Deal-Grove Model Predictions Once B and B/A are determined, we can predict the thickness of the oxide versus time 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 Barrier Diffusion of As, B, P, and Sb are orders of magnitude less in oxide than in silicon 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 Oxide is excellent mask for high-temperature diffusion of impurities Boron Phosphorus Diffusion time (hr) Mask thickness (  m) 1200 C 1000 C 1200 C 1000 C 1100 C 900 C 1100 C 900 C B P

Other Models A variety of other models have been suggested, primarily to correct the deficiencies of the Deal-Grove model for thin oxides A variety of other models have been suggested, primarily to correct the deficiencies of the Deal-Grove model for thin oxides These include 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 Some of these models do a much better job for thin oxides None are widely accepted None are widely accepted

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

Example: 2D Growth

There are several interesting observations 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

Example: 2D Growth

Several physical mechanisms are needed to understand these results Several physical mechanisms are needed to understand these results 1.Crystal orientation 2.Oxidant diffusion 3.Stress due to volume expansion Kao et al suggested changes to the linear-parabolic (Deal-Grove) model to correct for these effects 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 Most of these effects are built into the modeling software such as SUPREM IV and ATHENA

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

Physical Measurements Simple step height technique (DekTak) Simple step height technique (DekTak) –Etch away oxide with HF –Use a small stylus to measure the resulting step height –The resolution is <10 nm More complex technique uses one or more of the SFM concepts (AFM, MFM, etc) More complex technique uses one or more of the SFM concepts (AFM, MFM, etc) –Technique has atomic resolution SEM or TEM (electron microscopy) SEM or TEM (electron microscopy) All require sample preparation that makes the tests destructive and not easy to use in production All require sample preparation that makes the tests destructive and not easy to use in production

Optical Measurements Most optical techniques use the concept of measuring reflected monochromatic light Most optical techniques use the concept of measuring reflected monochromatic light –If monochromatic light of wavelength shines on a transparent film of thickness x 0, 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 Minima and maxima of intensity are observed as is varied

Optical Techniques

Color Chart r_chart_thermal_silicon_dioxide.htm r_chart_thermal_silicon_dioxide.htm

Optical Measurements Instrument from Filmetrics ( Instrument from Filmetrics (

Optical Measurements The positions of the minima and maxima are given by m=1,2,3… for maxima and ½,3/2,5/2,… for minima The positions of the minima and maxima are given by m=1,2,3… for maxima and ½,3/2,5/2,… for minima This is called reflectometry and works well for thicknesses over a few 10’s of nm This is called reflectometry and works well for thicknesses over a few 10’s of nm

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

Optical Measurements Here, one uses polarized light. 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 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 <1 nm Fitting routines are necessary to take into account rough interfaces between Si and SiO 2 layers. Fitting routines are necessary to take into account rough interfaces between Si and SiO 2 layers.

Cauchy Equation Sellmeier Equation

Electrical Measurements These measure properties that correlate directly to the performance of the devices fabricated using the oxides These measure properties that correlate directly to the performance of the devices fabricated using the oxides The dominant techniques is the C—V measurement The dominant techniques is the C—V measurement –The basic structure for the measurement is the MOS capacitor –The usual combination is Si-SiO 2 -(Al or pSi) –Any conductor-dielectric-semiconductor can be used

MOS Capacitor t ox Al Si wafer V + -

C-V Plot

Differences between high frequency and low frequency C-V data 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 Voltage shift proportional to charged defects within oxide