Scale-Invariant Drain Current in Nano-FETs

Starting from a three-dimensional transport model in the Landauer-Buttiker formalism we derive a scale-invariant expression for the drain current in a nano-transistor. Apart from dimensionless external parameters representing temperature, gate-, and drain voltage the normalized drain current depends on two dimensionless transistor parameters which are the characteristic length l and -width w of the electron channel. The latter quantities are the physical length and -width of the channel in units of the scaling length = ~(2mF )1=2. Here F is the Fermi energy in the source contact and m is the eective mass in the electron channel. In the limit of wide transistors and low temperatures we evaluate the scale-invariant IDVD characteristics as a function of the characteristic length. In the strong barrier regime, i. e. for l & 20 long-channel behavior is found. At weaker barriers source-drain tunneling leads to increasingly signicant deviations from the long-channel behavior. We compare with experimental results.