Oxidation of Silicon “Oxide” is the term used to describe silicon dioxide, one of the main material components of silicon-based transistors, including our MOS devices: • Gate oxides - isolate the gate from the source and drain of the transistor. This oxide needs to be very high quality, with highly controllable thickness • Field oxides / device isolation - keeps components from experiencing cross talk from nearby components - does not have to be as high of quality but needs to be much thicker than gate oxides • Intermetal dielectrics - used to isolate the connecting wires between devices. Again, lower quality, but much thicker than gates. This material is not directly grown from substrate material Ways to grow an oxide: • Thermally grow oxide from the silicon substrate (Si, oxygen, heat) • Chemically grow oxide by exposing any material to a stoichiometric combination of Si and 2O in a chemical vapor deposition process Also used for many other devices and process steps not used in this class. Refer to figure 8-1 in your textbook. ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 1 of 10 Oxide Properties The Silicon Dioxide Molecule and it’s material structure • Tetrahedral structure with Si in the center and O at the corners • Crystalline quartz - aligns tetrahedra in a simple crystalline structure • Fused silica - tetrahedral bound together in a random pattern - this is the type of oxide grown on silicon through thermal processes. Fused silica is an amorphous material ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 2 of 10 Fused silica properties • Thermodynamically unstable below quartz melting point (~1710 C) - tries to become crystalline - devitrification - occurs above 1000 C (this is a big problem for furnace tubes - causes particles) • Tetrahedra joined by bridging oxygen. Nonbridging oxygen do not connect to other tetrahedral, like crystalline quartz o Makes fused silica less dense (2.2 g/cm3 compared to 2.65 g/cm3) o Allows for much easier interstitial and substitiutional diffusion § Substitutional impurities replace silicon in the structure - B and P also called network formers. These also have one extra or less electron - effect the number of bridging oxygen atoms (B increase P - decrease (make oxide better) Called a network former because the components can be a basis for a glassy structure (B2O3, P2O5) This creates an electrical imbalance, fixed by either creating or destroying a non-bridging oxygen site. • B3+ à creates non-bridging oxygens - degrades the quality of the oxide • P5+ à destroys non-bridging oxygens - can improve the quality of the oxide § Interstitial impurities - also called network modifiers - Oxides of certain metals: Na, K, Pb, Ba - oxygen from metal oxide replaces oxygen in the system - produce more non-bridging oxygens ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 3 of 10 § Hydroxyl group - replace oxygen in the system: H20 + Si-O-Si à Si-OH + OH-Si - decreases oxide quality but increases oxidation rate if constantly present (wet oxidation) Growing a thermal oxide - the Deal Grove model (linear-parabolic model) • Two oxidants used - dry oxygen and water (dry oxidation and wet oxidation respectively) Dry oxidation: Wet oxidation: Sisolid + O2vapor à SiO2solid Sisolid + H2Ovapor à SiO2solid + 2H2gas • Reactions occur on the Si/SiO2 surface - oxide grows into the silicon and consumes the substrate - for every 1000nm of oxide grown, 440nm of Si is consumed • Deal-Grove model operating conditions o Oxide thicknesses between 30-500nm o Temperatures 700C - 1300C o Oxidant partial pressures 0.2atm - 25atm • Deal-Grove assumptions o Process occurs due to two fluxes that sequentially transport oxidizers from the ambient gas to the Si/Oxide interface o A third flux represents the consumption of the oxidant o Flux = # of particles/cm2/sec o Three fluxes (again) ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 4 of 10 1. the flux of the oxidizing species as moving from the bulk of the gas phase to the gas/oxide interface (F1) 2. the flux of the oxidizing species as it diffuses through the existing oxide to the Si/SiO2 interface (F2) 3. the flux of the oxidizing species as it is consumed by reaction at the Si/SiO2 interface (F3) o Steady state condition: F1 = F2 = F3 • F1 - caused by the mass transport created by oxidant density gradients at the wafer surface ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 5 of 10 • F1 α Cg - Cs à Need a proportionality constant à use the mass transfer coefficient hg: F 1 = h g (C g − C s ) (1) hg is related to the diffusivity of the oxidizing species into the oxide layer (D) and the thickness of the boundary layer Boundary layer à discussed on page 158 of textbook. Is the transition region between solid surface (gas velocity = 0) and the bulk gas region, where vg > 0 • Need to equate F1, F2, and F3 à Need like variables à use Henry’s Law Henry’s Law à the concentration of a species dissolved into a