![Physics 9826a
Deal-Grove model
Recall: from ideal gas law, Cg=pg /kT
Henry’s law: C0=H ps
F1 = h(C*-C0), where h=hg/HkT
F2 = D(O2) [(C0-Ci)/x0] (from Fick’s law)
If we let rate at interface be proportional to concentration of oxidant at the SiO2/Si
interface, then:
F2 = ksCi
Assuming steady state approximation: F1 = F2 = F3
h(C*-C0) = D(O2) [(C0-Ci)/x0] = ks Ci
… algebra then, solve for concentration at the interface…
k x
C * 1 + S 0
C*
; Co =
D
Ci =
k S k S x0 k S k S x0
1+ + 1+ +
h D h D
B. E. Deal and A. S. Grove, J. Appl. Phys., 36 (1965) 3770
Lecture 17 17
Deal-Grove model (linear-parabolic regime)
dx F3
Rate of growth = , where N is the number of oxygen atoms incorporated
dt N
per unit volume (2.2 ×1022 cm-3 for SiO2)
dx F3 Hk s p g
= =
dt N k k x
N 1 + s + s o
h D
for x0 = x(t = 0) solution is
x0 + Ax0 = B(t + τ )
2
1 1 2 DC * x 2 + Axi
A = 2 D + ; B =
k h ;τ = 0
s N B
For very thin oxides, we can neglect quadratic term, and we have :
B
x0 ≈ (t + τ ) linear regime
A
For thick oxides
xo ≈ B(t + τ )
2
parabolic regime
Lecture 17 18
Lecture 17 9](https://image.slidesharecdn.com/mechanismsofcorrosionandoxidation-lecture-130121164637-phpapp01/85/Mechanisms-of-corrosion-and-oxidation-lecture-9-320.jpg)
Mechanisms of corrosion and oxidation lecture
- 1. Physics 9826a Lecture 17 Mechanisms of Corrosion and Oxidation 17.1 Corrosion (thermodynamics and kinetics) 17.2 Surface and Interface reactions in oxidation of metals 17.3 Model oxidation of Si: Deal-Grove 17.4 Diffusion in metal oxide thin films References: 1) Zangwill, p.104-109 2) S.A. Campbell, The Science ad Engineering of Microelectronic Fabrication, 1995 3) B. E. Deal and A. S. Grove, J. Appl. Phys., 36 (1965) 3770 4) C.Y. Chang, S.M. Sze, VLSI Technology, McGraw Hill Lecture 17 1 17.1 Corrosion Corrosion is the deterioration of a material resulting from chemical reaction with its environment - temperature, pressure - concentration of the reactions and products - mechanical stress and erosion Can be regarded as reverse extractive metallurgy Metallurgy, reduction Metal oxide (silicate, carbonate) Metal Corrosion, Lower energy state oxidation Higher energy state Spontaneous process Metals: electrochemical process Nonmetals: direct chemical reaction (with salts, water, organic solvents, oxygen plus UV) Lecture 17 2 Lecture 17 1
- 2. Physics 9826a Oxidation Reduction Reactions of Metals Zn + 2HCl → ZnCl2 + H2 Simplified ionic form: Zn0 + 2H+ → Zn2+ + H2↑ Two “half reactions”: Zn0 → Zn2+ + 2e- (oxidation half reaction) 2H+ + 2e- → H2 (reduction half reaction) 1. Oxidation reaction: metals form ions that go into aqueous solution, also called the anodic reaction; electrons are produced and remain in the metal 2. Reduction reaction: metals or nonmetals consume electrons and they are reduced into zero-charge state, also called the cathodic reaction Both oxidation and reduction reactions must occur at the same time Lecture 17 3 Standard Electrode Half-Cell Potential for Metals • Every metal has a different tendency to corrode in a particular environment • Standard Electrode Half-Cell Potential for metals gives a universal way to compare the tendency for metals to form ions – if the potential is negative, metal oxidizes to ions – If the potential is positive, less tendency to corrode – measured against “standard hydrogen electrode” Assign 0V to the reaction: 2H+ + 2e- → H2 Lecture 17 4 Lecture 17 2
- 3. Physics 9826a Standard electrode potentials at 250 Lecture 17 5 Galvanic cells • Galvanic couple (cell): is constructed with two dissimilar metal electrodes each immersed in a solution of their own ions, and separated by a porous wall (membrane) to prevent their mechanical mixing and an external wire to connect the two electrodes Zn → Zn2+ + 2e- Eo = -0.763 V Cu → Cu2+ + 2e- Eo = +0.337 V Overall reaction: Zn + Cu2+ → Zn2+ + Cu Ecello = - 1.100 V Recall: Nernst equation connects half-cell reaction potentials with the metal ion concentrations 0.0592 E = Eo + log Cion , n where C ion is molar concentrat ion of ions Lecture 17 6 Lecture 17 3
- 4. Physics 9826a Galvanic Cells with NO metal ions present Consider a galvanic cell in which Fe and Cu electrodes are immersed in an aqueous acidic electrolyte (no metals ions present) Fe → Fe2+ + 2e- Eo = -0.440 V Cu → Cu2+ + 2e- Eo = +0.337 V Fe has the more negative half-cell potential, will oxidize Fe → Fe2+ + 2e- (anodic half reaction) If acidic: 2H+ + 2e- → H2 (cathodic half reaction) If neutral or basic solution: O2 + 2H2O + 4e- → 4 OH- Lecture 17 7 Common cathode reactions for aqueous galvanic cells Lecture 17 8 Lecture 17 4
