public override SpinResolved_Data Get_ChargeDensity_Deriv(ILayer[] layers, SpinResolved_Data carrier_density_deriv, SpinResolved_Data dopent_density_deriv, Band_Data chem_pot)
{
for (int i = 0; i < nz; i++)
{
double z = dz * i + zmin;
// get the relevant layer and if it's frozen out, don't recalculate the dopent charge
ILayer current_Layer = Solver_Bases.Geometry.Geom_Tool.GetLayer(layers, z);
ZeroD_Density charge_calc = new ZeroD_Density(current_Layer, temperature);
if (!current_Layer.Dopents_Frozen_Out(temperature))
{
double local_dopent_density_deriv = charge_calc.Get_DopentDensityDeriv(chem_pot.vec[i]);
dopent_density_deriv.Spin_Up.vec[i] = 0.5 * local_dopent_density_deriv;
dopent_density_deriv.Spin_Down.vec[i] = 0.5 * local_dopent_density_deriv;
}
else
{
dopent_density_deriv.Spin_Up.vec[i] = 0.0;
dopent_density_deriv.Spin_Down.vec[i] = 0.0;
}
carrier_density_deriv.Spin_Up.vec[i] = 0.5 * charge_calc.Get_CarrierDensityDeriv(chem_pot.vec[i]);
carrier_density_deriv.Spin_Down.vec[i] = 0.5 * charge_calc.Get_CarrierDensityDeriv(chem_pot.vec[i]);
}
return carrier_density_deriv + dopent_density_deriv;
}
public Band_Data Get_XC_Potential(SpinResolved_Data charge_density)
{
Band_Data result;
Band_Data charge_dens_spin_summed = charge_density.Spin_Summed_Data;
int dim = charge_dens_spin_summed.Dimension;
if (dim == 1)
{
int nx = charge_dens_spin_summed.vec.Length;
result = new Band_Data(nx, 0.0);
for (int i = 0; i < nx; i++)
{
result.vec[i] = Get_XC_Potential(charge_dens_spin_summed.vec[i]);
}
return(result);
}
else if (dim == 2)
{
int nx = charge_dens_spin_summed.mat.Rows;
int ny = charge_dens_spin_summed.mat.Cols;
result = new Band_Data(nx, ny, 0.0);
for (int i = 0; i < nx; i++)
{
for (int j = 0; j < ny; j++)
{
result.mat[i, j] = Get_XC_Potential(charge_dens_spin_summed.mat[i, j]);
}
}
return(result);
}
else if (dim == 3)
{
int nx = charge_dens_spin_summed.vol[0].Rows;
int ny = charge_dens_spin_summed.vol[0].Cols;
int nz = charge_dens_spin_summed.vol.Length;
result = new Band_Data(nx, ny, nz, 0.0);
for (int k = 0; k < nz; k++)
{
for (int i = 0; i < nx; i++)
{
for (int j = 0; j < ny; j++)
{
result.vol[k][i, j] = Get_XC_Potential(charge_dens_spin_summed.vol[k][i, j]);
}
}
}
return(result);
}
else
{
throw new NotImplementedException();
}
}
public Band_Data DFT_diff(SpinResolved_Data car_dens)
{
if (alpha_dft == 0.0)
{
return(0.0 * dft_pot);
}
else
{
return(dft_pot - Get_XC_Potential(car_dens));
}
}
void Print_VP(Band_Data band_energy, Band_Data x, SpinResolved_Data car_dens, SpinResolved_Data dop_dens, IPoisson_Solve pois_solv, IDensity_Solve dens_solv)
{
StreamWriter sw = new StreamWriter("vp");
int count_max = 100;
double dt = 0.01;
for (int i = 0; i < count_max; i++)
{
sw.WriteLine(calc_vp(i * dt, band_energy, x, car_dens, dop_dens, pois_solv, dens_solv).ToString());
}
sw.Close();
}
public void Update_DFT_Potential(SpinResolved_Data car_dens)
{
if (this.dft_pot == null && alpha_dft != 0.0)
{
this.dft_pot = Get_XC_Potential(car_dens);
}
else if (alpha_dft == 0.0)
{
this.dft_pot = 0.0 * car_dens.Spin_Summed_Data.DeepenThisCopy();
}
else
{
this.dft_pot = (1.0 - alpha_dft) * dft_pot + alpha_dft * Get_XC_Potential(car_dens);
}
}
protected virtual double calc_vp(double t, Band_Data phi, Band_Data x, SpinResolved_Data car_dens, SpinResolved_Data dop_dens, IPoisson_Solve pois_solv, IDensity_Solve dens_solv)
{
double vp;
SpinResolved_Data tmp_dens = dens_solv.Get_ChargeDensity(layers, car_dens, dop_dens, Physics_Base.q_e * (phi + t * x));
Band_Data V_Prime = -1.0 * (phi.Laplacian + t * x.Laplacian) - tmp_dens.Spin_Summed_Data;
vp = 0.0;
for (int i = 0; i < x.Length; i++)
{
vp += V_Prime[i] * x[i];
}
// multiply by volume element (this works in all dimensions as default dx, dy, dz are 1.0)
return(vp * dx_dens * dy_dens * dz_dens);
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data density, Band_Data chem_pot)
{
// send data to client
NetworkComms.SendObject("layers", clientIP, clientPort, layers);
NetworkComms.SendObject("density", clientIP, clientPort, density);
NetworkComms.SendObject("chem_pot", clientIP, clientPort, chem_pot);
// Call the save_density routine
//NetworkComms.AppendGlobalIncomingPacketHandler<SpinResolved_Data>("new_density", Save_Density);
