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Project Title Mechanics of thin film on wafer R91943100 詹孫戎
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Project Title Mechanics of thin film on wafer Basic mechanics Axial stress , strainPoisson’s ratio Poisson’s ratio Shear stress , strain , modulus Stress-strain Thermal strain Mechanical properties of microelectronic material Effective Young’s modulus of composite layers Substrate warpage Biaxial stress in thin film on thick substrate Mechanics of film-on-foil electronics Failure resistance of amorphous silicon transistors Mobility in thin-film under compressive strain Reference
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Project Title Axial stress Load P (Newton) : Internal resultant normal force Area A (m 2 ) : Cross-section area of the bar Stressσ (N/m 2 ; Pa) : Average normal stress at any point on the cross-sectional area σ > 0 tensile σ < 0 compressive Source:Mechanics of materials by R.C.Hibbeler
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Project Title Axial strain Strainε (dimensionless) : Deformation changes in length Average elongation / Original length Yong’s modulus E (N/m 2 ; Pa) : E (GPa) Si190 SiO 2 73 Diamond1035
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Project Title Poisson’s ratio Poisson’s ratio ν : Transverse strain / Longitudinal strain ν= 0.5 → volume conserved Source:Mechanics of materials by R.C.Hibbeler
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Project Title Shear stress , strain , modulus Shear stress τ (N/m 2 ; Pa) : V (Newton) ; internal result shear force A (m 2 ) : area at the section Shear strain γ (rad) Shear modulus G (N/m 2 ; Pa) : Source:Mechanics of materials by R.C.Hibbeler
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Project Title Stress-strain Low stress Elastic stress / strain = constant σ y = yield stress Ultimate stress – material break Si (brittle) ; ultimate stress ~ yield stree MaterialYield Strength(Mpa) Al170 Steel2,100 W4,000 Si7,000 Quartz8,400 Diamond53,000 Source:UC Berkeley EE143,Lec 25
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Project Title Thermal strain 1ε th = ∫[α f (T) – α s (T)] dT ≒ (α f – α s )(T Dep – T room ) Source:UC Berkeley EE143,Lec 25
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Project Title Mechanical properties of microelectronic material E(Gpa)ν α(1 /℃ ) σ o (residual stress) Substrate - silicon1900.232.6×10 -6 - alumina~415 - 8.7×10 -6 - silica730.170.4×10 -6 Films polysilicon1600.232.8×10 -6 varies thermal SiO 2 700.200.35×10 -6 compressive PECVD SiO 2 -- 2.3×10 -6 - LPCVD Si 3 N 4 2700.271.6×10 -6 tensile aluminum700.3525×10 -6 (high!)varies tungsten(W)410(stiff!)0.284.3×10 -6 varies polyimide3.20.4220~70 ×10 -6 (very high!)tensile
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Project Title Effective Young’s modulus of composite layers Stressing along x-direction All layers takes the same strain Ex = f A E A + f B E B Material with lager E takes larger stress Stressing along y-direction All layers takes the same stress Material with small E takes larger strain Source:UC Berkeley EE143,Lec 25
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Project Title Substrate warpage Radius of curvature of warpage Stoney’s equation t s : substrate thickness t f : film thickness E s : Young’s modulus of substrate υ s : Posson’s ratio of subsrate Source:UC Berkeley EE143,Lec 25
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Project Title Biaxial stress in thin film on thick substrate σ z = 0 No stress direction normal to substrate Assume isotropic film ε x = ε y = ε → σ x = σ y = σ Source:UC Berkeley EE143,Lec 25
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Project Title Mechanics of film-on-foil electronics When sheet is bent Top surface in tension Bottom surface in compression Neutral surface : one surface inside the sheet has no strain Strain in top surface : d f : film thickness d s : substrate thickness Circuit sandwiched between substrate and encapsulation layer Circuit in the neutral surface if Source:Z.Sue,E.Y.Ma,H.Gleskova, and S.Wagner, Appl.Phys.Lett.74,1177(1999)
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Project Title Mechanics of film-on-foil electronics Film and substrate have different Young’s moduli η = d f / d s χ = Y f / Y s Two kids of substrate Steel : Y f / Y s ≒ 100 Plastic : Y f / Y s ≒ 1 Source:Z.Sue,E.Y.Ma,H.Gleskova, and S.Wagner,Appl.Phys.Lett.74,1177(1999)
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Project Title Failure resistance of amorphous silicon transistors a-Si:H TFTs 51-μm-thick polyimide Both side coated 0.5-μm-thick SiN x 100-nm-thick Ti / Cr layer electrode 360nm gate SiN x 100nm undoped a-Si:H 180nm passivating SiN x 50nm (n+) a-Si:H 100nm Al for source-drain contact Compliant substrate Without SiN x back layer Stiff substrate With SiN x back layer Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)
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Project Title Failure resistance of amorphous silicon transistors TFT bent to a radius R χ= Y f / Y s ; η 1 = d f1 / d s ; η 2 = d f2 / d s Y f ≒ 200GPa ; Y s ≒ 5GPa TFT Compressed by at least 2% without failing Tensile 0.5% Source:H.Gleskova,S.Wagner,and Z.Sue, Appl.Phys.Lett.75,3011(1999)
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Project Title Failure resistance of amorphous silicon transistors Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)
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Project Title Mobility in thin-film under compressive strain Electronic mobility in amorphous silicon thin-film transistor under compressive strain Source:H.Gleskova,S.Wagner,Appl.Phys.Lett.79,3347(2001)
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Project Title Reference UC Berkeley EE143,Lec 25 Mechanics of materials by R.C.Hibbeler Z.Sue,E.Y.Ma,H.Gleskova,and S.Wagner,Appl.Phys.Lett.74,1177(1999) H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999) H.Gleskova,S.Wagner,Appl.Phys.Lett.79,3347(2001)
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