FLOOXS » TclLib » Device
107 documented proc(s) in TclLib/Device/.
3DTensorListToFlooxsTensor · 3DTensorListToFlooxsTensorAdd · 3DTensorTo2D · __alpha · __alphaInv · __approxFirstToSecondOrderRotation · __BuildHFromGeneric · __CompareBands · __CrowellSzeHole · __Det2x2 · __DetNxN · __DirectStatistics · __DOS1D · __DOS2D · __EllipsoidalMassTensor · __EnsureParams · __FirstKandaHallTensor · __IndirectStatistics · __interpolate_linear_vec · __Inv2x2 · __Inv3x3 · __InvNxN · __Make2x2 · __MapExpr · __MillerToRotation · __mult_sweep · __MultAx · __MultNxN · __ParseMillerDigits · __RotateTensor · __RotateTensorDiag · __RotateVector3 · __rotTen_F_Mat · __SolutionExpandRecursive · __Stats1D · __Stats2D · __Transpose · __xyzalpha · AddSolution · AddStressVector6 · BandGap · BandGapGamma · BandGapL · BandGapX · BandOverlapLoop · BuildH · BuildH110 · BuildHRot · ComputeModes · ComputeModesFull · CplxMult · Cubic::CubicSpline · Cubic::SolveTridiag · DGEquation · DimMap · DirectTunnelEnergy · ElecMobility · ElecMobility · ElecMobility · EllipsoidalMassTensor · Eqns · Eqns · EqnsLegacy · EqnsLegacy · EqnsSimple · Get3DHoleDPTensor · Get3DHoleDPTensor · GetAnisoCarrierTensor · GetConductivityTensor · GetdU · getHmobs · getHmobs0 · GetMobilityTensor · HoleMobility · HoleMobility · HoleMobility · Init · InterpBowing · InterpLinear · KKDiscretize · LatticeStrain · Ltun · MapTerm · Masetti · Masetti · Nc · NcGamma · NcL · NcX · PoissonSchrodinger · PolarizationCharge · Schenk · Schrodinger100Solve · SchrodingerDirectCurrent · SchrodingerDirectCurrentKPMeff · SchrodingerIndirectUnscaledTransmission · SchrodingerSolveEllipsoidal · SchrodingerSolveLVal · SchrodingerSolveXVal · Solve · SortLowHigh · SRH · ThermalConductivity · Transpose · Trapezoidal · UniformStress · VoxelVolumeTest
Input: 3x3 Tensor/ Matrix list (3 dimensional list where the first two dimensions are the 2D matrix and the 3rd dimension are other matricies) All matricies are multiplied together by component Returns: Flooxs tensor alagator expression
Input: 3x3 Tensor/ Matrix list (3 dimensional list where the first two dimensions are the 2D matrix and the 3rd dimension are other matricies) All matricies are added together by component Returns: Flooxs tensor alagator expression
Convert a 3D tensor to 2D by chopping off the z component
Build rotation matrix from XYZ Euler angles (degrees)
Inverse of XYZ rotation (negate angles, reverse order)
Build 6x6 Bond matrix from a 3x3 rotation matrix. Converts first-order (vector) rotation to second-order (Voigt tensor) rotation.
Build discretized Hamiltonian equations from the generic symbolic matrix. R: rotation matrix (empty string for unrotated).
Deduplicate equivalent bands
proc CrowellSze { driveForce Qfn Qfp Elec Hole Emob Hmob }
returns the determinate of a 2x2 matrix
puts [__Inv2x2 {{1 1} {1 -1}}]
laplace formula for determinate
returns the determinate of an NxN matrix
A is a matrix and N is the length of the sides
Statistics used in direct band to band tunneling quantum calculations Takes an energy, quasi fermis, and temperature
Returns the 1D Density of states value for a given temperature and effective mass
Returns the 2D Density of states value for a given temperature and effective mass
Legacy alias — older decks (and the auto-loaded tclIndex) reference the underscored name.
