Schematic of the polysilicon microbridge devices tested. A long, slender beam is suspended above a substrate. The bond pads support each end of the beam and provide an anchor to the substrate.
Cross section showing the computational model for the bond pad fabricated using the SUMMiT V™ process. The material layers are polysilicon, silicon dioxide, silicon nitride, and aluminum. The beam plane represents the location where the microbridge attaches to the bond pad.
(a) Predicted temperatures in a SUMMiT V™ bond pad due to thermal resistance at an ambient temperature of 295 K. In the simulation, the polysilicon thermal conductivity is 70 W/(m K) and the applied power is 1 mW. (b) Temperature and thermal conductivity dependent thermal resistance of the bond pad. Equation (11) is fit to each set of constant thermal conductivity data.
(a) Predicted temperatures in a SUMMiT V™ bond pad due to Joule heating at an ambient temperature of 295 K. In the simulation, the polysilicon thermal conductivity is 70 W/(m K) and the applied current is 1 mA. (b) Temperature and thermal conductivity dependent Joule heating of the bond pad. Equation (12) is fit to each set of constant thermal conductivity data.
Theoretical temperature profiles calculated according to basic steady state theory (Eq. (3) ) and modified theory that accounts for thermal resistance and Joule heating in the bond pad (Eq. (8) ). Experimental data was obtained at 303 K and 298 K for the 200 μm and 400 μm long beams, respectively, using Raman thermometry. 36 The applied power was 10.8 mW for the 200 μm beam and 4.0 mW for the 400 μm beam. The value of k is taken to be 71 W/(m K) in Eqs. (3) and (8) .
Schematic of the steady state thermal conductivity measurement system. The polysilicon microbridges are packaged and housed inside a radiation shielded cryostat that is evacuated to a pressure below 1 mTorr and cooled with a pressurized 10 L LN2 dewar. A heating element in the cryostat is used to maintain a constant temperature as set using the temperature controller. A computer is used to control a data acquisition (DAQ) unit that is connected to the current source and digital multimeter. 11
Thermal conductivity variation with beam length from experimental (T = 303 K) data showing the effect of data analysis procedure. The uncorrected data show clear length dependence and underpredict thermal conductivity. With electrical resistance, thermal resistance and Joule heating corrections, the length dependence is minimized resulting in a thermal conductivity of 71 W/(m K).
Measured temperature dependent thermal conductivity of polysilicon (filled circles) compared to reported values in the literature for single crystalline silicon (filled shapes) and polysilicon (unfilled shapes).
Reported values of doped polysilicon thermal conductivity at 300 K as a function of layer thickness.
Dimensions of geometric features used in the computational model.
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