LanTraP: User Manual
Contents
1. Emin dE and Emax default 1eV 0 001 eV 1 eV respectively The next 3 options are Emin dE and Emax which allow any value to be entered in eV These values determine the energy range from Emin to Emax as well as the resolution dE for which modes will be calculated There will always be 0 modes where no band exists so choose the energy range near the range of eigenvalues in the dispersion Note that using a dE that is too large may lead to significant errors Thus it is good practice to decrease dE to ensure the distribution of modes is converged and accurate Some suggested values are Electrons dE should be in the range of 0 01 eV to 0 001 eV Phonons dE should be in the range of 0 0001 eV to 0 000001 eV After all of these options have been modified the TE options button in the lower right will move the tool onto the next slide 2 3 TE Options OTE Options Particle Electron Temperature K an 300K Transport type Quasi Ballistic y Ef min eY 0 5e delta Ef ev o otey Ef Max eV 0 5e 0 MFP CB nm 10 CB scattering parameter o Conduction Band Minimum e MFP VB nm ho VB scattering parameter o valence Band Maximum leV Conductor Length nm 10 lt Modes Options Simulate gt Figure 4 A screen shot of the TE Options slide If on the Load Data slide the user chose TE or Modes and TE this slide will ha2. the user will see This slide will allow the user to upload the electron or phonon dispersion to calculate the thermoelectric properties and or the distribution of modes or a pre calculated distribution of modes to calculate the TE properties only The first input is the Upload drop down box This is where the input data in a txt file is uploaded From the drop down menu select upload This selection will prompt a pop up window allowing the user to select the desired file After selecting the file and pressing upload the data will appear in the Data file box Load Data Upload Uploaded data Ek for a 3D parabolic conduction band set on the origin 0k UE A Assuming that the effective mass is the eletron rest mass _ Box length is 5 nm in all dimensions and there are 51 k points determined by the Mo nkhurst Pack scheme 337140 223796 115078 010987 911522 816683 726471 640884 559925 483591 411883 344802 282348 224519 171317 122741 078791 039468 004771 974700 Z What to calculate Modes and TE gt Modes Options gt Data file E k or modes DO O LJ LI Gd OI O9 LI LI LJ LJ OJ G9 b3 L h bee e Figure 1 A screen shot of the Load Data slide The Data file text box shows what has been uploaded and allows the user to edit the file for example to remove a header from the data Note that the user can simply copy and paste data into the Data file b
3. the valence band Eyer E Eyp in Equation 1 where Ey is the Valence Band Maximum The Conduction Band Minimum and Valence Band Maximum are required to be different values with Valence Band Maximum being less than Conduction Band Minimum for the calculation to occur For electrons the tool will calculate electrical conductivity Seebeck coefficient electron thermal conductivity power factor and electronic zT where K is assumed to be 0 Phonons For phonon diffusive transport only a single mean free path and scattering parameter are required since E E in Equation 1 e MFP Phonon default 10 nm The mean free path of phonons A in Equation 1 e Scattering Parameter default 0 The scattering exponent r in Equation 1 for phonons For phonons the tool will calculate the lattice thermal conductivity 2 3 3 Quasi Ballistic Transport For quasi ballistic transport the options are the same as diffusive transport including the ballistic transport options for electrons but with the following added parameter e Conductor length default 10 nm This is the length of the material in nm along the transport direction The tool will calculate the same values as diffusive transport when quasi ballistic transport is selected However transport in this case can be in between fully ballistic and fully diffusive 3 Simulate After the TE Options slide the calculatio
4. LanTraP User Manual Kyle Conrad Jesse Maassen Mark Lundstrom 1 Introduction LanTraP is an online tool aimed at assisting research and education The tool allows for a txt file containing band structure information to be uploaded from which the thermoelectric TE transport coefficients for electrons and phonons can be calculated LanTraP supports any general band structure from simplified parabolic linear dispersions to accurate full band descriptions to perform thermoelectric calculations within the Landauer formalism In this manual the basics of the calculation method are outlined and all of the input parameters are described For more information about transport and the Landauer formalism see Near Equilibrium Transport Fundamentals and Applications by M Lundstrom amp C Jeong World Scientific Singapore 2013 2 Input Parameters There are a few ways to use LanTraP By uploading a dispersion relation E k for electrons or E q for phonons the user may then decide to calculate i just the distribution of modes or ii calculate the distribution of modes and the transport coefficients simultaneously Alternatively the user may upload a distribution of modes file and proceed to calculate the transport coefficients directly When the calculation is complete the tool produces plots and tables of the modes and transport coefficients which are available for download 2 1 Load Data When starting LanTraP this is first slide
