ThresholdSearch2D

<meta solver="ThresholdSearch2D">

Corresponding Python class: meta.shockley.ThresholdSearch2D.

Solver for threshold search of semiconductor laser in 2D Cartesian geometry.

This solver performs thermo-electrical computations followed by determination ot threshold current and optical analysis in order to determine the threshold of a semiconductor laser. The search is performed by scipy root finding algorithm in order to determine the voltage and electric current ensuring no optical loss in the laser cavity.

The optical computations are done with effective index method.

Attributes:

  • name (required) – Solver name.

Contents:
<geometry>

Geometry settings for all solvers.

Attributes:

  • thermal (required) – Geometry used by the thermal solver. (Cartesian2D geometry)

  • electrical (required) – Geometry used by the electrical, diffusion, and gain solvers. (Cartesian2D geometry)

  • optical (required) – Geometry used by the optical solver. (Cartesian2D geometry)

<mesh>

Mesh settings for all solvers.

Attributes:

  • thermal (required) – Mesh used by the thermal solver. (mesh)

  • electrical (required) – Mesh used by the electrical solver. (mesh)

  • diffusion – Mesh used by the carriers diffusion solver. (mesh)

  • optical – Mesh used by the optical solver. (mesh)

  • empty-elements – Should empty regions (e.g. air) be included into electrical computations? (default, include, or exclude, default is default)

<optical>

Configuration of the optical solver

Attributes:

  • polarization – Mode polarization. (TE or TM, default is TE)

  • mn – Lateral mode number (int, default 0)

  • lam (required) – Emission wavelength. The effective index is searched for this wavelength. (float (nm))

  • dneff – Step, by which the effective index is swept while searching for the approximate mode. (float, default 0.02)

  • vneff – “Vertical effective index” i.e. the effective index what would be in the absence of lateral confinement; setting this value helps to find modes in very long resonators. (float)

  • vat – Horizontal position of at which the vertical part of the field is calculated. (float (µm))

  • emission – Direction of the useful light emission. Necessary for the over-threshold model to correctly compute the output power. (front or back, default is front)

<root>

Configuration of the root-finder used in threshold search.

Attributes:

  • bcond (required) – Number of the voltage boundary condition to vary during the threshold search. (int)

  • vmin – Minimum voltage to search threshold for. It should be below the threshold. (float)

  • vmax – Maximum voltage to search threshold for. It should be above the threshold. (float)

  • vtol – Tolerance on voltage in the root search. (float (V), default 1e-05 V)

  • maxiter – Maximum number of root finding iterations. (int, default 50)

<voltage>

Voltage boundary conditions. See subsection Boundary conditions.

<temperature>

Temperature boundary conditions. See subsection Boundary conditions.

<heatflux>

Heat Flux boundary conditions. See subsection Boundary conditions.

<convection>

Convective boundary conditions. See subsection Boundary conditions.

This boundary condition does not have value attribute. Use coeff for convection coefficient and ambient for ambient temperature instead.

<radiation>

Radiative boundary conditions. See subsection Boundary conditions.

This boundary condition does not have value attribute. Use emissivity for surface emissivity and ambient for ambient temperature instead.

<junction>

Configuration of the effective model of p-n junction.

Attributes:

  • beta# – Junction coefficients. This is an inverse of the junction thermal voltage. (float (1/V))

  • js# – Reverse bias current densities. (float (A/m2))

  • pnjcond – Initial vertical conductivity of the junctions. (float (S/m), default 5.0 S/m)

<contacts>

Properties of the contact layers.

Attributes:

  • pcond – p-contact conductivity. (float (S/m), default 5.0 S/m)

  • ncond – n-contact conductivity. (float (S/m), default 50.0 S/m)

<loop>

Configuration of the self-consistent thermo-electric loop.

