# Photodiode bandwidth: why does power decrease with frequency

• I
• Jalo
In summary, the photocurrent in a p-i-n photodiode is directly proportional to the average power of the incident light signal. However, when the signal is modulated at a certain frequency, the instantaneous photocurrent response will not reproduce the waveform due to delays in the linear response of the photodiode. This results in a frequency response with a characteristic high frequency roll-off, and the bandwidth of the response is determined by the delay in the response. The linear response function can be modeled using an empirical function such as ## m(t)=\frac{A}{\tau} e^{-t/\tau} ##, where ## t>0 ##, and ## \tau ## is a constant.
Jalo
Hi,

I'm studying p-i-n photodiode (PD) at the moment and understand that the photodiode's response will depend on the frequency of the light signal going into it. I am struggling however to understand the concept of bandwidth, and why is it that the photocurrent at the PD decreases with higher frequencies.

1. What exactly is bandwidth? My understanding it that when we launch light into the PD, it will be absorbed in the PD's depletion region, originating an electron-hole pair that will be swept across the depletion range (drift) and afterwards diffuse through the bulk semiconductor region (diffusion) until it reaches the metal contacts. If we have an oscillating light signal going into the PD, how exactly does the signal's frequency change this process, or make it less effective? Is the collection of electrons/holes less efficient at high frequencies somehow? If so, why?

2. When we talk about 3dB bandwidth, am I correct in that this is the frequency at which the photocurrent measured in the PD is half of that measured when the signal is not oscillating (0 Hz)? If so, is the process of measuring bandwidth a matter of sending first a constant signal into the PD and then simply increase the signal's frequency, keeping it's amplitude, and waiting until the photocurrent collected at the PD halves?

Apologies if the questions are a bit daft, but I've just started studying this and am struggling to get a good intuition of the PD's dependency on the light signal's frequency. Thank you very much.

For a photodiode in the linear region, you will get a total photocurrent generated that is proportional to the average power of the incident signal, (the total charge that results is proportional to the incident energy), but if the incident signal is modulated at some frequency, in general you can not expect the instantaneous photocurrent of the photodiode to respond in such away that it reproduces the waveform. The linear response of the photodiode to a delta function incident power input, in the case of a perfectly linear response, will experience some delays. The result is linear response theory works very well, but do expect a frequency response with a characteristic high frequency roll-off. ## \\ ## To express this mathematically , photocurrent ## I(t)=\int\limits_{- \infty}^{t} P(t')m(t-t') \, dt' ##, where ## m(t) ## is the linear response function, and ## P(t) ## is the incident power. ##\\ ## The convolution theorem says ## \tilde{I}(\omega)=\tilde{P}(\omega) \tilde{m}(\omega) ##, where the Fourier transform ## \tilde{F}(\omega)=\int\limits_{-\infty}^{+\infty} F(t)e^{-i \omega t} \, dt ##. ## \\ ## (So that ## \tilde{m}(\omega)=\int\limits_{-\infty}^{+\infty} m(t)e^{-i \omega t} \, dt ##, and similarly for ## \tilde{I}(\omega) ##, and ## \tilde{P}(\omega)## ). ## \\ ## (The photocurrent response at any frequency will be proportional to the incident power at that frequency). ## \\ ## If ## m(t) ## is not instantaneous (i.e. if it is not a delta function), then there will be a (finite) frequency response associated with ## \tilde{m}(\omega) ## with a high frequency roll-off in the response.## \\ ## If ## m(t ) ## is instantaneous=a delta function, in that case the bandwidth of the response is infinite, and ## \tilde{m}(\omega) ## is a constant, independent of frequency. ## \\ ## ( For the sake of completeness, the inverse Fourier transform ## F(t)=\frac{1}{2 \pi} \int\limits_{-\infty}^{+\infty} \tilde{F}(\omega) e^{+i \omega t} \, d \omega ## ). ## \\ ## And note: This is the same kind of linear response that is used in ac circuit theory. The response of the photodiode is assumed to be perfectly linear. Any delay in the response that is spread out over time results in a frequency dependent response. ## \\ ## For a quick review: In the ac circuit linear response theory, we write ## V_{out}(t)=\int\limits_{-\infty}^{t} V_{in}(t') m(t-t') \, dt' ##, and ## \tilde{V}_{out}(\omega)=\tilde{V}_{in}(\omega) \tilde{m}(\omega) ##. ## \\ ## e.g. For a simple RC circuit, ## \tilde{m}(\omega)= \frac{-i/(\omega C)}{R-i/(\omega C ) } ## by simply using known impedances, etc., where ## V_{out} ## is measured across the capacitor. Alternatively, it could be computed from ## m(t)=(\frac{1}{RC})e^{-t/(RC)} ## for ## t>0 ##. ## \\ ## Also note of ## M(t) ## is the response to a unit step input for ## V_{in}(t) ##, then ##m(t)=\frac{dM(t)}{dt} ##, and ## m(t) ## is the response when ## V_{in}(t) ## is a delta function. ## \\ ## For the above photodiode, the empirical function ## m(t)=\frac{A}{\tau} e^{-t/\tau} ##, (## t>0 ##), for constants ## A ## and ## \tau ## can be a good starting point for simple modeling of the response.

Last edited:
hagopbul

## 1. What is a photodiode bandwidth?

A photodiode bandwidth refers to the range of frequencies of light that a photodiode can detect and convert into an electrical signal. It is typically measured in hertz (Hz) and can vary depending on the design and materials of the photodiode.

## 2. Why does the power decrease with frequency in a photodiode?

The power decrease with frequency in a photodiode is due to the inherent capacitance of the device. As the frequency of the light increases, the capacitance of the photodiode decreases, resulting in a decrease in the amount of charge that can be collected and therefore a decrease in the power output.

## 3. How does the bandwidth affect the performance of a photodiode?

The bandwidth of a photodiode directly affects its response time and sensitivity. A wider bandwidth allows the photodiode to detect and respond to a larger range of frequencies, resulting in a faster response time and higher sensitivity. A narrower bandwidth may limit the photodiode's ability to detect certain frequencies of light.

## 4. Can the bandwidth of a photodiode be increased?

Yes, the bandwidth of a photodiode can be increased by optimizing the design and materials of the device. This can include reducing the capacitance and increasing the surface area of the photodiode, as well as using materials with higher carrier mobility and lower recombination rates.

## 5. How does temperature affect the bandwidth of a photodiode?

The bandwidth of a photodiode can be affected by temperature due to changes in the device's capacitance and carrier mobility. As temperature increases, the capacitance decreases, resulting in a narrower bandwidth. Additionally, carrier mobility may also decrease at higher temperatures, further affecting the bandwidth and overall performance of the photodiode.

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