pynitride.physics.phonons module

class pynitride.physics.phonons.AcousticPhonon(solvmesh, rmesh, num_eigs, keepmesh=None, first_level=0, vecform='XYZ', deformation=True, piezo=False)

Bases: PhononModel

Superclass for acoustic phonons.

Parameters:

  • solvmesh – see PhononModel

  • rmesh – see PhononModel

  • keepmesh – see PhononModel

  • first_level – see PhononModel

  • vecform (str) – Format for the vecs, ‘XZ’, ‘XYZ’, or ‘Y’

  • deformation (bool) – whether to include deformation potential effects in matrix elements

  • piezo (bool) – whether to solve for the piezoelectric potential induced by the phonon and use it in matrix elements

I2(carrier, psii, psij, iq, thetaq, l)

The matrix element squared between two wavefunctions

See PhononModel.I2() for arguments and returns.

Note: if both piezo and deformation potentials are included, they are combined coherently (ie inside the squaring).

deformation

Whether to include deformation potential effects in matrix elements

piezo

Whether to solve for the piezoelectric potential induced by the phonon and use it in matrix elements

strain(iq, thetaq, l)

The strain profile

The strains returned are physicist strains, not engineering strains, eg \(e_{xy}=\frac{1}{2}\left(\partial_xu_y+\partial_yu_x\right)\)

Parameters:

  • iq (int) – index into the q array

  • thetaq – in-plane angle of the phonon propagation (from X toward Y)

  • l – which eigenvalue to use of those solved for

Returns:

a tuple of six MidFunctions (exx,exy,exz,eyy,eyz,ezz)

u(iq, thetaq, l)

The displacement profile

Parameters:

  • iq (int) – index into the q array

  • thetaq – in-plane angle of the phonon propagation (from X toward Y)

  • l – which eigenvalue to use of those solved for

Returns:

a tuple of three NodFunctions (ux,uy,uz)

vecform

Format for the vecs, ‘XZ’, ‘XYZ’, or ‘Y’

class pynitride.physics.phonons.DielectricContinuum_BulkWurtzite(solvmesh, rmesh, num_eigs, thickness, matname, keepmesh=None, first_level=0, pol='L')

Bases: OpticalPhonon

Solves the Dielectric Continuum model for the bulk phonon dispersion

Parameters:

  • solvmesh – mesh to solve on [ignored, but kept for compatibility with non-bulk signatures]

  • rmesh – the reciprocal mesh on which to solve

  • num_eigs – number of eigenvalues total to solve for

  • thickness – normalization thickness to use for the modes

  • matname – material name to look up for the parameters

  • keepmesh – mesh on which to produce the solution vectors

  • first_level – index of the first eigenvalue to solve for (if solving with this object, must be zero, but if this is just inheriting an RMesh from an already solved model, can be non-zero to pick out a different part of the spectrum)

  • pol – ‘L’ or ‘T’ to choose which branch to solve (nearly longitudinal or nearly transverse)

solve(just_energies=False, print_count=False, mode_iqs=None)
class pynitride.physics.phonons.DielectricContinuum_SWH(solvmesh, rmesh, num_spec_eigs, num_eigs=None, first_level=0, keepmesh=None)

Bases: OpticalPhonon

Solves for the extraordinary PO phonons in a Single Wurtzite Heterojunction.

See the Dielectric Continuum Binary Wurtzite Heterojunction model for the relevant mathematics.

Parameters:

  • solvmesh – The mesh to solve on, should contain one Wurtzite material block, which has two layers of uniform molefraction.

  • rmesh – The RMesh_1D which specifies the \(q\) points

  • num_spec_eigs – should be a dictionary indicating how many eigenvalues are desired for each mode type, ie mapping the names ‘TOl’,’TOIF’,’TOu’,’LOl’,’LOIF’,’LOu’ to integers. ‘l’,’IF’,’u’ refer to the lower-region confined, interface, and upper-region confined modes respectively

  • num_eigs – if specified, only this many contiguous eigenvalues will be used out of the modes specified by num_spec_eigs

  • first_level – can be used in combination with num_eigs to select which set of num_eigs eigenvalues will be used.

  • keepmesh – the mesh on which to actually store the solved phi

get_mode_by_name(name, num, iq=None)

Convenience function to pull particular modes from the phi array by name.

Parameters:

  • name (str) – name of the mode type, eg ‘TOu’ for the TO mode confined to the upper region

  • num – which of the modes solved for to return (indexed from 0 being the first solved-for mode of this type)

  • iq – if specified, will return only for the given \(q\) index (may be integer or slice)

Returns:

a tuple of the energy(ies), potential(s)

property rmesh
solve(just_energies=False, print_count=False, mode_iqs=None)

Actually solve for the modes.

w_IF(pol='T')

Finds the inteface resonant frequency.

