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Deal-Grove Model Predictions

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Deal-Grove Model Predictions Once B and B/A are determined, we can predict the thickness of the oxide versus time Deal-Grove Model of Oxidation Oxide as a Diffusion ... – PowerPoint PPT presentation

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Title: Deal-Grove Model Predictions


1
Deal-Grove Model Predictions
  • Once B and B/A are determined, we can predict the
    thickness of the oxide versus time

2
Deal-Grove Model of Oxidation
3
Oxide as a Diffusion Barrier
  • Diffusion of As, B, P, and Sb are orders of
    magnitude less in oxide than in silicon
  • Oxide is excellent mask for high-temperature
    diffusion of impurities

10
10
Boron
Phosphorus
1
1
0.1
0.1
0.01
0.01
0.1
0.1
1.0
10
100
1.0
10
100
4
Other Models
  • A variety of other models have been suggested,
    primarily to correct the deficiencies of the
    Deal-Grove model for thin oxides
  • These include
  • The Reisman power law model
  • The Han and Helms model with parallel oxidation
    paths
  • The Ghez and van Meulen model to account for the
    effect of oxygen pressure
  • Some of these models do a much better job for
    thin oxides
  • None are widely accepted

5
Other Topics
  • Several topics other than the simple planar
    growth of wet and dry oxide are important
  • These include
  • Thin oxide growth kinetics
  • Dependence on oxygen pressure
  • Dependence on crystal orientation
  • Mixed ambient growth kinetics
  • 2D growth kinetics

6
Example 2D Growth
7
Example 2D Growth
8
Example 2D Growth
  • There are several interesting observations
  • There is significant retardation of the oxide
    growth in sharp corners
  • The retardation is more pronounced for low
    temperature oxidation than for high temperature
    oxidation
  • Interior (concave) corners show a more pronounces
    retardation that exterior (convex) corners

9
Example 2D Growth
10
Example 2D Growth
  • Several physical mechanisms are needed to
    understand these results
  • Crystal orientation
  • Oxidant diffusion
  • Stress due to volume expansion
  • Kao et al suggested changes to the
    linear-parabolic (Deal-Grove) model to correct
    for these effects
  • Most of these effects are built into the modeling
    software such as SUPREM IV and ATHENA

11
Measurement Methods
  • The parameters of interest include
  • Thickness
  • Dielectric constant and strength
  • Index of refraction
  • Defect density
  • There are three classes of measurement
  • Physical (usually destructive)
  • Optical (usually nondestructive)
  • Electrical (usually nondestructive)

12
Physical Measurements
  • Simple step height technique (DekTak)
  • Etch away oxide with HF
  • Use a small stylus to measure the resulting step
    height
  • The resolution is lt10 nm
  • More complex technique uses one or more of the
    SFM concepts (AFM, MFM, etc)
  • Technique has atomic resolution
  • SEM or TEM (electron microscopy)
  • All require sample preparation that makes the
    tests destructive and not easy to use in
    production

13
Optical Measurements
  • Most optical techniques use the concept of
    measuring reflected monochromatic light
  • If monochromatic light of wavelength ? shines on
    a transparent film of thickness x0, some light is
    reflected directly and some is reflected from the
    wafer-film interface
  • For some wavelengths, the light will be in phase
    and for others it will be out of phase
  • constructive and destructive interference
  • Minima and maxima of intensity are observed as ?
    is varied

14
Optical Techniques
15
Color Chart
  • http//www.htelabs.com/appnotes/sio2_color_chart_t
    hermal_silicon_dioxide.htm

16
Optical Measurements
  • Instrument from Filmetrics(http//www.filmetrics.
    com)

17
Optical Measurements
  • The positions of the minima and maxima are given
    bym1,2,3 for maxima and ½,3/2,5/2, for
    minima
  • This is called reflectometry and works well for
    thicknesses over a few 10s of nm

18
Optical Measurements
  • If one does not know n, or if the film is very
    thin, then ellipsometry is better
  • When multiple wavelengths of light are used, the
    instrument is known as a spectroscopic
    ellipsometer

19
Optical Measurements
  • Here, one uses polarized light.
  • The measurement may be performed at multiple
    angles of incidence to obtain a higher degree of
    accuracy
  • One can get the index of refraction as a function
    of wavelength as well as the extinction
    coefficient
  • Can be used to measure thickness to lt1 nm
  • Fitting routines are necessary to take into
    account rough interfaces between Si and SiO2
    layers.

20
Cauchy Equation
Sellmeier Equation
21
http//en.wikipedia.org/wiki/Cauchy27s_equation
22
Electrical Measurements
  • These measure properties that correlate directly
    to the performance of the devices fabricated
    using the oxides
  • The dominant techniques is the CV measurement
  • The basic structure for the measurement is the
    MOS capacitor
  • The usual combination is Si-SiO2-(Al or pSi)
  • Any conductor-dielectric-semiconductor can be
    used

23
MOS Capacitor

Al
tox
V
Si wafer
Al
-
24
http//www.mtmi.vu.lt/pfk/funkc_dariniai/transisto
r/mos_capacitors.htm
25
C-V Plot
http//ece-www.colorado.edu/bart/book/book/chapte
r6/ch6_3.htmfig6_3_5
26
C-V Plot
  • Differences between high frequency and low
    frequency C-V data
  • Doping concentration in Si near Si-oxide
    interface
  • Voltage shift proportional to charged defects
    within oxide
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