Theoretical study of the lineshape of inelastic electron tunneling spectroscopy

We have studied the lineshape of the inelastic electron tunneling spectroscopy (IETS) theoretically. In order to calculate vibronic currents including the inelastic effect, we have adopted the Keldysh Green's function method and the self-consistent Born approximation, which is applied to the electron-intramolecular-vibration couplings. The second derivative of the vibronic current taken against the bias voltage has peak and dip structures in the IETS. In this paper, we discuss intrinsic and extrinsic mechanisms which control and modify the lineshape of the IETS. The effect of the intrinsic physical parameters, i.e., the contact transfer integral between the molecule and the electrode and the energy gap between the molecular orbital energy and the Fermi level of the electrode, on the lineshape will be discussed first. Next, we will discuss an extrinsic factor, i.e., the effect of the macroscopic shape of the electrode. In order to take into account the shape effect, we use the envelope function method. Our theoretical study will be useful as a guideline to understand various lineshapes of the IETS observed in various experimental situations.