From 71d584ca77dc34bcb46a7ea06a714afd888ee6ae Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?B=C3=A1lint=20Aradi?= Date: Wed, 6 Mar 2019 19:31:40 +0100 Subject: [PATCH] Add transport part of CECAM tutorial --- .../agr-nonscc/ideal/2cell_7.gen | 74 + .../agr-nonscc/ideal/dftb_in.hsd | 51 + .../agr-nonscc/vacancy1/device_7.gen | 409 ++++++ .../agr-nonscc/vacancy1/dftb_in.hsd | 51 + .../agr-nonscc/vacancy2/device_7.gen | 409 ++++++ .../agr-nonscc/vacancy2/dftb_in.hsd | 51 + .../agr-scc/contacts/device_7.gen | 410 ++++++ .../agr-scc/contacts/dftb_in.hsd | 44 + .../carbon2d-trans/agr-scc/ideal/device_7.gen | 410 ++++++ .../carbon2d-trans/agr-scc/ideal/dftb_in.hsd | 63 + .../agr-scc/vacancy1/device_7.gen | 409 ++++++ .../agr-scc/vacancy1/dftb_in.hsd | 66 + .../agr-scc/vacancy2/device_7.gen | 409 ++++++ .../agr-scc/vacancy2/dftb_in.hsd | 66 + .../recipes/transport/carbon2d-trans/slako | 1 + .../transport/carbon2d-trans/2cell-7.png | Bin 0 -> 97032 bytes .../transport/carbon2d-trans/4cell-7.png | Bin 0 -> 80082 bytes .../transport/carbon2d-trans/clip-pot.png | Bin 0 -> 88310 bytes .../transport/carbon2d-trans/clip-vac-pot.png | Bin 0 -> 103401 bytes .../carbon2d-trans/color-device-7.png | Bin 0 -> 113350 bytes .../transport/carbon2d-trans/device-7-vac.png | Bin 0 -> 140205 bytes .../carbon2d-trans/device-7-vac2.png | Bin 0 -> 127099 bytes .../carbon2d-trans/nonscc-dos-semilog.png | Bin 0 -> 36774 bytes .../transport/carbon2d-trans/nonscc-dos.png | Bin 0 -> 37206 bytes .../transport/carbon2d-trans/nonscc-tunn.png | Bin 0 -> 25167 bytes .../carbon2d-trans/nonscc-vac-dos.png | Bin 0 -> 34484 bytes .../carbon2d-trans/nonscc-vac-semilog-dos.png | Bin 0 -> 36076 bytes .../carbon2d-trans/nonscc-vac-tunn.png | Bin 0 -> 34563 bytes .../carbon2d-trans/nonscc-vac2-dos.png | Bin 0 -> 37682 bytes .../carbon2d-trans/nonscc-vac2-tunn.png | Bin 0 -> 40961 bytes .../transport/carbon2d-trans/plotline-pot.png | Bin 0 -> 21004 bytes .../carbon2d-trans/scc-tunn-comparison.png | Bin 0 -> 42967 bytes .../transport/carbon2d-trans/scc-tunn.png | Bin 0 -> 23647 bytes .../transport/carbon2d-trans/scc-vac-dos.png | Bin 0 -> 35706 bytes .../transport/carbon2d-trans/scc-vac-tunn.png | Bin 0 -> 33305 bytes .../transport/carbon2d-trans/scc-vac2-dos.png | Bin 0 -> 36803 bytes .../carbon2d-trans/scc-vac2-tunn.png | Bin 0 -> 33224 bytes docs/transport/carbon2d-trans.rst | 1251 +++++++++++++++++ docs/transport/index.rst | 1 + 39 files changed, 4175 insertions(+) create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/2cell_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/ideal/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/ideal/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/dftb_in.hsd create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/device_7.gen create mode 100644 docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/dftb_in.hsd create mode 120000 docs/_archives/recipes/transport/carbon2d-trans/slako create mode 100644 docs/_figures/transport/carbon2d-trans/2cell-7.png create mode 100644 docs/_figures/transport/carbon2d-trans/4cell-7.png create mode 100644 docs/_figures/transport/carbon2d-trans/clip-pot.png create mode 100644 docs/_figures/transport/carbon2d-trans/clip-vac-pot.png create mode 100644 docs/_figures/transport/carbon2d-trans/color-device-7.png create mode 100644 docs/_figures/transport/carbon2d-trans/device-7-vac.png create mode 100644 docs/_figures/transport/carbon2d-trans/device-7-vac2.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-dos-semilog.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-tunn.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-vac-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-vac-semilog-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-vac-tunn.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-vac2-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/nonscc-vac2-tunn.png create mode 100644 docs/_figures/transport/carbon2d-trans/plotline-pot.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-tunn-comparison.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-tunn.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-vac-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-vac-tunn.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-vac2-dos.png create mode 100644 docs/_figures/transport/carbon2d-trans/scc-vac2-tunn.png create mode 100644 docs/transport/carbon2d-trans.rst diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/2cell_7.gen b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/2cell_7.gen new file mode 100644 index 00000000..0159e249 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/2cell_7.gen @@ -0,0 +1,74 @@ +68 S +C H +1 1 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21.844634110000001 -20.000000000000000 7.100000000000000 +65 2 20.880312109999998 -20.000000000000000 5.169169877300000 +66 2 20.880312109999998 -20.000000000000000 7.610830123000000 +67 2 40.025607919999999 -20.000000000000000 5.169106264300000 +68 2 40.025607919999999 -20.000000000000000 7.610893736000000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 59.676097169999998 0.000000000000000 0.000000000000000 + 0.000000000000000 -40.000000000000000 0.000000000000000 + 0.000000000000000 0.000000000000000 8.520000000000000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/dftb_in.hsd new file mode 100644 index 00000000..2956e6a9 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/ideal/dftb_in.hsd @@ -0,0 +1,51 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 136 + FirstLayerAtoms = 1 69 + } + Contact { + Id = "source" + AtomRange = 137 272 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 273 408 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } +} + +Hamiltonian = DFTB { + SCC = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Eigensolver = TransportOnly{} + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.5 -3.0 + EnergyStep [eV] = 0.01 + Region = { + Atoms = 1:136 + } + } +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/device_7.gen b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/device_7.gen new file mode 100644 index 00000000..aff7e4a6 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/device_7.gen @@ -0,0 +1,409 @@ + 407 C +C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 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00000000..25428d51 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/dftb_in.hsd @@ -0,0 +1,51 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } +} + +Hamiltonian = DFTB { + SCC = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Eigensolver = TransportOnly{} + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.5 -3.0 + EnergyStep [eV] = 0.01 + Region = { + Atoms = 1:136 + } + } +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/device_7.gen 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-20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/dftb_in.hsd new file mode 100644 index 00000000..25428d51 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/dftb_in.hsd @@ -0,0 +1,51 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } +} + +Hamiltonian = DFTB { + SCC = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Eigensolver = TransportOnly{} + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.5 -3.0 + EnergyStep [eV] = 0.01 + Region = { + Atoms = 1:136 + } + } +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/device_7.gen b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/device_7.gen new file mode 100644 index 00000000..b28124bc --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/device_7.gen @@ -0,0 +1,410 @@ + 408 C +C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + 4 1 37.831463060000 -20.000000000000 3.550000000000 + 5 1 35.371950920000 -20.000000000000 0.710000000000 + 6 1 36.601706990000 -20.000000000000 1.420000000000 + 7 1 36.601706990000 -20.000000000000 2.840000000000 + 8 1 35.371950920000 -20.000000000000 3.550000000000 + 9 1 32.912438770000 -20.000000000000 0.710000000000 + 10 1 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-9.940000000000 + 62 1 23.074390180000 -20.000000000000 -9.230000000000 + 63 1 21.844634110000 -20.000000000000 -11.360000000000 + 64 1 21.844634110000 -20.000000000000 -9.940000000000 + 65 2 20.880312110000 -20.000000000000 -11.870830122700 + 66 2 20.880312110000 -20.000000000000 -9.429169877000 + 67 2 40.025607920000 -20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/dftb_in.hsd new file mode 100644 index 00000000..be306cd3 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/contacts/dftb_in.hsd @@ -0,0 +1,44 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 136 + } + Contact { + Id = "source" + AtomRange = 137 272 + } + Contact { + Id = "drain" + AtomRange = 273 408 + } + Task = ContactHamiltonian{ + ContactId = "source" + } 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23.074390180000 -20.000000000000 -12.070000000000 + 60 1 24.304146260000 -20.000000000000 -11.360000000000 + 61 1 24.304146260000 -20.000000000000 -9.940000000000 + 62 1 23.074390180000 -20.000000000000 -9.230000000000 + 63 1 21.844634110000 -20.000000000000 -11.360000000000 + 64 1 21.844634110000 -20.000000000000 -9.940000000000 + 65 2 20.880312110000 -20.000000000000 -11.870830122700 + 66 2 20.880312110000 -20.000000000000 -9.429169877000 + 67 2 40.025607920000 -20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/ideal/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/ideal/dftb_in.hsd new file mode 100644 index 00000000..706802d0 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/ideal/dftb_in.hsd @@ -0,0 +1,63 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 136 + FirstLayerAtoms = 1 69 + } + Contact { + Id = "source" + AtomRange = 137 272 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 273 408 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Task = UploadContacts { + } +} + +Hamiltonian = DFTB { + SCC = Yes + SCCTolerance = 1e-6 + ReadInitialCharges = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Electrostatics = Poisson { + Poissonbox [Angstrom] = 40.0 30.0 30.0 + MinimalGrid [Angstrom] = 0.5 0.5 0.5 + SavePotential = Yes + } + + Eigensolver = GreensFunction { + } + + Mixer = Broyden { + MixingParameter = 0.02 + } + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.0 -3.0 + EnergyStep [eV] = 0.01 +} +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/device_7.gen b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/device_7.gen 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-9.429106264000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/dftb_in.hsd new file mode 100644 index 00000000..1565fd58 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy1/dftb_in.hsd @@ -0,0 +1,66 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Task = UploadContacts { + } +} + +Hamiltonian = DFTB { + SCC = Yes + SCCTolerance = 1e-6 + ReadInitialCharges = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Filling = Fermi { + Temperature [Kelvin] = 150.0 + } + + Electrostatics = Poisson { + Poissonbox [Angstrom] = 40.0 40.0 30.0 + MinimalGrid [Angstrom] = 0.5 0.5 0.5 + SavePotential = Yes + } + + Eigensolver = GreensFunction { + } + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.0 -3.0 + EnergyStep [eV] = 0.025 + Region = { + Atoms = 1:135 + } +} +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/device_7.gen b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/device_7.gen new file mode 100644 index 00000000..20277bde --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/device_7.gen @@ -0,0 +1,409 @@ + 407 C +C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + 4 1 37.831463060000 -20.000000000000 3.550000000000 + 5 1 35.371950920000 -20.000000000000 0.710000000000 + 6 1 36.601706990000 -20.000000000000 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-12.070000000000 + 60 1 24.304146260000 -20.000000000000 -11.360000000000 + 61 1 24.304146260000 -20.000000000000 -9.940000000000 + 62 1 23.074390180000 -20.000000000000 -9.230000000000 + 63 1 21.844634110000 -20.000000000000 -11.360000000000 + 64 1 21.844634110000 -20.000000000000 -9.940000000000 + 65 2 20.880312110000 -20.000000000000 -11.870830122700 + 66 2 20.880312110000 -20.000000000000 -9.429169877000 + 67 2 40.025607920000 -20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 diff --git a/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/dftb_in.hsd b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/dftb_in.hsd new file mode 100644 index 00000000..1565fd58 --- /dev/null +++ b/docs/_archives/recipes/transport/carbon2d-trans/agr-scc/vacancy2/dftb_in.hsd @@ -0,0 +1,66 @@ +Geometry = GenFormat { +<<< 'device_7.gen' +} + +Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Task = UploadContacts { + } +} + +Hamiltonian = DFTB { + SCC = Yes + SCCTolerance = 1e-6 + ReadInitialCharges = No + MaxAngularMomentum = { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Filling = Fermi { + Temperature [Kelvin] = 150.0 + } + + Electrostatics = Poisson { + Poissonbox [Angstrom] = 40.0 40.0 30.0 + MinimalGrid [Angstrom] = 0.5 0.5 0.5 + SavePotential = Yes + } + + Eigensolver = GreensFunction { + } + +} + +Analysis = { +TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.0 -3.0 + EnergyStep [eV] = 0.025 + Region = { + Atoms = 1:135 + } +} +} + diff --git a/docs/_archives/recipes/transport/carbon2d-trans/slako b/docs/_archives/recipes/transport/carbon2d-trans/slako new file mode 120000 index 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using DFTB+. We +will then calculate the density of states and the transmission coefficients and +analyse the results in comparison with the previous periodic calculations. + + +Non-SCC pristine armchair nanoribbon +==================================== + +[Input: `recipes/transport/carbon2d-trans/agr-nonscc/ideal/`] + + +Preparing the structure +------------------------ + +When we run a transport calculation with open boundary conditions, the geometric +structure specified in the input needs to obey some rules. The system must +consist of an extended device (or molecule) region, and two or more +semi-infinite bulk contacts. The bulk contacts are described by providing two +*principal layers* for each contact. + +A *Principal Layer (PL)* is defined as a contiguous group of atoms that have +finite interaction only with atoms belonging to adjacent PLs. In a sense, a PL +is a generalisation of the idea of nearest neighbour atoms to the idea of +nearest neighbour blocks. The PL partitioning in the electrodes is used by the +code to retrieve a description of the bulk system. PLs may be defined, as we +will see, in the extended device region to take advantage of the iterative Green +function solver algorithm. + +Additional information about the definition of PLs, contacts and extended device +region can be found in the manual and in the on-line recipes. + +In the case of an ideal one-dimensional system, all the PLs are identical. The +system we start with is an infinite armchair graphene nanoribbon (AGR), +therefore the partitioning into device and contact regions is somewhat +arbitrary. We will therefore start from a structure file containing a single PL +(`2cell_7.gen`), which has been previously relaxed. The PL can be converted to +XYZ format by using the `gen2xyz` script and visualised with `Jmol`:: + + gen2xyz 2cell_7.gen + jmol 2cell_7.xyz + +The structure is shown in Figure :ref:`fig_transport_carbon2d-trans_2cell-7` + +.. _fig_transport_carbon2d-trans_2cell-7: +.. figure:: ../_figures/transport/carbon2d-trans/2cell-7.png + :width: 60% + :align: center + :alt: Armchair nanoribbon PL + + Armchair nanoribbon principal layer (PL) + +As you may notice, we did not take a single unit cell length as a PL, but rather +two unit cells. This choice is dictated by the definition of the PL itself, as +we want to avoid non-zero interactions between second-neighbour PLs. This is +better explained by referring to Figure +:ref:`fig_transport_carbon2d-trans_4cell-7`. The red carbon atoms represent the +closest atoms which would belong to non-nearest neighbour PLs, and these have a +separation of 0.568 nm, as shown in Figure +:ref:`fig_transport_carbon2d-trans_4cell-7`. The carbon-carbon interaction is +non zero up to a distance of 6 a.u., therefore the interaction between the two +red atoms would be small, but non zero. Hence this is too small a separation for +a one unit cell long section of nanoribbon to be used as the PL. + +.. _fig_transport_carbon2d-trans_4cell-7: +.. figure:: ../_figures/transport/carbon2d-trans/4cell-7.png + :width: 80% + :align: center + :alt: Layer definition + + Layer definition + +As currently there is no way to damp out small interactions, the PL must contain +two unit cells in this case, as shown in figure +:ref:`fig_transport_carbon2d-trans_4cell-7`. It follows that the correct +definition of a PL depends both on the geometry of the system and the +interaction cut-off distance. + +After having defined a proper PL, we then build a structure consisting of a +device region with 2 PLs and contacts at each end of this region, each with 2 +PLs. + +*Note*: For the pristine system, the equilibrium results should not depend on +the length of the device region, as the represented system is an infinite ideal +nanoribbon with discrete translational symmetry along the ribbon. + +The input atomic structure must be defined according to a specific ordering: the +device atoms come first, then each contact is specified, starting with the PL +closer to the device region. For an ideal system defined by repetition of +identical PLs, the tool `buildwire` (distributed with the code) can be used to +build a 1D geometry with the right ordering. + +When you type:: + + buildwire 2cell_7.gen + +you will be asked to type the name of the file containing the input supercell +(`2cell_7.gen`) and the number of principal layers in the device region (we will +set this to be 2). `buildwire` will always give its output as a supercell +structure, but in some cases we will need to manually modify this structure file +so that it corresponds to the ordering explained in the previous paragraph. + +The following output will be visualised:: + + Insert PL .gen file name: + 2cell_7.gen + Insert number of PLs in channel: 2 + structure built + *iatc= + 137 272 0 + 273 408 0 + *PLs= + 1 69; + +The indexes **iatc** and **PLs** define the atoms belonging to the contacts, to +the device region and to the PLs of the device region, and will be useful when +we will write the input files. You should take a note of them (the iterative +algorithm used in solving the Green function requires these values). A file +`Ordered_2cell_7.gen` will have been created, and defined as a supercell format +GEN file (``S``), which we will rename `device_7.gen` for the following:: + + mv Ordered_2cell_7.gen device_7.gen + +We can better understand the ordering of the atomic indexes if we convert this +structure to XYZ, open it with jmol and then change the colours of specific +ranges of atoms by using the following syntax in the jmol console (for example, +we select here the first contact and split it into two sub-ranges containing its +first and second PLs):: + + > select atomno>136 && atomno<205 + > color yellow + > select atomno>204 && atomno<273 + > color red + +In Figure :ref:`fig_transport_carbon2d-trans_color-device-7` a `Jmol` export of +the structure is shown. + +.. _fig_transport_carbon2d-trans_color-device-7: +.. figure:: ../_figures/transport/carbon2d-trans/color-device-7.png + :width: 80% + :align: center + :alt: PLs in contact 1 + + The PLs of contact 1 + +The yellow and red atoms represent the first and second PLs of the first +contact. When you build a structure yourself, it is always a good idea to use a +visualiser and verify that the atomic indices are consistent with the transport +setup definitions. + +The last step is to change the supercell definition in the gen structure +file. From the point of view of an open boundary condition calculation, +Supercell (``S``) and Cluster (``C``) have a slightly different meaning with +respect to a canonical DFTB calculation. By Supercell we mean any structure +which is *periodic in any direction transverse to the transport direction*, +while for cluster we mean any structure *not periodic in any direction +transverse to transport*. It follows that purely 1D systems, like nanowires and +nanoribbons, should be regarded as clusters (``C``). Therefore we edit the +structure file `device_7.gen`, changing in the first line the ``S`` (supercell) +to be ``C`` (cluster) and remove the last four lines, which would normally only +be defined for periodic systems. + +This is the file we get after running `buildwire`:: + + 408 S + C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + 4 1 37.831463060000 -20.000000000000 3.550000000000 + 5 1 35.371950920000 -20.000000000000 0.710000000000 + 6 1 36.601706990000 -20.000000000000 1.420000000000 + 7 1 36.601706990000 -20.000000000000 2.840000000000 + 8 1 35.371950920000 -20.000000000000 3.550000000000 + ........ + 65 2 20.880312110000 -20.000000000000 -11.870830122700 + 66 2 20.880312110000 -20.000000000000 -9.429169877000 + 67 2 40.025607920000 -20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 + 0.000000000000000 0.000000000000000 0.000000000000000 + 59.676097169999998 0.0000000000000000 0.0000000000000000 + 0.0000000000000000 -40.000000000000000 0.0000000000000000 + 0.0000000000000000 0.0000000000000000 51.119999999999997 + +Note that the numbering of atoms at the start of each line, as output by +`buildwire` are sequential according to the numbering of the initial structure, +not its global position in the output file. + +The corrected definition for the 1D ribbon with open boundary conditions is +then:: + + 408 C + C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + 4 1 37.831463060000 -20.000000000000 3.550000000000 + 5 1 35.371950920000 -20.000000000000 0.710000000000 + 6 1 36.601706990000 -20.000000000000 1.420000000000 + 7 1 36.601706990000 -20.000000000000 2.840000000000 + 8 1 35.371950920000 -20.000000000000 3.550000000000 + ........ + 65 2 20.880312110000 -20.000000000000 -11.870830122700 + 66 2 20.880312110000 -20.000000000000 -9.429169877000 + 67 2 40.025607920000 -20.000000000000 -11.870893735700 + 68 2 40.025607920000 -20.000000000000 -9.429106264000 + + +Now the file `device_7.gen` contains the correct structure, defined as a cluster +and with the proper atom ordering. Next, we set up the input file for a +tunnelling calculation. + + +Transmission and density of states +---------------------------------- + +In the DFTB+ input format, settings related to a transport calculation may be +required to appear in separate sections of the `dftb_in.hsd` file, depending on +the functionality they invoke. In the following we will set up the simplest open +boundary condition calculation: a calculation of transmission coefficients +according to the Landauer-Caroli formula, assuming a non-SCC DFTB +hamiltonian. We will analyse and comment the different sections contained in the +file `dftb_in.hsd`. + +First, we have the specification of the geometry:: + + Geometry = GenFormat { + <<< 'device_7.gen' + } + +This follows the same rule as in a regular DFTB+ calculation, except for the +fact that the structure should follow the specific partitioning structure +explained in the previous section. + +Whenever an open boundary system is defined, we have to specify a block named +``Transport`` which contains information on the system partitioning and +additional information about the contacts to the device:: + + Transport { + Device { + AtomRange = 1 136 + FirstLayerAtoms = 1 69 + } + Contact { + Id = "source" + AtomRange = 137 272 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 273 408 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + } + +Here we have used the indexes printed by `buildwire`. ``Device`` contains two +fields: ``AtomRange`` specifies which atoms belong to the extended device region +(1 to 136) and ``FirstLayerAtoms`` specify the starting index of the PLs in the +device region. This field is optional, but if not specified the iterative +algorithm will not be applied and the calculation will be slower, even though +the result will be still correct. Then we have the definitions of the +contacts. In this example we define a two terminal system, but in general N +contacts are allowed. A contact is defined by an ``Id`` (mandatory), the range +of atoms belonging to the contact specified in ``AtomRange`` (mandatory) and a +``FermiLevel`` (mandatory). The potential is set by default to 0.0, therefore +need not be specified in this example. Note that according to equilibrium Green +function theory, the Fermi level and the contact potential are not necessary to +calculate the