flash memory devices.
This calculator uses Deal-Grove as the backbone for the calculation, and incorporates the work of other research for more accurate prediction.

To use, go to:
http://www.lelandstanfordjunior.com/thermaloxide.html

Why the new look?

You may have used the calculator that has resided here since early 2001. This new calculator has all of the functionality of the old one, and a whole lot more. Much of this is described below.

In order to accomodate different models in one format, many new fields were added.

To help avoid confusion, many of the fields are "greyed out" by your browser if they are not applicable. If you wonder why you can't enter in a particular field, it's probably because something else you've selected is inconsistent with that field

The calculator now helps you to decide which model is best, but ultimately lets you have control over the models used.
In the past, the forward calculation (thickness from time) was on a different page than the reverse calculation (time from desired thickness). They are now integrated in the same page.
Likewise, all models are now accessible from the same page, instead of different pages.
The code has become very large, making client-side calculations slow on poor connections. It's now entirely server-side, so only a small amount of data is transferred over the internet. This means that the result is presented on a separate page from the input form.
The calculator now makes iterative calculations that were not practical before.

I liked the old one. What if I want to use that one?

The old Deal-Grove calculator that used to reside here is built in to this calculator. Just select the "use Strict Deal Grove" model option, and un-select the other model options and it will give you the same result as before. It is generally not recommended to do this, but if you want to use the old calculator for legacy reasons, it is maintained for such backward compatibility.

Has the calculator been tested?

Yes, but not for all possible cases. To give some idea of the range, users have reported up to eighteen DAYS of oxidation, with very close agreement. Short oxidations have been run down to a few tens of angstrom with excellent agreement to the Massoud model. Results for thin doped oxides, while not perfect, are better than what's been obtained in advanced process simulators such as SUPREM for the tests we've run.
If you are an SNF labmember, you can help by logging your oxidation data in the electronic logs at: http://www.lelandstanfordjunior.com/eData.html. At the present time, these logs are specific to SNF, but if you have some interesting data you'd like to share, please email me. You can find my full email address when you run the calculator.

How do I use it?

