# Where do photons excite electrons in the PN junction?

Assuming a Si-Boron P-type, and Si-Phosphorous N-type solar cell.

N-type is on top and P-type is bottom.

I understand that after both semiconductors are layered a depletion zone is formed. Where e- from N-type move to P-type. This results in an electric field.

Then I'm not clear what happens. Photons come in through the N-type and strike atoms where exactly? Are they striking Si, P, or B, and in which part of the PN junction.

Thank you for clarifying!

• The material has a band structure, so asking about hitting individual atoms is not a useful question. Photons are generating electron-hole pairs throughout the material, until the photons are all absorbed. In and near the depletion layer is where you separate charge. – Jon Custer Feb 26 '19 at 14:07
• but these cells efficiency is calculated based on the band gap of silicon/ SQ limit, so photons are probably exciting electrons in the valence shells of silicon. And is the charge separation occurring in P side of the depletion zone? Also what does the silicon orbitals in these bonds look like, are they sp3 hybridized? – dlight Feb 26 '19 at 20:37
• The photons are exciting electrons from the crystal’s valence band. These are extended states not associated with specific atoms. Solid state physics, not atomic physics. – Jon Custer Feb 26 '19 at 21:09
• I see. How would I determine the band gap for the silicon-boron crystal? Can you try to indicate the molecular orbital which the e- are in before and which antibonding orbital they are in after excitation – dlight Feb 27 '19 at 16:08
• I meant the typical silicon doped with boron used for P-type side. so not degenerately doped. – dlight Feb 28 '19 at 8:39

When a silicon photodiode or photovoltaic cell is exposed to visible light, for example a solar spectrum where almost all of the intensity is well above the band gap, the conversion of photons to electron-hole pairs starts right at the front entrance, and decays exponentially inwards.

It's then the job of diffusion, plus any electric fields produced by self-bias (due to doping) or externally applied bias (in the case of biased photodiodes) to separate the electrons from the holes so that each can be collected at one of the electrodes.

The P-N junction produces a natural electric field within the silicon, and results in the drift of the electrons in one direction and the holes in the other.

From PV Education.org's Optical Properties of Silicon we can see the absorptivity is very strong for blue light around 450 nm, and much weaker for red light at 650 nm. The most likely place for photons to be converted to electron-hole pairs is always the entrance face of the silicon, but the average depth is a strong function of wavelength.

Here's a plot of the normalized conversion rate based on this simple model for three different visible wavelengths. Most of the power available to silicon in sunlight is within this range.

Here's the script so that you can look it in more depth:

info = """250   1.84E+06   1.694   3.666
260   1.97E+06   1.800   4.072
270   2.18E+06   2.129   4.690
280   2.36E+06   3.052   5.258
290   2.24E+06   4.426   5.160
300   1.73E+06   5.055   4.128
310   1.44E+06   5.074   3.559
320   1.28E+06   5.102   3.269
330   1.17E+06   5.179   3.085
340   1.09E+06   5.293   2.951
350   1.04E+06   5.483   2.904
360   1.02E+06   6.014   2.912
370   6.97E+05   6.863   2.051
380   2.93E+05   6.548   0.885
390   1.50E+05   5.976   0.465
400   9.52E+04   5.587   0.303
410   6.74E+04   5.305   0.220
420   5.00E+04   5.091   0.167
430   3.92E+04   4.925   0.134
440   3.11E+04   4.793   0.109
450   2.55E+04   4.676   0.091
460   2.10E+04   4.577   0.077
470   1.72E+04   4.491   0.064
480   1.48E+04   4.416   0.057
490   1.27E+04   4.348   0.050
500   1.11E+04   4.293   0.045
510   9.70E+03   4.239   0.039
520   8.80E+03   4.192   0.036
530   7.85E+03   4.150   0.033
540   7.05E+03   4.110   0.030
550   6.39E+03   4.077   0.028
560   5.78E+03   4.044   0.026
570   5.32E+03   4.015   0.024
580   4.88E+03   3.986   0.023
590   4.49E+03   3.962   0.021
600   4.14E+03   3.939   0.020
610   3.81E+03   3.916   0.018
620   3.52E+03   3.895   0.017
630   3.27E+03   3.879   0.016
640   3.04E+03   3.861   0.015
650   2.81E+03   3.844   0.015
660   2.58E+03   3.830   0.014
670   2.38E+03   3.815   0.013
680   2.21E+03   3.800   0.012
690   2.05E+03   3.787   0.011
700   1.90E+03   3.774   0.011
710   1.77E+03   3.762   0.011
720   1.66E+03   3.751   0.010
730   1.54E+03   3.741   0.009
740   1.42E+03   3.732   0.008
750   1.30E+03   3.723   0.008
760   1.19E+03   3.714   0.007
770   1.10E+03   3.705   0.007
780   1.01E+03   3.696   0.006
790   9.28E+02   3.688   0.006
800   8.50E+02   3.681   0.005
810   7.75E+02   3.674   0.005
820   7.07E+02   3.668   0.005
830   6.47E+02   3.662   0.004
840   5.91E+02   3.656   0.004
850   5.35E+02   3.650   0.004
860   4.80E+02   3.644   0.003
870   4.32E+02   3.638   0.003
880   3.83E+02   3.632   0.003
890   3.43E+02   3.626   0.002
900   3.06E+02   3.620   0.002
910   2.72E+02   3.614   0.002
920   2.40E+02   3.608   0.002
930   2.10E+02   3.602   0.002
940   1.83E+02   3.597   0.001
950   1.57E+02   3.592   0.001
960   1.34E+02   3.587   0.001
970   1.14E+02   3.582   0.001
980   9.59E+01   3.578   0.001
990   7.92E+01   3.574   0.001
1000   6.40E+01   3.570   0.001"""
# https://www.pveducation.org/pvcdrom/materials/optical-properties-of-silicon
# M. A. Green and Keevers, M. J., Optical properties of intrinsic silicon at 300 K, Progress in Photovoltaics: Research and Applications, vol. 3, pp. 189-192, 1995
# M. A. Green, Self-consistent optical parameters of intrinsic silicon at 300 K including temperature coefficients, Solar Energy Materials and Solar Cells, vol. 92, pp. 1305-1310, 2008

import numpy as np
import matplotlib.pyplot as plt

splitlines = [[float(x) for x in line.split()] for line in info.splitlines()]
lam, a_cm, n, k = np.array(zip(*splitlines))

if True:
plt.plot(lam, 1E-04 * a_cm)
plt.yscale('log')
plt.xlabel('wavelength (nm)', fontsize=16)
plt.ylabel('atten. coeff. (um^-1)', fontsize=16)
plt.show()

lams     = (450, 550, 650)
a_cms    = (2.55E+04, 6.39E+03, 2.81E+03)
a_ums    = [1E-04 * x for x in a_cms]
depth_um = np.arange(0, 10, 0.01)
curves   = [np.exp(-depth_um * a_um) for a_um in a_ums]

if True:
colors = ('b', 'g', 'r')
labels = ((1, 0.125, '450nm'), (2.5, 0.225, '550nm'), (3.5, 0.40, '650nm'))
for curve, color, (x, y, text) in zip(curves, colors, labels):
plt.plot(depth_um, curve, color, linewidth=2)
plt.text(x, y, text, fontsize=14)
plt.xlabel('depth into silicon (um)', fontsize=16)
plt.ylabel('remaining intensity (normalized)', fontsize=16)
plt.show()