//Start listening for incoming connections
TCPConnection.StartListening(true);
//Print out the IPs and ports we are now listening on
Console.WriteLine("Server listening for TCP connection on:");
foreach (System.Net.IPEndPoint localEndPoint in TCPConnection.ExistingLocalListenEndPoints()) Console.WriteLine("{0}:{1}", localEndPoint.Address, localEndPoint.Port);
throw new NotImplementedException();
}
public void Output(SpinResolved_Data data, string filename, bool with_warnings)
{
StreamWriter sw = new StreamWriter(filename);
if (with_warnings)
{
sw.WriteLine("Warning - The data has been written out serially and there is no information as to which order the dimensions come in.");
sw.WriteLine("Warning - Ordering compared to Band_Data objects is not guaranteed!");
}
// output the charge density
Band_Data tot_charge = data.Spin_Summed_Data;
for (int i = 0; i < tot_charge.Length; i++)
{
sw.WriteLine(tot_charge[i].ToString());
}
sw.Close();
}
public Band_Data Get_XC_Potential_Deriv(SpinResolved_Data charge_density)
{
Band_Data result;
Band_Data charge_dens_spin_summed = charge_density.Spin_Summed_Data;
int dim = charge_dens_spin_summed.Dimension;
if (dim == 1)
{
int nx = charge_dens_spin_summed.vec.Length;
result = new Band_Data(new DoubleVector(nx));
for (int i = 0; i < nx; i++)
{
result.vec[i] = Get_XC_Potential_Deriv(charge_dens_spin_summed.vec[i]);
}
return(result);
}
else if (dim == 2)
{
int nx = charge_dens_spin_summed.mat.Rows;
int ny = charge_dens_spin_summed.mat.Cols;
result = new Band_Data(new DoubleMatrix(nx, ny));
for (int i = 0; i < nx; i++)
{
for (int j = 0; j < ny; j++)
{
result.mat[i, j] = Get_XC_Potential_Deriv(charge_dens_spin_summed.mat[i, j]);
}
}
return(result);
}
else if (dim == 3)
{
throw new NotImplementedException();
}
else
{
throw new NotImplementedException();
}
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
double[,] xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
double beta = 1.0 / (Physics_Base.kB * temperature);
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density.Spin_Up.vol[k][i, j] *= g_2d * Math.Log(1.0 + Math.Exp(-1.0 * beta * xy_energy[i, j])) / beta;
charge_density.Spin_Down.vol[k][i, j] *= g_2d * Math.Log(1.0 + Math.Exp(-1.0 * beta * xy_energy[i, j])) / beta;
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data density, Band_Data chem_pot)
{
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
double x = dx * i + xmin;
double y = dy * j + ymin;
double z = dz * k + zmin;
// get the relevant layer
ILayer current_Layer = Solver_Bases.Geometry.Geom_Tool.GetLayer(layers, x, y, z);
// calculate the density at the given point
ZeroD_Density charge_calc = new ZeroD_Density(current_Layer, temperature);
double local_charge_density = charge_calc.Get_CarrierDensity(chem_pot.vol[k][i, j]);
// as there is no spin dependence in this problem yet, just divide the charge into spin-up and spin-down components equally
density.Spin_Down.vol[k][i, j] = 0.5 * local_charge_density;
density.Spin_Up.vol[k][i, j] = 0.5 * local_charge_density;
}
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data density, Band_Data chem_pot)
{
// send data to client
NetworkComms.SendObject("layers", clientIP, clientPort, layers);
NetworkComms.SendObject("density", clientIP, clientPort, density);
NetworkComms.SendObject("chem_pot", clientIP, clientPort, chem_pot);
// Call the save_density routine
//NetworkComms.AppendGlobalIncomingPacketHandler<SpinResolved_Data>("new_density", Save_Density);
//Start listening for incoming connections
TCPConnection.StartListening(true);
//Print out the IPs and ports we are now listening on
Console.WriteLine("Server listening for TCP connection on:");
foreach (System.Net.IPEndPoint localEndPoint in TCPConnection.ExistingLocalListenEndPoints())
{
Console.WriteLine("{0}:{1}", localEndPoint.Address, localEndPoint.Port);
}
throw new NotImplementedException();
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data carrier_density, ref SpinResolved_Data dopent_density, Band_Data chem_pot)
{
Band_Data car_dens_spin_summed = carrier_density.Spin_Summed_Data;
Band_Data dop_dens_spin_summed = dopent_density.Spin_Summed_Data;
for (int i = 0; i < nz; i++)
{