There are two types of calculations you can make:
- Calculate the resultant thickness of a particular oxidation run, or
- Calculate the time required to achieve a desired thickness.
Select this first with the buttons at the top of the page. Time is specified in HH:MM:SS format. Thickness is specified in Angstrom. The appropriate field will become active (time entry or thickness entry) awaiting your input.
Select the following conditions for your run:
- Initial oxide thickness:
  - General: This is the amount of oxide already on the surface before the process begins.
  - Purpose: If you have an oxide layer already grown, specify this here.
  - Options: Any positive thickness.
  - Units: Angstrom
  - Default: This defaults to a reasonable "native" oxide thickness of 10Å.
  - limitations: (none)
  - specifics/details: The thermal oxidation process does not follow superposition, and is not linear. In other words, an oxidation run which grows 1000Å of oxide on a bare Si wafer would not simply add 1000Å of oxide thickness to a wafer already having 5000Å before the oxidation. In fact, it would add much less than 1000Å to the existing 5000Å. The calculator will take care of this calculation for you if you enter the initial oxide thickness here.
- Temperature:
  - General: This is the Temperature, in degrees Celcius, at which the oxidation is carried out.
  - Purpose: The oxidation process is highly sensitive to temperature.
  - Options: 750°C-1150°C in 50°C increments.
  - Units: degrees Celcius
  - Default: set to 1000°C, for no particular reason.
  - limitations: general calculator from 750°C-1150°C. Massoud Model limited to 800°C-1000°C^[2] As more data outsside of this limit is explored, the temperature window may be widened.
  - specifics/details: Massoud only took his data in the 800°C-1000°C regime. It may be extensible to other regimes, but since it has not been verified, this calculator doesn't extrapolate until we have data to support it.
- Crystal Orientation:
  - General: This is the orientation of the silicon crystal surface on which you are growing the oxide.
  - Purpose: Deal and Grove recognized the orientation dependence, and postulated that it was due to a difference in atomic surface density. ^[3]
  - Options: <100>, <111>, <110>, or poly.
  - Units: (standard miller indices for crystal orientation)
  - Default: <100> orientation. The most common orientation for silicon wafers is <100>, generally because MOS transistors built on this surface yield oxides with the best electrical properties.
  - limitations: <100>, <111>, <110> and polysilicon.
  - specifics/details: Vertical (diffused base) Bipolar transistors are generally built on <111> wafers (actually, slightly off-cut, which is beyond the scope of this discussion). <110> wafers are rare, but this calculation might be useful if, for instance you wish to know the oxide thickness which has grown on an etched sidewall of a structure you are building- you may not be able to easily measure this oxide, but the calculator can estimate its thickness easily. The poly model is not ideal since the grain structure, grain size, dominant orientation, etc are not known. This is a first-order guess for poly oxidation.^[4]
- Ambient:
  - General: This is the ambient (gas composition) in which the oxidation is carried out.
  - Purpose: The oxidizing species is significant in the diffusion of the oxidant through the growing oxide, and in the surface reaction once it reaches the Si/SiO₂ interface.
  - Options: wet or dry
  - Units: (none: just oxidizing species)
  - Default: wet
  - limitations: Massoud Model only supports a dry ambient, and will not run if you select wet.
  - specifics/details: Dry oxidation is 100% pure oxygen (O₂) gas. In experimental reality, O₂ gas from the cylinder or from liquid boil-off is not perfectly dry, but is usually close.^[5] Massoud, in his experiments, went to great pains to ensure the gas was pure dry O₂, so as to make a physcially-correct experiment. In the case of Wet ambient, this calculator is calibrated for Pyrogenic Steam. This is the most common form of wet oxidation in use today, which involves the reaction of hydrogen (H₂) and Oxygen (O₂) gas at high temperature to form water (H₂0) vapor. Most systems are tuned to approximately 92% partial pressure of water, which is the calculator default. This is done for several reasons, including safety- It is less safe to have an abundance of hydrogen than to have an abundance of oxygen. Some processes run a DRY-WET-DRY sequence to improve oxide quality. Other systems use a bubbler (nitrogen gas bubbled through a heated vial of liquid water) to produce steam for wet oxidations. The defaults used are not well suited to bubbler-type wet oxidations, but could be tuned with the partial pressure parameter.
- Partial Pressure:
  - General: Part of the ambient specification, this is the component of pressure in the oxidation system that comprises the oxidizing species.
  - Purpose: If your gas composition is different, or your ambient pressure is different than one standard atmosphere (760 Torr, 101 kPa, 1 Bar), then you should adjust this value.
  - Options: Can be less than 1.0 for reduced pressure or diluted oxidant. Can be greater than 1.0 for high-pressure oxidations.^[6]
  - Units: Atmosphere or Bar
  - Default: 1.0 for dry oxidations (ie: the tube is at 1 atmosphere of pressure, and is 100% oxygen)
    0.92 for wet oxidations (ie: the tube is at 1 atmosphere and the composition of gas is 92% water vapor).
  - limitations: Presently not used in the Massoud Model. If specified, Massoud may still calculate if appropriate, but will ignore the value entered for partial pressure. Not used in the Strict Deal-Grove Model. Partial Pressure option is disabled if you select strict Deal-Grove.
  - specifics/details: If your lab is in the mountains, you'll need to adjust the partial pressure. Use of a bubbler for wet oxidations would likely require partial pressure calibration.
- Active Doping Concentration:
  - General: This is the concentration of active dopants in the silicon at the region where the oxidation will occur.
  - Purpose: Deal also noticed a dependence on doping. ^[7] The enhancement in thermal oxidation is related to the electrical carriers (electrons and holes) in silicon, not the actual dopant atoms directly.
  - Options: Value up to silicon atomic density (though this may not be realistic).
  - Units: atomic concentration, or more correctly extrinsic electrical carrier concentration per cubic centimeter. (eg: 1e21 /cm³)
  - Default: Defaults to 1e14, which is below the level of having any impact on thermal oxidation. This default is set when a doping type is selected, only to illustrate the entry format (ie: exponential notation).
  - limitations: Will not be used in strict Deal-Grove model. The advanced Doping Model option will be turned off if the strict Deal-Grove model is selected. Due to limited data, the doping model in the Massoud Model is "first order".
  - specifics/details: Specify the active carrier concentration, not the chemical doping level to get the correct answer. If the concentration that you specify is below the intrinsic carrier concentration at the oxidation condition, then the calculator will decide not to use doping models. You must select the "use Advanced Doping Models" option for this model to be invoked. It is important to specify only the ELECTRICALLY ACTIVE doping. It is up to you to account for solid solubility, clustering, or other effects which might limit the dopant activation.
- Doping Type:
  - General: This is the type of dopant (n-type or p-type) that is quantified in the Active Doping Concentration.
  - Purpose: Both dopant types enhance thermal oxidation rates, but in different ways.
  - Options: p-type (acceptor, eg: boron) or n-type (donor, eg: phosphorus, arsenic, antimony) dopant.
  - Units: (none: only doping type)
  - Default: (none)
  - limitations: Will not be used in strict Deal-Grove model. The advanced Doping Model option will be turned off if the strict Deal-Grove model is selected.
  - specifics/details: If you choose to invoke the Advanced Doping Models, you must specify which doping type.
Select the Model Options: You can select or exclude certain models from the calculation. The calculator will do its best to determine the correct answer, but it will do so within the constraints that you specify in this section. It will not apply a model that it believes is totally inappropriate. The recommended (and default) settings are to "use Massoud Model if appropriate", and NOT to use Strict Deal Grove, and also to NOT apply doping models.
- use Massoud Model, if appropriate^[8] Deal-Grove does not work well for thin dry oxides,^[9] so a different model is needed. It is recommended to keep this option "on". The calculator will check to see if the massoud model is appropriate or not. If not, it will stick to the Modified Deal Grove model, or strict Deal Grove if you've specified this restriction. Massoud limitations are: dry ambient only, Temperature: 800°C-1000°C, and not thick. Massoud will not run partial pressure calculations, but the fact that you have specified partial pressure will not stop Massoud from running. Massoud model now runs a doping model.
- use Strict Deal-Grove This option is not recommended, but is included for Legacy reasons. Some people like to do things the old way, so this "pure" Deal-Grove model is retained as an option.
- use Advanced doping models, if possible This option is turned off by default. Turning it on will enable the doping fields in the form, and will also turn off the "strict Deal Grove" option, since it can only run with Modified Deal Grove and Massoud Models. It is recommended to leave this off unless you have high doping concentrations. In any case, if you attempt to invoke this model, but specify a doping that is "low" (below the intrinsic carrier concentration under the conditions specified), the doping models will be ignored, and you will be notified as such.

