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 ide 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 + O O Wet Oxidation + H O O + 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 idation 1μm O.17 μm 1μm idized.17 μm O X si = X N N si molecular density of O atomic density of.3 10 5 10 molecules / cm atoms / cm 3 = X = 0. 46 X 3
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: ygen flux the number of ygen 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 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 X = k s C i Mass transfer coefficient [cm/sec]. Fick s Law of Solid-state Diffusion Diffusivity [cm /sec] Oxidation reaction rate constant
E = exp A D DO kt E A = Diffusivity: the diffusion coefficient activation energy k = Boltzmann's constant = 1.38 x10 T = absolute temperature -3 J/K The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O 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 idant 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 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 = C H s = ( kt ) C o HkT partial pressure of idant at surface [in gaseous form]. C s from ideal gas law PV= NkT The Deal-Grove Model of Oxidation (cont d) C G stagnant layer C s O Note C s s C o o C o Ci X 0x Define F 1 F F 3 C A h F = G 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 We therefore can solve for C o and C i 1 EE143 Ali Javey
The Deal-Grove Model of Oxidation (cont d) We have: Co Ci F D X At equilibrium: F 1 =F =F 3 Solving, we get: F3 = k s C F 1 = h(c A C o ) i C i CA = k kx 1+ + h D s s C k = + s X Ci D o 1 F ( = F = F = F ) 1 Where h=h g /HkT 3 = k s C i = ksc A ks ksx 1+ + h D The Deal-Grove Model of Oxidation (cont d) We can convert flux into growth thickness from: F N 1 = dx dt ΔX 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 = X i O Solution A B X 1 D( k DC N 1 s A + AX = B( t +τ ) + 1 h g ) Note: h g >>k s for typical idation condition τ = X i + O AX B i x Dry / Wet Oxidation Note : dry and wet idation have different N1 factors N 1 N 1 3 = 3. 10 / cm for O as idant + O O 3 = 46. 10 / cm for H O as idant + H O O + H
X Summary: Deal-Grove Model t dx dt X X = t + AX 0 x dx + dt B A + X = B ( t + τ ) dx A dt = B Oxide Growth Rate slows down with increase of ide thickness t Solution: Oxide Thickness Regimes X A t + τ = 1+ 1 A 4B (Case 1) Large t [ large X ] X Bt (Case ) Small t [ Small X ] X B A t
Thermal Oxidation on <100> licon Thermal Oxidation on <111> licon
Thermal Oxidation Example A <100> silicon wafer has a 000-Å ide on its surface (a) How long did it take to grow this ide at 1100 o C in dry ygen? (b)the wafer is put back in the furnace in wet ygen at 1000 o C. How long will it take to grow an additional 3000 Åof ide? Thermal Oxidation Example Graphical Solution (a) According to Fig. 3.6, it would take.8 hr to grow 0. μm ide in dry ygen at 1100 o C.
Thermal Oxidation Example Graphical Solution (b) The total ide thickness at the end of the idation would be 0.5 μm which would require 1.5 hr to grow if there was no ide 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 ide is 1.5-0.4 = 1.1 hr. Thermal Oxidation Example Mathematical Solution (a) From Table 3.1, 1.3 μm B 6.00 μm B = 7.7x10 exp = 3.71x10 exp kt hr A kt hr 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 X i = 5nm
Thermal Oxidation Example Mathematical Solution (b) From Table 3.1, 0.78 μm B 7.05 μm B = 3.86x10 exp = 9.70x10 exp kt hr A kt hr 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) t = μm 0.314 hr 0.5μm + 0.398hr = 1.07 hr μm 0.74 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 ide grown less consumed more ide 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 idation at 900 o C as function of surface Phosphorus concentration Dry idation, 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 idation 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 idation 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 ide 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, idize 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 b Overall growth rate is higher than single-crystal
-Dimensional idation effects (100) cylinder (110) (100) Thinner ide (100) (110) Thicker ide Top view Mechanical stress created by O volume expansion also affects ide growth rate