module particles ! Number of carriers 
    integer, parameter :: DIM = 3                                ! dimension
    ! For each particle 
    real ( kind = 8 ), dimension(:,:), allocatable :: Par_pos, Par_wvk, Par_vel ! carrier position and wave vector k 
    integer, dimension(:), allocatable :: Par_valley
    real ( kind = 8 ), dimension(:), allocatable :: Par_ene, Par_tau 
    ! for TempUse
!    real ( kind = 8 ), dimension(DIM) :: Temp_pos, Temp_wvk ! carrier position and wave vector k 
!    integer :: Temp_valley_i, Temp_valley_f
!    real ( kind = 8 ) :: Temp_ene, Temp_tau
    real ( kind = 8 ) :: ParCharge ! charge of sampled particles 
end

module scattering
! for valley - 
integer, parameter :: num_Valley = 3   ! G - 1, L - 2, X - 3
integer, parameter :: num_ScatMech = 10   !  max for each ... G 1~10, L 11~, X polar_ab 1, 
real ( kind = 8 ), dimension(num_Valley) :: nonParabolPara, nonParabolPara2, nonParabolPara4
real ( kind = 8 ), dimension(num_Valley) :: eff_mass,rel_eff_mass,semh,hhem,tau_max ! Nonparbolic parameter, Effective <ass 
integer, dimension(num_Valley) :: max_scatt_mech
integer:: num_EnergyLevel !  total # of energy level 
real ( kind = 8 ) :: MaxE_eV, StepE_eV
integer:: acoustic_G,polar_G,intervalley_G_L,intervalley_G_X ! Consider G
integer:: acoustic_L,polar_L,intervalley_L_G,intervalley_L_L,intervalley_L_X ! Consider L
integer:: acoustic_X,polar_X,intervalley_X_G,intervalley_X_L,intervalley_X_X ! Consider X
!   Scattering Parameters 
real ( kind = 8 ) :: eps_high,eps_low !dielectric constant 
real ( kind = 8 ) :: acou_sigma_G,acou_sigma_L,acou_sigma_X ! Acoustic Coupling Const[eV] G/L/X = 7.01/9.2/9.0
real ( kind = 8 ) :: DefPot_G_L,DefPot_G_X,DefPot_L_G,DefPot_L_L,DefPot_L_X ! GL1.8E10  GX10.E10 LG 1.8E10 LL 5.E10 LX 1.E10  DefPot_G_L,DefPot_G_X,DefPot_L_G,DefPot_L_L,DefPot_L_X, DefPot_X_G,DefPot_X_L,DefPot_X_X
real ( kind = 8 ) :: DefPot_X_G,DefPot_X_L,DefPot_X_X   ! XG  10.E10   XL 1.E10  XX 10.E10  Intervalley Deformation Potential [eV/m] 
real ( kind = 8 ) :: polar_Ep_G,polar_Ep_L,polar_Ep_X ! phonon energy for Polaroptical /eV/ 0.03536, 0.03536, 0.03536    
real ( kind = 8 ) :: IntVal_Ep_G_L,IntVal_Ep_G_X,IntVal_Ep_L_G,IntVal_Ep_L_L ! phonon energy for IV /eV/ 0.0278, 0.0299, 0.0278, 0.029
real ( kind = 8 ) :: IntVal_Ep_L_X,IntVal_Ep_X_G,IntVal_Ep_X_L,IntVal_Ep_X_X ! phonon energy for IV /eV/ 0.0293, 0.0299, 0.0293, 0.0299
real ( kind = 8 ) :: split_L_G,split_X_G,eq_valleys_G,eq_valleys_L,eq_valleys_X ! Ee level diff (0.29,0.48), # of eq valleys 1/4/3 !!! later need to consider change
real ( kind = 8 ) :: rho_GaAs, u_sound ! = 5370.  = 5.22E3
! real ( kind = 8 ), dimension(:), allocatable :: scatTable  
! real ( kind = 8 ), dimension(num_ScatMech, num_EnergyLevel) :: 
real ( kind = 8 ), dimension(:,:,:), allocatable :: scatt_table 
real ( kind = 8 ), dimension(:,:,:), allocatable :: ren_scatt_table 
integer, dimension(num_ScatMech,num_Valley):: flag_mech 
real ( kind = 8 ), dimension(num_ScatMech,num_Valley):: E_change
integer, dimension(num_ScatMech,num_Valley):: i_valley
integer, dimension(num_ScatMech,num_Valley):: ScatMechFreq
real ( kind = 8 ) :: max_scat ! MaxScattering Rate
real ( kind = 8 ), dimension(:), allocatable :: RelCumFreqDist, FreqDist, CumFreqDist ! distribution function
end

