Deal-Grove Model Deal-Grove Model PredictionsPredictions

Once B and B/A are determined, we Once B and B/A are determined, we can predict the thickness of the oxide can predict the thickness of the oxide versus timeversus time

Deal-Grove Model of Deal-Grove Model of OxidationOxidation

Oxide as a Diffusion BarrierOxide as a Diffusion Barrier Diffusion of As, B, P, and Sb are orders of magnitude Diffusion of As, B, P, and Sb are orders of magnitude

less in oxide than in siliconless in oxide than in silicon Oxide is excellent mask for high-temperature Oxide is excellent mask for high-temperature

diffusion of impuritiesdiffusion of impurities

BoronPhosphorus

10

1

0.1

0.010.1 1.0 10 100

Diffusion time (hr)

Mask thickness(m) 1200 C

1000 C

1200 C

1000 C 1100 C

900 C

1100 C

900 C

BP

10

1

0.1

0.010.1 1.0 10 100

Other ModelsOther Models A variety of other models have been suggested, A variety of other models have been suggested,

primarily to correct the deficiencies of the Deal-primarily to correct the deficiencies of the Deal-Grove model for thin oxidesGrove model for thin oxides

These includeThese include– The Reisman power law modelThe Reisman power law model– The Han and Helms model with parallel The Han and Helms model with parallel

oxidation pathsoxidation paths– The Ghez and van Meulen model to account for The Ghez and van Meulen model to account for

the effect of oxygen pressurethe effect of oxygen pressure Some of these models do a much better job for Some of these models do a much better job for

thin oxidesthin oxides None are widely acceptedNone are widely accepted

Other TopicsOther Topics

Several topics other than the simple Several topics other than the simple planar growth of wet and dry oxide planar growth of wet and dry oxide are importantare important

These includeThese include– Thin oxide growth kineticsThin oxide growth kinetics– Dependence on oxygen pressureDependence on oxygen pressure– Dependence on crystal orientationDependence on crystal orientation– Mixed ambient growth kineticsMixed ambient growth kinetics– 2D growth kinetics2D growth kinetics

Example: 2D GrowthExample: 2D Growth

Example: 2D GrowthExample: 2D Growth

Example: 2D GrowthExample: 2D Growth

There are several interesting There are several interesting observationsobservations– There is significant retardation of the There is significant retardation of the

oxide growth in sharp cornersoxide growth in sharp corners– The retardation is more pronounced for The retardation is more pronounced for

low temperature oxidation than for high low temperature oxidation than for high temperature oxidationtemperature oxidation

– Interior (concave) corners show a more Interior (concave) corners show a more pronounces retardation that exterior pronounces retardation that exterior (convex) corners(convex) corners

Example: 2D GrowthExample: 2D Growth

Example: 2D GrowthExample: 2D Growth

Several physical mechanisms are needed to Several physical mechanisms are needed to understand these resultsunderstand these results

1.1. Crystal orientationCrystal orientation

2.2. Oxidant diffusionOxidant diffusion

3.3. Stress due to volume expansionStress due to volume expansion Kao et al suggested changes to the linear-Kao et al suggested changes to the linear-

parabolic (Deal-Grove) model to correct for these parabolic (Deal-Grove) model to correct for these effectseffects

Most of these effects are built into the modeling Most of these effects are built into the modeling software such as SUPREM IV and ATHENA software such as SUPREM IV and ATHENA

Measurement MethodsMeasurement Methods

The parameters of interest includeThe parameters of interest include– ThicknessThickness– Dielectric constant and strengthDielectric constant and strength– Index of refractionIndex of refraction– Defect densityDefect density

There are three classes of measurementThere are three classes of measurement– Physical (usually destructive)Physical (usually destructive)– Optical (usually nondestructive)Optical (usually nondestructive)– Electrical (usually nondestructive)Electrical (usually nondestructive)

Physical MeasurementsPhysical Measurements Simple step height technique (DekTak)Simple step height technique (DekTak)

– Etch away oxide with HFEtch away oxide with HF– Use a small stylus to measure the resulting Use a small stylus to measure the resulting

step heightstep height– The resolution is <10 nmThe resolution is <10 nm

More complex technique uses one or more of the More complex technique uses one or more of the SFM concepts (AFM, MFM, etc)SFM concepts (AFM, MFM, etc)– Technique has atomic resolutionTechnique has atomic resolution