5. culate electrical conductance Seebeck coefficient electron thermal conductance power factor and electronic zT where K is assumed to be 0 Phonons For phonon ballistic transport there are no other options to modify and the tool will calculate the lattice thermal conductance 2 3 2 Diffusive Transport For diffusive transport there are more options especially when the particle being considered is an electron The tool allows for an energy dependent mean free path with the form ACE Ag FA 1 where E ef depends on the case considered and is defined below Electrons For electron diffusive transport all of the options for ballistic transport still need to be set in addition to the following scattering parameters e MFP CB default 10 nm The mean free path of electrons in the conduction band A in Equation 1 e CB scattering parameter default 0 The scattering exponent r in Equation 1 of the conduction band e Conduction Band Minimum default 0 eV The minimum energy of the conduction band For the conduction band Eyer E Ecg in Equation 1 where Ecg is the Conduction Band Minimum e MFP VB default 10 nm The mean free path of electrons in the valence band A in Equation 1 e VB scattering parameter default 0 The scattering exponent r in Equation 1 of the valence band e Valence Band Maximum default 1 eV The minimum energy of the valence band For
6. lculate drop down box either Modes or Modes and TE was selected the user will need to specify a number of parameters to calculate the modes displayed on the Modes Options slide Modes Options Monkhorst Pack k grid jum yes Dimensionality 3 Ml Transport direction zo Spin Degeneracy P Emin ev ey gE eV oe Emax eV 1e lt Load Data TE Options gt Figure 3 A screen shot of the Modes Options slide e Monkhorst Pack k grid default yes The Monkhorst Pack k grid boolean option allows for one of two uniformly spaced k grid organization schemes to be chosen The Monkhorst Pack k grid is chosen so that there are no duplicates in the Brillouin zone If no is selected the tool assumes that the first and last points of the k grid are duplicates at the edge of the Brillouin zone in k ky and k directions Dimensionality default 3 The user may select between 1 2 and 3 dimensions from the drop down box The choice of dimensionality is important in determining the units of the distribution of modes and the TE characteristics Lx Ly and Lz default 1 nm These values correspond to the lengths of the simulation box used in creating the dispersion relation in nm If the user selects less than 3 dimensions the tool will determine which lengths are used based on the number of k points in each dimension with the largest numbers being the dimensions used Nu
7. llows see Figure 2 e Each row corresponds to a list of eigenvalues e The rows iterate over all the k points in the Brillouin zone e The sequence of k points iterates over k ky kz in this order k point Row vector of r t lt st YT n eigenvalues P ik 1 iky 1 ik 1 En Loop through all iky ik 2 ik 1 ik 1 n ik n ik 1 ik 1 i Increment ik second B Me i each time loop through ikan ik 2 ik 1 3 3 all ik first k 1 ik 3 kt 3 a Increment ik third IkK 1 iky 1 ik 2 each time loop through all ik first and A ik second ik n ikj ny ik 2 3 a 3 a 3 3 3 Only the eigenvalues are included in the file Figure 2 The proper format for an uploaded dispersion file 2 1 2 Format for a distribution of modes file For a pre calculated distribution of modes the uploaded file has 2 columns the first is an energy vector in eV in increasing order and the second is the distribution of modes in units of m where d is the dimensionality at each energy The output Modes Table from the tool automatically has the correct format 2 2 Modes Options If on the Load Data slide TE was chosen from the What to calculate drop down box this slide has no options and prompts the user to select the TE Options button If from the What to ca
