Joule Heating of MEMS Beam Ansys Simulation October 2011
Problem Find power required to heat silicon beam by ~100°C with the geometry below Ambient temperature = 7 Kelvin Heat convection and conduction are modeled in the simulation 10 μm w Fixed @ 7 Kelvin Fixed @ 7 Kelvin 10 μm α° L μm Top View t = 5 μm 3D view Front View
Si Material Properties [Karlmann, 2006] Thermal Expansion coef. Resistivity α < 0 ! Thermal Conductivity [Asheghi 2002] [Li 1978]
Si Material Parameters (From previous slide) Resistivity [Ohm-m] = ~10^-3 For boron-doped Si (NA = 3*10^17 cm^-3) Young’s Mod: 169 GPa Temp [K] Thermal Expans. High purity p-type [1/K] [Karlmann,2006] 35 -0.11e-6 50 -0.29e-6 70 -0.46e-6 110 -0.22e-6 130 0.11e-6 150 0.49e-6 190 1.24e-6 210 1.56e-6 250 2.1e-6 300 2.65e-6 400 3.21e-6 Temp [K] Thermal Cond. 10^17 B/cm^3 [W/(m-K)] [Aseghi, 2002] 20 170 30 300 50 600 80 500 100 400 150 200 146 74 *Interesting note: Thermal expansion of silicon is NEGATIVE below 120 K
Simulation Results – Temp. & Displ. Max Temp: 367 K Power: 19 mW (3000 x 5 x 5 μm3 beam, 2° angle) Max Temp: 207.6 K Power: 11 mW (3000 x 5 x 5 μm3 beam, 2° angle) Displacement: 19 μm Power: 19 mW (3000 x 5 x 5 μm3 beam, 2° angle) Displacement: 4.4 μm Power: 11 mW (3000 x 5 x 5 μm3 beam, 2° angle)
Simulation Results - Temperature Max temperature (at middle of beam) LxWxT (α deg)
Simulation Results - Displacement Max displacement (at middle of beam) LxWxT (α deg)
Simulation Results – Displ. Vs Temp LxWxT (α deg)