Initialize from Silicon if SetParams hasn't been called
pi_mat is the calculated pi coefficeint matrix X_Vect is the stress vector(xx,yy,zz,yz,xz,xy), and uB is mobility times magnetic field vector (x,y,z)
Statistics used in indirect band to band tunneling quantum calculations Takes an energy, quasi fermis, temperature, and phonon energy
Vectorized linear interpolation for a sorted list of query points. Single pass O(n+m) where n = len(x), m = len(xv). Values outside the data range are clamped to the nearest endpoint.
returns the inverse of a 2x2 matrix
puts [MultNxN {{1 2} {3 4}} {{1 2} {4 3}} 2]
Returns the inverse of a 3x3 matrix
Generic NxN inverse via Gauss-Jordan elimination with partial pivoting.
Takes 4 scalars and returns a 2x2 matrix [a b] [c d]
Discretize a full expression (sum of terms) using MapTerm.
Build a 3x3 rotation matrix from Miller indices. Syntax: (hkl)<uvw> — default: () → column 2 (z), <> → column 0 (x) (axis:hkl)<axis:uvw> — explicit axis assignment Examples: (001)<100> — (001) surface, [100] channel. Normal→z, channel→x (x:001)<y:100> — (001) surface normal along x, [100] along y (x:110)<z:1-10> — (110) normal along x (1D quantum), [-110] along z The third direction is always the cross product of the other two, placed in whichever column remains. The rotation matrix rows are crystal [100],[010],[001] directions. The columns are device x,y,z directions.
Multiplicative (geometric) sweep — same interface as __linear_sweep but steps by multiplication instead of addition. step is a factor (e.g. 1.2).
Matrix A times vector x multiplication Returns a vector
multiplies two NxN matricies
Parse a signed Miller index string (e.g., "001", "-110", "1-10") into a list of 3 integers.
Takes a 3x3 Tensor list and crystal rotation vector returns a rotated tensor
Same procedure but only outputs Diag
Takes a 3 length list and crystal rotation vector
Rotate a 4th order tensor (stored as 6x6 Voigt matrix) by angle psi around Z. Full contraction: T'_ijkl = a_im a_jn a_ko a_lp T_mnop
Recursively expand solution variable references in an expression string. Replaces solution names with their stored expressions until no more remain. mater: material name for material-specific solution lookup name: the solution variable to expand
Returns the 1D Density of states with integral function for a given temperature, effective mass and potential
Returns the 2D Density of states with integral function for a given temperature, effective mass and potential
Returns the transpose of matrix A
Build 3x3 rotation matrix: Rz(Z) * Ry(Y) * Rx(X)
Input: {X Y Z} angles in degrees
Returns 6x6 Bond matrix for Voigt tensor rotation
to do pod we need a set of solutions this procedure adds a solution as a function of bias
Add vectors
Effective (minimum) bandgap — for ni calculations At x<~0.85 the X-valley is lowest; above that, L takes over. We return a smooth minimum via Alagator ternary.
Gamma-valley (direct gap) — matters for optical transitions and direct tunneling
L-valley — dominant conduction band for Ge-rich alloys
X-valley (Delta minimum) — dominant conduction band for Si-rich alloys
Loop over energies from the bottom of the conduction band to the top of the valance band. Only produces values if the bands overlap fxn is a function that is called at every point in the loop with that energy dU is the energy step size mat is the material used
Build the LK 6-band k.p Hamiltonian, returning a list of 6 expression strings for aschro / kaschro. k_units: "m" (default) — broadcast k-parameters expected in 1/m. "cm" — broadcast k-parameters in 1/cm (matches the BEATS-3 KGrid convention; lifts free-k factors by ×1e2 per free k inside KKDiscretize).
Legacy (110) rotation — calls generic BuildHRot Rotates yz plane: ky→(ky-kz)/√2, kz→(ky+kz)/√2, kx unchanged Surface normal (0-11) along z, channel [100] along x
Build rotated LK Hamiltonian for arbitrary crystal orientation. miller: Miller index string, e.g., (001)<100>, (001)<1-10>, (x:001)<z:100> The Hamiltonian is built in the crystal frame then rotated to the device frame. k_units: see BuildH for unit-convention details.