double z = dz * i + zmin;
double local_dopent_density;
double local_carrier_density = car_dens_spin_summed.vec[i];
// get the relevant layer and if it's frozen out, don't recalculate the charge
ILayer current_Layer = Solver_Bases.Geometry.Geom_Tool.GetLayer(layers, z);
// calculate the density at the given point
ZeroD_Density charge_calc = new ZeroD_Density(current_Layer, temperature);
if (!current_Layer.Dopents_Frozen_Out(temperature))
{
local_dopent_density = charge_calc.Get_DopentDensity(chem_pot.vec[i]);
local_carrier_density = charge_calc.Get_CarrierDensity(chem_pot.vec[i]);
}
else
{
// if the density is frozen out, on the first step, this will add the carrier density to the dopent density
// to give a total, frozen-out charge. After that, the local carrier density is set to zero and so this value
// should not change
local_dopent_density = dop_dens_spin_summed.vec[i];
local_carrier_density = charge_calc.Get_CarrierDensity(chem_pot.vec[i]);
}
// as there is no spin dependence in this problem yet, just divide the charge into spin-up and spin-down components equally
dopent_density.Spin_Down.vec[i] = 0.5 * local_dopent_density;
dopent_density.Spin_Up.vec[i] = 0.5 * local_dopent_density;
carrier_density.Spin_Down.vec[i] = 0.5 * local_carrier_density;
carrier_density.Spin_Up.vec[i] = 0.5 * local_carrier_density;
}
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
DoubleHermitianEigDecomp eig_decomp = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
double[] dens_x = new double[nx];
// and generate a density for the y-direction
for (int i = 0; i < nx; i++)
for (int k = 0; k < max_wavefunction; k++)
dens_x[i] += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i]) * Get_OneD_DoS(energies[k], no_kb_T);
// multiply the z-densities by the y-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
{
charge_density.Spin_Up.mat[i, j] *= 0.0;
charge_density.Spin_Down.mat[i, j] *= 0.0;
}
charge_density.Spin_Up.mat[i, j] *= dens_x[i];
charge_density.Spin_Down.mat[i, j] *= dens_x[i];
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data density, Band_Data chem_pot)
{
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
continue;
double x = dx * i + xmin;
double y = dy * j + ymin;
// get the relevant layer
ILayer current_Layer = Solver_Bases.Geometry.Geom_Tool.GetLayer(layers, plane, x, y, pos_z);
// calculate the density at the given point
ZeroD_Density charge_calc = new ZeroD_Density(current_Layer, temperature);
double local_charge_density = charge_calc.Get_CarrierDensity(chem_pot.mat[i, j]);
// as there is no spin dependence in this problem yet, just divide the charge into spin-up and spin-down components equally
density.Spin_Down.mat[i, j] = 0.5 * local_charge_density;
density.Spin_Up.mat[i, j] = 0.5 * local_charge_density;
}
}
protected override void Initialise_DataClasses(Dictionary<string, object> input_dict)
{
if (initialise_from_restart)
{
// initialise data classes for the density and chemical potential
this.carrier_charge_density = new SpinResolved_Data(nz_dens);
this.dopent_charge_density = new SpinResolved_Data(nz_dens);
this.chem_pot = new Band_Data(nz_dens, 0.0);
Initialise_from_Restart(input_dict);
// and instantiate their derivatives
carrier_charge_density_deriv = new SpinResolved_Data(nz_dens);
dopent_charge_density_deriv = new SpinResolved_Data(nz_dens);
chem_pot.Laplacian = pois_solv.Calculate_Phi_Laplacian(chem_pot);
return;
}
else if (hot_start)
{
Initialise_from_Hot_Start(input_dict);
}
// try to get and the carrier and dopent density from the dictionary... they probably won't be there and if not... make them
if (input_dict.ContainsKey("Carrier_Density")) this.carrier_charge_density = (SpinResolved_Data)input_dict["Carrier_Density"];
else this.carrier_charge_density = new SpinResolved_Data(nz_pot);
if (input_dict.ContainsKey("Dopent_Density")) this.dopent_charge_density = (SpinResolved_Data)input_dict["Dopent_Density"];
else this.dopent_charge_density = new SpinResolved_Data(nz_pot);
// and instantiate their derivatives
carrier_charge_density_deriv = new SpinResolved_Data(nz_pot);
dopent_charge_density_deriv = new SpinResolved_Data(nz_pot);
// and finally, try to get the chemical potential from the dictionary...