- 5. Physics 9826a Microscopic Galvanic Cell Corrosion Electrochemical reactions for (a) Zn in dilute hydrochloric acid; (b) Fe immersed in oxygenated neutral water solution (rusting of iron) 2Fe + 2H2O + O2 → 2 Fe2+ + 4OH- → 2 Fe(OH)2 ↓ 2 Fe(OH)2 + H2O + ½ O2 → 2 Fe(OH)3 ↓ (rust) Lecture 17 9 Galvanic Cells created by differences in Composition, Structure, and Stress 1. Grain – grain-boundary galvanic cell (grain boundaries are typically more chemically active (anodic) than the grain matrix) 2. Multiple-phase galvanic cells (e.g. Fe and Fe3C in gray cast iron) 3. Impurity cells (higher corrosion resistance for purer metals) Types of corrosion • Uniform chemical attack corrosion (whole surface area is affected) • Galvanic or two-metal pair corrosion • Pitting and perforation • Intergranular • Stress and Erosion • Cavitation • Selective leaching or dealloying Lecture 17 10 Lecture 17 5
- 6. Physics 9826a Corrosion Rate (Kinetics) • So far we discussed equilibrium conditions and thermodynamic tendencies of metals to corrode • Corroding systems are not at equilibrium Kinetics - Faraday’s equation (electrochemistry) ItM iAtM w= = ; nF nF where w is weight of corroded or electroplated metal in time t; I = curretn flow, A; M = atomic mass of the metal, g/mol; n = number of electrons produced or consumed, F = 96500C/mol; i = curretn density, A/cm 2 ; A = area of electrode, cm 2 How to measure corrosion rate: - a weight loss per unit area; - change in thickness of material per unit time; - as a current density Lecture 17 11 17.2 Oxidation of metals Protective oxide films: 1. The volume ratio of oxide to metal after oxidation should be close to 1:1 or Pilling-Bedworth ratio = 1 (ration of oxide volume produced by oxidation to the volume of metal consumed by oxidation) 2. The oxide film should have good adherence, high-temperature plasticity to prevent fracture 3. The melting point of the oxide should be high 4. The oxide films should have a low vapor pressure and thermal coefficient of expansion comparable to the one of the metal 5. Low conductivity and low diffusion coefficient for metal ions and oxygen are desired Lecture 17 12 Lecture 17 6
- 7. Physics 9826a Mechanisms of Oxidation • When cations diffuse, the initially formed oxide drifts towards the metal • When anions diffuse, the oxide drifts in the opposite direction Lecture 17 13 Oxidation Rate (Kinetics) • During the oxidation of different metals, various empirical rate laws have been observed • Linear law: w = kL t Typical for metals with porous or cracked oxide films (⇒ transport of reactant ions occurs at faster rates than the chemical reaction), e.g., K, Ta • Parabolic law: w2 = kpt + C Typical for metals with thick coherent oxides, e.g. Cu, Fe • Logarithmic rate: w = ke log (Ct + A) For oxidation at elevated temperature, e.g., Fe, Cu, Al; fast oxidation at the start, the rate decreases to a very low value w – weight gain per unit area; or • Catastrophic at high T: rapid exothermal reactions, oxides are oxide thickness volatile, e.g. Mo, W, V Lecture 17 14 Lecture 17 7
- 8. Physics 9826a 17.3 Thermal oxidation of silicon Si grows a high quality oxide Si(s) + O2 (g) = SiO2 (s) Si(s) + H2 O (g) = SiO2 (s) +2H2 Lecture 17 15 17.3 Thermal oxidation of silicon • Diffusivity of Si in SiO2 much smaller than that of O2 ⇒ molecular O2 diffusion (opposite to metal oxidation or anodic oxidation of Si , in which cations moves out to surface) gas SiO2 Si cg csurf c0 ci F1 F2 F3 0 xo Depth (x) F1 – incident flux to surface; F1=hg (Cg-Cs) hg – mass transfer coefficient F2 – flux through the oxide; F3 – reaction flux of oxide growth at interface Lecture 17 16 Lecture 17 8
