  A numerical modeling study based on 3D finite element method (FEM) simulation
and 1D analytical solutions has been carried out to evaluate the capabilities
of two ac methods for measuring in-plane thermal conductivity of thin film
deposited on the back of a suspended SiNx membrane setup. Two parallel metal
strips are present on the top of the dielectric membrane. One strip (S1) serves
as both heater and thermometer, while another one (S2) acts as thermometer
only. For a modified phase shift (MPS) method, it is crucial to extract the
in-plane thermal diffusivity from the phase shift of the temperature
oscillation on S2. It was found that the frequency window for carrying out the
data fitting became narrower as the in-plane thermal diffusivity of the
composite membrane (${\alpha_{\parallel ,C}}$) increased, primarily due to the
failure of the semi-infinite width assumption in the low frequency region. To
ensure the validity of the method, the upper limit of ${\alpha_{\parallel ,C}}$
should not exceed ~1.8$ \times $10-5 m2 s-1 for the specific membrane dimension
under consideration (1$\times $1 mm2). On the other hand, inspired by a
modified Angstrom method proposed by Zhu recently, we suggest a new data
reduction methodology which takes advantage of the phase shift on both S1 and
S2 as well as the amplitude on S1. Based on the simulation results, it is
expected that the non-ideality associated with the three observables may be at
least partially cancelled out.Therefore, the frequency window selection for
carrying out the data fitting is not sensitive to the magnitude of
${\alpha_{\parallel ,C}}$. For typical specimen films whose in-plane thermal
conductivity ranges from 0.84 W m-1 K-1 to 50 W m-1 K-1, the method proposed
here yields a theoretical measurement uncertainty of less than 5%.