if (input_dict.ContainsKey("Chemical_Potential")) this.chem_pot = (Band_Data)input_dict["Chemical_Potential"];
}
public void Write_Out_Density(SpinResolved_Data h, string outfile)
{
Band_Data h_spin_summed = h.Spin_Summed_Data;
System.IO.StreamWriter sw = new System.IO.StreamWriter(outfile);
for (int i = 0; i < h_spin_summed.mat.Cols; i++)
for (int j = 0; j < h_spin_summed.mat.Rows; j++)
{
sw.Write(h_spin_summed.mat[j, i].ToString() + '\t');
if (j == h_spin_summed.mat.Rows - 1)
sw.WriteLine();
}
sw.Close();
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data g_phi)
{
DoubleTriDiagMatrix lap_mat = -1.0 * Generate_Laplacian(exp.Layers);
Band_Data rho_prime_spin_summed = rho_prime.Spin_Summed_Data;
// check that lap_mat and rho_prime have the same dimension
if (rho_prime_spin_summed.Length != lap_mat.Rows)
throw new Exception("Error - the Laplacian generated by pois_solv has a different order to rho_prime!");
for (int i = 0; i < rho_prime_spin_summed.Length; i++)
lap_mat[i, i] -= rho_prime_spin_summed.vec[i];
DoubleTriDiagFact lu_newt_step = new DoubleTriDiagFact(lap_mat);
// calculate newton step and its laplacian
Band_Data result = new Band_Data(lu_newt_step.Solve(-1.0 * g_phi.vec));
result.Laplacian = Calculate_Phi_Laplacian(result);
return result;
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi)
{
Save_Data(gphi, gphi_filename);
Save_Data(rho_prime.Spin_Summed_Data, densderiv_filename);
Create_NewtonStep_File(top_length, split_width, split_length, flexpde_script, T);
return Get_Data_From_External(newton_location, flexpde_options, newton_result_filename);
}
public void Update_DFT_Potential(SpinResolved_Data car_dens)
{
// set the dft potential for the electrons and holes separately
// NOTE!!!!! V_xc is set using the total carrier density so its value includes the density due to electrons
// this is a bug, but shouldn't be a problem as there should be no chance of getting holes where there are electrons and vice versa
electron_dens_calc.Update_DFT_Potential(car_dens);
hole_dens_calc.Update_DFT_Potential(car_dens);
}
public void Output(SpinResolved_Data data, string filename)
{
throw new NotImplementedException();
}
/// <summary>
/// calculates an optimal t based on bisection
/// </summary>
/// <param name="t"></param>
/// <param name="phi"></param>
/// <param name="x"></param>
/// <param name="car_dens"></param>
/// <param name="dop_dens"></param>
/// <param name="pois_solv"></param>
/// <param name="dens_solv"></param>
/// <returns></returns>
protected double Calculate_optimal_t(double t, Band_Data phi, Band_Data x, SpinResolved_Data car_dens, SpinResolved_Data dop_dens, IPoisson_Solve pois_solv, IDensity_Solve dens_solv, double minval)
{
double maxval = 3.0;
SpinResolved_Data car_dens_copy = car_dens.DeepenThisCopy();
SpinResolved_Data dop_dens_copy = dop_dens.DeepenThisCopy();
double vpa = calc_vp(t, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv);
double vpb = calc_vp(div_fact * t, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv);
double t_orig = t;
// work out whether this is going in the right direction (assuming vp is monotonic)
if (Math.Abs(vpb) < Math.Abs(vpa))
{
// if 0.5 * t was going downhill, first, halve t seeing as you've already done this step
t = div_fact * t;
// then halve the damping parameter and check whether you've found a root yet
while (Math.Sign(vpb) == Math.Sign(vpa))
{
t = div_fact * t;
if (t < minval)
{
if (Math.Sign(calc_vp(1.0, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv)) == Math.Sign(vpb))
{
return(0.5);
}
//return 1.0 / div_fact;
else
{
return(Calculate_optimal_t(1.0, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv, minval));
}
}
vpa = vpb;
vpb = calc_vp(t, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv);
}
//return 0.5 * (1.0 + (1.0 / div_fact)) * t;
return(t - t * (1.0 - 1.0 / div_fact) * vpb / (vpa - vpb));
}
else
{
// if 0.5 * t was going uphill, then we need to be doubling t and looking for the root
while (Math.Sign(vpb) == Math.Sign(vpa))
{
t = (1.0 / div_fact) * t;
if (t > maxval)
{
return(maxval);
}
vpa = vpb;
vpb = calc_vp(t, phi, x, car_dens_copy, dop_dens_copy, pois_solv, dens_solv);
}
//return 0.5 * (1.0 + div_fact) * t;
return(t - t * (1.0 - div_fact) * vpb / (vpb - vpa));
}
}
/// <summary>
/// returns an eigenvector decomposition for the xy-plane after having calculated the density in the
