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.
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