added plasmaFrequencySTO

libhreels/dielectrics20.py

@@ -4,18 +4,18 @@ import numpy as np
 from scipy import constants
 from scipy.integrate import cumulative_trapezoid
 
-def plasmaFrequency(n,eps_inf=1): 
-    '''Returns the plasma frequency for a given doping n in charge/m³.'''
-    # Note that the function parameter is actually n/m, the charge carrier density 
-    # over the band mass in units of electron mass in vacuum.
+def plasmaFrequency(n,eps_inf=1, m=1): 
+    # Returns the plasma frequency in cm^-1 for a given charge carrier density n in e/m³
+    # and a polarisable medium described by eps_infinity 
+    # and a band mass m in units of electron mass in vacuum.
     eps_0 = constants.value("vacuum electric permittivity")
     e = constants.value('elementary charge')
     m_e = constants.value('electron mass')
     # Careful: There is a factor of 2 pi between omega and nue:
     # If the plasma oscillates in a polarisable medium eps_infinity will reduce the restoring fields
-    w_P = np.sqrt(n*e*e/(eps_0*eps_inf*m_e))        #
+    w_P = np.sqrt(n*e*e/(eps_0*eps_inf*m_e*m))        #
     nue_P = w_P /1E+12 * 33.35641 /2 /np.pi   #Hz -> THz -> cm^-1
-    return nue_P
+    return nue_P        # in units of cm-1
 
 def chargeDensitySTO(x):
     # Calculates the charge density per m^3 for SrTi_(1-x)Nb_xO_3 
@@ -23,6 +23,13 @@ def chargeDensitySTO(x):
     vol = 3.91*3.91*3.91 * 1E-30    # unit cell volume in m^3 
     return x/vol
     
+def plasmaFrequencySTO(x,eps_inf=5.14,m=15):
+    # Calculates the plasma frequency in cm^-1 for SrTi_(1-x)Nb_xO_3 
+    # assuming doping by one electron per Nb atom 
+    # and an effective mass m=15
+    vol = 3.91*3.91*3.91 * 1E-30    # unit cell volume in m^3 
+    return plasmaFrequency(x/vol,eps_inf, m=m)
+    
 
 def loss(eps):
     '''Returns the loss function for a given eps'''