only take a subset of modes with this proc for ramping purposes
Next we need to compute the POD modes, fit the data and build the alagator equations for each solution pde
Multiply complex numbers that are stored as two separate values
#+########################################################################## CubicSpline - returns the x,y coordinates of the cubic spline using xy control points. xy => {{x0 y0} {x1 y1} .... {xn yn}} XY points MUST BE SORTED by increasing x
#+##########################################################################
SolveTriDiag -- solves the linear system for tridiagoal NxN matrix A
using Gaussian elimination (no pivoting). Since A is sparse, we pass
in three diagonals:
sub(i) => a(i,i-1) diag(i) => a(i,i) sup(i) => a(i,i+1)
Result is returned in b[1:n]
# Full Density Gradient Correction:
Legacy DimMap — compatibility wrapper for ellipsoidal.tcl
Computes the direct tunneling energy using the effective mass approximation Takes an conduction band sub band energy Eci Conduction band effective mass Takes an valance band sub band energy Evi Valance band effective mass
set low field electron mobility via analytical expression from Farahmand for low field mobility
set low field electron mobility via analytical expression from Farahmand for low field mobility paramters for AlN for low field mobility from Farahmand
set low field electron mobility via analytical expression from Farahmand for low field mobility paramters for GaN for low field mobility from Farahmand
Build the 3x3 inverse mass tensor for an ellipsoidal valley
with longitudinal mass ml along direction {dx dy dz} and
transverse mass mt perpendicular.
Multi-valley FEQF via unified SiGe model. Requires the mesh region to be named "SiGe". For a "Germanium" region, use Germanium::EqnsLegacy.
Multi-valley FEQF via unified SiGe model. Requires the mesh region to be named "SiGe". For a "Silicon" region, use Silicon::EqnsLegacy.
Legacy single-valley Germanium equations with Hall tensor.
Legacy multi-valley equations with Si-specific strain polynomial coefficients. Call Silicon::EqnsLegacy T=Temp after FEQFDevicePackage in decks that need the fitted piezoresistance tensor and strain-dependent hole k.p model.
Single-valley GaN equations with Farahmand mobility and Caughey-Thomas velocity saturation. No satellite valley transfer. Simpler to converge, suitable for low-field or DC characterization.
set kp [GetKP $StressVector6 $StressRotation $CrystalRotation ]
set kp [GetKP $StressVector6 $StressRotation $CrystalRotation ]
takes a carrier vector returns a tensor 3x3 list
takes a mobility vector, carrier type returns a tensor 3x3 list
Get dU from the number of integration points that you want
This really doesn't work...
This really doesn't work...
takes a mobility vector returns a tensor 3x3 list
set hole mobility as constant
set hole mobility as constant
set hole mobility as constant
lastly we can make guesses using the POD equations for each solution
Quadratic interpolation with bowing parameter for alloy properties. Returns an Alagator expression: (1-x)*valA + x*valB - bow*x*(1-x) x can be a numeric constant or an Alagator field name.
Linear interpolation returning an Alagator expression. x can be a numeric constant or an Alagator field name.
Discretize ka*kb*s directly by index. a,b: 0=x, 1=y, 2=z. dim: number of discretized spatial dimensions. hasI: 1 if the original term had an i* prefix on the k-product. k_units: "m" (default, legacy) or "cm". "m": free (broadcast) k-parameters are expected in 1/m, matching the eV·m² C constants in Peqn/Qeqn/Reqn/Seqn directly. Confined directions get the existing 1e4 / 1e2 factors that lift the cm-meshed Grad/Vel back into m-units. "cm": broadcast k-parameters are in 1/cm (matches KGrid). Each free k contributes one extra ×1e2 so the C·k product still lands in eV.
linear interpolation of strain using the starting lattice constant and linearly interpolaring the change from the mole fraction
Compute the tunneling length in 1D all parameters are optional units are nm or um Econd_o is an offset value for the conduction band Eval is the name of the valance band Econd is the name of the conduction band
Discretize a single Hamiltonian term, optionally applying rotation R. Parses coeff*[i*]ki*kj*s patterns; strain/constant terms pass through. Returns a list of discretized terms (one for unrotated, up to 9 for rotated).
Masetti Mobility Model from Sentaurus, P at end of parameter is Phospherous, B at end of parameter is Boron See paper titled Electrical TCAD Simulations of a Germanium pMOSFET Technology
Masetti Mobility Model from Sentaurus, P at end of parameter is Phospherous, B at end of parameter is Boron
Aggregate electron DOS for ohmic contact calculations. Returns X-valley Nc, which is the dominant valley in Si-rich compositions and provides the correct contact boundary condition.