Attributes:

  • skip-thermal – Skip thermal computations. The structure is assumed to have a constant temperature inittemp. This can be used to look for the threshold under pulse laser operation. (bool, default is no)

  • tfreq – Number of electrical iterations per single thermal step. As temperature tends to converge faster, it is reasonable to repeat thermal solution less frequently. (int, default 6)

  • inittemp – Initial temperature used for the first computation. (float (K), default 300 K)

  • maxterr – Maximum allowed temperature error. (float (K), default 0.05 K)

  • maxcerr – Maximum allowed current density error. (float (%), default 0.05 %)

<tmatrix>

Matrix configuration for the thermal solver.

Attributes:

  • algorithm – Algorithm used for solving set of linear positive-definite equations. (cholesky, gauss, or iterative, default is cholesky)

<iterative>

Parameters for iterative matrix solver. PLaSK uses NSPCG package for performing iterations. Please refer to its documentation for explanation of most of the settings.

Attributes:

  • maxit – Maximum number of iterations. (int, default 1000)

  • maxerr – Maximum iteration error. (float, default 1e-6)

  • noconv – Desired behavior if the iterative solver does not converge. (error, warning, or continue, default is warning)

  • accelerator – Accelerator used for iterative matrix solver. (cg, si, sor, srcg, srsi, basic, me, cgnr, lsqr, odir, omin, ores, iom, gmres, usymlq, usymqr, landir, lanmin, lanres, cgcr, or bcgs, default is cg)

  • preconditioner – Preconditioner used for iterative matrix solver. (rich, jac, ljac, ljacx, sor, ssor, ic, mic, lsp, neu, lsor, lssor, llsp, lneu, bic, bicx, mbic, or mbicx, default is ic)

  • nfact – This number initializes the frequency of partial factorizations. It specifies the number of linear system evaluations between factorizations. The default value is 1, which means that a factorization is performed at every iteration. (int, default 10)

  • ndeg – Degree of the polynomial to be used for the polynomial preconditioners. (int, default 1)

  • lvfill – Level of fill-in for incomplete Cholesky preconditioners. Increasing this value will result in more accurate factorizations at the expense of increased memory usage and factorization time. (int, default 0)

  • ltrunc – Truncation bandwidth to be used when approximating the inverses of matrices with dense banded matrices. An increase in this value means a more accurate factorization at the expense of increased storage. (int, default 0)

  • omega – Relaxation parameter. (float, default 1.0)

  • nsave – The number of old vectors to be saved for the truncated acceleration methods. (int, default 5)

  • nrestart – The number of iterations between restarts for the restarted acceleration methods. (int, default 100000)

Preconditioner choices:

rich

Richardson’s method

jac

Jacobi method

ljac

Line Jacobi method

ljacx

Line Jacobi method (approx. inverse)

sor

Successive Overrelaxation

ssor

Symmetric SOR (can be used only with SOR accelerator)

ic

Incomplete Cholesky (default)

mic

Modified Incomplete Cholesky

lsp

Least Squares Polynomial

neu

Neumann Polynomial

lsor

Line SOR

lssor

Line SSOR

llsp

Line Least Squares Polynomial

lneu

Line Neumann Polynomial

bic

Block Incomplete Cholesky (ver. 1)

bicx

Block Incomplete Cholesky (ver. 2)

mbic

Modified Block Incomplete Cholesky (ver. 1)

mbicx

Modified Block Incomplete Cholesky (ver. 2)
Accelerator choices:

cg

Conjugate Gradient acceleration (default)

si

Chebyshev acceleration or Semi-Iteration

sor

Successive Overrelaxation (can use only SOR preconditioner)

srcg

Symmetric Successive Overrelaxation Conjugate Gradient Algorithm (can use only SSOR preconditioner)

srsi

Symmetric Successive Overrelaxation Semi-Iteration Algorithm (can use only SSOR preconditioner)

basic

Basic Iterative Method

me

Minimal Error Algorithm

cgnr

Conjugate Gradient applied to the Normal Equations

lsqr

Least Squares Algorithm

odir

ORTHODIR, a truncated/restarted method useful for nonsymmetric systems of equations

omin

ORTHOMIN, a common truncated/restarted method used for nonsymmetric systems

ores

ORTHORES, another truncated/restarted method for nonsymmetric systems

iom

Incomplete Orthogonalization Method

gmres

Generalized Minimal Residual Method

usymlq

Unsymmetric LQ

usymqr

Unsymmetric QR

landir

Lanczos/ORTHODIR

lanmin

Lanczos/ORTHOMIN or Biconjugate Gradient Method

lanres

Lanczos/ORTHORES or “two-sided” Lanczos Method

cgcr

Constrained Generalized Conjugate Residual Method

bcgs

Biconjugate Gradient Squared Method
<ematrix>

Matrix configuration for the electrical solver.

