1. Joule Heating of MEMS Beam Ansys Simulation October 2011

2. 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
7 Kelvin
7 Kelvin
10 μm α°
L μm
Top View
t = 5 μm
3D view
Front View

3. Si Material Properties
[Karlmann, 2006] 
Thermal Expansion coef.
Resistivity
α < 0 !
Thermal Conductivity
[Asheghi 2002]
[Li 1978]

4. 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

5. Simulation Results – Temp. & Displ.
Max Temp: 367 K
Power: 19 mW
(3000 x 5 x 5 μm3 beam, 2° angle)
Max Temp: 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)

6. Simulation Results - Temperature
Max temperature (at middle of beam)
LxWxT (α deg)

7. Simulation Results - Displacement
Max displacement (at middle of beam)
LxWxT (α deg)

8. Simulation Results – Displ. Vs Temp
LxWxT (α deg)