Transmission curve, but are required to calculate the current via +the Landauer formula, as they would determine the occupation distribution in the +contacts. + +Then we have the ``Hamiltonian`` block, which describes how the initial +Hamiltonian and the SCC component, if any, will be calculated:: + + Hamiltonian = DFTB { + SCC = No + MaxAngularMomentum { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + Eigensolver = TransportOnly{} + + } + +In this example we will calculate the transmission according to Caroli (referred +by some authors as Fisher Lee) formula in a non-SCC approximation, i.e. the +Hamiltonian is directly assembled from the Slater-Koster files and used "as is" +to build the contact self energies and the extended device Green function. The +definition of an eigensolver is not meaningful in an open boundary setup, as the +system is instead solved by the Green function technique. Therefore we just use +a keyword ``TransportOnly`` to indicate that we do not want to solve an +Eigenvalue problem. The other fields are filled up in the same way as for a +regular DFTB calculation. + +In general, in DFTB+ an Eigensolver is regarded as a calculator which can +provide charge density in the SCC cycle, therefore we will define a Green +function based eigensolver later, but only for SCC calculations. + +Note that as C-H bonds are present in the system, charge transfer should occur, +hence the result will not be accurate at the non-SCC level. It is not *a-priori* +trivial to predict whether this affects qualitatively or quantitatively the +transmission. We will therefore later compare these results with an SCC +calculation - at the moment we will stay at the level of a non-SCC calculation, +because it is faster to execute and also allows us to use the simplest input +file possible. + +Finally, the implementation of the Landauer-Caroli formula is regarded as a +post-processing operation and specified by the block ``TunnelingAndDos`` inside +``Analysis``:: + + Analysis { + TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.5 -3.0 + EnergyStep [eV] = 0.01 + Region { + Atoms = 1:136 + } + } + } + +``TunnelingAndDos`` allows for the calculation of Transmission coefficient, +Local Density of States (LDOS) and current. A transmission is always calculated +using the energy interval and energy step specified here. The LDOS is only +calculated when sub-blocks ``Region`` are defined. ``Region`` can be used to +select some specific subsets of atoms or orbitals, according to the syntax +explained in the manual. In this example, we are specifying the whole extended +device region (atoms 1 to 136). Note that the energy range of interest is not +known a priori. Either you have a reference band structure calculation, +therefore you know where the first sub-bands are (this is the correct way to do +this), or you can run a quick calculation with a large energy step and on the +basis of the transmission curve then refine the range of interest. + +Now that the input file is complete, we have to complete one last step. During a +transport run, DFTB+ will look for two directories named `GS` and `contacts`. We +have to create these directories in advance:: + + mkdir GS + mkdir contacts + +We can then start the calculation:: + + dftb+ dftb_in.hsd | tee output.log + +We can take advantage of parallelisation over the energy points in the +calculation by running the code with `mpirun`:: + + mpirun -n 4 dftb+ dftb_in.hsd | tee output.log + +where ``4`` should be substituted by the number of available nodes. Note that +NEGF is parallelised over energy points, therefore a number of nodes larger than +the energy grid will not improve performances and secondly that the memory +consumption is proportional to the number of nodes used - this may be critical +in shared memory systems with a small amount of memory per node. + +When the calculation has finished, the transmission and density of states are +saved to both the `detailed.out` file and to two separate `tunneling.dat` and +`localDOS.dat` files. These additional files both contain the energy points in +the first column and the desired quantities as additional columns. + +We can plot the transmission by using the `plotxy` script:: + + plotxy --xlabel 'Energy [eV]' --ylabel 'Transmission' -L tunneling.dat + +The plot is shown in Figure :ref:`fig_transport_carbon2d-trans_nonscc-tunn`: + +.. _fig_transport_carbon2d-trans_nonscc-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-tunn.png + :width: 80% + :align: center + :alt: Non-SCC transmission in pristine AGR + + Non-SCC transmission through a pristine AGR + +The ribbon is semiconducting, therefore we can see a zero transmission at +energies corresponding to the band gap. As the system is ideal, outside of the +band gap we can observe the characteristic conductance steps where the value of +the transmission is 1.0 for every band which crosses a given energy. This is a +normal signature of ideal 1D systems with translational invariance. + +Similarly, we can visualise the density of states by typing (the x and y axis +limits are chosen to focus on the first few sub-bands):: + + plotxy --xlabel 'Energy [eV]' --ylabel 'DOS [arbitrary units]' -L \ + --xlimits -6.5 -3 --ylimit 0 1400 localDOS.dat + +The result is shown in Figure :ref:`fig_transport_carbon2d-trans_nonscc-dos`: + +.. _fig_transport_carbon2d-trans_nonscc-dos: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-dos.png + :width: 80% + :align: center + :alt: Non-SCC density of states in pristine AGR + + Non-SCC density of states for a pristine AGR + +You can plot the transmission or the density of states on a semi-logarithmic +scale:: + + plotxy --xlabel 'Energy [eV]' --ylabel 'Transmission' -L \ + --xlimits -6.5 -3 --logscale y localDOS.dat + +If you do so, you will obtain the plot shown in Figure +:ref:`fig_transport_carbon2d-trans_nonscc-dos-semilog`. + +.. _fig_transport_carbon2d-trans_nonscc-dos-semilog: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-dos-semilog.png + :width: 80% + :align: center + :alt: Non-SCC density of states in logarithmic scale + + Non-SCC density of states on logarithmic scale + +The density of states in the band-gap is not zero, but decreases by several +orders of magnitude. This is a natural consequence of the quasi-particle nature +of the Green function formalism: every state in the system has a finite +broadening in energy. + + +Non-SCC armchair nanoribbon with vacancy (A) +============================================ + +[Input: `recipes/transport/carbon2d-trans/agr-nonscc/vacancy1/`] + + +Transmission and Density of States +---------------------------------- + +Now that we have a calculation of the reference pristine system, we will +introduce a scattering centre by producing a vacancy in the system. In order to +do so, we directly modify the structure file `device_7.gen` and the input file +`dftb_in.hsd`. We remove atom number 48 from the structure file. Note that DFTB+ +ignores the indexes in the first column of the .gen file, therefore we do not +need to adjust them. We have, however, to remember to change the total number of +atoms in the first line from 408 to 407:: + + 407 C + C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + ..... + 46 1 32.912438770000 -20.000000000000 7.810000000000 + 47 1 30.452926620000 -20.000000000000 4.970000000000 + 49 1 31.682682700000 -20.000000000000 7.100000000000 + 50 1 30.452926620000 -20.000000000000 7.810000000000 + ... + +The resulting structure should look like this: + +.. figure:: ../_figures/transport/carbon2d-trans/device-7-vac.png + :width: 80% + :align: center + :alt: Geometry with vacancy on sublattice A + + Geometry with vacancy on sublattice A + +We then also adjust the dftb_in.hsd file accordingly. As we have removed an +atom, all the indexes in the transport block need to be adjusted properly. Note +that we removed an atom in the first PL of the extended device, therefore we +also need to adjust the values of FirstLayerAtoms. The ``Transport`` block now +reads:: + + Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.7103 + potential [eV] = 0.0 + } + } + +Compared to the pristine system, we have modified ``AtomRange`` in all the +blocks and the values of ``FirstLayerAtoms``. + +After running the