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Quantum Transport in GaSb / InAs Tunneling FET

Quantum Transport in GaSb / InAs Tunneling FET . Yu He, Zhengping Jiang, Daniel Mejia, Tillmann Kubis , Michael Povolotskyi , Jean Michel Sellier , Jim Fonseca, Gerhard Klimeck

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Quantum Transport in GaSb / InAs Tunneling FET

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  1. Quantum Transport in GaSb/InAs Tunneling FET Yu He, Zhengping Jiang, Daniel Mejia, TillmannKubis, Michael Povolotskyi, Jean Michel Sellier, Jim Fonseca, Gerhard Klimeck Network for Computational Nanotechnology (NCN)Electrical and Computer EngineeringPurdue University, West Lafayette IN, USA Summer School 2012

  2. What is GaSb-InAs TFET • TFET is promising for low-power logic design -> low SS and high Ion/Ioff ratio. TFET concept (taken from MIND) • L-shape GaSb-InAstunneling FET • Broken gap bandstructure – mixture of electrons/holes • 2D transport (nonlinear geometry) Conduction band Conduction band Valence band Valence band GaSb InAs

  3. Set up the simulation task (A/nm) • We use Meta_nTFET.in • We will use a sp3s* tight binding model • GaSb will be p-type doped with density 4e18 cm-3 • InAs will be n-type doped with density 5e17 cm-3 • A Lshaped structure is used • It will produce an I-V curve and local DOS shown on left cm-3 1020 1018 1016 1014

  4. Details of simulation structure Periodic boundary in plane Gate Oxide 4nm InAs 60nm 15nm drain GaSb Source 10nm

  5. Define a hetero-structure Structure { Material { tag = pGaSb name = GaSb crystal_structure = zincblende Bands:BandEdge:Ec = 1.531 Bands:BandEdge:Eg = Ec - Ev Bands:BandEdge:Ev = 0.4865 Bands:BandEdge:mstar_v_dos = 1.2523 regions = (1) doping_type = P doping_density = 4E18 } ...... • Define GaSb for regions (1) • Bands:BandEdge define the necessary options for semiclassical density solver • Doping_type defines the type of doping: P • Doping_density defines the doping density as 4E18

  6. Define a hetero-structure Structure { Material { tag = nInAs name = InAs crystal_structure = zincblende Bands:BandEdge:Ec = 0.5337 Bands:BandEdge:Eg = Ec - Ev Bands:BandEdge:Ev = -0.1929 Bands:BandEdge:mstar_c_dos = 0.1455 regions = (2, 5) doping_type = N doping_density = 5E17 } ...... • Define InAs for regions (2,5) • Bands:BandEdge define the necessary options for semiclassical density solver • Doping_type defines the type of doping: N • Doping_density defines the doping density as 5E17

  7. Define an Oxide region Structure { Material { tag = Oxide name = SiO2 crystal_structure = zincblende Lattice:epsilon_dc = 3.9 Lattice:cation = "Si" Lattice:anion = "O" regions = (3, 4) } ...... • Define SiO2 for regions (3,4) • Lattice:epsilon_dc define the dielectric constant

  8. Domains for transport Domain { name = device …… // names of leads domain leads = (source_contact, drain_contact) } Domain { name = source_contact lead_direction = -2 …… } Domain { name = drain_contact lead_direction = 1 …… } • Source_contact and drain_contact domains have to be defined, and lead_direction is defined for each lead • In device domain, we have to specify the leads as source_contact,drain_contact oxide InAs y drain GaSb x source

  9. Domains for Poisson • We have to define a continuum domain for poisson solver, whose type is finite_elements • Finite element mesh is defined at device domain • Periodic boundary condition is not applied to Poisson by setting neglect_periodicity as true Domain { name = continuum type = finite_elements mesh_from_domain = device neglect_periodicity = true }

  10. Define the Lshaped geometry Geometry { Region // p-GaSb { shape = cuboid region_number = 1 priority = 1 min = (-100, -100, -100) max = (10.14, 15, 100) } …… 60nm Domains (device, source ,drain) 30nm Region 1 15nm 10.14 nm y x

