EE143 F05 Lecture 5 Thermal Oxidation of Si General Properties of SiO2 Applications of thermal SiO2 Deal Grove Model of Oxidation SiO2 Thermal SiO2 is amorphous Weight Density 2 20 gm cm3 Molecular Density 2 3E22 molecules cm3 Si Crystalline SiO2 Quartz 2 65 gm cm3 Professor N Cheung U C Berkeley 1 EE143 F05 Lecture 5 Thermal SiO2 Properties 1 Excellent Electrical Insulator Resistivity 1E20 ohm cm Energy Gap 9 eV 2 High Breakdown Electric Field 10MV cm 3 Stable and Reproducible Si SiO2 Interface 4 Conformal oxide growth on exposed Si surface SiO2 Thermal Oxidation Si Professor N Cheung U C Berkeley Si 2 EE143 F05 Lecture 5 Thermal SiO2 Properties cont 5 SiO2 is a good diffusion mask for common dopants Dsio 2 Dsi e g B P As Sb SiO2 exceptions exceptionsare areGa Ga a ap type p typedopant dopant and andsome some metals metals e g e g Cu Cu Au Au Si 6 Very good etching selectivity between Si and SiO2 SiO2 Si Professor N Cheung U C Berkeley HF dip Si 3 EE143 F05 Lecture 5 Steam generation for wet oxidation Professor N Cheung U C Berkeley 4 EE143 F05 Lecture 5 Thickness of Si consumed during oxidation original surface Si SiO2 Xsi Xox Si Nox X si X ox Nsi X ox molecular density of SiO2 atomic density of Si 2 3 10 22 molecules cm 3 0 46 X ox 22 3 5 10 atoms cm Professor N Cheung U C Berkeley 5 EE143 F05 Lecture 5 For 1 dimensional planar oxide growth 1 m Si oxidized 2 17 m SiO2 Suggested calculation exercise 1 m diameter Si sphere Professor N Cheung U C Berkeley Si completely oxidized 1 3 m diameter SiO2 sphere SiO2 6 EE143 F05 Lecture 5 Kinetics of SiO2 Growth Oxidant Flow O2 or H2O Gas Diffusion Gas Flow Stagnant Layer Solid state Diffusion SiO2 SiO2 Formation Si Substrate Professor N Cheung U C Berkeley 7 EE143 F05 Lecture 5 Deal Grove Model CG stagnant layer Cs Note Note CCss CCoo SiO2 Si Co Ci X0x F2 F1 gas transport flux Professor N Cheung U C Berkeley diffusion flux through SiO2 F3 reaction flux at interface 8 EE143 F05 F1 hG CG CS Lecture 5 Mass transfer coefficient cm sec C F2 D x Fick s Law of Solid state Diffusion C o Ci D X ox Diffusivity cm2 sec F3 ks Ci Surface reaction rate constant cm sec Comment The derivation used in Jaeger textbook assumes F1 is large not a rate limiting factor for growth rate Hence the algebra looks simpler However the lecture notes derivation includes gas transport effect and can be directly applied to CVD growth rate which will be discussed in later weeks Professor N Cheung U C Berkeley 9 EE143 F05 Lecture 5 How to solve the oxidant concentrations CS and Co are related by Henry s Law CG is a controlled process variable proportional to the input oxidant gas pressure Only OnlyCCooand andCCi iare arethe the22unknown unknownvariables variables which whichcan canbe besolved solvedfrom fromthe thesteady state steady statecondition condition FF11 FF22 F F33 22equations equations Professor N Cheung U C Berkeley 10 EE143 F05 Lecture 5 Derivation of Oxidation Growth Rate C o H Ps Henry s constant partial pressure of oxidant at surface in gaseous form H kT Cs Henry s Law from ideal gas law PV NkT Co Cs HkT Professor N Cheung U C Berkeley 11 EE143 F05 Lecture 5 Derivation of Oxidation Growth Rate cont C A HkT C G Define F1 can be re written as This is a control process variable For a given oxidant pressure CA is known hG F1 C A Co HkT h Using the steady state condition Conservation of mass flux F1 F2 F3 1 Professor N Cheung U C Berkeley 22equations equationsto tosolve solvethe the 22unknowns unknowns CCoo CCi i 2 12 EE143 F05 Lecture 5 Derivation of Oxidation Growth Rate cont Therefore CA Ci ks ks X ox 1 h D k s X ox C o Ci 1 D ksC A F F1 F2 F3 k s Ci k s k s X ox 1 D h Professor N Cheung U C Berkeley 13 EE143 F05 Lecture 5 Now convert F into Oxide Thickness Growth Rate dX ox F N1 dt Oxidant molecules unit volume required to form a unit volume of SiO2 X ox SiO2 Si F Therefore we have the oxide growth rate eqn N1 t Professor N Cheung U C Berkeley dX ox dt k sC A k s k s X ox 1 h D 14 EE143 F05 Lecture 5 Initial Condition At t 0 Xox Xi SiO2 SiO2 Si xox Si Solution Xox AX ox B t 2 1 1 A 2D ks h 2 DC A B N1 Professor N Cheung U C Berkeley Note h ks for typical oxidation condition 2 X i AXi B 15 EE143 F05 Lecture 5 Note dry and wet oxidation have different N1 factors N1 2 3 10 cm Si O2 SiO2 for O2 as oxidant N1 4 6 1022 cm3 for H2O as oxidant 22 3 Si 2 H2 O SiO2 2 H2 Professor N Cheung U C Berkeley 16 EE143 F05 Lecture 5 Summary of Deal Grove Model Xox t t X ox AX 2 2 X ox 0x B t dx ox dx ox A B dt dt dxox B dt A 2 X ox Professor N Cheung U C Berkeley t Oxide OxideGrowth GrowthRate Rateslows slows down downwith withincrease increaseof ofoxide oxide thickness thickness 17 EE143 F05 Lecture 5 A t X ox 1 2 1 A 2 4 B Case 1 Large t large Xox Xox Bt Case 2 Small t Small Xox X ox Professor N Cheung U C Berkeley B t A 18 EE143 F05 Lecture 5 Deal Grove Model Parameters 1 B 2 D C N1 2 B A A 1 D C A 1 1 N 1 h k s D e Q kT Q activation energy for diffusion Q ks e kT Q activation energy for interface reaction For Forthermal thermaloxidation oxidationof ofSi Si hhisistypically typically kkss B A B A isis kkss i e i e FF11isisrarely rarelythe therate limiting rate limitingstep step Professor N Cheung U C Berkeley 19 EE143 F05 Lecture 5 B Parabolic Constant B A Linear Constant Professor N Cheung U C Berkeley 20 EE143 F05 Lecture 5 Oxidation Charts The Thecharts chartsare are based basedon on XXi 00 i Professor N Cheung U C Berkeley 21 EE143 F05 Lecture 5 Two Ways to Calculate Oxide Thickness Grown by Thermal Oxidation E g SiO2 xi 4000A Si 1100oC 33min steam SiO2 xo x Si Method 1 Find B B A from Charts Solve Professor N Cheung U C Berkeley Xox AX ox B t 2 22 EE143 F05 Lecture 5 Two Ways to Calculate Oxide Thickness Grown by Thermal Oxidation Method 2 Use Oxidation Charts Xox oC 0 110 6500oA T3 The Thecharts chartsare are based basedon on T2 T1 XXi 0 i 0 4000oA 0 24 33 5 7 time min X i 4000 A 24 min at 1100oC …
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