Attributes:

  • algorithm – Algorithm used for solving set of linear positive-definite equations. (cholesky, gauss, or iterative, default is cholesky)

<iterative>

Parameters for iterative matrix solver. PLaSK uses NSPCG package for performing iterations. Please refer to its documentation for explanation of most of the settings.

Attributes:

  • maxit – Maximum number of iterations. (int, default 1000)

  • maxerr – Maximum iteration error. (float, default 1e-6)

  • noconv – Desired behavior if the iterative solver does not converge. (error, warning, or continue, default is warning)

  • accelerator – Accelerator used for iterative matrix solver. (cg, si, sor, srcg, srsi, basic, me, cgnr, lsqr, odir, omin, ores, iom, gmres, usymlq, usymqr, landir, lanmin, lanres, cgcr, or bcgs, default is cg)

  • preconditioner – Preconditioner used for iterative matrix solver. (rich, jac, ljac, ljacx, sor, ssor, ic, mic, lsp, neu, lsor, lssor, llsp, lneu, bic, bicx, mbic, or mbicx, default is ic)

  • nfact – This number initializes the frequency of partial factorizations. It specifies the number of linear system evaluations between factorizations. The default value is 1, which means that a factorization is performed at every iteration. (int, default 10)

  • ndeg – Degree of the polynomial to be used for the polynomial preconditioners. (int, default 1)

  • lvfill – Level of fill-in for incomplete Cholesky preconditioners. Increasing this value will result in more accurate factorizations at the expense of increased memory usage and factorization time. (int, default 0)

  • ltrunc – Truncation bandwidth to be used when approximating the inverses of matrices with dense banded matrices. An increase in this value means a more accurate factorization at the expense of increased storage. (int, default 0)

  • omega – Relaxation parameter. (float, default 1.0)

  • nsave – The number of old vectors to be saved for the truncated acceleration methods. (int, default 5)

  • nrestart – The number of iterations between restarts for the restarted acceleration methods. (int, default 100000)

Preconditioner choices:

rich

Richardson’s method

jac

Jacobi method

ljac

Line Jacobi method

ljacx

Line Jacobi method (approx. inverse)

sor

Successive Overrelaxation

ssor

Symmetric SOR (can be used only with SOR accelerator)

ic

Incomplete Cholesky (default)

mic

Modified Incomplete Cholesky

lsp

Least Squares Polynomial

neu

Neumann Polynomial

lsor

Line SOR

lssor

Line SSOR

llsp

Line Least Squares Polynomial

lneu

Line Neumann Polynomial

bic

Block Incomplete Cholesky (ver. 1)

bicx

Block Incomplete Cholesky (ver. 2)

mbic

Modified Block Incomplete Cholesky (ver. 1)

mbicx

Modified Block Incomplete Cholesky (ver. 2)
Accelerator choices:

cg

Conjugate Gradient acceleration (default)

si

Chebyshev acceleration or Semi-Iteration

sor

Successive Overrelaxation (can use only SOR preconditioner)

srcg

Symmetric Successive Overrelaxation Conjugate Gradient Algorithm (can use only SSOR preconditioner)

srsi

Symmetric Successive Overrelaxation Semi-Iteration Algorithm (can use only SSOR preconditioner)

basic

Basic Iterative Method

me

Minimal Error Algorithm

cgnr

Conjugate Gradient applied to the Normal Equations

lsqr

Least Squares Algorithm

odir

ORTHODIR, a truncated/restarted method useful for nonsymmetric systems of equations