8. mber of k points default 51 for kx ky and kz The Number of k points for k ky and k are used to correctly interpret the uploaded file If there is no periodicity along any of the directions set the number of k points along those directions to 1 Note that the distribution of modes may not be accurate if the k grid is too coarse By increasing the k point density eventually the modes will converge to the correct values and will no longer change with further increases in k point density Number of Bands default 1 Along with Number of k points Number of Bands is used to correctly interpret the uploaded file Note that the number of bands must be the same for all k points Transport direction default Z The Transport direction drop down menu is used to identify the transport direction and assigns the other directions as perpendicular k points when calculating modes Spin Degeneracy default 2 The Spin Degeneracy drop down box allows for either 1 or 2 to be chosen The spin degeneracy parameter is set to 1 2 when each band should only hold 1 2 electron This ensures that the calculated distribution of modes for electrons is per spin i e identical spin up and spin down states will count as a single mode In the case of phonons the Spin Degeneracy should always be 2 different by definition from electrons the polarization of phonons is included in the calculation of the distribution of modes
9. n begins after pressing the simulate button in the lower right On the screen simulation information will appear such as which calculation is being performed or any errors that may occur Commonly the most time consuming part is the calculation of the distribution of modes The computation time will increase with the size of the uploaded data file and the resolution of the Fermi energy grid The tool will typically run for anywhere between a few seconds to several minutes before completion Once the simulation is complete the final slide will have a plot and the Result drop down menu From the drop down menu all of the calculated values can be selected to be plotted within the tool If multiple simulations were run in the same instance of the tool the results may be compared against each other If an output was not calculated due to the choice of What to calculate the plot will only contain one point at 0 0 As well the Modes Table TE Table and Phonon Lattice Thermal Conductivity Conductance show the results in table form Each output may be downloaded from the tool using the button next to the Result drop down The tables are designed to be downloaded and directly loaded into programs such as MATLAB Simulate Result Distribution of Modes x F 2e 17 1e 17 Number of Modes 1 m d 1 where d dimension oO Si 05 os 1 0 Energy eV 1 result Clear lt TE Options Figure 5 A screen sho
10. ox The uploaded data must have a specific format depending on the data type described below The final option on this page is the What to calculate drop down box The options here are Modes TE and Modes and TE Depending on the data file only certain options should be chosen If an electron or phonon dispersion file has been uploaded choose either Modes or Modes and TE since a distribution of modes is required to calculate the transport coefficients If the uploaded data was a pre calculated distribution of modes the user should only select TE Once completed select the Modes Options button in the bottom right corner to move to the next slide 2 1 1 Format for the electron or phonon dispersion file The basic format of a dispersion relation file is the following each row vector lists the eigenvalues in increasing order corresponding to a specific k ky Kz point with the rows iterating over all the k points in the Brillouin zone The k grid mesh must be uniform within the Brillouin zone along a given direction gt to gt where l is the box size in a given direction but the density may be different along kx ky and kz Note that the simulation box must be rectangular with one direction corresponding to the transport direction By labeling the k points by the number from smallest to largest ik 1 corresponding to the minimum k and ik n corresponding to the max k the order of k points in the dispersion file is as fo
11. t of the Simulate slide after calculation has completed
12. ve options otherwise the slide will show a message that there are no options to modify Particle default Electron The Particle drop down box has two options Electron or Phonon This determines what properties are calculated Temperature K default 300K The lattice temperature in K Transport type default Ballistic Transport type is a drop down box with choices of Ballistic Diffusive and Quasi Ballistic where the last option allows the user to set the length of the transport region The choice of Particle and Transport type changes the options available which are detailed below 2 3 1 Ballistic Transport Electrons Ef min default 0 5 eV Ef min should be chosen such that Ef min gt 15 k T Emin where Emin is the minimum energy of the distribution of modes delta Ef default 0 001 eV The value of delta Ef is the resolution of the Fermi energy range for which transport coefficients are calculated over Ef max default 0 5 eV Ef max should be chosen such that Ef max lt Emax 15 k T where Emax is the maximum energy of the distribution of modes The reason for the restrictions on the Ef grid is to insure the tool performs a proper integration If the Fermi energy range is too wide an error will occur and the calculation will stop without completion For electron ballistic transport the tool will cal
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