Chapter 2: Electron Emission from Solids

Example 1, Page 19

In [6]:
import math
#Variable declaration
A=6.02*(10**5)#A=thermionic emission constant in A(m^(-2))(K^(-2))
Ew=4.54#Ew=work function in eV
T=2500#T=temperature in Kelvin
kB=1.38*10**(-23)#kB=Boltzmann's constant in J/K
e=1.6*10**(-19)#e=charge of anelectron in C

#Calculations&Results
b=(e*Ew)/kB#b=thermionic emission constant in K
print "b=%.3e K"%b
Jx=A*(T**2)*math.exp(-b/T)#Jx=emission current density in A/m^(2)
print "Jx=%.f A/(m^2)"%Jx
n=Jx/e#n=number of electrons emitted per unit area per second in (m^-2)(s^-1)
print "n=%.3e (m^-2)(s^-1)"%n

b=5.264e+04 K
Jx=2700 A/(m^2)
n=1.688e+22 (m^-2)(s^-1)

Example 2, Page 20

In [9]:
import math

#Variable declaration
T=2673#T=temperature in Kelvin
dT=10.#dT=change in temperature in Kelvin
Ew=4.54#Ew=work function in eV
e=1.6*10**(-19)#e=charge of anelectron in C
kB=1.38*10**(-23)#kB=Boltzmann's constant in J/K

#Calculations&Results
#I=(S*A*(T^2))*exp(-((e*Ew)/(kB*T))#I=emission current,S=surface area of the filament,dI=change in emission current
d=((2*dT)/T)+(((e*Ew)/(kB*(T**2))*dT))#d=change in emission current
print "d=%.4f"%d
d*100#percent change in emission current
print "d*100=%.2f %%"%(d*100)

d=0.0812
d*100=8.12 %

Example 3, Page 20

In [12]:
import math

#Variable declaration
kB=1.38*10**(-23)#kB=Boltzmann's constant in J/K
#A=6.02*(10**5)#A=thermionic emission constant in A(m^(-2))(K^(-2))
#Ew1,Ew2=thermionic work function of 2 emitters in eV
e=1.6*10**(-19)#e=charge of anelectron in C
T=2000#T=temperature in Kelvin

#Calculations&Results
#Jx1=A*(T^2)*exp(-(a/(kB*T)))#Jx=emission current density in A/m^(2)
#Jx2=A*(T^2)*exp(-(b/(kB*T)))
#(Jx1/Jx2)=2
#(Jx1/Jx2)=exp((Ew2-Ew1)/(kB*T))
#exp((Ew2-Ew1)/(kB*T))=2
d=(kB*T*math.log(2))#d=(Ew2-Ew1)=difference in thermionic work functions of 2 emitters
print "d=%.3e J"%d
d/e
print "d/e=%.4f eV"%(d/e)

d=1.913e-20 J
d/e=0.1196 eV

Example 4, Page 20

In [13]:
#Variable declaration
#Ia=(K*(Va^(3/2)));Ia=space charge limited current ,Va=anode voltage,K=proportionality constant
Ia1=300#Ia1=space charge limited current of 1st anode in A
Ia2=200.#Ia2=space charge limited current of 2nd anode in A
Va1=200#Va=anode voltage of 1st anode in V

#Calculations
Va2=(Va1*((Ia2/Ia1)**(2./3)))#Va2=anode voltage of 2nd anode in V

#Result
print "Va2=%.2f V"%Va2

Va2=152.63 V