  We report on experiments performed in vacuum and at cryogenic temperatures on
a tri-port nano-electro-mechanical (NEMS) device. One port is a very non-linear
capacitive actuation, while the two others implement the magnetomotive scheme
with a linear input force port and a (quasi-linear) output velocity port. We
present an experimental method enabling a full characterization of the
nanomechanical device harmonic response: the non-linear capacitance function
$C(x)$ is derived, and the normal parameters $k$ and $m$ (spring constant and
mass) of the mode under study are measured through a careful definition of the
motion (in meters) and of the applied forces (in Newtons). These results are
obtained with a series of purely electric measurements performed without
disconnecting/reconnecting the device, and rely only on known DC properties of
the circuit, making use of a thermometric property of the oscillator itself: we
use the Young modulus of the coating metal as a thermometer, and the
resistivity for Joule heating. The setup requires only three connecting lines
without any particular matching, enabling the preservation of a high impedance
NEMS environment even at MHz frequencies. The experimental data are fit to a
detailed electrical and thermal model of the NEMS device, demonstrating a
complete understanding of its dynamics. These methods are quite general and can
be adapted (as a whole, or in parts) to a large variety of elecromechanical
devices.