Parameters:

pol – the polarization ‘T’ or ‘L’

Returns:

a tuple of the interface resonant frequency and +1/-1 indicating the mode is found above/below this frequency respectively

class pynitride.physics.phonons.ElasticContinuum(solvmesh, rmesh, num_eigs, keepmesh=None, vecform='XYZ', first_level=0, parallel=True, deformation=True, piezo=False, dirichelet_bottom=False)

Bases: AcousticPhonon

Note: this parallel is not the same as the one in solve()

solve(just_energies=False, parallel=True, print_count=True, mode_iqs=None, tasksize=600)
solve_one_q(q, iq=None, just_energies=False)
class pynitride.physics.phonons.ElasticContinuum_BulkWurtzite(solvmesh, rmesh, num_eigs, thickness, matname, keepmesh=None, first_level=0, vecform='XYZ', polXZ='all')

Bases: AcousticPhonon

Solves the Elastic Continuum model for the bulk phonon dispersion

Parameters:

  • solvmesh – mesh to solve on [ignored, but kept for compatibility with non-bulk signatures]

  • rmesh – the reciprocal mesh on which to solve

  • num_eigs – number of eigenvalues total to solve for

  • thickness – normalization thickness to use for the modes

  • matname – material name to look up for the parameters

  • keepmesh – mesh on which to produce the solution vectors

  • first_level – index of the first eigenvalue to solve for (if solving with this object, must be zero, but if this is just inheriting an RMesh from an already solved model, can be non-zero to pick out a different part of the spectrum)

  • vecform – see AcousticPhonon

  • polXZ – for XZ modes, can specify whether to include only ‘TA’ or only ‘LA’ or ‘all’

solve(just_energies=False, print_count=False, mode_iqs=None)

Solve the phonon problem, populating the energies and possibly vectors.

Parameters:

  • just_energies – whether to only solve the energies

  • print_count – (ignored)

  • mode_iqs – can limit the indices (into the rmesh) at which to solve

class pynitride.physics.phonons.OpticalPhonon(solvmesh, rmesh, num_eigs, keepmesh=None, first_level=0)

Bases: PhononModel

Superclass for all optical phonon models.

I2(carrier, psii, psij, iq, thetaq, l)

The matrix element squared between two wavefunctions

See PhononModel.I2() for arguments and returns.

Note:thetaq does not actually matter for optical phonons.

class pynitride.physics.phonons.PhononModel(solvmesh, rmesh, num_eigs, keepmesh=None, first_level=0)

Bases: object

Superclass for all phonon models.

Parameters:

  • solvmesh – the direct mesh on which to perform the phonon solve

  • rmesh – the 1-D reciprocal mesh on which to perform the phonon solve

  • num_eigs – the number of eigenvalues to solve for

  • keepmesh – the direct mesh on which phonon modes will actually be desired, eg for a scattering problem, just the region where the carriers are. This should be a submesh of solvmesh.

  • first_level – the index of the first eigenvalue which should be solved for.

I2(carrier, psii, psij, iq, thetaq, l)

The matrix element squared between two wavefunctions

Parameters:

  • psii – the two wavefunctions (as 2-D NodFunctions)

  • psij – the two wavefunctions (as 2-D NodFunctions)

  • iq (int) – index into the q array

  • thetaq – in-plane angle of the phonon propagation (from X toward Y)

  • l – which eigenvalue to use of those solved for

Returns:

the squared matrix element

en(iq=slice(None, None, None), l=None)

Returns the l-th energy at q-index iq.

Note: l is an absolute index, ie l should not be lower than first_level

first_level

The index of the first eigenvalue to solve for

interp_energy(absk, l, bounds_check=True)

Returns the interpolated energy at a point in reciprocal space

Parameters:

  • absk (float) – the point in reciprocal space

  • l (int) – the mode index (absolute)

  • bounds_check (bool) – whether to complain if absk is out of interpolation bounds

interp_radial_group_velocity(absk, l, bounds_check=True)

Returns the interpolated radial group velocity at a point in reciprocal space

Parameters:

  • absk (float) – the point in reciprocal space

  • l (int) – the mode index (absolute)

  • bounds_check (bool) – whether to complain if absk is out of interpolation bounds

num_eigs

The number of eigenvalues to solve for

phi(iq=slice(None, None, None), l=slice(None, None, None))

Returns the l-th potential at q-index iq.

Note: l is an absolute index, ie l should not be lower than first_level

property q

The q values of the self.rmesh.

read(name, just_energies=False)

Reads the phonon solve from a file.

If reading mode vectors and/or potentials, checks the dimensions. If dimensions are incorrect, any new keys in rmesh will be cleared away and then an error will be raised.

Parameters:

  • filename (str) – the file to save to

  • just_energies (bool) – if True, read only the energies, otherwise read energies, mode vecs and/or potentials.

property rmesh

The reciprocal mesh on which to solve

save(filename, just_energies=False)

Saves the phonon solve to a file.

Parameters:

  • filename (str) – the file to save to

  • just_energies (bool) – if True, save only the energies, otherwise save energies, mode vecs and/or potentials.

solve(mode_iqs=None)
vecs(iq=slice(None, None, None), l=None)

Returns the l-th mode vector at q-index iq.

Note: l is an absolute index, ie l should not be lower than first_level

class pynitride.physics.phonons.PiezoPotential(pm, parallel=True)

Bases: object

Helper for ElasticContinuum to calculate the piezo potential`

Parameters:

  • pm – the ElasticContinuum model this calculator will help

  • parallel – whether to spawn parallel processes

property q
property rmesh
solve_one_q(q, iq, vec)

Solve the piezo potential at one q

Parameters:

  • q – the wavevector

  • iq – if supplied, use this iq to determine the q, and use precalculated FEM matrices

  • vec – the elastic continuum solution

Returns:

the electric potential function for this mode