168 lines
5.6 KiB
Fortran
168 lines
5.6 KiB
Fortran
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!=======================================================================
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!
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MODULE IMFP
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!
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USE ACCURACY_REAL
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE MEAN_FREE_PATH(EK,MFP)
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!
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! This subroutine computes the electron inelastic mean free path
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!
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!
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! Reference: (1) D. R. Penn, Phys. Rev. B 13, 5248-5254 (1976)
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! (2) B. Da, H. Shinotsuka, H. Yoshikawa, Z.J. Ding and
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! S. Tanuma, Phys. Rev. Lett. 113, 063201 (2014)
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!
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!
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! Input parameters:
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!
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! * EK : electron kinetic energy (in SI)
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!
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!
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! Output variables :
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!
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! * IMPF : inelastic mean free path (in SI)
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!
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!
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! Note: eps(q,omega) is in fact stored as a function of Y = q / k_F
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! and V = hbar omega / E_F
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!
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! Therefore, in order to be consistent, the integrations have
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! to be performed in Y and V
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!
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 30 Apr 2021
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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!
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USE Q_GRID, ONLY : Q_MIN
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USE E_GRID, ONLY : E_MIN
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!
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USE REAL_NUMBERS, ONLY : ZERO,ONE,TWO,HALF,FOURTH,SMALL,TTINY,INF
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USE PI_ETC, ONLY : PI
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USE FERMI_SI, ONLY : EF_SI,KF_SI
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USE CONSTANTS_P1, ONLY : BOHR,H_BAR,M_E
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USE ENE_CHANGE, ONLY : EV
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!
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USE DF_VALUES, ONLY : D_FUNC
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!
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USE INTEGRATION, ONLY : INTEGR_L
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USE INTEGRATION4
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USE DFUNCL_STAN_DYNAMIC
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!
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IMPLICIT NONE
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!
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INTEGER :: IQ,IE
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INTEGER :: ID
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INTEGER :: I_ZQ,I_ZE
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!
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INTEGER, PARAMETER :: NE_MAX = 2000 ! max. number of points in e-grid
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INTEGER, PARAMETER :: NQ_MAX = 1000 ! max. number of points in q-grid
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!
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REAL (WP), INTENT(IN) :: EK
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REAL (WP), INTENT(OUT):: MFP
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REAL (WP) :: MIN_E,MAX_E,MIN_Q,MAX_Q
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REAL (WP) :: STEP_E,STEP_Q
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REAL (WP) :: E,Q
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REAL (WP) :: X,V,Z,EKF,KOEF
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REAL (WP) :: EPSR,EPSI
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REAL (WP) :: ELF(NSIZE),IN(NSIZE)
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REAL (WP) :: A,B
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!
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REAL (WP) :: FLOAT,SQRT
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!
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EKF = EK / EF_SI ! in units of E_F
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!
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KOEF = EKF * PI * BOHR / RS !
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!
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MIN_E = E_MIN ! in units of E_F
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MAX_E = EKF - ONE ! in units of E_F
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STEP_E = (MAX_E - MIN_E) / FLOAT(NE_MAX - 1) ! in units of E_F
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!
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! Constructing the e-grid
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!
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DO IE = 1, NE_MAX ! E_F
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!
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E = MIN_E + FLOAT(IE - 1) * STEP_E ! in units of
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V = E ! hbar * omega / E_F
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!
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! Constructing the q-grid
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!
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MIN_Q = MAX( Q_MIN, SQRT(EKF) - SQRT(EKF - V) ) ! for Z to be defined
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MAX_Q = SQRT(EKF) + SQRT(EKF - V) ! in units of k_F
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STEP_Q = (MAX_Q - MIN_Q) / FLOAT(NQ_MAX - 1) ! in units of k_F
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!
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I_ZQ = 0 ! switch for integrand = 0
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!
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DO IQ = 1, NQ_MAX !
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!
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Q = MIN_Q + FLOAT(IQ - 1) * STEP_Q ! in units of k_F
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!
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X = HALF * Q ! (q / 2k_F)
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Z = FOURTH * V / (X * X) ! omega / omega_q
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!
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! Computing the dielectric function epsilon(q,E)
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!
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CALL DFUNCL_DYNAMIC(X,Z,RS,T,D_FUNC,IE,EPSR,EPSI) !
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!
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! Computing the loss function ELF = Im [ -1 / epsilon(q,E) ]
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!
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ELF(IQ) = EPSI / ( (EPSR * EPSR + EPSI * EPSI) * Q) ! integrand function
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!
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! IF(ELF(IQ) /= ZERO) I_ZQ = IQ !
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IF(ELF(IQ) == ZERO) ELF(IQ) = SMALL !
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!
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END DO ! end of q-grid
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!
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! IF(I_ZQ > 0) THEN !
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!
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! Performing the q-integration
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!
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ID = 1 ! EPSI = 0 at origin
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CALL INTEGR_L(ELF,STEP_Q,NSIZE,NQ_MAX,A,ID) !
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!
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! ELSE ! ELF always = 0
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!
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! A = TTINY !
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!
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! END IF !
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!
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! Constructing the e-integrand
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!
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IN(IE) = A !
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!
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! IF(A /= ZERO) I_ZE = IE !
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IF(IN(IE) == ZERO) IN(IE) = SMALL !
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!
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END DO ! end of e-grid
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!
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! IF(I_ZE > 0) THEN !
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!
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! Performing the e-integration
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!
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ID = 1 !
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CALL INTEGR_L(IN,STEP_E,NSIZE,NE_MAX,B,ID) !
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!
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! ELSE ! IN always = 0
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!
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! B = TTINY !
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!
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! END IF !
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!
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MFP = KOEF / B ! ref. (2) eq. (2)
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!
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END SUBROUTINE MEAN_FREE_PATH
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!
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END MODULE IMFP
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