EE 143 Microfabrication Technology Fall 2014

Transcription

1 EE 143 Microfabrication Technology Fall 2014 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 1 xidation EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 2

2 Thermal xidation of Silicon Achieved by heating the silicon wafer to a high temperature (~900 o C to 1200 o C) in an atmosphere containing pure oxygen or water vapor Enabling reactions: For dry oxygen: Si + 2 Si 2 For water vapor: Si + 2H 2 Si 2 + 2H 2 Si Wafer Schematically: High T (~900 o C 1200 o C) In dry 2 or Water vapor 56% 44% Si Wafer EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 3 xidation Modeling (1) Initially: (no surface) gas stream Si Growth rate determined by reaction the surface (2) As oxide builds up: gas stream oxide Si Reactant must diffuse to Si surface where the oxidation reaction takes place Growth rate governed more by rate of diffusion to the silicon-oxide interface EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 4

3 N N surface xidation Modeling (cont.) reactant concentration Si 2 X ox J Si N i Si-Si 2 interface N = reactant conc. at oxide surface [in cm -2 ] N i = reactant conc. at Si-Si 2 interface N( x, t) J = reactant flux = D x distance from surface Diffusion coeff. [in µm/hr or m/s] [Fick s 1 st Law of Diffusion] In the Si 2 : J ( N N ) D X i = = constant [in # particles/(cm 2 s)] (1) Assumption that the reactant does not accumulate in the oxide. EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 5 xidation Modeling (cont.) At the Si-Si 2 interface: xidation rate N i J N i J = k s N (2) i Reaction rate constant Combining (1) and Si-Si 2 interface N J J k s Ni = J = D ks X DJ D JX = DN J X = DN k + s k s DN J = D X + k s = Flux of reactants EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 6

4 Rate of change of oxide layer thickness w/time xidation Modeling (cont.) Find an expression for X (t): dx dt J M oxidizing flux DN M X + D k = = = (3) s # of molecules of oxidizing species incorporated into a unit volume of oxide = cm for = cm for H2 Solve (3) for X (t) : [Initial condition X ( t = 0) = X i ] dx dt DN M = X + D ks t DN D ( X + ) dx dt X ks = X 0 i M EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 7 xide Thickness Versus Time Result: additional time required to go from X i X 1 A 4B 2 X ( t) = 1+ ( t + τ ) A 2 Xi Xi A = 2D τ = + k s B ( B A) 2DN E B = D = D A exp M kt where time required to grow X i [X i = initial oxide thickness] i.e., D governed by an Arrhenius relationship temperature dependent EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 8

5 For shorter times: 2 A 4B xidation Modeling (cont.) B A ( t + τ ) << X ( t) = ( t + τ ) oxide growth limited by reaction at the Si-Si 2 interface Taylor expansion (first term after 1 s cancel) linear growth rate constant For long oxidation times: oxide growth diffusion-limited 2 A 4B ( t + τ ) >> X ( t) = B( t + τ ) t >>τ EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 9 Bt Parabolic rate constant xidation Rate Constants Above theory is great but usually, the equations are not used in practice, since measured data is available Rather, oxidation growth charts are used EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 10

6 xidation Growth Charts EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 11 Using the xidation Growth Charts Example: <100> silicon Starting oxide thickness: X i =100nm Want to do wet 1000 o C to achieve X ox =230nm What is the time t required for this? Growth Chart for <100> Silicon EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 12

7 Factors Affecting xidation In summary, oxide thickness is dependent upon: 1. Time of oxidation 2. Temperature of oxidation 3. Partial pressure of oxidizing species ( N o ) Also dependent on: 4. Reactant type: Dry 2 Water vapor faster oxidation, since water has a higher solubility (i.e., D) in Si 2 than 2 5. Crystal orientation: <111> faster, because there are more bonds available at the Si-surface <100> fewer interface traps; smaller # of unsatisfied Si-bonds at the Si-Si 2 interface EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 13 Factors Affecting xidation 6. Impurity doping: P: increases linear rate const. no affect on parabolic rate constant faster initial growth surface reaction rate limited B: no effect on linear rate const. increases parabolic rate const. faster growth over an initial oxide diffusion faster EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 14

8 Dopant Redistribution During xidation This must be considered and designed for when generating any process flow, especially for transistor circuits, e.g., CMS During oxidation, the impurity concentration at the Si-Si 2. interface can increase (pile-up) or deplete, depending upon the dopant type Whether a particular impurity depletes or piles the interface depends on: 1. Diffusion coefficient, D (of the impurity in Si 2 ) 2. Segregation coefficient, m: m = impurity equil. conc. in Si impurity equil. conc. in Si 2 EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 15 Dopant Behavior During xidation Segregation coefficient (m) and diffusion constant (D) combine to determine dopant behavior during oxidation: Impurity m D in Si 2 Dopant Behavior During xidation B <0.3 (small) Small depl. f/si surface, pile up in oxide B (oxidation w/h 2 ) <0.3 (small) Large depl. f/si surface, depl. from oxide P, Sn, As ~10 (large) Small pile up in Si, very little diff. into Si 2 Ga 20 (large) Large depl. f/si, depl. from oxide e.g., wet oxidation where H 2 is present as a by-product. So large that it depletes the the Si surface despite EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 16

9 Dopant Redistribution During xidation B B (oxidation w/ H 2 ) P, Sn, As Ga EE 143: Microfabrication Technology LecM 2 C. Nguyen 2/14/10 17