- 9. Physics 9826a Deal-Grove model Recall: from ideal gas law, Cg=pg /kT Henry’s law: C0=H ps F1 = h(C*-C0), where h=hg/HkT F2 = D(O2) [(C0-Ci)/x0] (from Fick’s law) If we let rate at interface be proportional to concentration of oxidant at the SiO2/Si interface, then: F2 = ksCi Assuming steady state approximation: F1 = F2 = F3 h(C*-C0) = D(O2) [(C0-Ci)/x0] = ks Ci … algebra then, solve for concentration at the interface… k x C * 1 + S 0 C* ; Co = D Ci = k S k S x0 k S k S x0 1+ + 1+ + h D h D B. E. Deal and A. S. Grove, J. Appl. Phys., 36 (1965) 3770 Lecture 17 17 Deal-Grove model (linear-parabolic regime) dx F3 Rate of growth = , where N is the number of oxygen atoms incorporated dt N per unit volume (2.2 ×1022 cm-3 for SiO2) dx F3 Hk s p g = = dt N k k x N 1 + s + s o h D for x0 = x(t = 0) solution is x0 + Ax0 = B(t + τ ) 2 1 1 2 DC * x 2 + Axi A = 2 D + ; B = k h ;τ = 0 s N B For very thin oxides, we can neglect quadratic term, and we have : B x0 ≈ (t + τ ) linear regime A For thick oxides xo ≈ B(t + τ ) 2 parabolic regime Lecture 17 18 Lecture 17 9
- 10. Physics 9826a Deal-Grove Model Physical significance of 2 regimes: - in linear regime for thin films, the oxidant concentration is assumed constant throughout the system, C0 ~ Ci, rate is controlled by interface (surface) reaction; - in the parabolic (thick film) regime, Ci →0, and C0 ~ C* ; and B ∝ D, and diffusion through the oxide dominates growth kinetics Lecture 17 19 Problems with DG model: • Steady state growth? • Interface growth assumes first order gas phase type reaction, why? • What is the true O2 profile? • Is the interface a sharp well-phase-segregated plane (strain in Si, suboxides, roughness? • No good physical interpretation of accelerated initial growth • Ions, radicals, surface reaction/exchange? Lecture 17 20 Lecture 17 10
- 11. Physics 9826a The role of SiO formation during the SiO2 growth Overall reaction route is dependent on the oxygen (water) pressure and temperature used - at low T, high po2 ⇒ Si(s) + O2(g) = SiO2 (s) - “passive” oxidation regime - at high T, low po2 ⇒ Si(s) + O2(g) = 2SiO (g) – “active” oxidation Starodub D. Surf. Rev. Lett. 6 (1999) 45-52 Lecture 17 21 Oxygen reactions with oxide films Some possible types of reactions: (i) exchange without a change in (ii) Oxide growth with additional O total oxygen concentration incorporation oxide O2 substrate Exchange Oxide growth Lecture 17 22 Lecture 17 11
- 12. Physics 9826a Oxygen transport mechanisms examined by ion scattering and isotopes 16 18 O O H+ marker tracer (first) (last) Oxygen lattice transport (O or vacancy exchange) Direct oxygen transport (no O- exchange) to interface Energy Concentration vs “Raw” ion scattering depth spectra (for two Lecture 17 isotopes) 23 Oxygen isotope experiments: SiO2 growth mode Q: Why use isotopes? A: To study processes, not just structures!! 900 °C 1. 18O uptake at the surface! 2. Growth at the interface 3. 16O loss at the surface 800 °C 4. 16O movement at the interface! Lecture 17 Gustafsson, Garfunkel, PRB 52, 1759 (1995) Gusev, Lu, 24 Lecture 17 12
- 13. Physics 9826a Schematic model for ultra-thin films Surface exchange SiO2 Transition zone, Growth SiOx Si (crystalline) Lecture 17 Deal and Grove 25 17.4 Diffusion in metal oxide thin films Oxygen (O2) transport in SiO2 Atomic oxygen (O) in metal oxide films No O-exchange SiO2 growth + O-diffusion and MOx growth, O-exchange O-exchange O2 decomp. exchange in bulk O-exchange in bulk of oxide in surface at interface at surface of oxide at interface layer Si-substrate O Substrate O2 O2 MOx SiO2 films: • amorphous after annealing • molecular O2 transport in SiO2 • decomposition by SiO desorption (Many) transition metal and lantinide films: • tend to crystallize at low T • high oxygen mobility Lecture 17 26 Lecture 17 13
- 14. Physics 9826a Plan-view HRTEM and HAADF-STEM 3042513A-12, HAADF-STEM ZrO2 /Si(001) As deposited 5 nm 5 nm 3042513A-12, HAADF-STEM HRTEM shows no discrete crystallization, though some regions do show lower-ordering structure HAADF-STEM shows density variations suggestive of either roughening or partial phase- separation Lecture 17 2 nm 27 Elementary steps during metal oxidation Lecture 17 28 Lecture 17 14
- 15. Physics 9826a Microscopic oxidation pathways J. Appl. Phys. 85 (1999) 7646 Lecture 17 29 Oxygen diffusion in ultrafine grained monoclinic ZrO2 Objective: find the difference in diffusivities of O in crystalline ZrO2 and grain-boundary region - prepare samples with different grain-to-grain boundary ratio, - analyze by SIMS Lecture 17 J. Appl. Phys. 85 (1999) 7646 30 Lecture 17 15
- 16. Physics 9826a 18O profiles in crystalline ZrO2 • Dv= 2.5x10-7m2/s; • Db= 3.3x10-5m2/s; Lecture 17 31 Comparison of 18O diffusion in metal oxides J. Appl. Phys. 85 (1999) 7646 Lecture 17 32 Lecture 17 16