omin

ORTHOMIN, a common truncated/restarted method used for nonsymmetric systems

ores

ORTHORES, another truncated/restarted method for nonsymmetric systems

iom

Incomplete Orthogonalization Method

gmres

Generalized Minimal Residual Method

usymlq

Unsymmetric LQ

usymqr

Unsymmetric QR

landir

Lanczos/ORTHODIR

lanmin

Lanczos/ORTHOMIN or Biconjugate Gradient Method

lanres

Lanczos/ORTHORES or “two-sided” Lanczos Method

cgcr

Constrained Generalized Conjugate Residual Method

bcgs

Biconjugate Gradient Squared Method
<diffusion>

Diffusion solver configuration.

Attributes:

  • fem-method – Order of the finite-element method. (linear or parabolic, default is parabolic)

  • accuracy – Required relative accuracy. (float (%), default 0.01 %)

  • abs-accuracy – Required absolute minimal concentration accuracy. (float (cm-3), default 5000000000000000.0 cm-3)

  • maxiters – Maximum number of allowed iterations before attempting to refine mesh. (int, default 20)

  • maxrefines – Maximum number of allowed mesh refinements. (int, default 5)

  • interpolation – Current density interpolation method name. (linear or spline, default is spline)

<gain>

Gain solver parameters.

Attributes:

  • lifetime – Average carriers lifetime. This parameter is used for gain spectrum broadening. (float (ps), default 0.1 ps)

  • matrix-elem – Value of the squared matrix element in gain computations. If it is not set it is estimated automatically. (float (eV×m0))

  • strained – Boolean attribute indicating if the solver should consider strain in the active region. If set to yes then there must a layer with the role “substrate“ in the geometry. The strain is computed by comparing the atomic lattice constants of the substrate and the quantum wells. (bool, default is no)

<optical-root>

Parameters of the horizontal root-finding algorithm.

Attributes:

  • method – Root finding algorithm. (muller, broyden, or brent, default is muller)

  • tolx – Maximum change of the effective frequency parameter which is allowed for convergent solution. (float, default 1e-06)

  • tolf-min – Minimum value of the determinant sufficient to assume convergence. (float, default 1e-07)

  • tolf-max – Maximum value of the determinant required to assume convergence. (float, default 2e-05)

  • maxstep – Maximum step in one iteration of root finding. Significant for the Broyden’s method only. (float, default 0.1)

  • maxiter – Maximum number of root finding iterations. (int, default 500)

  • alpha – Parameter ensuring sufficient decrease of determinant in each step (Broyden method only). (float, default 1e-07)

  • lambda – Minimum decrease ratio of one step (Broyden method only). (float, default 1e-08)

  • initial-range – Initial range size (Muller method only). (complex, default 0.001)

<optical-stripe-root>

Parameters of root-finding algorithm for one stripe.

Attributes:

  • method – Root finding algorithm. (muller, broyden, or brent, default is muller)

  • tolx – Maximum change of the effective frequency parameter which is allowed for convergent solution. (float, default 1e-06)

  • tolf-min – Minimum value of the determinant sufficient to assume convergence. (float, default 1e-07)

  • tolf-max – Maximum value of the determinant required to assume convergence. (float, default 1e-05)

  • maxstep – Maximum step in one iteration of root finding. Significant for the Broyden’s method only. (float, default 0.1)

  • maxiter – Maximum number of root finding iterations. (int, default 500)

  • alpha – Parameter ensuring sufficient decrease of determinant in each step (Broyden method only). (float, default 1e-07)

  • lambda – Minimum decrease ratio of one step (Broyden method only). (float, default 1e-08)

  • initial-range – Initial range size (Muller method only). (complex, default 0.001)

<output>

Settings for the solver output.

Attributes:

  • optical-res-x – Number of points along the horizontal axis for the saved and plotted optical field. (int, default 800)

  • optical-res-y – Number of points along the vertical axis for the saved and plotted optical field. (int, default 600)