Simulation of transport in silicon devices at atomistic level

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

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

3. Construction of Hamiltonian of Silicon devices • We start with studies of relatively simple structures, like homogeneous silicon, pn junction, MOS capacitors • Parameterize the obtained • 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.: and various • “Assemble” Hamiltonian of complex structure with above parameters: “MOSFET” = “pure silicon” + “pn junctions” + “MOS capacitors”

4. Properties of homogeneous siliconBand structure obtained with sp3 atomic basis

5. Properties of homogeneous siliconTemperature 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.

6. Properties of homogeneous siliconDoping 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.

7. Properties of homogeneous siliconConduction band structure Theoretical Results: • The minima in <100> direction • The minima at K=0.68(2π/a) • Effective mass m║=0.78(1.14) m┴=0.167(0.246) Experimental Results: • The minima in <100> direction • The minima at K=0.85(2π/a) • Effective mass m║=0.92 m┴=0.197

8. Properties of homogeneous siliconValence band structure Experimental Results: • The valence bands consist of three overlapping bands • The maxima all at Γpoint • Δ= 44 meV • Effective mass mlh = 0.16 mhh= 0.48 msh= 0.24 Theoretical Results: • The valence bands consist of three overlapping bands • The maxima all at Γpoint • Δ= 9 meV • Effective mass mlh = 0.22(0.32) mhh= 0.22(0.32) msh= 0.14(0.21)

9. Properties of pn junctionThe energy band diagram, before being joined

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

11. Properties of pn junctionThe charge distribution

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

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

14. Properties of pn junctionCurrent flow in a pn junction diode

15. 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

16. Properties of MOSFETThe energy band diagram at equilibrium

17. Properties of MOSFETThe energy band diagram along the channel for various VGS

18. Properties of MOSFETCurrent flow along the channel, a lake analogy to FET operation

19. Properties of MOSFETCurrent flow along the channel, a toy model result