/// z-direction and storing it in "charge_density"
/// </summary>
private double[,] Solve_Eigenvector_Problem(Band_Data dft_pot, ref SpinResolved_Data charge_density)
{
DoubleHermitianEigDecomp eig_decomp;
double[,] xy_energy = new double[nx, ny];
Band_Data dens_up = new Band_Data(nx, ny, nz, 0.0);
Band_Data dens_down = new Band_Data(nx, ny, nz, 0.0);
// cycle over xy-plane calculating the ground state energy and eigenstate in the growth direction
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
// pull out the chemical potential for this slice
double[] z_dft_pot = new double[nz];
for (int k = 0; k < nz; k++)
z_dft_pot[k] = dft_pot.vol[k][i, j];
// calculate its eigendecomposition
DoubleHermitianMatrix h_z = Create_Hamiltonian(z_dft_pot, tz, nz);
eig_decomp = new DoubleHermitianEigDecomp(h_z);
// insert the eigenstate into density and record the local confinement energy
xy_energy[i, j] = eig_decomp.EigenValue(0);
for (int k = 0; k < nz; k++)
{
double dens_tot = DoubleComplex.Norm(eig_decomp.EigenVector(0)[k]) * DoubleComplex.Norm(eig_decomp.EigenVector(0)[k]);
dens_up.vol[k][i, j] = 0.5 * dens_tot;
dens_down.vol[k][i, j] = 0.5 * dens_tot;
}
}
// put the calculated densities into charge_density
charge_density = new SpinResolved_Data(dens_up, dens_down);
return xy_energy;
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
double[,] xy_energy = new double[nx, ny];
xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density);
/*int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
double[,] dens_xy = new double[nx, ny];
// and generate a density for the y-direction
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < max_wavefunction; k++)
dens_xy[i, j] += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_Fermi_Function(energies[k]);
*/
IExperiment exp_green;
exp_green = new Iterative_Greens_Function_Test.Experiment();
Iterative_Greens_Function_Test.Iterative_Greens_Function iter = new Iterative_Greens_Function_Test.Iterative_Greens_Function(exp_green, xy_energy);
double[,] dens_xy = new double[nx, ny];
double max_energy = Physics_Base.kB * temperature * no_kb_T;
DoubleMatrix xy_energy_mat = new DoubleMatrix(xy_energy);
double min_energy = xy_energy_mat.Min();
double dE = 0.1;
//double min_energy = -1.0 * max_energy;
int n_slices = (int)((max_energy - min_energy) / dE);
for (int n = 1; n < n_slices-1; n++)
{
double energy = min_energy + n * dE;
double[,] dens_per_E = iter.GetDoS(energy);
double fermi_func = Get_Fermi_Function(energy);
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
dens_xy[i, j] += dens_per_E[i,j] * fermi_func;
}
}
//double fermi_fact_max = Math.Exp(max_energy / (Physics_Base.kB * temperature)) + 1;
//double fermi_fact_min = 2.0;
double[,] dens_per_E_max = iter.GetDoS(max_energy);
double[,] dens_per_E_min = iter.GetDoS(min_energy);
double fermi_func_max = Get_Fermi_Function(max_energy);
double fermi_func_min = Get_Fermi_Function(min_energy);
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
dens_xy[i, j] += 0.5*(dens_per_E_max[i, j] * fermi_func_max + dens_per_E_min[i,j] * fermi_func_min);
}
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density.Spin_Up.vol[k][i, j] *= dens_xy[i, j];
charge_density.Spin_Down.vol[k][i, j] *= dens_xy[i, j];
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
public abstract SpinResolved_Data Get_ChargeDensity_Deriv(ILayer[] layers, SpinResolved_Data carrier_charge_density, SpinResolved_Data dopent_charge_density, Band_Data chem_pot);
public void Print_DFT_diff(SpinResolved_Data car_dens)
{
Console.WriteLine("Maximum absolute difference in DFT potentials = " + DFT_diff(car_dens).InfinityNorm().ToString("F6"));
}
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
throw new NotImplementedException();
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi)
{
Save_Data(rho_prime.Spin_Summed_Data, densderiv_filename);
Save_Data(gphi, gphi_filename);
Band_Data x = Get_Data_From_External(newton_location, "-p " + newton_parameterfile, newton_result_filename);
return x;
}
public abstract void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot);
public abstract Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi, SpinResolved_Data carrier_density, Band_Data dft_pot, Band_Data dft_calc);
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
double[,] xy_energy = Solve_Eigenvector_Problem(dft_pot, ref charge_density_deriv);
