Simulation of transport in silicon devices at atomistic level Introduction Properties of homogeneous silicon Properties of pn junction Properties of MOSFET

Structure, circuit symbol and I-V characteristic of an nMOSFET

Construction of Hamiltonian of Silicon devices Split contributions to electrostatic potential in the silicon devices into intrinsic silicon part and the part due to charge redistribution caused by applied voltage, match of Fermi energies, etc.: We start with studies of relatively simple structures, like homogeneous silicon, pn junction, MOS capacitors Parameterize the obtained and various “Assemble” Hamiltonian of complex structure with above parameters: “MOSFET” = “pure silicon” + “pn junctions” + “MOS capacitors”

Properties of homogeneous silicon Band structure obtained with sp 3 atomic basis

Properties of homogeneous silicon Temperature dependence of the energy band gap With increasing temperature, interatomic distance increases, interaction of an atomic orbital with its neighbors decreases, and then band gap tends to decrease.

Properties of homogeneous silicon Doping dependence of the energy band gap The wavefunctions of the electrons bound to the impurity atoms start to overlap as the density of impurities increase, and cause the band gap to shrink.

Properties of homogeneous silicon Conduction band structure Experimental Results: The minima in direction The minima at K=0.85(2π/a) Effective mass m ║ =0.92 m ┴ =0.197 Theoretical Results: The minima in direction The minima at K=0.68(2π/a) Effective mass m ║ =0.78(1.14) m ┴ =0.167(0.246)

Properties of homogeneous silicon Valence band structure Theoretical Results: The valence bands consist of three overlapping bands The maxima all at Γpoint Δ= 9 meV Effective mass m lh = 0.22(0.32) m hh = 0.22(0.32) m sh = 0.14(0.21) Experimental Results: The valence bands consist of three overlapping bands The maxima all at Γpoint Δ= 44 meV Effective mass m lh = 0.16 m hh = 0.48 m sh = 0.24

Properties of pn junction The energy band diagram, before being joined

Properties of pn junction The energy band diagram at equilibrium A built-in potential δV(r) is established due to the charge redistribution

Properties of pn junction The charge distribution

Properties of homogeneous silicon Charge distribution of p- and n-type silicon The distribution of charge (hole) is not uniform!

Self-consistent LDA calculation of the band bending profile over a PN junction The profile depends on density of dopants and bias voltage Atomic orbital can not “see” the detailed structure of the charge distribution, Hamiltonian elements change smoothly across the pn junction!

Properties of pn junction Current flow in a pn junction diode

IV curve of a pn junction:Tight-binding results The fitting curve (predicted by diffusion theory): J = J0(exp(eV/kT)-1) With J0 = 1.0e-18(A) And T = 420K

Properties of MOSFET The energy band diagram at equilibrium

Properties of MOSFET The energy band diagram along the channel for various V GS

Properties of MOSFET Current flow along the channel, a lake analogy to FET operation

Properties of MOSFET Current flow along the channel, a toy model result