Modeling of p-type MOS transistors

Fig. 1: Illustration of the multi-band effect on the local density of states and transmission coefficient in a Si p-type double-gate MOSFET whose transport direction is along [100]. VDS = -0.4V and VG = 0V. For sake of clarity the bandstructures and potentials are represented in terms of hole energy [1,2].

Complementary metal oxide semi-conductor technology is experiencing a generalized scaling strategy, where strain engineering, crystallographic orientation, and the use of alternative channel materials are being evaluated as possible means to improve transistor performance. Several quantum simulation tools have been developed for n-type metal-oxide-semiconductor (nMOS) transistors. Simulator implementation for p-type MOS (pMOS) devices is less advanced than for their nMOS counterparts, which can be explained by the lack of an accurate one-band model for the valence band, like the effective mass approximation for electrons. Indeed the hole bandstructure is strongly nonparabolic and anisotropic due to the coupling of the three first valence bands known as heavy hole, light hole, and split-off. The situation is even more complicated when confinement and strain effects are included. A rigorous description of nanostructure valence bands requires thus a multiband approach based on k.p or tight-binding Hamiltonian.
A correct description of the valence subbands requires at least six bands (the twice spin-degenerate three first valence bands). It has been shown that the main physical effects obtained in a full-band model can be captured by the much simpler six-band k. p approach. Indeed, within this method the bandstructure description around the Brillouin zone center is still accurate for reasonable applied drain voltages (VDS=0.6 V). Therefore, six-band k. p model has been used for semiclassical mobility calculations in uniform hole inversion layer. Nevertheless at nanometer scale, quantum mechanism prevalence makes semiclassical approaches inadequate.
Since 2009 we develop 6-bands quantum transport models in 2D [1,2] and 3D [3] with ionized impurities [4] and hole-phonon scatterings [5].

1) N. Cavassilas, S. d’Ambrosio, M. Bescond
“Quantum simulation of hole transport in Si, Ge, SiGe and GaAs double-gate pMOSFETs : orientation and strain effects”
IEDM Tech. Digest (IEEE), Baltimore (USA), December 2009.

2) N. Cavassilas, N. Pons, F. Michelini, M. Bescond
“Multiband quantum transport simulations of ultimate p-type double-gate transistors: influence of the channel orientation”
Appl. Phys. Lett. 96, 102102 (2010).
DOI: 10.1063/1.3352558

3) N. Pons, N. Cavassilas, F. Michelini, L. Raymond, M. Bescond
“Original shaped nanowire metal-oxide-semiconductor field-effect transistor with enhanced current characteristics based on three-dimensional modeling”
J. Appl. Phys. 106, 53711 (2009).
DOI: 10.1063/1.3204550

4) N. Pons, N. Cavassilas, L. Raymond et al.
“Three-dimensional k.p real-space quantum transport simulations of p-type nanowire transistors: Influence of ionized impurities”
Appl. Phys. Lett. 99, 082113 (2011).
DOI: 10.1063/1.3628316

5) N. Cavassilas, F. Michelini, M. Bescond
“Multiband quantum transport simulations of ultimate p-type double-gate transistors: Effects of hole-phonon scattering”
J. Appl. Phys. 109, 073706 (2011).
DOI: 10.1063/1.3556457