Gamma-valley electron DOS (1-fold degeneracy) Si: mGamma ≈ 0.036 (very light, high in the band structure) Ge: mGamma ≈ 0.041
L-valley electron DOS (4-fold degeneracy) Ge: ml=1.59, mt=0.0815 Si: L-valley masses ml=1.42, mt=0.13 Computed inline (same method as Germanium::Nc) to match endpoint exactly.
X-valley electron DOS (6-fold degeneracy) Si: ml=0.9161, mt=0.1905 → md = 6^(2/3)*(ml*mt^2)^(1/3) ≈ 1.084 Ge: X-valley masses ml=1.35, mt=0.29 → md = 6^(2/3)*(ml*mt^2)^(1/3) ≈ 1.42
Silicon Electron and Hole Poisson-Schrodinger loop with predictor corrector T is temperature, er is the oxide relative permittivity
Set polarization charge at a III-N heterointerface. Creates the 2DEG at AlGaN/GaN interfaces via fixed sheet charge. interface: the interface name (e.g., "AlGaN_GaN") charge: sheet charge density in cm^-2 (positive = donor-like)
The driving force, SRH, band gap, and thermal voltage are arguments This expression modifies an SRH like expression
Solve the sub bands along the [100] direction
Computes direct tunnel current using the Bigelow method Ec is the gamma electron sub band energies EVc is the gamma electron eigen vector base names mc is the gamma electron effective mass Evlh is the light hole sub band energies EVvlh is the light hole eigen vector base names mvlh is the light hole effective mass Evhh is the heavy hole sub band energies EVvhh is the heavy hole eigen vector base names mvhh is the heavy hole effective mass Eg is the direct band gap T is the temperature
Computes direct tunnel current using the Bigelow method assuming kp Ec is the gamma electron sub band energies EVc is the gamma electron eigen vector base names mc is the gamma electron effective mass Ev is the hole sub band energies EV is the hole eigen vector base names mv is the hole effective mass Eg is the direct band gap T is the temperature
Computes indirect tunneling transmission for a given conduction and valance band Ev is list of eigenvalues for the valance band EVv is the valance band eigenvector base name Ec is list of eigenvalues for the conduction band EVc is the conduction band eigenvector base name hw is the phonon energy Mat is the material name T is the temperature value or field N is the Number of integration points Returns units of inverse cm
Solve the Schrodinger equation for a set of ellipsoidal valleys.
Arguments:
Econd - band edge potential name (Alagator field)
ml - longitudinal effective mass (m0 units)
mt - transverse effective mass (m0 units)
directions - list of valley direction vectors, e.g., {{1 0 0} {0 1 0} {0 0 1}}
dotransport - compute transport mass if true
nev - number of eigenvalues
prefix - solution variable prefix (e.g., "EVX" or "EVL")
alpha - 3x3 crystal-to-device rotation matrix
L-valley solver: 4 valleys along <111> directions
X-valley solver: 6 valleys along <100> directions
Run a Galerkin POD-projected Newton solve using the per-variable bases stored in this namespace. Returns the iteration count. The caller is expected to have already set up an initial guess (e.g. via POD::Init) so the warm start lives in the column space of V.
Sort a tcl list of numbers low to high
SRH recombination
Thermal properties (temperature-dependent for GaN) k(T) = 2.6725 - 4.25e-3*T + 3.0e-6*T^2 W/cm·K c(T) = 1.395 + 5.14e-3*T - 3.67e-6*T^2 J/cm³·K
Transpose a tcl list that is holding numeric matrix data
Simple trapezoidal integration formula U is a list of evenly spaced values dU is the separation of the values
Goal is to use this function
VoxelVolumeTest — volume-integration regression check for voxel decks. Loops over the FieldServer's currently-meshed bulk materials, integrates each material's volume (`integrate eqn=Material($mat)`), and compares against a stored gold-value dict. Drift > `bound` percent on any single material fails the test. Platform-independent metric — replaces the old structure-to-structure CompareStruct gating in voxel test decks. Requires the deck to have called `meshvoxel` first (integrate operates on the tet mesh, not the voxel brick).