solid is proportional to the partial pressure of the species in the gas phase at the surface C 0 = HPs (2) C * = HPg (3) C0 is the equilibrium concentration of the oxidizing species at the surface Ps is the partial pressure of the oxidizing species at the surface C* is the equilibrium concentration of the oxidizing species in the oxide bulk Pg is the partial pressure of oxidizing species in the bulk of the gas phase • Assume the ideal gas law (PV=kT) Cg = Pg (4) kT P Cs = s kT (5) • Combine equations 1-5 F1 = h(C* - C0) (6) h à new mass transfer coefficient related to hg by: h= hg HkT (7) • Now we move into the oxide layer itself, look at F2 using Fick’s Law of Diffusion: ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 6 of 10 F2 = − D (C − Ci ) dC =− D 0 dxox xox (8) D is the diffusion coefficient of oxidation species in the oxide layer Ci is the interface concentration xox is the oxide thickness • The flux at the oxide/silicon interface, F3, is determined by the reaction rate coefficient, and is what ties in oxide growth to the fluxes of the oxidant at the wafer surface F3 = ksCi (9) ks is the first order reaction rate coefficient • Recall that F1 = F2 = F3. This sets up a system of equations from which we can solve for unknowns: Ci = C* k k x 1 + s + s ox h D  k x  C * 1 + s ox  D  C0 =  k k x 1 + s + s ox h D (10) (11) • Look at limiting cases o D is small à flux of oxidant through oxide is small compared to reaction flux at interface § Oxidant consumed as quick as it can get there § “Diffusion limited case” § Ci = 0, C0 = C* o D is big à reaction rate limited Ci = C0 = C* k 1+ s h (12) • From these relationships, you can determine the growth rate o Use two solution cases ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 7 of 10 o Include # of oxidant molecules incorporated per unit volume of oxide (Ni) Typical oxide: 2.2 x 1022 [SiO2]cm-3 2 O’s per molecule For O2 2.2 x 1022 /cm3 For H2O 4.4 x 1022 /cm3 o Combine equations 9 and 10, recall that flux is density x velocity Ni dx ox = dt k sC * k k x 1 + s + s ox h D (13) Solving this differential equation: Set Boundary Conditions xox = xi at t = 0 (note that xi can include oxide already on the surface) xox2 + Axox = B(t + τ ) (14) τ is the time displacement to account for the initial oxide on the system  1 1 A = 2 D k + h    s  (15) 2 DC * B= Ni (16) τ= xi2 + Axi B (17) • From this equation, we can see the linear and parabolic regimes: o t >> τ, Diffusion Controlled, xox2 = Bt B à Depends on Diffusion, Parabolic, “Parabolic Rate Constant” o A2 B , Linear Regime, xox = (t + τ ) 4B A B/A is the linear rate constant, independent of diffusion (t + τ )<< ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 8 of 10 k h C *  B  = s   A ks + h   N1  (18) Note that h >> ks, therefore 18 can be simplified: C *  B = ks   N  A  1 (19) • Of course, these values can either be calculated or looked up in a table. For calculations, refer to Figures 8-4 to 8-6 in Wolf and Tauber Factors that can contribute to oxidation growth NOT covered by the Deal-Grove model: • Crystal Orientation - depending on the Si orientation, the surface density of Si atoms can differ, impacting the rate constant for oxidation. This only serious impacts the linear, reaction rate limited case Refer to Table 8-6 for modified DG constants • Dopant effects - tend to increase oxidation rates Boron will incorporate into the oxide, increase NBO concentration, providing easier oxidant diffusion to the interface. Phosphorus will not incorporate into the surface, but increases the vacancy ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 9 of 10 density in the Si, providing enhanced oxidation by increasing the number density of available sites. • Water in a dry oxidation process à 25ppm of water can measurably increase both linear and parabolic oxidation • There are many other things which impact oxidation rates which are beyond the context of this class. Please refer to Chapter 8.5 of Wolf and Tauber for a more detailed discussion. Optical measurements of oxide thickness • Interference patterns - oxides are typically grown to thicknesses on the same order of magnitude of the wavelength of visible light. • This produces constructive and destructive interference patterns • Plotting the intensity of reflected light vs. wavelength can provide a thickness measurement • Ellipsometry uses polarized light and the differences in interference for tangential and parallel polarized light, incident at some angle, to make an even more detailed measurement of thickness • Spectral ellipsometry uses both phenomena to provide an optical measurement of both thickness and dielectric constant. Electrical measurements - measure the capacitance of the oxide layer, treat as a parallel plate capacitor: C= ε0ε ox Area xox (20) ______________________________________________________________ SCS Lecture Notes © Thermal Oxidation of Silicon - MatE 129, Integrated Circuit Manufacturing Page 10 of 10