Python을 이용한 Hecht equation fitting

운반자의 이동도와 수명의 곱을 계산하기 위한 파이썬 프로그래밍의 예제이다.

 

import matplotlib

import matplotlib.pyplot as plt

from matplotlib import style

from matplotlib import pylab

import numpy as np

from scipy.optimize import curve_fit

# bias data and peak position channel data

xs=np.array([35,100,150,200,250,300])

ys=np.array([100,133,145,152,159,162])

#detector thickness in cm.

det_thick=0.2

#define fitting function

def expo_func(x, m, t):

return m*x*(1 - np.exp(-t/x) )

popt, pcov = curve_fit(expo_func, xs, ys, p0=(30, 40))

a, b = popt

c=det_thick*det_thick/b

xx = np.linspace(0.1,400,1000)

yy = expo_func(xx, *popt)

# calculation of R squared

r2 = 1. - sum((expo_func(xs, *popt) - ys) ** 2) / sum((ys - np.mean(ys)) ** 2)

plt.plot(xs,ys,'o',label="data")

plt.plot(xx, yy,'--',label="fitting")

pylab.title('Hecht equation fitting')

ax = plt.gca()

ax.set_ylim(0,300)

ax.set_xlim(0,350)

fig = plt.gcf()

plt.legend(loc='upper left')

plt.xlabel(r'Bias (V)')

plt.ylabel(r'Peak position (channel)')

plt.text(150,250, "R$^2$: {}".format(r2))

plt.text(150,200,"($\mu$$\\tau$)$_e$ = {:.5f} cm$^2$/V".format(c))

plt.show()

결과물은 다음과 같다.