\begin{figure}[!t]
\centering
{\includegraphics[width=8.5cm]{./figure/fig1-tnano.eps}
}
\caption{(a-c) Methodology flow. A) an OPV molecule with oxygen linkers is the input for the three models:  semi-empirical look-up table SE-LUT, Transmission Spectrum based (TSB) model and FET-based equivalent model FBE. They evaluate the conduction of the molecule in different  conditions of applied bias (Vds) and gate voltage (Vg). 
B) An engine  based on VHDL-AMS, elaborates the results obtained by the three models, generates the related I-V characteristics and provides a VHDL-AMS description of the MOL-FET. 
C) Logic circuits  can be hierarchically and modularly implemented 
and then simulated to evaluate the circuit correct behavior and performance.}
\label{fig:main}
\vspace{0.0em}
\end{figure}
%

Emerging future nanoelectronics is being extensively explored for several
applications
\cite{datta2005quantum,csaba2009read,gas1,Chiolerius1,study2,magn1}. More
specifically
molecular devices can play an important role both for sensing and for
computational applications
with huge advantages in terms of integration capabilities, functional density
and performance. Recently, molecular
electronics has gained a great interest from both applied electronics and
theoretical point of view
\cite{datta2005quantum,zahid2005self,mahmoud2012designing,AzzuACM,AzzuTnano,
reed2014molecular,wheeler2008molecular,csaba2009read,perrine2008gating}. 
Here we focus on Molecular-FET (MOL-FET), however the concepts we are
developing can be extended to any other molecular device. 
Methodologies on molecular device modeling are fragmented, it is extremely
difficult to compare models, the scenario offers only a few examples on how MOL-FET can be 
integrated in circuits and systems for computation and sensing, and,
especially the literature does not offer a thorough analysis of MOL-FET models 
impact at circuit level in terms of flexibility and computation requirements. 

This article presents our proposals to advance the state of the art in the
key points outlined in the following.
{\bf 1)} We introduce a new
modular framework (Fig.~\ref{fig:main}(a-c)) based on VHDL-AMS that enables to
compare different MOL-FET models within the same simulation engine and in
the same conditions. 
The method allows first of all to compare the models at device
level in terms of their capability to generate the I-V characteristics
comparable to those used
as a reference. Here we refer to Atomistic simulations
\cite{Qwise,soler2002siesta} as later explained (ATK Fig.~\ref{fig:func-atk}), but in general any reference data, for example
experimental values, could be considered the term of comparison and included
in the simulation framework.  
{\bf 2)} In this case three models, developed by the
authors and partially new, are being compared and discussed later on: a) a new semi-empirical
look-up table model (SE-LUT, Fig.~\ref{fig:func-lut}; b) a new transmission
spectrum based model (TSB Fig.~\ref{fig:func-ts}), evolved w.r.t 
\cite{zahir2014molecular}; c) FET-based equivalent model (FBE
Fig.~\ref{fig:func-fbe}), partially based on \cite{ahmed2014spice} and
partially new.  The three models I-V characteristics are compared to the
reference ATK simulations (ATK Fig.~\ref{fig:func-atk}) and show an excellent agreement\IEEEpubidadjcol . 
{\bf 3)} Another fundamental novelty of this work consists in the possibility to
verify the MOL-FET correct behavior when used in a logic circuit. Several are the possible
topologies, that in this case we limit to a
Resistance-N-MOLFET crossbar that we use to design elementary logic cells. 
{\bf 4)} Moreover, the framework allows to analyze the circuit proper behavior and
to verify to what extent it is posible to use each elementary logic cell in
a complex architecture organized as a cascade of basic
crossbars. Here we implement as a benchmark circuit a complex up-to-date
16 bits tree adder (sparse tree used in Pentium4 family). The steps 3 and 4 evidence
i) whether the molecule used has the correct properties for being used in
realistic circuits; ii) the impact of the different
technological choices (i.e.  molecules, gate coupling) on the circuit
behavior; iii) the capabilities at circuit level offered by the different
modeling featuresof the involved models, i.e.  the sensitivity to parameters and the capability to
capture physical quantities, among which technological variations due to the
immaturity and the extreme varaibility of molecular electronics
iii) the models computational requirements both in terms of simulation time
and in terms of setting-up of all the data and parameters necessary when a
new molecule or condition is taken into consideration.

The rest of the paper is organized as follows: in Sec. \ref{sec:vhdlams} we
present the VHDL-AMS framework
while Sec. \ref{sec:method} describes the
the three models used.
In Sec. \ref{sec:circuit} we use an example logic gate ({\sc exor}) to
discuss the circuit organization, its behavior and to describe the models
capabilities. 
Sec. \ref{sec:p4} finally presents the architecture of the adder and details
the simulations results and discusse the performance.