What's not accounted for in this calculator?

Stress, and 3-D effects: This calculator assumes that the oxide is growing on a planar surface, with no external forces. Only the intrinsic stress of a planar oxidation process is considered.
Mixed kinetics: Oxides grown in partial chlorine ambients, for example, are not modeled.^[10]

Under what conditions might the calculator have significant error?

Thin oxidation other than Massoud regime: Massoud's data nailed the DRY 800-1000°C regime. Outside of this temperature range and ambient, results on thin oxides (less than 500Å) may vary.
Doping models: As the oxide grows, dopant segregates into the oxide, diffuses into the silicon, piles up at the interface, etc. Your doping may have been ion-implanted, or grown into the silicon, or diffused into the silicon. These factors will alter the observed oxidation rate.^[11] It's often difficult to pinpoint your actual surface concentration with an ion implant if you are on the steep gaussian curve. The most reliable data has been taken with uniformly doped substrates doped above solid solubility.
As always, Garbage-in/Garbage-out: If your furnace ambient is not known or controlled, or temperature is poorly calibrated, experiment will not agree with this calculator. If your silicon is not pure, or has significant damage (perhaps from an ion implant), rates will change. Any source of point defects in the crystal can alter oxidation.
Short-time, tube furnace runs (where wafers are loaded into a hot furnace, and gasses are switched after thermal equilibration) are usually dominated by gas transients and also oxide growth in push/pull, so results will vary. Sometimes this can be modeled by two perturbations: Change the initial oxide parameter, AND alter the time used in the calculator (different from the recipe time) to account for the gas turn-on/turn-off transients. For example, on oxidations less than about 40Å, we've used a slightly thicker (14Å) native oxide thickness, and a simulation time that is 2 minutes greater than the actual recipe time.
Rapid Thermal Oxidations (where the chamber is filled with gas before the temperature is ramped) are usually limited by transient temperature control.

References:

^[1]B.E. Deal and A.S. Grove, J. Appl. Phys. 36, 3770 (1965).

^[2]H.Z. Massoud, et. al, J. Electrochem. Soc. 132, 2685 (1985).

^[3]B.E. Deal, J. Electrochem. Soc. 125, 576 (1978).

^[4]H. Sunami, J. Electrochem. Soc. 125, 892 (1978).

^[5]E. A. Irene, J. Electrochem. Soc. 120, 1613 (1974).

^[6]R. R. Razouk, J. Electrochem. Soc. 128, 2214 (1981).

^[7]B.E. Deal and M. Sklar, J. Electrochem. Soc. 112, 430 (1965).

^[8]H.Z. Massoud, Ph.D. Dissertation, Stanford Electronics Labs, Tech. Rep. No. G502-1, Stanford Univ., Stanford, CA (1983).

^[9]E. A. Irene, J. Electrochem. Soc. 125, 1708 (1978).

^[10]H. L. Tsai, et. al, J. Electrochem. Soc. 131, 411 (1984).

^[11]A.S. Grove, et. al., J. Appl. Phys. 35, 2629 (1964).

Send comments or suggestions to Eric Perozziello ericp@snf (run the calculator to get my full email).