Calculate responsivity, photocurrent, shot noise, thermal noise, SNR, NEP, and specific detectivity D* for Si PD, InGaAs PD, APD, and PMT. Includes responsivity vs wavelength chart.
Parameters
Wavelength λ (nm)
nm
Optical power P (µW)
μW
Bandwidth BW (MHz)
MHz
Temperature T (°C)
°C
APD Gain M
Results
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R (A/W)
—
Ip (µA)
—
SNR (dB)
—
NEP (pW/√Hz)
—
D* (×10¹⁰ Jones)
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i_shot (pA/√Hz)
Resp
SNR vs Incident Power
Theory & Key Formulas
Responsivity: $R = \frac{QE \cdot e \cdot \lambda}{h c}$
What exactly is "responsivity" in this simulator? I see it changes when I slide the wavelength.
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Basically, responsivity ($R$) tells you how good your detector is at converting light into electrical current. It's measured in Amps per Watt (A/W). In practice, a higher $R$ means more current for the same amount of light. Try moving the wavelength slider above from 400 nm to 1000 nm for a Silicon detector. You'll see $R$ increase because each photon has less energy, so you get more electrons per watt of optical power.
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Wait, really? So if I increase the optical power ($P$) in the simulator, the photocurrent just goes up proportionally? What limits this?
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Exactly right—photocurrent $I_p = R \times P$. But the limit is noise. Even in total darkness, there's tiny random current called dark current. And the signal itself has "shot noise" because light arrives as discrete photons. A common case is in fiber-optic receivers: even with a strong signal, this inherent noise sets the minimum detectable power. Adjust the "Bandwidth" and "Temperature" sliders to see how they affect the noise values in the results.
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Okay, so NEP and D* in the results... they seem to get worse with more noise. Which one should I look at to choose the best detector for a low-light application?
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Great question! NEP (Noise-Equivalent Power) is the signal power that gives a signal-to-noise ratio of 1. Lower NEP is better. D* (pronounced "D-star") normalizes NEP for the detector's area and bandwidth, so you can compare different sized sensors. For instance, choosing between a small, sensitive APD and a large-area PMT for a LIDAR system? Compare their D* values in this simulator by switching the detector type and keeping other parameters the same.
Physical Model & Key Equations
The core relationship is the responsivity, which converts incident optical power into photocurrent. It depends on the quantum efficiency (QE) and the photon energy.
$$R = \frac{I_p}{P}= \frac{QE \cdot e \cdot \lambda}{h c}$$
Where $R$ is responsivity (A/W), $QE$ is quantum efficiency (unitless, set per detector material), $e$ is electron charge ($1.602 \times 10^{-19}$ C), $\lambda$ is wavelength (m), $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s), and $c$ is the speed of light ($3 \times 10^8$ m/s).
The total noise current determines the minimum detectable signal. It combines shot noise from the signal and dark current, plus thermal (Johnson) noise from the load resistor.
Where $I_d$ is dark current (A), $BW$ is electrical bandwidth (Hz), $k$ is Boltzmann's constant, $T$ is temperature (K), and $R_L$ is load resistance (Ω). From this, we derive NEP = $i_{noise}/ R$ and D* = $\sqrt{A \cdot BW} / $NEP, where $A$ is detector area.
Frequently Asked Questions
Are you calculating the wavelength dependence of quantum efficiency QE using the default values? For Si PDs and InGaAs PDs, the absorption coefficient of the material varies with wavelength, so QE is not constant. If you want to match the catalog, manually re-enter the representative QE value at the wavelength of interest.
First, increasing the load resistance RL reduces thermal noise and improves SNR. Next, if the dark current Id is large, assume cooling and set the Id value to a smaller value. Also, narrowing the bandwidth BW to the necessary minimum is effective. If you cannot increase the signal optical power, try reducing these noise sources.
Since APDs and PMTs internally multiply the photocurrent, the output current becomes M times. However, shot noise also increases during the multiplication process (considering the excess noise factor F), so simply multiplying by M does not necessarily improve SNR. This tool calculates NEP and SNR reflecting M and F, allowing you to obtain a guideline for the optimal multiplication factor.
