Project Title Mechanics of thin film on wafer R 詹孫戎

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

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

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

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

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

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

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

Project Title Mechanical properties of microelectronic material E(Gpa)ν α(1 ／℃ ) σ o (residual stress) Substrate － silicon ×10 -6 － alumina~415 － 8.7×10 -6 － silica ×10 -6 Films polysilicon ×10 -6 varies thermal SiO ×10 -6 compressive PECVD SiO 2 －－ 2.3×10 -6 － LPCVD Si 3 N ×10 -6 tensile aluminum ×10 -6 (high!)varies tungsten(W)410(stiff!) ×10 -6 varies polyimide ~70 ×10 -6 (very high!)tensile

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

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

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

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)

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)

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)

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)

Project Title Failure resistance of amorphous silicon transistors Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)

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)

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)