impurity_scattering.hpp

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#ifndef VIENNASHE_SHE_SCATTERING_IMPURITY_SCATTERING_HPP
#define VIENNASHE_SHE_SCATTERING_IMPURITY_SCATTERING_HPP
 
/* ============================================================================
   Copyright (c) 2011-2022, Institute for Microelectronics,
                            Institute for Analysis and Scientific Computing,
                            TU Wien.
 
                            -----------------
     ViennaSHE - The Vienna Spherical Harmonics Expansion Boltzmann Solver
                            -----------------
 
                    http://viennashe.sourceforge.net/
 
   License:         MIT (X11), see file LICENSE in the base directory
=============================================================================== */
 
// viennashe
#include "viennashe/math/constants.hpp"
#include "viennashe/materials/all.hpp"
#include "viennashe/physics/constants.hpp"
#include "viennashe/physics/dispersion.hpp"
#include "viennashe/physics/physics.hpp"
 
#include "viennashe/log/log.hpp"
#include "viennashe/she/log_keys.h"
#include "viennashe/she/scattering/common.hpp"
 
namespace viennashe
{
  namespace she
  {
 
 
    template <typename DeviceType>
    class ionized_impurity_scattering : public scattering_base<DeviceType>
    {
        typedef scattering_base<DeviceType>                     base_type;
        typedef typename base_type::FacetType                   FacetType;
        typedef typename base_type::CellType                    CellType;
 
      public:
        typedef typename base_type::scatter_processes_type      scatter_processes_type;
        typedef scatter_processes_type                          value_type;
 
        explicit ionized_impurity_scattering(DeviceType const & device,
                                             viennashe::config const & conf) : base_type(device, conf), params_(conf.scattering().ionized_impurity()) {  }
 
        scatter_processes_type operator()(CellType const & elem,
                                          double kinetic_energy,
                                          viennashe::carrier_type_id ctype) const
        {
          return this->get(elem, kinetic_energy, ctype);
        }
 
        scatter_processes_type operator()(FacetType const & elem,
                                          double kinetic_energy,
                                          viennashe::carrier_type_id ctype) const
        {
          return this->get(elem, kinetic_energy, ctype);
        }
 
        scatter_process_id id() const { return IMPURITY_SCATTERING; }
 
      private:
 
        template <typename ElementType>
        scatter_processes_type get(ElementType const & elem,
                                   double kinetic_energy,
                                   viennashe::carrier_type_id ctype) const
        {
          scatter_processes_type result(1);
 
          // Final energy is always equal to initial energy:
          result[0].initial_energy(kinetic_energy);
          result[0].final_energy(kinetic_energy);
          result[0].rate( getScatteringRate(elem, kinetic_energy, ctype) );
          result[0].generation_rate(0);
 
          return result;
        }
 
 
        template <typename ElementType>
        double getScatteringRate(ElementType const & elem,
                                 double kinetic_energy,
                                 viennashe::carrier_type_id ctype) const
        {
           double ND = base_type::device_.get_doping_n(elem);
           double NA = base_type::device_.get_doping_p(elem);
           const double temp = base_type::device_.get_lattice_temperature(elem);
 
           double NI = NA + ND;
 
           return getScatteringRate(NI, kinetic_energy, temp, ctype);
        }
 
        double getScatteringRate(double NI,
                                 double kinetic_energy, double T, viennashe::carrier_type_id ctype) const
        {
          const double kB = viennashe::physics::constants::kB;
          const double hbar = viennashe::physics::constants::hbar;
          const double q = viennashe::physics::constants::q;
          const double eps = viennashe::materials::si::permittivity();
          const double pi = viennashe::math::constants::pi;
 
          const double prefactor = (2.0 * pi * NI * q * q * q * q) / (hbar * eps * eps);
 
          const double norm_k = base_type::conf_.dispersion_relation(ctype).norm_k(kinetic_energy);
 
          //avoid singularity in the following expression
          if (norm_k <= 0.0)
            return 0.0;
 
          const double lambda_sq = (eps * kB * T) / (q * q * NI );
          const double a = 4.0 * lambda_sq * norm_k * norm_k;
 
          const double scattering_rate = prefactor
                                         * 0.5 * (std::log(1.0 + a) - (a / (1.0 + a)) ) / 4.0 / std::pow(norm_k, 4.0);
 
          if (scattering_rate < 0.0) //the above formula may in some corner cases become negative, so we truncate it
            return 0.0;
 
          return scattering_rate;
        }
 
        ionized_impurity_scattering_parameters  params_;
 
    };
 
  } //namespace she
} //namespace viennashe
 
#endif