Thermal expansion coefficient of polycrystalline silicon thin film was measured by microgauge method and microbridge method. In both methods, test patterns were made from polycrystalline silicon thin film and driven by applying hundreds of microampere of current. When current is applied to the test pattern, Joule heating is occurred and test pattern is deflected due to thermal expansion of the test pattern.
Polycrystalline silicon thin film with 3㎛ thickness was used as device material. The thin film was doped with phosphorus and has resistivity of $5.7 × 10^{-4} ~ 6.4 × 10^{-4}Ωㆍm$ at room temperature.
Test patterns have Vernier gauge which has resolution of 0.2㎛ in order we can measure the deflection of the test pattern exactly. In microgauge method, deflection and resistance at the driving point were measured. Average temperature can be calculated from measured resistance. By relationship between measured displacement at the Vernier gauge and calculated average temperature, thermal expansion coefficient of polycrystalline silicon thin film was calculated. In microbridge method, thermal expansion coefficient of polycrystalline silicon thin film was calculated by ANSYS simulation that satisfied measured displacement at the Vernier gauge and calculated average temperature from measured resistance.
Average temperature of the test pattern can be calculated if we know temperature dependence of resistivity of polycrystalline silicon thin film and contact resistance of the test patterns. The test patterns were driven in the vacuum chamber in order to eliminate heat dissipation to the air. Neglecting the heat dissipation to the air simplifies the work to calculate average temperature of the test patterns.
Driving current was applied by HP 4145B Semiconductor Analyzer. Driving voltage and driving current were measured simultaneously. Displacement at the Vernier gauge was measured by optical microscope with CCD camera.
To calculate average temperature of the test patterns at the driving point, temperature characteristics of resistivity of polycrystalline silicon thin film was investigated. Bridges width of 3, 5, 7㎛ and length of 200, 300, 400, 500㎛ were used to measure the resistivity. To make uniform temperature throughout the test pattern, we dropped silicon oil to the microbridge enough to immerse it entirely. Temperature dependence of resistivity was measured on the hot chuck. 1 mil thick Aluminum wire was bonded to the contact pads so that current can be applied through the silicon oil to the microbridge. The current was limited under 10 μA to minimize Joule heating effect of microbridge.
Measured bridge resistance is consists of two factors. One is resistance of microbridge itself and the other is contact resistance at the bridge pads. To measure the contact resistance, some bridges which have the same width and thickness but have different lengths were used. Extrapolating the linear line obtained from total resistance vs. bridge length graph to the point where the bridge length equals zero, we get contact resistance at that point considering contact area.
From experiments, we get temperature dependence of resistivity of polycrystalline thin film from room temperature up to 200 centigrade as below.
$ρ = ρ_{0} [1+ξ(T-T_{0})]$
Initial resistivity $(ρ_{0})$ at room temperature $(T_{0})$ was $5.7 × 10^{-4} ~ 6.4 × 10^{-4} Ωㆍm$ and temperature coefficient of resistivity (TCR, ξ) was $-1.73 × 10^{-3}$/℃.
We simulated temperature profile of the test patterns at driving point on the basis of measured temperature characteristics of polycrystalline silicon thin film and contact resistance. Integrating the temperature profile and divide it by test pattern length, we can obtain average temperature of test patterns.
Thermal expansion coefficient of polycrystalline silicon thin film was calculated by relationship between average temperature and measured displacement.
Thermal expansion coefficient of polycrystalline silicon thin film was $2.9 × 10^{-6}$/℃ by microgauge method and standard deviation was $0.24 × 10^{-6}$. By microbridge method, Thermal expansion coefficient was calculated as $2.6 × 10^{-6}$/℃.