  11. Define the Lshaped geometry Geometry { …… Region // n-InAs { shape = cuboid region_number = 2 priority = 2 min = (30, 15, -100) max = (300,19.1, 100) } Region // n-InAs { shape = cuboid region_number = 5 priority = 2 min = (-100,15, -100) max = (30, 19.1, 100) } …… Domains (device, source ,drain) Region 2 & 5 4.1 nm Region 1 y x

  12. Define the Lshaped geometry Geometry { …… Region //SiO2 { shape = cuboid region_number = 3 priority = 1 min = (-100, 19.1, -100) max = (20.14,21, 100) } …… Domains (device, source ,drain) 2 nm Region 3 Region 2 & 5 Region 1 y x

  13. Define the Lshaped geometry Geometry { …… Region { shape = cuboid region_number = 4 priority = 1 min = (20.14, 19, -100) max = (30.14, 100, 100) } Region 4 10nm Domains (device, source ,drain) Region 3 Region 2 & 5 Region 1 oxide y InAs drain x GaSb source

  14. Define the gate for Poisson gate Geometry { …… Boundary_region // gate { shape = cuboid region_number = 1 priority = 1 min = (-100, 20, -100) max = (20.5, 100, 100) } Region 4 Domains (device, source ,drain) Region 3 Region 2 & 5 Region 1 y x

  15. Simulation flow cm-3 1021 1020 1019 1018 1017 • Ballistic simulation  cannot fill triangular well  quantum self-consistency not converge • Include phonon scattering  numerically expensive Due to high doping S/D, depleted channel and separation of conduction / valence band density, semiclassical model provides good approximation and is much faster. Ballistic/Phonon Impurity Roughness, etc. Electrostatic Potential Step1. Semiclassical density + Poisson Step2. Quantum transport (NEGF) • Semiclassical model: effective mass, quasi-fermilevel, quantum corrections • Simulation flow =>

  16. Transport solver options Solver options: Option meaning: name = Transport Solver name type = MetaTransportSemiPotential Solver type (NEMO5 will look for “MetaTransportSemiPotential.py” in. / Meta) Transport_type = transfer_matrix (optional) Default: NEGF domain = device Area the solver will explicitly work on active_regions = (1, 2, 5) Defines on which regions the solver works output_name = nTFET Prefix for all outputfile names contact_domains = (source_contact, drain_contact,gate) Names of the lead domains source_contact_voltages = (0.0, 0.0, …) List of voltages to apply drain_contact_voltages = (0.3, 0.3, …) List of voltages to apply gate_voltages = (-0.1, 0.0, …) List of voltages to apply to the gate (Boundary_region with region_number = 1)

  17. Transport solver options Solver options: Option meaning: use_Poisson_potential = true if true, Poisson potential is used (otherwise,Φ=0) tb_basis = sp3sstar Tight binding basis representation charge_self_consistent= false if true, iterative solution (requires use_potential=true) use_semiclassical_potential = trueif true, use semiclassical density relative_maximum_energy = -0.9 Emax=max(Ef) - band_margin relative_minimum_energy = 0.6 Emin=min(Ef) + bandgap_margin use_adaptive_grid = false (optional) adaptive mesh for fixed number of energy points use_adaptive_grid1 = false adaptive mesh for variable number of energy points number_of_energy_points = 960 (optional) Number of points in energy add_constant_potential = 0.0 Add a constant to the potential momentum_space_degeneracy = 2 degeneracy of k-space (inverse fraction of calculated Brillouin zone) momentum_intervals = [(0, 0.2)] List of intervals of resolved k-space number_of_momentum_points = 31 Number of momentum points for each k-interval

  18. Transport solver options Write multidimensional data to disc: Poisson potential in 3D, space charge in cm-3 in 3D, transmission energy resolved, Spectral function energy resolved, electron LDOS in space and energy, hole LDOS in space and energy output = (potential, free_charge_cm-3,transmission, spectral_density, ldosn1d, ldosp1d) Write to disc data along a path: output_along_path = (cb_band, vb_band, potential, free_charge_cm-3) path_points = [(5, 0, 0), (9, 15, 0), (11, 17, 0), (70, 17, 0) ] List of points on the path in nm number_of_path_points = (80, 16, 120) List of number of points between two path points enable_structure = true Structure output is added gate oxide drain source

