Appendix

Python program example (He+H implanted sample for example) for solving Eq. (17) is given here. Two methods were tried to solve Eq. (17). One is Newton iteration method and another is directly plotting the curve. Here we paste the program to illustrate the solving of Eq. (17) by directly plotting, which may be the simplest and most effective method.

#Python 3.6 #Filename: Cal Em by using Numerical Method plot curve of Em

import numpy as np import pandas as pd import matplotlib.pyplot as plt

print('---------------------------------------------') print('Import the growth rate data of He+H implantation...')

(t,v)=np.loadtxt('.\\loop growth rate\_He+H.txt', skiprows=1, unpack=True)

```
print('T(K)',' V(nm/min)')
print(t[0],v[0])
print(t[1],v[1])
print(t[2],v[2])
```

```
v0=(v[0]-v[1])/(v[1]-v[2])
v0=float('%.5f'%v0)
print('\nV0 is:',v0)
```

```
a1=(v[0]*v[0])/((1+v0)*v[1]*v[1])
a1=float('%.5f'%a1)
a2=(v0*v[2]*v[2])/((1+v0)*v[1]*v[1])
a2=float('%.5f'%a2)
b1=100000*(1/t[0]-1/t[1])/8.6
b1=float('%.5f'%b1)
b2=100000*(1/t[2]-1/t[1])/8.6
b2=float('%.5f'%b2)
```

```
print('\ny=a1*exp(E*b1)+a2*exp(E*b2)-1')
print('a1 ','b1 ','a2 ','b2')
print(a1,b1,a2,b2)
```
#Plotting of Em of He+H-implanted sample x=np.arange(0,1.1,0.000005)

#y=a1\*exp(x\*b1)+a2\*exp(x\*b2)-1, is not available here, use y=y1+y2 y1=a1\*np.exp(x\*b1)

Measurement of Vacancy Migration Energy by Using HVEM DOI: http://dx.doi.org/10.5772/intechopen.87131

```
y2=a2*np.exp(x*b2)-1
  y=y1+y2
  i=len(x)-1
  while y[i]>0.00001:
    i=i-1
  else:
    print('Em:',2*x[i]) #M. Kiritani, H. Takata, K. Moriyama, et al., Philos. Mag. A,
40 (1979) 779-802.
    print('y:',y[i])
  He+H_data={'y=a1*exp(x*b1)+a2*exp(x*b2)-1':y,
              'Em':x}
  df1=pd.DataFrame(He+H_data)
  df1.to_csv('.\\He+H_data.csv')
  plot1=plt.plot(x,y,'r',label='He+H implanted')
  plt.xlabel('E')
  plt.ylabel('y in the equation')
  plt.legend(loc=2)
  plt.show()
  plt.savefig('p1.png')
```