physics.hpp

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#ifndef VIENNASHE_PHYSICS_PHYSICS_HPP
#define VIENNASHE_PHYSICS_PHYSICS_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
=============================================================================== */
 
// std
#include <math.h>
#include <cmath>
 
// viennashe
#include "viennashe/forwards.h"
#include "viennashe/math/constants.hpp"
#include "viennashe/physics/constants.hpp"
#include "viennashe/physics/exception.hpp"
#include "viennashe/materials/all.hpp"
 
 
namespace viennashe
{
  namespace physics
  {
 
    namespace convert
    {
 
      //
      // Replace this by a sane unit framework!
      //
 
      inline double joule_to_eV(const double eps)
      {
        return eps / viennashe::physics::constants::q;
      }
 
      inline double eV_to_joule(const double eps)
      {
        return eps * viennashe::physics::constants::q;
      }
    }
 
    inline double get_thermal_potential(double T)
    {
      return (constants::kB * T) / constants::q;
    }
 
    inline double get_optical_phonon_number(double eps_optical, double temperature = 300.0 /* Kelvin */)
    {
      const double kB = constants::kB;
      return 1.0 / (std::exp(eps_optical / (kB * temperature)) - 1.0);
    }
 
    inline double get_band_weight(double temperature, viennashe::carrier_type_id ctype)
    {
      const double Ncv0 = 2.50933670314359713002e19 * 100 * 100 * 100;
      // Insert carrier mass model here
      const double me = (ctype == viennashe::ELECTRON_TYPE_ID) ? 0.33 : 0.6;
      return Ncv0 * std::pow(me * (temperature / 300.0), 1.5) * 6.0;
    }
 
    inline double get_band_edge(viennashe::carrier_type_id const & ctype)
    {
      return ((ctype == viennashe::ELECTRON_TYPE_ID) ? 1.0 : -1.0) * viennashe::materials::si::band_gap() * 0.5;
    }
 
 
    inline double get_thermal_velocity(double temperature, viennashe::carrier_type_id ctype)
    {
      // TODO: use carrier mass model
      (void)ctype; // fix unused parameter warning
      const double kBT = viennashe::physics::constants::kB * temperature;
      return std::sqrt(8.0 * kBT / (viennashe::math::constants::pi * viennashe::physics::constants::mass_electron) );
    }
 
    inline double get_auxilary_concentration(double temperature, viennashe::carrier_type_id ctype)
    {
      const double kbT  = viennashe::physics::constants::kB * temperature;
      const double band_edge   = viennashe::physics::get_band_edge(ctype);
      const double band_weight = viennashe::physics::get_band_weight(temperature, ctype);
      const double polarity = (ctype == viennashe::ELECTRON_TYPE_ID) ? -1.0 : 1.0;
 
      return band_weight * std::exp(polarity * band_edge / kbT);
    }
 
    inline double built_in_potential(double temperature, double doping_n, double doping_p)
    {
      if (doping_n <= 0 && doping_p <= 0) return 0;
 
      const double net_doping = (doping_n - doping_p);
      const double T    = temperature;
      const double naux = viennashe::physics::get_auxilary_concentration(T, viennashe::ELECTRON_TYPE_ID);
      const double paux = viennashe::physics::get_auxilary_concentration(T, viennashe::HOLE_TYPE_ID);
 
      double x = std::sqrt(net_doping * net_doping + 4.0 * naux * paux);
 
      if ( net_doping >= 0.0 )
      {
        x = (x + net_doping) * 0.5 / naux;
        return  T * std::log(x) * viennashe::physics::constants::kB / viennashe::physics::constants::q;
      }
      else
      {
        x = (x - net_doping) * 0.5 / paux;
        return -T * std::log(x) * viennashe::physics::constants::kB / viennashe::physics::constants::q;
      }
 
    }
 
    inline double contact_carrier_ohm(double temperature, double doping_n, double doping_p, viennashe::carrier_type_id ctype)
    {
      const double q    = viennashe::physics::constants::q;
      const double kbT  = viennashe::physics::constants::kB * temperature;
      const double phiB = viennashe::physics::built_in_potential(temperature, doping_n, doping_p);
 
      const double band_edge   = viennashe::physics::get_band_edge(ctype);
      const double band_weight = viennashe::physics::get_band_weight(temperature, ctype);
      const double polarity    = (ctype == viennashe::ELECTRON_TYPE_ID) ? -1.0 : 1.0;
 
      return band_weight * std::exp( polarity * ( band_edge - q * phiB ) / kbT ) ;
    }
 
 
  } //namespace physics
} //namespace viennashe
 
#endif