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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 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 B PPhosphorus 11 1200 C Mask thickness (mm) 1200 C 1100 C 0.1 0.1 1000 C 1100 C 900 C 1000 C 900 C 0.01 0.01 0.1 0.1 1.0 1.0 10 10 Diffusion time (hr) 100 100 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 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 Example: 2D Growth Example: 2D Growth 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 Example: 2D Growth Example: 2D Growth 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 Most of these effects are built into the modeling software such as SUPREM IV and ATHENA 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) 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 <10 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 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 Optical Techniques Color Chart http://www.htelabs.com/appnotes/sio2_colo r_chart_thermal_silicon_dioxide.htm Optical Measurements Instrument from Filmetrics (http://www.filmetrics.com) Optical Measurements The positions of the minima and maxima are given by 2n1 x0 cos min, max m 1 n0 sin sin n1 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 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 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 <1 nm Fitting routines are necessary to take into account rough interfaces between Si and SiO2 layers. Cauchy Equation B C n( ) A 2 4 ... Sellmeier Equation B3 B1 B2 n( ) 1 2 2 2 ... C1 C2 C3 2 2 2 http://en.wikipedia.org/wiki/Cauchy%27s_equation Electrical Measurements 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 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 MOS Capacitor Al + tox Si wafer Al V - http://www.mtmi.vu.lt/pfk/funkc_dariniai/transistor/mos_capacitors.htm C-V Plot http://ece-www.colorado.edu/~bart/book/book/chapter6/ch6_3.htm#fig6_3_5 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