My research has dealt with the computation and application of real and complex electronic bandstructure in the modeling of nanoelectronic semiconductor devices.

Real Bandstructure : Confined Bloch Wave method

It is known that computing the electronic energy levels of a finite system or nanostructure is more difficult than computing those of an infinite system or bulk material. In the literature, a technique for simplifying this computation has been proposed, wherein energy levels of a finite system are derived from those of the corresponding infinite system. So far, this method has been validated only for finite length one-dimensional systems and for higher-dimensional systems at k = 0. We have established [IWPSD_2009, JPCM_2010] that this technique, referred to as the confined Bloch wave (CBW) method, is valid for higher-dimensional symmorphic systems over the entire Brillouin zone, provided some symmetry requirements are satisfied. Using this method, we have computed the subbands of zigzag ribbons of one type patterned in artificial graphene and have shown that the CBW method predicts all the important subbands in these ribbons. We intend to extend these results to the case of ultra-thin semiconductor films.

Complex Bandstructure and tunneling

Zone unfolding of complex bands

Complex bands k (E) in a semiconductor crystal, along a general direction n, can be computed by casting Schrodingers equation as a generalized polynomial eigenvalue problem. When working with primitive lattice vectors, the order of this eigenvalue problem can grow large for arbitrary n. It is, however, possible to always choose a set of non-primitive lattice vectors such that the eigenvalue problem is restricted to be quadratic. The complex bands so obtained need to be unfolded onto the primitive Brillouin zone. We have developed [JPCM_2012] a unified method to unfold real and complex bands. This method ensures that the measure associated with the projections of the non-primary wavefunction onto all candidate primary wavefunctions is invariant with respect to the energy E.

Complex bandstructure of SiGe and direct bandgap III-V compounds

Over the last decade, Si1x Gex has increasingly been used as a channel material in MOSFETs. Though many studies have dealt with the real bandstructure of Si1x Gex , the effect of germanium mole fraction x on complex bandstructure has been unexplored. Complex bands fundamentally determine band to band tunneling (BTBT) current. BTBT contributes significantly to off-current in conventional MOSFETs, via the mechanism of gate induced drain leakage (GIDL). Additionally, BTBT determines the on-current in tunneling FETs, which have been suggested as next generation devices. Further, BTBT is more dominant in Si1x Gex than silicon, owing to a narrower bandgap. We have determined the orientation dependent complex bandstructure of Si1x Gex along common crystallographic directions and predicted trends in BTBT current [DRC_2011].

We have also computed [IWPSD_2011] the orientation dependent complex bandstructure of InSb, InAs, GaSb, InP and GaAs, and the orientation dependent probability of band to band tunneling in these materials. These direct bandgap III-V materials are attractive candidates for Tunnel FETs. Comparison of our results with Kane’s two-band model commonly used in TCAD simulation, demonstrates the inaccuracies of the latter. Our results will be useful in the design of better performing Tunnel FETs in these materials.

Band to band tunneling in heterojunctions

TCAD tools must be able to handle BTBT through heterojunctions, since for example, an appropriately designed heterojunction can boost on-current significantly in Tunnel FETs. It is known that a multiscale approach which captures the complex bandstructure within the bandgap is critical to reliably predict BTBT current through homojunctions. Evanescent states in heterojunctions depend on both materials forming the junction. However, semi-classical schemes to handle BTBT through heterojunctions simply follow a region based approach, stitching together the complex bands of the two materials. The accuracy of computing BTBT current using this idea is not known. We have compared [IWCE_2012] this semi-classical approach against the results of an accurate quantum computation.

Multiscale Modeling of phonon assisted band-to-band tunneling

We have developed [JAP_2013] a TCAD compatible multiscale model of phonon-assisted band-to-band tunneling in semiconductors, which incorporates the non-parabolic nature of complex bands within the bandgap of the material. This model is shown capture the measured current-voltage data in silicon, for current transport along the [100], [110], and [111] directions. Our model will be useful to predict band-to-band tunneling phenomena to quantify on and off currents in tunnel FETs and in small geometry MOSFETs and FINFETs.