Transient modelling of temperature field in planar and 3D microvolume LTCC and thick-film resistors

Transient simulations of planar and 3D microvolume resistors on/in alumina and LTCC substrates are presented in the paper. The first test sample had five planar resistors with effective dimensions from 50×200 μm² to 800×200 μm² placed on/in 9.5×4.0 mm² substrate chip. The second one consisted of single 3D resistor with diameter from 100 to 500 μm placed in 5×5 mm² alumina or LTCC substrates with 150 to 635 μm thickness (resistor length). Simulations were performed for maximal microresistors´ temperature of about 160°C. Well-known ANSYS finite element method software was used. Proper boundary conditions guaranteed physically acceptable distributions of temperature in simulated microcomponents. The first 40 seconds were simulated starting from the point when the power is applied to the microresistor. Examples of calculated temperature fields and their analyses are shown in the paper. Meaning of such distributions on reliability and stability is discussed, as well. Moreover, a simple model of thermal wave propagation in considered microstructures is presented.