LED based avalanched photodetector

3. Analysis and Result

Author: Cai Shijie Date: April 2025

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

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Average photon current pulse number vs voltage of power supply

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

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Average photon current pulse height vs voltage of power supply

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

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Pulse number distribution vs Poisson distribution

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by 0.245%. The Python, Arduino code, and QE calculation are attached in the appendix.

In conclusion, the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

Appendix

QE Estimation

Given Parameters

• Blue LED optical power: $P_{\text{blue}}=1\mu \text{W}=1\times 10^{-6}\text{W}$
• Wavelength of blue light: ${\lambda }_{\text{blue}}=450\text{nm}$
• Photon energy:

$E_{\text{ph}}=\frac{hc}{\lambda }=\frac{6.626\times 10^{-34}\cdot 3.0\times 10^8}{450\times 10^{-9}}\approx 4.42\times 10^{-19}\text{J}$

• Photon emission rate:

$N_{\text{emit}}=\frac{P_{\text{blue}}}{E_{\text{ph}}}=\frac{1\times 10^{-6}}{4.42\times 10^{-19}}\approx 2.26\times 10^{12}\text{photons/s}$

• Emission duration: $\mathrm{\Delta }t=50\text{ms}=0.05\text{s}$
• Distance between LEDs: $d=0.1\text{m}$
• Red LED pn-junction radius: $r=17\mu \text{m}=1.7\times 10^{-5}\text{m}$
• Entrance area of the pn-junction:

$A=\pi r^2=\pi (1.7\times 10^{-5}{)}^2\approx 9.08\times 10^{-10}{\text{m}}^2$

• Solid angle covered by receiving junction:

$\mathrm{\Omega }=\frac{A}{d^2}=\frac{9.08\times 10^{-10}}{(0.1{)}^2}=9.08\times 10^{-8}\text{sr}$

• Fraction of photons geometrically intercepted:

$f=\frac{\mathrm{\Omega }}{4\pi }=\frac{9.08\times 10^{-8}}{4\pi }\approx 7.23\times 10^{-9}$

• Shell transmission rate at 450 nm (approximate): $T_{\text{shell}}=0.2$
• Number of detected photo-pulses: $N_{\text{detected}}=4$

Photons Reaching the pn-Junction in 50 ms: $N_{\text{incident}}=N_{\text{emit}}\cdot \mathrm{\Delta }t\cdot f\cdot T_{\text{shell}}=2.26\times 10^{12}\cdot 0.05\cdot 7.23\times 10^{-9}\cdot 0.2\approx 1.63\times 10^3$

$\eta =\frac{N_{\text{detected}}}{N_{\text{incident}}}=\frac{4}{1.63\times 10^3}\approx 2.45\times 10^{-3}=0.245\mathrm{\%}$

Conclusion: Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately 0.245%. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

Code Listings

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Arduino code