quantum transport in gasb / inas tunneling fet
DESCRIPTION
Quantum Transport in GaSb / InAs Tunneling FET . Yu He, Zhengping Jiang, Daniel Mejia, Tillmann Kubis , Michael Povolotskyi , Jean Michel Sellier , Jim Fonseca, Gerhard Klimeck - PowerPoint PPT PresentationTRANSCRIPT
Network for Computational Nanotechnology (NCN)UC Berkeley, Univ.of Illinois, Norfolk State, Northwestern, Purdue, UTEP
Quantum Transport in GaSb/InAs Tunneling FET
Yu He, Zhengping Jiang, Daniel Mejia, Tillmann Kubis, Michael Povolotskyi, Jean Michel Sellier, Jim Fonseca,
Gerhard KlimeckNetwork for Computational Nanotechnology (NCN)
Electrical and Computer EngineeringPurdue University, West Lafayette IN, USA
Summer School 2012
Yu HeGaSb InAs
Conduction band
Conduction band
Valence bandValence band
L-shape GaSb-InAs tunneling FET Broken gap bandstructure – mixture of
electrons/holes 2D transport (nonlinear geometry)
TFET concept (taken from MIND)
What is GaSb-InAs TFETTFET is promising for low-power logic design -> low SS and high Ion/Ioff ratio.
Yu He
Set up the simulation task
• 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
(A/n
m)
1020
1018
1016
1014
cm-3
Yu He
Details of simulation structure
15nm
Gate
Source
drainGaSb
InAsOxide
10nm
4nm
60nm
Periodic boundary in plane
Yu He
Define a hetero-structureStructure{ Material {
tag = pGaSb
name = GaSbcrystal_structure = zincblendeBands: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 = Pdoping_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
Yu He
Define a hetero-structureStructure{ Material {
tag = nInAs
name = InAscrystal_structure = zincblendeBands: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 = Ndoping_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
Yu He
Define an Oxide region
Structure{ Material {
tag = Oxide
name = SiO2crystal_structure = zincblendeLattice: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
Yu He
Domains for transportDomain{
name = device……// names of leads domainleads = (source_contact, drain_contact)
}Domain{
name = source_contactlead_direction = -2……
}Domain{
name = drain_contactlead_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
source
drain
x
y
oxide
GaSb
InAs
Yu He
Domain{
name = continuumtype = finite_elementsmesh_from_domain = deviceneglect_periodicity = true
}
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
Yu He
Define the Lshaped geometryGeometry{
Region // p-GaSb{
shape = cuboidregion_number = 1priority = 1min = (-100, -100, -100)max = (10.14, 15, 100)
}……
Domains (device, source ,drain)
Region 1
60nm
30nm
10.14 nm
15nm
x
y
Yu He
Define the Lshaped geometryGeometry{
……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 1
Region 2 & 5 4.1 nm
x
y
Yu He
Define the Lshaped geometryGeometry{
……Region //SiO2 {
shape = cuboid region_number = 3 priority = 1
min = (-100, 19.1, -100) max = (20.14,21, 100)
}……
Domains (device, source ,drain)
Region 1
Region 2 & 5Region 3 2 nm
x
y
Yu He
Define the Lshaped geometryGeometry{
……Region{
shape = cuboid region_number = 4 priority = 1
min = (20.14, 19, -100) max = (30.14, 100, 100)
}
Domains (device, source ,drain)
Region 1
Region 2 & 5Region 3
Region 4
10nm
x
y
oxide
source
drain
GaSb
InAs
Yu He
Define the gate for PoissonGeometry{
……Boundary_region // gate{
shape = cuboidregion_number = 1priority = 1min = (-100, 20, -100)max = (20.5, 100, 100)
}
Domains (device, source ,drain)
Region 1
Region 2 & 5Region 3
Region 4
gate
x
y
Yu He
Ballistic simulation cannot fill triangular well quantum self-consistency not converge
Include phonon scattering numerically expensive
Semiclassical model: effective mass, quasi-fermi level, quantum corrections Simulation flow =>
Step1. Semiclassical
density + Poisson
Step2. Quantum transport (NEGF)
ElectrostaticPotential
Ballistic/PhononImpurity
Roughness, etc.
Due to high doping S/D, depleted channel and separation of conduction / valence band density, semiclassical model provides good
approximation and is much faster.