  19. Transport solver – output list Output files: File content: nTFET.log monitored output (defined in global section nTFET_potential_* preliminary results (overwritten by subsequent bias points) For the first voltage point: nTFET_ramper_0.vtk all atomistic quantities nTFET_ramper_0.xy nTFET_ramper_0_TRANS_0.dat transmission nTFET_ramper_0_ldosn1d_0.dat electron LDOS along output path nTFET_ramper_0_ldosp1d_0.dat hole LDOS along output path nTFET_ramper_0_nE_0.dat energy resolved charge density nTFET_ramper_0_potential.xy potential For the second voltage point… nTFET_ramper_1.vtk nTFET_ramper_1.xy… … nTFET_ramper_current.dat IV characteristics nTFET_structure.vtk Structure output

  20. Understand the output files nTFET_ramper_current.dat : % V_0; I_0; V_1; I_1; ... 0 -4.73015e-10 0.3 4.73015e-10 -0.1 0 0 -1.97807e-23 0.3 1.97807e-23 0 0 0 -8.14723e-27 0.3 8.14723e-27 0.1 0 0 -1.56303e-18 0.3 1.56303e-18 0.2 0 0 -1.3812e-15 0.3 1.3812e-15 0.3 0 …… source source current drain drain current gate gate current bias biasbias

  21. Understand the output files nTFET_ramper_x.xy: % NEMO5 1D-interpolated atomistic data: 0 0.985862 -0.0586379 0.545138 1.25433e+19 0.194052 0.985862 -0.0586379 0.545138 1.25433e+19 0.388104 0.985862 -0.0586379 0.545138 1.25433e+19 0.582157 0.985862 -0.0586379 0.545138 1.25433e+19 0.776209 0.98568 -0.0588204 0.54532 1.24054e+19 …… distance; CB_band[eV]; VB_band[eV]; potential[V]; free_charge_cm-3;

  22. Understand the output files nTFET_ramper_x_ldosp1d.dat; nTFET_ramper_x_ldosn1d; -0.6 3.44E+11 3.44E+113.44E+113.44E+11 …… -0.599062 3.59E+11 3.59E+113.59E+113.59E+11 …… -0.598123 3.78E+11 3.78E+113.78E+113.78E+11 …… -0.597185 3.94E+11 3.94E+113.94E+113.94E+11 …… -0.596246 4.07E+11 4.07E+114.07E+114.07E+11 …… …… Energy (eV) position resolved LDOS at each energy point

  23. Exercise I: Plot I-V curve • NEMO5 will produce nTFET_ramper_current.dat • Start MATLAB on your workspace • Load nTFET_ramper_current.dat file into matlab workspace, enter the following script: • xlabel('Voltage (V)' ) • ylabel(‘Current (A/nm)' ) • Semilogy(nTFET_ramper_current(:,1), nTFET_ramper_current(:,2), ‘rx—’) • You will have the figure on the left (A/nm)

  24. Exercise II: Plot I-V curve • NEMO5 will produce nTFET_ramper_13_ldosp1d.dat nTFET_ramper_13_ldosn1d.dat nTFET_ramper_13.xy • Load the three above files into matlab workspace, enter the following script: • pos = nTFET_ramper_13(:,1); • egrid = nTFET_ramper_13_ldosn1d(:,1); • meshgrid(pos,egrid); • [hChC] = contourf(pos,egrid, log10(nTFET_ramper_13_ldosn1d(:,2:end)+ nTFET_ramper_13_ldosp1d(:,2:end)+1e-3),50); • set(hC,'LineStyle','none'); • hold on, plot(nTFET_ramper_13(:,1),nTFET_ramper_13(:,2),'k'); • hold on, plot(nTFET_ramper_13(:,1),nTFET_ramper_13(:,3),'k'); • xlabel('Position (nm)' ) • ylabel('Energy (eV)' ) • caxis([13 21]); • You will have the figure on the right cm-3 1020 1018 1016 1014

  25. How to interpret your results? GaSb InAs Ec cm-3 cm-3 1020 1018 1016 1014 1020 1018 1016 1014 Ec (A/nm) Ev Ev GaSb InAs

  26. Conclusion • Transport calculations • Calculate quantum transport using NEGF or transfer matrix method • Self-consistently iterate with Poisson, or use a semiclassical density to speed up • Can handle arbitrary geometries; • Can be used to study complicated structures like Band-to-Band tunneling device • We have more than that … • Random alloy • Surface and interface roughness • … Thank you.

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