double beta = 1.0 / (Physics_Base.kB * temperature);
// multiply the z-densities by the xy-density
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
for (int k = 0; k < nz; k++)
{
charge_density_deriv.Spin_Up.vol[k][i, j] *= g_2d * Get_Fermi_Function(xy_energy[i, j]);
charge_density_deriv.Spin_Down.vol[k][i, j] *= g_2d * Get_Fermi_Function(xy_energy[i, j]);
}
// and multiply the density derivative by e to get the charge density and by e to convert it to d/dphi (as increasing phi decreases the charge: dn/dphi*-e^2 )
charge_density_deriv = unit_charge * unit_charge * charge_density_deriv;
}
public Band_Data Get_XC_Potential_Deriv(SpinResolved_Data charge_density)
{
throw new NotImplementedException();
}
/// <summary>
/// for this method, it is assumed that the dopent density is frozen out (and therefore not altered) unless overriden
/// </summary>
public virtual void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data carrier_charge_density, ref SpinResolved_Data dopent_charge_density, Band_Data chem_pot)
{
Get_ChargeDensity(layers, ref carrier_charge_density, chem_pot);
}
public void Print_DFT_diff(SpinResolved_Data car_dens)
{
}
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, Band_Data chem_pot)
{
Get_SOI_parameters(chem_pot);
// if (dV_x == null)
// throw new Exception("Error - Band structure derivatives are null! Have you initiated this type properly by calling Get_SOI_parameters(Band_Data chem_pot)?");
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
// reset charge density
charge_density_deriv = 0.0 * charge_density_deriv;
// integrate up density from k = 0 to k = k_F
int count = 0;
double k = 0;
// create initial hamiltonian and eigendecomposition
int max_wavefunction_old_p, max_wavefunction_old_m;
DoubleHermitianMatrix hamiltonian_p = Create_H_Using_SOIP(dft_pot, k);
DoubleHermitianEigDecomp eig_decomp_old_p = Diagonalise_Hamiltonian(hamiltonian_p, out max_wavefunction_old_p);
DoubleHermitianEigDecomp eig_decomp_old_m = Diagonalise_Hamiltonian(hamiltonian_p, out max_wavefunction_old_m);
while (k < kmax)
{
// increment the wavevector
k += delta_k;
count += 1;
// create new decompositions for forwards and backwards analysis
int max_wavefunction_p, max_wavefunction_m;
DoubleHermitianEigDecomp eig_decomp_p = Diagonalise_Hamiltonian(Create_H_Using_SOIP(dft_pot, k), out max_wavefunction_p);
DoubleHermitianEigDecomp eig_decomp_m = Diagonalise_Hamiltonian(Create_H_Using_SOIP(dft_pot, -1.0 * k), out max_wavefunction_m);
SpinResolved_Data new_charge_deriv = new SpinResolved_Data(nx, ny);
// cycle over each of the positive bands
for (int i = 0; i < max_wavefunction_p; i++)
new_charge_deriv += Calculate_Density_Derivative(eig_decomp_old_p, eig_decomp_p, i);
// and negative bands
for (int i = 0; i < max_wavefunction_m; i++)
new_charge_deriv += Calculate_Density_Derivative(eig_decomp_old_m, eig_decomp_m, i);
// set new eigenvalue decompositions and max_wavefunctions to the old ones
eig_decomp_old_m = eig_decomp_m; eig_decomp_old_p = eig_decomp_p;
max_wavefunction_old_m = max_wavefunction_m; max_wavefunction_old_p = max_wavefunction_p;
// and finally, add the charge density calculated
charge_density_deriv += new_charge_deriv;
}
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi, SpinResolved_Data car_dens, Band_Data dft_pot, Band_Data dft_calc)
{
Save_Data(car_dens.Spin_Summed_Data, dens_filename);
Save_Data(dft_pot, xc_pot_filename);
Save_Data(dft_calc, "xc_pot_calc.dat");
return(Calculate_Newton_Step(rho_prime, gphi));
}
bool Check_Integration_Convergence(SpinResolved_Data density_k, double eps)
{
// checks whether the maximum (negative) density is less than eps
double max_dens = 0.0;
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
if (density_k.Spin_Up.mat[i, j] + density_k.Spin_Down.mat[i, j] < max_dens)
max_dens = density_k.Spin_Up.mat[i, j] + density_k.Spin_Down.mat[i, j];
return eps > -1.0 * max_dens;
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi, SpinResolved_Data carrier_density, Band_Data dft_pot, Band_Data dft_calc)
{
throw new NotImplementedException();
}
public Band_Data DFT_diff(SpinResolved_Data car_dens)
{
throw new NotImplementedException();
}
/// <summary>
/// Calculate the charge density for this potential
/// NOTE!!! that the boundary potential is (essentially) set to infty by ringing the density with a set of zeros.