SEM or TEM (electron microscopy)SEM or TEM (electron microscopy) All require sample preparation that makes the All require sample preparation that makes the

tests destructive and not easy to use in tests destructive and not easy to use in productionproduction

Optical MeasurementsOptical Measurements Most optical techniques use the concept of Most optical techniques use the concept of

measuring reflected monochromatic lightmeasuring reflected monochromatic light– If monochromatic light of wavelength If monochromatic light of wavelength shines shines

on a transparent film of thickness xon a transparent film of thickness x00, some , some light is reflected directly and some is reflected light is reflected directly and some is reflected from the wafer-film interfacefrom the wafer-film interface

– For some wavelengths, the light will be in For some wavelengths, the light will be in phase and for others it will be out of phasephase and for others it will be out of phase constructive and destructive interferenceconstructive and destructive interference

Minima and maxima of intensity are observed as Minima and maxima of intensity are observed as is varied is varied

Optical TechniquesOptical Techniques

Color ChartColor Chart

http://www.htelabs.com/appnotes/sio2http://www.htelabs.com/appnotes/sio2_color_chart_thermal_silicon_dioxide.ht_color_chart_thermal_silicon_dioxide.htmm

Optical MeasurementsOptical Measurements

Instrument from Instrument from FilmetricsFilmetrics(http://www.filmetrics.com)(http://www.filmetrics.com)

Optical MeasurementsOptical Measurements

The positions of the minima and maxima The positions of the minima and maxima are given byare given by

m=1,2,3… for maxima and ½,3/2,5/2,… for minimam=1,2,3… for maxima and ½,3/2,5/2,… for minima

This is called reflectometry and works well This is called reflectometry and works well for thicknesses over a few 10’s of nmfor thicknesses over a few 10’s of nm

1

01

01maxmin,

sinsin

cos2

n

n

m

xn

Optical MeasurementsOptical Measurements

If one does not know n, or if the film is very thin, If one does not know n, or if the film is very thin, then ellipsometry is betterthen ellipsometry is better

When multiple wavelengths of light are used, the When multiple wavelengths of light are used, the instrument is known as a spectroscopic instrument is known as a spectroscopic ellipsometerellipsometer

Optical MeasurementsOptical Measurements

Here, one uses polarized light.Here, one uses polarized light.– The measurement may be performed at The measurement may be performed at

multiple angles of incidence to obtain a higher multiple angles of incidence to obtain a higher degree of accuracydegree of accuracy

One can get the index of refraction as a One can get the index of refraction as a function of wavelength as well as the function of wavelength as well as the extinction coefficientextinction coefficient– Can be used to measure thickness to <1 nmCan be used to measure thickness to <1 nm

Fitting routines are necessary to take into Fitting routines are necessary to take into account rough interfaces between Si and account rough interfaces between Si and SiOSiO22 layers. layers.

Cauchy EquationCauchy Equation

...)(42

CB

An

Sellmeier EquationSellmeier Equation

...1)(3

2

23

22

22

12

21

C

B

C

B

C

Bn

http://en.wikipedia.org/wiki/Cauchy%27s_equation

Electrical MeasurementsElectrical Measurements

These measure properties that correlate directly These measure properties that correlate directly to the performance of the devices fabricated to the performance of the devices fabricated using the oxidesusing the oxides

The dominant techniques is the C—V The dominant techniques is the C—V measurementmeasurement– The basic structure for the measurement is the MOS The basic structure for the measurement is the MOS

capacitorcapacitor

– The usual combination is Si-SiOThe usual combination is Si-SiO22-(Al or pSi)-(Al or pSi)

– Any conductor-dielectric-semiconductorAny conductor-dielectric-semiconductor can be usedcan be used

MOS CapacitorMOS Capacitor

tox

Al

Al

Si wafer V

+

-

http://www.mtmi.vu.lt/pfk/funkc_dariniai/transistor/mos_capacitors.htm

http://ece-www.colorado.edu/~bart/book/book/chapter6/ch6_3.htm#fig6_3_5

C-V PlotC-V Plot

C-V PlotC-V Plot

Differences between high frequency Differences between high frequency and low frequency C-V dataand low frequency C-V data– Doping concentration in Si near Si-oxide Doping concentration in Si near Si-oxide

interfaceinterface Voltage shift proportional to charged Voltage shift proportional to charged

defects within oxidedefects within oxide