module simulation
    ! Basic Parameters
    real ( kind = 8 ), parameter :: pi = 3.141592653589793239
    real ( kind = 8 ), parameter :: kB = 1.3806503D-23
    real ( kind = 8 ), parameter :: r_o = 1.0D-10 ! Angstrom
    real ( kind = 8 ), parameter :: m_o = 1.675D-27  !neutron mass  %kg
    real ( kind = 8 ), parameter :: m_e = 9.10938188D-31 !electron mass  
    real ( kind = 8 ), parameter :: e_c = 1.60217646D-19 
    real ( kind = 8 ), parameter :: eps_o = 8.8541878176D-12 ! dielectric C^2/N-m^2 
    real ( kind = 8 ), parameter :: N_a = 6.0221415D26 ! Avogadro
    real ( kind = 8 ), parameter :: hbar = 1.05457148D-34 ! J-s 
    real ( kind = 8 ) :: echbar ! J-s 
    ! Simulation Condition 
    integer:: num_Carriers, step_output1, step_output2 !  total sampled # of carriers
    real ( kind = 8 ) :: time, time_max, time_step, time_early ! time step fs
    real ( kind = 8 ) :: Te, Tp, Tsys ! in K
    real ( kind = 8 ) :: Te_eV, Tp_eV, Tsys_eV ! in eV
    real ( kind = 8 ), dimension(3) :: EField ! electric field V/m
    ! Properties Check
    ! energy - all valley, for each valley, 
    real ( kind = 8 ) :: TotParEne, AveParEne, TimeAveParEne ! energy
    real ( kind = 8 ), dimension(:), allocatable :: TotEneValley, AveEneValley, TimeAveEneValley ! 
    ! freq - valley, 
    integer, dimension(:), allocatable :: FreqValley ! How many particles in the whole area in each valley
    real ( kind = 8 ), dimension(:), allocatable :: RelFreqValley, TimeFreqValley, TimeRelFreqValley ! How many particles in the whole area in each valley - time average
    ! velocity - all valleys, each valley
    real ( kind = 8 ), dimension(3) :: AveParVel, TimeAveParVel ! average particle velocity for x,y,z direction
    real ( kind = 8 ), dimension(:,:), allocatable :: AveParValleyVel, TimeAveParValleyVel
    ! Energy Histogram - for all energy valleys, for each valley 
    integer, dimension(:), allocatable :: EneLevelHist
    real ( kind = 8 ), dimension(:), allocatable :: RelEneLevelHist, TimeRelEneLevelHist  ! EneLevelHist-number 
    integer, dimension(:,:), allocatable :: EneLevelValleyHist
    real ( kind = 8 ), dimension(:,:), allocatable :: RelEneLevelValleyHist, TimeRelEneLevelValleyHist  ! EneLevelHist-number 
      
    real ( kind = 8 ) :: E_F
    real ( kind = 8 ) :: n_d, n_i, primV
    real ( kind = 16 ) :: RandomNum ! Generated Random number
end

module nodes ! Node Grid, System configuration
    integer :: num_Nodes
end