/// this prevents potential solvers from extrapolating any residual density at the edge of the eigenstate
/// solution out of the charge density calculation domain
/// </summary>
/// <param name="layers"></param>
/// <param name="charge_density_deriv"></param>
/// <param name="chem_pot"></param>
public override void Get_ChargeDensity_Deriv(ILayer[] layers, ref SpinResolved_Data charge_density_deriv, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
DoubleHermitianMatrix hamiltonian = Create_Hamiltonian(layers, dft_pot);
DoubleHermitianEigDecomp eig_decomp = new DoubleHermitianEigDecomp(hamiltonian);
double min_eigval = eig_decomp.EigenValues.Min();
int max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
double dens_val_deriv = 0.0;
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
{
charge_density_deriv.Spin_Up.mat[i, j] = 0.0;
charge_density_deriv.Spin_Down.mat[i, j] = 0.0;
continue;
}
for (int k = 0; k < max_wavefunction; k++)
{
// and integrate the density of states at this position for this eigenvector from the minimum energy to
// (by default) 50 * k_b * T above mu = 0
dens_val_deriv += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_OneD_DoS_Deriv(eig_decomp.EigenValue(k), no_kb_T);
}
// just share the densities (there is no spin polarisation)
charge_density_deriv.Spin_Up.mat[i, j] = 0.5 * dens_val_deriv;
charge_density_deriv.Spin_Down.mat[i, j] = 0.5 * dens_val_deriv;
}
// and multiply the density derivative by e to get the charge density and by e to convert it to d/dphi (as increasing phi decreases the charge: dn/dphi*-e^2 )
charge_density_deriv = unit_charge * unit_charge * charge_density_deriv;
}
public void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
SpinResolved_Data electron_density = charge_density.DeepenThisCopy();
SpinResolved_Data hole_density = charge_density.DeepenThisCopy();
// remove the electron density from the hole density SpinResolved_Data and vice versa
for (int i = 0; i < electron_density.Spin_Summed_Data.Length; i++ )
{
if (electron_density.Spin_Summed_Data.vec[i] > 0.0)
{
electron_density.Spin_Up[i] = 0.0;
electron_density.Spin_Down[i] = 0.0;
}
if (hole_density.Spin_Summed_Data.vec[i] < 0.0)
{
hole_density.Spin_Up[i] = 0.0;
hole_density.Spin_Down[i] = 0.0;
}
}
electron_dens_calc.Get_ChargeDensity(layers, ref electron_density, chem_pot);
hole_dens_calc.Get_ChargeDensity(layers, ref hole_density, chem_pot);
charge_density = electron_density + hole_density;
}
/// <summary>
/// Calculate the charge density for this potential
/// NOTE!!! that the boundary potential is (essentially) set to infty by ringing the density with a set of zeros.
