Section 4: Thermal Oxidation Jaeger Chapter 3
Properties of O Thermal O is amorphous. Weight Density =.0 gm/cm 3 Molecular Density =.3E molecules/cm 3 O Crystalline O [Quartz] =.65 gm/cm 3 <> (1) Excellent Electrical Insulator Resistivity > 1E0 ohm-cm Energy Gap ~ 9 ev () High Breakdown Electric Field > 10MV/cm (3) Stable and Reproducible /O Interface
Properties of O (cont d) (4) Conformal oxide growth on exposed surface O Thermal Oxidation (5) O is a good diffusion mask for common dopants D D sio << si e.g. B, P, As, Sb. O *exceptions are Ga (a p-type dopant) and some metals, e.g. Cu, Au
Properties of O (cont d) (6) Very good etching selectivity between and O. O HF dip
Thermal Oxidation of licon Dry Oxidation S i + O S O i Wet Oxidation S i + H O S O i + H Growth Occurs 54% above and 46% below original surface as silicon is consumed
Thermal Oxidation Equipment Horizontal Furnace Vertical Furnace
Kinetics of O growth Oxidant Flow (O or H O) Gas Diffusion Solid-state Diffusion O Formation Gas Flow Stagnant Layer O -Substrate
licon consumption during oxidation 1μm O.17 μm 1μm oxidized.17 μm O X si = X ox N N ox si molecular density of O atomic density of.3 10 5 10 molecules / cm atoms / cm 3 = X ox = 0. 46 X 3 ox
C G The Deal-Grove Model of Oxidation stagnant layer C s O Note C s s C o o C o Ci X 0x F 1 F F 3 gas transport flux diffusion flux through O reaction flux at interface F: oxygen flux the number of oxygen molecules that crosses a plane of a certain area in a certain time
The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O Note Note C s s C o o C o Ci X 0x F 1 F F 3 ( ) F1 = h C C F F 3 C = D x G G S Co Ci D Xox = k s C i Mass transfer coefficient [cm/sec]. Fick s Law of Solid-state Diffusion Diffusivity [cm /sec] Oxidation reaction rate constant
Diffusivity: the diffusion coefficient D E = exp A DO kt E A = activation energy k = Boltzmann's constant T = absolute temperature = 1.38 x10-3 J/K
The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O Note Note C s s C o o C o Ci X 0x F 1 F F 3 C S and C o are related by Henry s Law C G is a controlled process variable (proportional to the input oxidant gas pressure) Only Co and Ci are the unknown variables which can be solved from the steady-state condition: F1 = F =F3 ( equations)
The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O Note Note C s s C o o C o Ci X 0x F 1 F F 3 C = H o P s Henry s Law Henry s constant = H ( kt ) partial pressure of oxidant at surface [in gaseous form]. C s from ideal gas law PV= NkT C s = C o HkT
The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O Note Note C s s C o o C o Ci X 0x Define F 1 F F 3 C A hg F HkT C C 1 = A ( HkT C G ( o ) ) h G HkT h milarly, we can set up equations for F and F 3 Using the steady-state condition: F = 1 = F F 3 1 We therefore can solve for C o and C i EE143 Ali Javey
The Deal-Grove Model of Oxidation (cont d) We have: Co Ci F D Xox At equilibrium: F 1 =F =F 3 Solving, we get: F = k s C 3 i F 1 = h(c A C o ) C i CA = k kx 1+ + h D s s ox C k = + s X Ci D o 1 ox F ( = F = F = F ) 1 3 = k s C i = k 1+ k C s s A k X + s ox Where h=h g /HkT h D
The Deal-Grove Model of Oxidation (cont d) We can convert flux into growth thickness from: F N 1 = dx dt ox ΔX ox Oxidant molecules/unit volume required to form a unit volume of O. O F
The Deal-Grove Model of Oxidation (cont d) Initial Condition: At t = 0, X ox = X i O Solution A B 1 D( k X DC N 1 ox s A + AX = B( t + 1 h g ) ox τ = +τ Note: h g >>k s for typical oxidation condition X ) + i B O AX i x ox
Dry / Wet Oxidation Note : dry and wet oxidation have different N1 factors N 1 N 1 3 = 3. 10 / cm for O as oxidant + O O 3 = 46. 10 / cm for H O as oxidant + H O O + H
X ox Summary: Deal-Grove Model t dx dt X ox X ox = t ox + AX dx dt ox 0 x B A + X = + A ox B ( t dx dt ox + τ ) = B Oxide Growth Rate slows down with increase of oxide thickness t
Solution: Oxide Thickness Regimes X ox A t + τ = 1+ 1 A 4B (Case 1) Large t [ large X ox ] X ox Bt (Case ) Small t [ Small X ox ] B X t ox A
Thermal Oxidation on <100> licon
Thermal Oxidation on <111> licon
Thermal Oxidation Example A <100> silicon wafer has a 000-Å oxide on its surface (a) How long did it take to grow this oxide at 1100 o C in dry oxygen? (b)the wafer is put back in the furnace in wet oxygen at 1000 o C. How long will it take to grow an additional 3000 Å of oxide?