calculation, we can compare the transmission curve for this +structure with a single vacancy and the pristine ribbon by using plotxy:: + + plotxy --xlabel 'Energy [eV]' --ylabel 'Transmission' -L --xlimits -6.5 -3 \ + tunneling.dat ../ideal/tunneling.dat + +.. _fig_transport_carbon2d-trans_nonscc-vac-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-vac-tunn.png + :width: 80% + :align: center + :alt: Non-SCC Transmission in pristine (green) and single vacancy (blue) + ribbon + + Non-SCC Transmission in pristine (green) and single vacancy (blue) ribbons + +Clearly, the presence of a vacancy introduces some finite scattering which +reduce the transmission with respect to the ideal ribbon. In particular, the +effect is quite small in the first conductance band while it is more visible in +the first valence band and in higher bands. The reflection amplitude is +increased near the band edges. This is expected in 1D systems, as near the band +edges the density of states diverges (Van Hove singularities), hence the group +velocity is lower, and it is known from semi-classical transport theory that the +scattering probability is, when short range disorder is present, inversely +proportional to the group velocity. The absence of resonant features in the +transmission may point to the fact that the vacancy does not induce additional +states in the conduction or valence bands. This can be verified by visualising +the density of states, as in Figure +:ref:`fig_transport_carbon2d-trans_nonscc-vac-dos`. + +.. _fig_transport_carbon2d-trans_nonscc-vac-dos: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-vac-dos.png + :width: 80% + :align: center + :alt: Non-SCC DOS for single vacancy in sublattice A (linear scale) + + Non-SCC DOS for single vacancy in sublattice A (linear scale) + +The same density of states can be visualised on logarithmic scale as +well, as in Figure :ref:`fig_transport_carbon2d-trans_nonscc-vac-semilog-dos`. + +.. _fig_transport_carbon2d-trans_nonscc-vac-semilog-dos: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-vac-semilog-dos.png + :width: 80% + :align: center + :alt: non-SCC DOS for single vacancy on sublattice A (semilog scale) + + Non-SCC DOS for single vacancy on sublattice A (semilog scale) + +The vacancy is adding some close energy levels in the gap, as verified already +from the DFTB+ calculation in the first part of the tutorial. The Van Hove +singularities are partially suppressed as the system no longer possesses +translational symmetry along the transport direction. Even in a simple non-SCC +approximation, the qualitative picture is consistent with the previous SCC +periodic calculation. We will now consider a vacancy sitting on the other +sublattice (B) and try to understand whether the relative position of the +vacancy is relevant or not by calculating once more the non-SCC transmission and +density of states + + +Non-SCC armchair nanoribbon with vacancy (B) +============================================ + +[Input: `recipes/transport/carbon2d-trans/agr-nonscc/vacancy2/`] + + +Transmission and Density of States +----------------------------------- + +We will now consider a vacancy sitting on the other sublattice (B), i.e. we can +take the structure file we used for the ideal ribbon and delete the atom +number 47. The structure file is:: + + 407 C + C H + 1 1 37.831463060000 -20.000000000000 0.710000000000 + 2 1 39.061219140000 -20.000000000000 1.420000000000 + 3 1 39.061219140000 -20.000000000000 2.840000000000 + ..... + 46 1 32.912438770000 -20.000000000000 7.810000000000 + 48 1 31.682682700000 -20.000000000000 5.680000000000 + 49 1 31.682682700000 -20.000000000000 7.100000000000 + 50 1 30.452926620000 -20.000000000000 7.810000000000 + ..... + +The `jmol` rendering of the geometry: + +.. figure:: ../_figures/transport/carbon2d-trans/device-7-vac2.png + :width: 80% + :align: center + :alt: Geometry with vacancy on sublattice B + + Geometry with vacancy on sublattice B + +Also in this case we remove an atom from the first PL of the extended device +region, therefore the rest of the `dftb_in.hsd` input file is identical to the +one we used for the vacancy on sublattice A. We can therefore just copy it and +run the DFTB calculation. The transmission is shown in Figure +:ref:`fig_transport_carbon2d-trans_nonscc-vac2-tunn` (transmission for vacancy +on sublattice B in blue, transmission for vacancy on sublattice A in green and +pristine system in green): + +.. _fig_transport_carbon2d-trans_nonscc-vac2-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-vac2-tunn.png + :width: 80% + :align: center + :alt: Non-SCC Transmission for vacancy B (blue), pristine (green) and vacancy + A (green) + + Non-SCC Transmission for vacancy B (blue), pristine (green) and vacancy A + (green) + +We can see a very strong suppression of transmission in the first sub-bands, +especially in the first valence band. Again, the absence of resonances may be +due by gap states. In fact, we can verify it by plotting the density of states, +as shown in Figure :ref:`fig_transport_carbon2d-trans_nonscc-vac2-dos`. + +.. _fig_transport_carbon2d-trans_nonscc-vac2-dos: +.. figure:: ../_figures/transport/carbon2d-trans/nonscc-vac2-dos.png + :width: 80% + :align: center + :alt: Non-SCC DOS for vacancy in sublattice B + + Non-SCC DOS for vacancy in sublattice B + +We can clearly see that the vacancy induces some nearly degenerate gap states, +and that the density of states at higher energies is largely unaffected. It is +known that the relative position of a scattering centre in a graphene nanoribbon +with respect to different sub-lattices strongly affects its scattering +properties, as is shown in these non-SCC calculation. Qualitatively, the picture +is also consistent with periodic DFTB+ calculations, with the difference that we +obtain directly information on the effect on transport properties via +transmission function. This also ensures that we do not have to worry about +choosing the right supercell or k-point sampling as the open boundary conditions +represent exactly the infinite system with a single scattering centre. As +already pointed out earlier, there is no warranty that a non-SCC calculation +give the proper result in a system if relevant charge transfer is occurring, and +in general it will not. Therefore in the next section we will repeat the same +calculation by solving the SCC problem. + + +SCC Pristine armchair nanoribbon +================================ + +A DFTB Hamiltonian is in general given by two terms: + +.. math:: + H^{SCC} = H^{0} + H^{\text{shift}} + +Where the component :math:`H^{\text{shift}}` is the self-consistent (SCC) +correction. The SCC correction is in general needed whenever there is a finite +charge transfer between atoms, i.e. whenever there are bonds between atoms with +different chemical species or with different coordination numbers. In our case, +we can expect a finite charge transfer between the C and H atoms at the edges, +and an SCC component may be relevant. While in the previous sections, we have +only considered the non-SCC component :math:`H^{0}`, in the next sections we +will compute the same calculation by including the correction given by the +shifts :math:`H^{\text{shift}}`. + +Note that the equilibrium SCC problem can be tackled in two ways: we could apply +the Landauer-Caroli to an SCC Hamiltonian taken, for example, from a periodic +calculation (i.e. uploading the SCC component), or we can solve the problem as a +full NEGF setup with 0 bias. The code flow is currently such that this second +procedure has to be used (however, the first technique will be available in +future release). Therefore we will need to learn to set the input related to two +other components of the NEGF machinery: the real space Poisson solver and the +Green function density matrix. + +In this way we will introduce a first complete input file. It is important, from +a didactic point of view, to be clear that as long as the applied bias is zero +and we are interested in equilibrium properties, the two approaches are +equivalent and the results are only valid in the limit of linear response. + + +Contact calculation +------------------- + +[Input: `recipes/transport/carbon2d-trans/agr-scc/contacts/`] + +In order to run an SCC transport calculation, the code needs some additional +knowledge about the contact PLs. In particular, the SCC shifts and Mulliken +charges have to be saved somewhere to enable consistency between the calculation +of the self-energy and the calculation of the Poisson potential. To this end, we +have to introduce an additional step in the procedure: the contact calculation. + +The contact calculation is simply a periodic calculation for the contact PL. As +such, not all the field defined in the transport are meaningful and the input +file will of course look different. The ``Geometry`` block is identical:: + + Geometry = GenFormat { + <<< 'device_7.gen' + } + +While the ``Transport`` block needs to be modified as follows:: + + Transport { + Device { + AtomRange = 1 136 + } + Contact { + Id = "source" + AtomRange = 137 272 + } + Contact { + Id = "drain" + AtomRange = 273 408 + } + Task = ContactHamiltonian { + ContactId = "source" + } + } + +We first notice the addition of an option ``Task =ContactHamiltonian {...