Simulation flow1021
1020
1019
1018
1017
cm-3
Yu He
Solver options: Option meaning:name = Transport Solver nametype = MetaTransportSemiPotential Solver type (NEMO5 will look for
“MetaTransportSemiPotential.py” in. / Meta)
Transport_type = transfer_matrix (optional) Default: NEGFdomain = device Area the solver will explicitly work onactive_regions = (1, 2, 5) Defines on which regions the solver works output_name = nTFET Prefix for all outputfile namescontact_domains = (source_contact, drain_contact,gate) Names of the lead domainssource_contact_voltages = (0.0, 0.0, …) List of voltages to applydrain_contact_voltages = (0.3, 0.3, …) List of voltages to applygate_voltages = (-0.1, 0.0, …) List of voltages to apply to the gate
(Boundary_region with region_number = 1)
Transport solver options
Yu He
Solver options: Option meaning:use_Poisson_potential = true if true, Poisson potential is used (otherwise,Φ=0)tb_basis = sp3sstar Tight binding basis representationcharge_self_consistent = false if true, iterative solution (requires
use_potential=true)use_semiclassical_potential = true if true, use semiclassical densityrelative_maximum_energy = -0.9 Emax=max(Ef) - band_marginrelative_minimum_energy = 0.6 Emin=min(Ef) + bandgap_marginuse_adaptive_grid = false (optional) adaptive mesh for fixed number of
energy points use_adaptive_grid1 = false adaptive mesh for variable number
of energy pointsnumber_of_energy_points = 960 (optional) Number of points in energyadd_constant_potential = 0.0 Add a constant to the potential
Transport solver options
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-spacenumber_of_momentum_points = 31 Number of momentum points for each k-interval
Yu He
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 nmnumber_of_path_points = (80, 16, 120) List of number of points between
two path pointsenable_structure = true Structure output is added
Transport solver options
oxide
source
drain
gate
Yu He
Output files: File content:nTFET.log monitored output (defined in global sectionnTFET_potential_* preliminary results (overwritten by subsequent
bias points)For the first voltage point:nTFET_ramper_0.vtk all atomistic quantitiesnTFET_ramper_0.xynTFET_ramper_0_TRANS_0.dat transmissionnTFET_ramper_0_ldosn1d_0.dat electron LDOS along output path nTFET_ramper_0_ldosp1d_0.dat hole LDOS along output pathnTFET_ramper_0_nE_0.dat energy resolved charge density nTFET_ramper_0_potential.xy potentialFor the second voltage point…nTFET_ramper_1.vtknTFET_ramper_1.xy……nTFET_ramper_current.dat IV characteristicsnTFET_structure.vtk Structure output
Transport solver – output list
Yu He
Understand the output filesnTFET_ramper_current.dat : % V_0; I_0; V_1; I_1; ...0 -4.73015e-10 0.3 4.73015e-10 -0.1 00 -1.97807e-23 0.3 1.97807e-23 0 00 -8.14723e-27 0.3 8.14723e-27 0.1 00 -1.56303e-18 0.3 1.56303e-18 0.2 00 -1.3812e-15 0.3 1.3812e-15 0.3 0……
source source current drain drain current gate gate currentbias bias bias
Yu He
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;
Yu He
Understand the output files
nTFET_ramper_x_ldosp1d.dat; nTFET_ramper_x_ldosn1d;-0.6 3.44E+11 3.44E+11 3.44E+11 3.44E+11 ……-0.599062 3.59E+11 3.59E+11 3.59E+11 3.59E+11 ……-0.598123 3.78E+11 3.78E+11 3.78E+11 3.78E+11 ……-0.597185 3.94E+11 3.94E+11 3.94E+11 3.94E+11 ……-0.596246 4.07E+11 4.07E+11 4.07E+11 4.07E+11 …………Energy (eV) position resolved LDOS at each energy point
Yu He
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/n
m)
Yu He
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);[hC hC] = 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
1020
1018
1016
1014
cm-3
Yu He
1020
1018
1016
1014
cm-3
(A/n
m)
How to interpret your results?
GaSb InAs
Ec
Ec
EvEv
GaSb InAs
1020
1018
1016
1014
cm-3
Yu He
ConclusionTransport 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
Thank you.
We have more than that …−Random alloy−Surface and interface roughness−…