Thermal Oxidation Example Graphical Solution (a) According to Fig. 3.6, it would take.8 hr to grow 0. μm oxide in dry oxygen at 1100 o C.
Thermal Oxidation Example Graphical Solution (b) The total oxide thickness at the end of the oxidation would be 0.5 μm which would require 1.5 hr to grow if there was no oxide on the surface to begin with. However, the wafer thinks it has already been in the furnace 0.4 hr. Thus the additional time needed to grow the 0.3 μm oxide is 1.5-0.4 = 1.1 hr.
Thermal Oxidation Example Mathematical Solution (a) From Table 3.1, 1.3 μm B 6.00 B = 7.7x10 exp = 3.71x10 exp kt hr A kt μm B μm For T = 1373 K, B = 0.036 and = 0.169 hr A hr ( 0.05μm) 0.05μm τ = + = 0.174 hr μm μm 0.036 0.169 hr hr ( 0.μm) 0.μm t = + 0.174hr =.70 hr μm μm 0.036 0.169 hr hr μm hr X i = 5nm
Thermal Oxidation Example Mathematical Solution (b) From Table 3.1, 0.78 μm B 7.05 B = 3.86x10 exp = 9.70x10 exp kt hr A kt μm B μm For T = 173 K, B = 0.314 and = 0.74 hr A hr ( 0.μm) 0.μm τ = + = 0.398 hr μm μm 0.314 0.74 hr hr ( 0.5μm) 0.5μm t = + 0.398hr = 1.07 hr μm μm 0.314 0.74 hr hr μm hr X i = 0
Effect of Xi on Wafer Topography 1 3 O O X i
Effect of Xi on Wafer Topography 1 3 O O X i 1 less oxide grown less consumed more oxide grown more consumed 3
Factors Influencing Thermal Oxidation Temperature Ambient Type (Dry O, Steam, HCl) Ambient Pressure Substrate Crystallographic Orientation Substrate Doping
High Doping Concentration Effect Coefficients for dry oxidation at 900 o C as function of surface Phosphorus concentration Dry oxidation, 900 o C n + n O n + n
Transmission Electron Micrograph of /O Interface Amorphous O Crystalline
Thermal Oxide Charges potassium sodium
Oxide Quality Improvement To minimize Interface Charges Q f and Q it Use inert gas ambient (Ar or N) when cooling down at end of oxidation step A final annealing step at 400-450 o C is performed with 10%H +90%N ambient ( forming gas ) after the IC metallization step.
Oxidation with Chlorine-containing Gas Introduction of halogen species during oxidation e.g. add ~1-5% HCl or TCE (trichloroethylene) to O reduction in metallic contamination improved O / interface properties O Na + K + M + Cl MCl Cl Na + or K + in O are mobile!
Effect of HCl on Oxidation Rate HCl + O + H O Cl
Local Oxidation of [LOCOS] Oxidation ~100 A O (thermal) - pad oxide to release mechanical stress between nitride and. Nitride Etch
Local Oxidation of licon (LOCOS) Standard process suffers for significant bird s beak Fully recessed process attempts to minimize bird s beak
Dopant Redistribution during Thermal Oxidation conc. e. g. B, P, As, Sb. O C B (uniform) C 1 x C C B Segregation Coefficient Fixed ratio m = C C1 equilibrium dopant conc. in equilibrium dopant conc. in O (can be>1 or <1)
Four Cases of Interest (A) m < 1 and dopant diffuses slowly in O O C C B D e. g. B (m = 0.3) C 1 flux loss through O surface not considered here. B will be depleted near interface.
Four Cases of Interest (B) m > 1, slow diffusion in O. O C 1 C C B e.g. P, As, Sb dopant piling up near interface for P, As & Sb
Four Cases of Interest (C) m < 1, fast diffusion in O O C C B e. g. B, oxidize with presence of H C 1
Four Cases of Interest (D) m > 1, fast diffusion in O O C 1 C B e. g. Ga (m=0) C
Polycrystalline Oxidation O poly- grain boundaries (have lots of defects). fast slower O a roughness with X ox b Overall growth rate is higher than single-crystal
-Dimensional oxidation effects (100) cylinder (110) (100) Thinner oxide (100) (110) Thicker oxide Top view Mechanical stress created by O volume expansion also affects oxide growth rate