}``, +which was previously absent. This block specifies that we intend to calculate +the bulk contact SCC properties, and the field ``ContactId`` specifies which +contact we want to calculate. The field ``FirstLayerAtoms`` in the ``Device`` +block is absent (it does not make sense in a contact calculation) and so are the +fields ``FermiLevel`` and ``Potential`` in the two ``Contact`` sections, as they +are not meaningful during this step. In general, the philosophy of a DFTB+ input +file is that if input fields that would be useless or contradictory are present, +the code will halt with an error message. + +The Hamiltonian block shows some differences, too:: + + Hamiltonian = DFTB { + SCC = Yes + SCCTolerance = 1e-6 + EwaldParameter = 0.1 + MaxAngularMomentum { + C = "p" + H = "s" + } + + SlaterKosterFiles = Type2FileNames { + Prefix = "../../slako/" + Separator = "-" + Suffix = ".skf" + } + + KPointsAndWeights = SupercellFolding { + 25 0 0 + 0 1 0 + 0 0 1 + 0.0 0.0 0.0 + } + } + +The flags ``SCC = Yes`` and ``SCCTolerance = 1e-6`` enable the SCC calculation. +A small tolerance in the contact calculation, and in general in transport +calculation, helps to avoid artificial mismatches at device/contact boundaries. +The parameter ``EwaldParameter`` needs to sometimes be set when using parallel +calculations to reduce the size of the neighbour list. Typically, the code may +complain about a too small parameter: in that case, setting a value of 0.1 is +considered to be good practice. The other parameters are the usual ones, except +for the ``KPointsAndWeights``, which deserves special attention. + +The bulk contact is of course a periodic structure, hence we need to specify a +proper k-point sampling, as we would do in a regular periodic DFTB +calculation. However, you should be careful about the way the lattice vector is +internally defined. In the input system is a cluster (C), i.e. *it has no +periodicity in direction transverse to the transport directions*, the lattice +vector of the contact is internally reconstructed and assigned to be the first +lattice vector, *regardless the spatial orientation of the structure*. This +means that the ``KPointsAndWeights`` for a cluster system are always defined as +above: a finite number of k-points along the first reciprocal vector (according +to a 1D Monkhorst-Pack scheme) and a Gamma point sampling along the other two +directions. The reason for this choice is that we do not want to assign a +specific direction to the structures, i.e. at this level we do not assume in any +way that the structure must be oriented along x,y or z direction. + +Note also that as the contact information is used in the transport calculation, +it is a good idea to use a dense k point sampling and a low SCC tolerance, in +order to get a very well converged solution. The contact calculation will be +usually much faster than the transport calculation, so this does not usually +present a problem. + +On the other hand, this rule regarding k-points does not apply to periodic +transport calculations, as the periodicity along the transverse directions must +also be preserved (refer to the following section for a periodic system +example). We can run the calculation by typing:: + + dftb+ dftb_in.hsd | tee output.log + +After running the calculation, we notice that a file `shiftcont_source.dat` is +generated. This file contains the information useful for the transport +calculation (shifts and charges of a bulk contact). It is suggested you also +keep a copy of the `detailed.out` for later reference. We can obtain the value +of the Fermi energy, which we will later need, from `detailed.out` as -4.7103 +eV. + +We can now run the same calculation for the drain contact by just modifying the +``Task`` block:: + + Task = ContactHamiltonian { + ContactId = "drain" + } + +The contact are identical, therefore we expect the same results, also with the +same Fermi energy. We now have a file `shiftcont_drain.out`, which is equivalent +to `shiftcont_drain.dat` apart from small numerical error. In fact, we could +have simply copied the previous contact results into this file. + +Now that the contact calculation is available, we can set up the transport +calculation. + + +Transmission and Density of States +---------------------------------- + +[Input: `recipes/transport/carbon2d-trans/agr-scc/ideal/`] + +In order to calculate the transmission for the SCC system, we have to copy the +files `shiftcont_drain.dat` and `shiftcont_source.dat` into the current +directory:: + + cp ../contacts/shiftcont* . + +Then, we have to specify some additional blocks with respect to a non-SCC +calculation. We first look at the ``Transport`` block:: + + Transport { + Device { + AtomRange = 1 136 + FirstLayerAtoms = 1 69 + } + Contact { + Id = "source" + AtomRange = 137 272 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 273 408 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Task = UploadContacts { + } + } + + +The atom indices are of course the same, as the geometry of the system is not +changed. This time though, we explicitly specified a ``Task`` block named +``UploadContacts``, which declares that we are now running a full transport +calculation. ``Task = UploadContacts {}`` is the default and does not take any +additional parameters, therefore you can safely omit it. + +Now that we are solving the full SCC scheme, we will allow for charge transfer +between the open leads and the extended device region, therefore it is important +to set a well-defined Fermi energy. While this does not make any difference in a +non-SCC transmission calculation, it is crucial for the SCC calculation. A wrong +or unphysical Fermi energy will lead to unphysical charge accumulation or +depletion in the system. + +To this end, you will have to pay some attention to the definition of the Fermi +energy. As we are calculating a semiconductor system, the Fermi level should be +in the energy gap. By calculating a band structure or by inspection of the +eigenvalues in the file `detailed.out` you can verify that the value -4.7103 is +on the edge of the conduction band. This can be explained as numerically the +Fermi level is defined by filling the single particle states till the reference +density is reached, therefore its position inside the gap of a semiconductor is +arbitrary. Therefore, while in metallic system we may ensure consistency and use +a well calculated Fermi level at some specific temperature during all our +transport calculation, in the case of a semiconductor system we can manually set +the Fermi level in the middle of the energy gap (for this system, roughly at +-4.45 eV) and freely vary the temperature as long as the gap is larger than +several times the value of kT. + +We will see in the following that there are some ways to verify that the Fermi +level is defined consistently, as this is often source of confusion. Note also +that, differently from other codes, DFTB+ allows for different Fermi levels in +different contacts, which can be useful when heterogeneous contacts are defined +(for example, in a PN junction). In that case a built-in potential is internally +added to ensure no current flow at equilibrium. + +In the ``Hamiltonian`` block