  Molecular junctions and similar devices described by an energy dependent
transmission coefficient can have a high linear response thermoelectric figure
of merit. Since such devices are inherently non-linear, the full thermodynamic
efficiency valid for any temperature and chemical potential difference across
the leads is calculated. The general features in the energy dependence of the
tranmission function that lead to high efficiency and also high power output
are determined. It is shown that the device with the highest efficiency does
not necessarily lead to large power output. To illustrate this, we use a model
called the t-stub model representing tunneling through an energy level
connected to another energy level. Within this model both high efficiency and
high power output are achievable. Futhermore, by connecting many nanodevices it
is shown to be possible to scale up the power output without compromising
efficiency in an (exactly solvable) n-channel model even with tunneling between
the devices.