This occurs when the content inside the square root in the NEP calculation formula becomes negative. The main cause is that the dark current Id or signal photocurrent Ip values are extremely small, and although the thermal noise term (4kT·BW/RL) is not dominant, the settings for load resistance RL or bandwidth BW are unrealistic. Re-enter practical values for each parameter (especially RL and BW).
Real-World Applications
Fiber-Optic Communications: InGaAs photodetectors are standard in telecom receivers for 1310 nm and 1550 nm light. Engineers use calculations like these to balance responsivity and bandwidth to achieve the required data rate and bit-error rate for your internet backbone.
LIDAR and 3D Sensing: Avalanche Photodiodes (APDs) are favored here for their internal gain (M). Designing a LIDAR for a self-driving car requires optimizing the gain to amplify weak return signals without introducing excessive excess noise, which you can explore with the "APD Gain M" slider.
Scientific Spectroscopy: For analyzing faint starlight or fluorescent samples, Photomultiplier Tubes (PMTs) offer extremely high gain and low dark current. Their superior NEP and D* make them ideal for photon-counting applications where every single photon matters.
Consumer Electronics: Silicon photodiodes are everywhere, from the ambient light sensor in your phone that adjusts screen brightness to barcode scanners. The design trade-off is between sensitivity (high R) and speed (high BW), which are inversely related—a key relationship visible in the simulator outputs.
Common Misconceptions and Points to Note
First, while it's easy to think "a sensor with high sensitivity is a good sensor," this is a pitfall. For example, an InGaAs photodiode with high sensitivity R excels in the near-infrared but is inferior to silicon in the visible range. By using the tool to observe sensitivity while changing the wavelength, you can appreciate that "high sensitivity" is specific to a particular wavelength band. Next, understand the relationship between bandwidth BW and "response speed." A 10MHz bandwidth corresponds to a response time of approximately 35ns. For high-speed applications like communications, you would set a larger bandwidth, but you can use this simulator to confirm the trade-off of increased noise that comes with it. Finally, dark current Id is highly sensitive to temperature. Try lowering the tool's temperature T parameter from room temperature (300K) to a cooled state (e.g., 250K). You should see a significant improvement in NEP. In actual design, pursuing higher performance means considering the balance between cost and performance, as cooling mechanisms become necessary.
Select wavelength (400–1700 nm) and detector type (Si, InGaAs, APD, PMT) using the wavelength slider or numerical input
Enter incident optical power (1 pW to 100 mW) via the power slider to calculate photocurrent Ip and responsivity R
Set bandwidth (1 Hz to 1 GHz) and operating temperature (250–350 K) to compute shot noise, NEP, and detectivity D*
Read SNR in dB, noise equivalent power in pW/√Hz, and specific detectivity to assess detection limit performance
Worked Example
For an InGaAs photodetector at λ=1550 nm (telecom band): assume incident power P=1 µW, bandwidth BW=100 MHz, temperature T=300 K. Responsivity R ≈ 0.9 A/W yields photocurrent Ip = 0.9 µA. Shot noise current i_shot = √(2qIp·BW) ≈ 38 pA/√Hz. NEP = i_shot/R ≈ 42 pW/√Hz. Detectivity D* = √(A·BW)/NEP where active area A=100 µm² yields D* ≈ 7.5×10¹¹ Jones. At 1 µW signal, SNR ≈ 18 dB.
Practical Notes
Silicon detectors dominate <900 nm; switch to InGaAs or Ge for 900–1700 nm infrared telecommunications and LIDAR applications
APD and PMT gain amplification reduces NEP by 10–100× but increases dark current exponentially; validate operating voltage against avalanche multiplication factor M
Thermal noise dominates at frequencies <10 MHz and high temperatures (>320 K); cryogenic cooling (<200 K) recovers 3–6 dB SNR for sensitive spectroscopy
D* scales with √A; small 10 µm² detectors achieve D*>10¹³ Jones but require impedance matching to low-noise transimpedance amplifiers (noise figure <3 dB)