now an SCC calculation has to be specified:: + + Hamiltonian = DFTB { + SCC = Yes + SCCTolerance = 1e-6 + ReadInitialCharges = No + ... + +Differently from the non-SCC calculation, we now need to specify a way to solve +the Hartree potential and the charge density self-consistently. In a NEGF +calculation, we use a real-space Poisson solver to calculate the potential, and +a Green function integration method to calculate the density matrix:: + + ... + Electrostatics = Poisson { + PoissonBox [Angstrom] = 40.0 30.0 30.0 + MinimalGrid [Angstrom] = 0.5 0.5 0.5 + SavePotential = Yes + } + + Eigensolver = GreensFunction { + } + + Mixer = Broyden { + MixingParameter = 0.02 + } + } + ... + +The Poisson section contains the definition of the real space grid +parameters. Note that differently from a normal DFTB+ calculation, simulating +regions of vacuum is not for free, as the simulation domain must be spanned by +the real space grid. The grid is always oriented along the orthogonal cartesian +coordinate system. ``PoissonBox`` specifies the lateral length of the grid. The +length along the transport direction is ignored as it is automatically +determined by the code (in this case, z=30.0). The length along the transverse +direction are relevant and *should be carefully set*. In order not to force +unphysical boundary conditions, you may extend the grid at least 1 nm away. If a +strong charge transfer is present, you may go for a larger grid according to +your available computational resources. A poorly defined grid can lead to no +convergence at all, to a very strange (and slow) convergence path or to +unphysical results. ``MinimalGrid`` specifies the minimum step size for the +multigrid algorithm. Values between 0.2 and 0.5 are usually good, where a lower +value stands for higher precision. ``SavePotential = Yes`` will return a file +containing the potential and charge density profile, for later reference. These +files can be quite large, therefore the default is ``No``. + +The Eigensolver is now specified as ``GreensFunction``. With this definition, we +instruct the code not to solve an eigenvalue problem but rather to calculate the +density matrix by integration of the Keldysh Green function. This block provides +the SCC charge density with or without applied bias. The options define the +integration path. Usually the default options are good enough in most cases and +advanced users may refer to the manual and references therein. + +The ``Mixer`` options is present in DFTB+ calculations as well. Convergence is +known to be critical in NEGF schemes. In that case, a lower ``MixingParameter`` +value will help to avoid strong oscillation in the SCC iterations. + +The last block is ``Analysis``:: + + ... + Analysis { + TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.0 -3.0 + EnergyStep [eV] = 0.01 + } + } + +This block is identical to the non-scc calculation as the same task is +performed: calculation of Transmission, current and DOS by using the +Landauer-Caroli formula. The Transmission will be of course be different due to +the fact that the ground state charge density is now solution of the SCC +Hamiltonian and we have slightly changed the energy range as the SCC component +introduce a shift of the band-structure (try to compare the SCC and non-SCC +transmission results when you are done). We can now run the calculation (after +creating the directories GS and contacts):: + + mkdir GS + mkdir contacts + mpirun -n 4 dftb dftb_in.hsd | tee output.log + +Where ``-n 4`` should be adapted to the number of available nodes. As transport +calculations in DFTB+ are parallelised on energy points, a quantity larger than +40 (the default number of integration points at equilibrium) will not speed up +the calculation of the density matrix. + +An inspection of the file `detailed.out` reveals that we have additional +information with respect to the non-SCC calculation, including a list of atomic +charges and orbital population, as now the SCC density matrix has been +calculated. The transmission is also saved as separate file, and is shown in +Figure :ref:`fig_transport_carbon2d-trans_scc-tunn`. + +.. _fig_transport_carbon2d-trans_scc-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/scc-tunn.png + :width: 80% + :align: center + :alt: SCC transmission in pristine AGR + + SCC transmission in pristine AGR + +As you would expect, it still step-like as in the non-SCC calculation. This is +correct, as we're calculating an ideal 1D system. The bandwidth (i.e., the steps +width) may differ due to SCC contribution and the overall transmission is +shifted. Note that while the non-SCC calculation is very robust, meaning that +you will always get step-like transmission for a 1D system, in the SCC +calculation a poor definition of the boundary conditions, of the bulk contact +properties or of the additional ``GreensFunction`` and ``Poisson`` blocks may +induce numerical artifacts and scattering barriers which should not be there. As +a result, the transmission will not appear step-like but rather visibly smoothed +out. + +You can also verify the quality of the calculation by inspection of the +potential and charge density profiles. In a pristine periodic system we would +expect a periodic potential, without discontinuities at the boundary between +extended device and electrodes. The information needed to construct the real +space potential and charge density are contained in 5 files: `box3d.dat`, +`Xvector.dat`, `Yvector,dat`, `Zvector.dat`, `potential.dat` and +`charge_density.dat`. The first 4 files contain the grid information, and the +last two ones the list of potential and charge density values (following a row +major order). Those information can be converted to any useful with some simple +scripting, we provide an utility called `makecube` which can be used to convert +them to Gaussian `cube` format or a more flexible `vtk` format. There's plenty +of software to visualise `vtk` or `cube` files, but unluckily at present current +choices of software which are effective at visualising real space grid data are +weak at visualising atomistic structures, and vice versa. In the following we +will use `paraview` and work with the `vtk` format. `Paraview +`_ is freely available and is supplied with many +gnu/linux distributions as a compiled package. + +The `vtk` file can be obtained by simply running:: + + makecube potential.dat pot.vtk + +.. _fig_transport_carbon2d-trans_clip-pot: +.. figure:: ../_figures/transport/carbon2d-trans/clip-pot.png + :width: 80% + :align: center + :alt: Potential profile along the nanoribbon + + Potential profile along the nanoribbon + +An extensive explanation of `paraview` features is beyond the scope of this +tutorial. Following some easy steps, you can produce the potential map shown in +Figure :ref:`fig_transport_carbon2d-trans_clip-pot`. + +1. Open paraview and import the file `pot.vtk` from File->Open +2. Click on Properties->Apply (Properties are usually visualised on the left + side of the screen) and you should see the bounding box in the visualisation + windows. +3. In the Pipeline browser select the file `pot.vtk` by clicking once on it, and + then select the Clip filter from Filters->Alphabetical (or from the filter + toolbar). +4. In Properties, click on 'Y Normal' to produce a clip along the nanoribbon. +5. Click on Properties->Apply. + +The plot shown in Figure :ref:`fig_transport_carbon2d-trans_clip-pot` above is +the self-consistent potential along the nanoribbon. We can see that the charge +transfer between carbon and hydrogen at the edges results in a non-flat +potential. At a first glance, the potential looks quite homogeneous, meaning +that there are no clear discontinuities at the box boundary. This is important: +being it a homogeneous ribbon, the potential should have the same periodicity as +the lattice. We can verify this with a closer inspection by plotting a cut along +a line. We apply the following steps: + +1. We select `pot.vtk` in the Pipeline Browser and Filters->Alphabetical->Plot + Over Line +2. From the Properties window, we select 'Z Axis' and click on 'Apply' + +By following this procedure we obtain Figure +:ref:`fig_transport_carbon2d-trans_plotline-pot`. + +.. _fig_transport_carbon2d-trans_plotline-pot: +.. figure:: ../_figures/transport/carbon2d-trans/plotline-pot.png + :width: 80% + :align: center + :alt: Potential profile along the nanoribbon + + Potential profile along the nanoribbon + +As you can notice, there is a discontinuity at the interface. However, it is +quite small (~ 12 meV). Defining a 'perfect' interface between the bulk +semi-infinite contacts and the device region is very difficult, especially in a +semiconductor where no free charge can contribute to screen such an interface +potential. A smaller tolerance in the self-consistent charge during the contact +and the device calculation, a finer calculation of the Fermi level (in metallic +systems) and a finer Poisson grid can decrease the discontinuity: you should be +able to reach about 1 meV, but it is difficult to go below this value. However, +as you can see in the transmission plot, as long as the discontinuity is this +small, it hardly affects the transmission. + +However, it is important for you to verify that the behaviour at the boundaries +is reasonable. Otherwise, the extended region may be too small to allow to the +relevant physical quantities (charge, potential) to relax to bulk values. Be +aware that numerical errors are unavoidable, therefore it is important to +understand their relevance and the impact on the results. In the transmission +calculation we do not notice anything different because the energy step is close +to the mismatch at the boundaries. + +After running the calculation for the pristine system, we will introduce +vacancies as we did in the non-SCC calculation. The results should be now +directly comparable to the bulk periodic SCC calculation. + + +SCC armchair nanoribbon with vacancy (A) +======================================== + +[Input: `recipes/transport/carbon2d-trans/agr-scc/vacancy1/`] + +We will now calculate the SCC transmission for the nanoribbon with a vacancy on +the sublattice A, using the same input structure set up for the non-SCC +calculation. The contacts are identical to the pristine case, therefore in the +following we will only modify the extended device calculation. + + +Transmission and Density of States +----------------------------------- + +As previously done, the transport section must be modified in order to account +for the different number of atoms in the extended device region:: + + Transport { + Device { + AtomRange = 1 135 + FirstLayerAtoms = 1 68 + } + Contact { + Id = "source" + AtomRange = 136 271 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Contact { + Id = "drain" + AtomRange = 272 407 + FermiLevel [eV] = -4.45 + potential [eV] = 0.0 + } + Task = UploadContacts { + } + } + +We use the same Fermi level and the files `shiftcont_source.dat` and +`shiftcont_drain.dat` as in the pristine system calculation, as the contacts are +not modified. + +The ``Hamiltonian`` block is also not modified, except for an additional finite +temperature:: + + Hamiltonian = DFTB { + ... + Filling = Fermi { + Temperature [Kelvin] = 150.0 + } + ... + } + +A finite temperature is used to provide a finite temperature broadening, useful +if the vacancy induces partially filled gap states. In general, temperature +broadening may improve convergence and dump oscillations in the SCC iterations. + +The ``Analysis`` block is also similar, we add the DOS calculation to verify if +we can identify a vacancy state:: + + Analysis { + TunnelingAndDos { + Verbosity = 101 + EnergyRange [eV] = -6.0 -3.0 + EnergyStep [eV] = 0.025 + Region { + Atoms = 1:135 + } + } + } + +As usual, you can now create the `GS` and `contacts` directories, copy the +`shiftcont_source.dat` and `shiftcont_drain.dat` in the current directory and +run the calculation. The density of states and transmission are shown in Figure +:ref:`fig_transport_carbon2d-trans_scc-vac-dos` and +:ref:`fig_transport_carbon2d-trans_scc-vac-tunn`. + +.. _fig_transport_carbon2d-trans_scc-vac-dos: +.. figure:: ../_figures/transport/carbon2d-trans/scc-vac-dos.png + :width: 80% + :align: center + :alt: Density of states for vacancy (A) + + Density of states for vacancy (A) + +.. _fig_transport_carbon2d-trans_scc-vac-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/scc-vac-tunn.png + :width: 80% + :align: center + :alt: Transmission for vacancy (A) + + Transmission for vacancy (A) + +The vacancy states are located in the energy gap, consistently with the periodic +calculation, and that the tunneling curve is qualitative similar to the non-scc +calculation. The first conduction and valence band are weakly affected by the +vacancy which does not act as a strong scatterer. There is no signature of +resonances, as the additional levels are located in the gap. + +Note also that we previously recommended the use of large extended regions and +to verify that the potential and charge density are smooth at interfaces. As you +can see in Figure :ref:`fig_transport_carbon2d-trans_clip-vac-pot`, the impurity +is very close to the boundaries, resulting to a potential profile which varies +significantly close in to the boundary. It is left to the reader to verify that +the overall transmission does not change significantly if a longer extended +region is considered. + +.. _fig_transport_carbon2d-trans_clip-vac-pot: +.. figure:: ../_figures/transport/carbon2d-trans/clip-vac-pot.png + :width: 80% + :align: center + :alt: Potential profile for vacancy (A) + + Potential profile for vacancy (A) + + +SCC armchair nanoribbon with vacancy (B) +======================================== + +[Input: `recipes/transport/carbon2d-trans/agr-scc/vacancy2/`] + +We will now run the same calculation, but with the vacancy on the +sublattice B. As in the non-SCC case, the only difference with the previous +calculation is the location of the vacancy, therefore the input file is +absolutely identical. The contacts are the same, therefore all we have to do is +copy the `shiftcont_source.dat` and `shiftcont_drain.dat` files into the current +directory and run the calculation. + +The resulting transmission and density of states are shown in Figures +:ref:`fig_transport_carbon2d-trans_scc-vac2-dos` and +:ref:`fig_transport_carbon2d-trans_scc-vac2-tunn`. + +.. _fig_transport_carbon2d-trans_scc-vac2-dos: +.. figure:: ../_figures/transport/carbon2d-trans/scc-vac2-dos.png + :width: 80% + :align: center + :alt: Density of states for vacancy (B) + + Density of states for vacancy (B) + +.. _fig_transport_carbon2d-trans_scc-vac2-tunn: +.. figure:: ../_figures/transport/carbon2d-trans/scc-vac2-tunn.png + :width: 80% + :align: center + :alt: Transmission for vacancy (B) + + Transmission for vacancy (B) + +We immediately notice that the Van Hove singularities are strongly suppressed +and that the valence band is almost completely suppressed. Consistently with the +picture obtained by periodic calculation, a quasi-bounded vacancy level +hybridise with the valence band edge causing a strong back-scattering. A +comparison between all the three cases (see Figure +:ref:`fig_transport_carbon2d-trans_scc-tunn-comparison`) shows that the +scattering probability is deeply affected by the exact position of the +vacancy. This is, in graphene nanoribbon, generally true for other kinds of +short range scattering centres such as substitutional impurities. We can also +notice that, in this particular case, the non-scc approximation is qualitatively +consistent for two reasons: the vacancy level are not populated and the charge +transfer at the edges is not critical as the edges contribute poorly to the +transmission in an armchair ribbon. + +.. _fig_transport_carbon2d-trans_scc-tunn-comparison: +.. figure:: ../_figures/transport/carbon2d-trans/scc-tunn-comparison.png + :width: 80% + :align: center + :alt: Transmission for pristine system (blue), vacancy (A) (green) and + vacancy (B) (red) + + Transmission for pristine system (blue), vacancy (A) (green) and vacancy (B) + (red) diff --git a/docs/transport/index.rst b/docs/transport/index.rst index de5b8f0d..975ddf40 100644 --- a/docs/transport/index.rst +++ b/docs/transport/index.rst @@ -12,3 +12,4 @@ defect calculations which can be helpful to understand the following chapter. :maxdepth: 1 carbon2d-elec.rst + carbon2d-trans.rst

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