/// this prevents potential solvers from extrapolating any residual density at the edge of the eigenstate
/// solution out of the charge density calculation domain
/// </summary>
/// <param name="layers"></param>
/// <param name="charge_density"></param>
/// <param name="chem_pot"></param>
public override void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data charge_density, Band_Data chem_pot)
{
// convert the chemical potential into a quantum mechanical potential
Band_Data dft_pot = chem_pot.DeepenThisCopy();
Get_Potential(ref dft_pot, layers);
DoubleHermitianMatrix hamiltonian = Create_Hamiltonian(layers, dft_pot);
DoubleHermitianEigDecompServer eig_server = new DoubleHermitianEigDecompServer();
eig_server.ComputeEigenValueRange(dft_pot.mat.Min(), no_kb_T * Physics_Base.kB * temperature);
eig_server.ComputeVectors = true;
DoubleHermitianEigDecomp eig_decomp = eig_server.Factor(hamiltonian);
int max_wavefunction = 0;
if (eig_decomp.EigenValues.Length != 0)
{
double min_eigval = eig_decomp.EigenValues.Min();
max_wavefunction = (from val in eig_decomp.EigenValues
where val < no_kb_T * Physics_Base.kB * temperature
select val).ToArray().Length;
}
for (int i = 0; i < nx; i++)
for (int j = 0; j < ny; j++)
{
double dens_val = 0.0;
// do not add anything to the density if on the edge of the domain
if (i == 0 || i == nx - 1 || j == 0 || j == ny - 1)
{
charge_density.Spin_Up.mat[i, j] = 0.0;
charge_density.Spin_Down.mat[i, j] = 0.0;
continue;
}
for (int k = 0; k < max_wavefunction; k++)
{
// and integrate the density of states at this position for this eigenvector from the minimum energy to
// (by default) 50 * k_b * T above mu = 0
dens_val += DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * DoubleComplex.Norm(eig_decomp.EigenVector(k)[i * ny + j]) * Get_OneD_DoS(eig_decomp.EigenValue(k), no_kb_T);
}
// just share the densities (there is no spin polarisation)
charge_density.Spin_Up.mat[i, j] = 0.5 * dens_val;
charge_density.Spin_Down.mat[i, j] = 0.5 * dens_val;
}
// and multiply the density by -e to get the charge density (as these are electrons)
charge_density = unit_charge * charge_density;
}
public SpinResolved_Data Get_ChargeDensity(ILayer[] layers, SpinResolved_Data carrier_charge_density, SpinResolved_Data dopent_charge_density, Band_Data chem_pot)
{
SpinResolved_Data electron_density = carrier_charge_density.DeepenThisCopy();
SpinResolved_Data hole_density = carrier_charge_density.DeepenThisCopy();
// remove the electron density from the hole density SpinResolved_Data and vice versa
for (int i = 0; i < electron_density.Spin_Summed_Data.Length; i++)
{
if (electron_density.Spin_Summed_Data.vec[i] > 0.0)
{
electron_density.Spin_Up[i] = 0.0;
electron_density.Spin_Down[i] = 0.0;
}
if (hole_density.Spin_Summed_Data.vec[i] < 0.0)
{
hole_density.Spin_Up[i] = 0.0;
hole_density.Spin_Down[i] = 0.0;
}
}
// must remove one lot of dopents due to double counting
return electron_dens_calc.Get_ChargeDensity(layers, electron_density, dopent_charge_density, chem_pot) + hole_dens_calc.Get_ChargeDensity(layers, hole_density, dopent_charge_density, chem_pot)
- dopent_charge_density;
}
public void Output(SpinResolved_Data data, string filename)
{
Output(data, filename, true);
}
/// <summary>
/// for this method, it is assumed that the dopent density is frozen out (and therefore not altered) unless overriden
/// </summary>
public void Get_ChargeDensity(ILayer[] layers, ref SpinResolved_Data carrier_charge_density, ref SpinResolved_Data dopent_charge_density, Band_Data chem_pot)
{
Get_ChargeDensity(layers, ref carrier_charge_density, chem_pot);
}
public override Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi, SpinResolved_Data car_dens, Band_Data dft_pot, Band_Data dft_calc)
{
Save_Data(car_dens.Spin_Summed_Data, dens_filename);
Save_Data(dft_pot, xc_pot_filename);
Save_Data(dft_calc, "xc_pot_calc.dat");
return Calculate_Newton_Step(rho_prime, gphi);
}
public SpinResolved_Data Get_ChargeDensity_Deriv(ILayer[] layers, SpinResolved_Data carrier_density_deriv, SpinResolved_Data dopent_density_deriv, Band_Data chem_pot)
{
SpinResolved_Data electron_density_deriv = carrier_density_deriv.DeepenThisCopy();
SpinResolved_Data hole_density_deriv = carrier_density_deriv.DeepenThisCopy();
// remove the electron density from the hole density SpinResolved_Data and vice versa
for (int i = 0; i < electron_density_deriv.Spin_Summed_Data.Length; i++)
{
if (electron_density_deriv.Spin_Summed_Data.vec[i] > 0.0)
{
electron_density_deriv.Spin_Up[i] = 0.0;
electron_density_deriv.Spin_Down[i] = 0.0;
}
if (hole_density_deriv.Spin_Summed_Data.vec[i] < 0.0)
{
hole_density_deriv.Spin_Up[i] = 0.0;
hole_density_deriv.Spin_Down[i] = 0.0;
}
}
return electron_dens_calc.Get_ChargeDensity_Deriv(layers, electron_density_deriv, dopent_density_deriv, chem_pot) + hole_dens_calc.Get_ChargeDensity_Deriv(layers, hole_density_deriv, dopent_density_deriv, chem_pot);
}
public abstract Band_Data Calculate_Newton_Step(SpinResolved_Data rho_prime, Band_Data gphi);
public override SpinResolved_Data Get_ChargeDensity_Deriv(ILayer[] layers, SpinResolved_Data carrier_charge_density, SpinResolved_Data dopent_charge_density, Band_Data chem_pot)
{
throw new NotImplementedException();
}
