Understanding Rate Coefficients in SiO2 Oxidation: Deal Grove Model and Alternatives - Pro, Study notes of Electrical and Electronics Engineering

Download Understanding Rate Coefficients in SiO2 Oxidation: Deal Grove Model and Alternatives - Pro and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! 1 Review: The Linear and Parabolic rate coefficients (two limiting forms) • Case I: For very short oxidation time (thin oxides layer), the rate equation reduced to the linear form • Case II: when t>>τ, the oxide is sufficiently thick, the rate equation reduced to the simple parabolic expression, • B/A and B are often termed the linear and parabolic rate coefficients respectively because of the xo and x2o terms in which they appear. Physically, they represent the contribution of fluxes F3 (interface reaction) and F2 (oxidant diffusion), respectively. SiO2 growth on a bare Si wafer usually starts out with a linear xx versus x, which become parabolic as the oxide thickens. • In fact, B and B/A are normally determine experimentally by extracting them from growth rate. The reason for taking this approach is simply that we usually do not know all the parameters in Grove-Deal model equations. Ks (interface reaction rate constant) is particular contains a lot of “hidden” physics associate with the interface reaction. What we do, however, is compare experimental values of B and B/A with the model equations. To test the reasonableness of the liner parabolic model. )( / )( 0 2 02 τττ +≈⇒+=+⇒+=+ t A Bxt AB x B xtBAxx oo O BttBxt AB x B xo ≈+≈⇒+=+ )()( / 2 0 0 2 ττ Curves predicted by Deal Grove Model The general behavior of an initial linear growth rate that becomes parabolic as the oxide grows. SiO2 grows much faster in an H2O ambient than it does in dry O2. The principle reason for this is that oxidant solubility in H2O is much higher for H2O than for O2. Calculated dry O2 oxidation rates using deal-Grove model Calculated H2O oxidation rates using deal-Grove model Problems in Deal Grove model: Initial Oxidation Stage • A major problem with the Deal Grove model was recognized when it was first proposed - it does not correctly model thin O2 growth kinetics (0-30 nm). • Experimentally dry O2 oxides grow much faster for ≅ 200 Å than Deal Grove predicts. • MANY suggestions have been made in the literature about why. None have been widely accepted. • Since modern technologies emphasize this range of oxide thickness for MOSFETs and capacitors, intense work has been done to model the initial rapid stage of oxidation.According to the deal grove model the oxidation rate should apporch at constant value i. e. A B dt dxo t Lim = →0 Instead, the oxidation rate increased by a factor of 4 or more.       +≈ )( τt A Bxo 2 Models proposed to explain thin oxidation results • 1. Reisman et. al. Model • Simple power law “fits the data” over the whole range of oxide thicknesses. • a and b are experimentally extracted parameters just as Deal-Grove model has two (B and B/A). • Physically - interface reaction controlled, oxidation process at all time and viscous flow of SiO2 control volume expansion at the interface. Models proposed to explain thin oxidation results (cont.) 2. Han and Helms Model • Two Sio2 in parallel) - “fits the data” ” over the whole range of oxide thicknesses. Three parameters (one of the A values is 0). • Physically - second process may be outdiffusion of OV and reaction at the gas/SiO2 interface. • Initially, for very thin oxides, one of the two parallel process control the oxidation rate. • All of the rate constant in the above equation were found to fit Arrhenious expression of the form • separate but parallel reaction occur (perhaps O2 and O diffusing through the B1=C exp ( -EA/kT ) Models proposed to explain thin oxidation results (cont.) • 3. Massoud et. al. Model • Second term added to Deal Grove model which gives a higher dx/dt during initial growth. • L =70 Å so the second term disappears for thicker oxides. • Because it is simply implemented along with the Deal Grove model, this model has been used in process simulators. • Experimental data agrees with the Reisman, Han and Massoud models. (800°C dry O2 model comparison see Figure.) Dopants redistribution during oxidation • During oxidation, the impurity concentration changes in the silicon near the silicon-silicon dioxide interface. • Boron and gallium tend to be depleted from the surface, whereas • phosphorus, arsenic, and antimony pile up at the surface. • The profile depend on both the diffusion coefficient and the segregation coefficient m of the impurity in the oxide, where m is • m = concentration of impurity in Si/concentration of impurity in SiO2. 5 Trench Isolation • Trench isolation is utilized in most of the today’s advance MOS and bipolar process. • The trenches are etched using reactive ion etching and can be quite deep with very high aspect ratio. • The surface of the trenched is passivated with a thin layer of SiO2 , and then the trenched is refilled with polysilicon. • Similar structures are used to form trenched capacitor between the polysilicon and the substrate for use as DRAM technologies., 2. Repeat Problem 1 if the oxidation is done in a wet O, ambient. \ . . . . Complete Process Simulation of Oxidation « Many of the models described above (and others that are in Chapter 5), have been implemented in lol n) Lt Ubg # (CMa) programs like SUPREM. | qd: * FOI hae «In an integrated simulator, these models must work ir ‘ LY um", : harmony with each other. = 6V a s yo ove model has been extended to nelude 2D effets. ambie il