A photodetector (PD) converts received optical signals into electrical signals, thus completing the optical-to-electrical signal conversion. The basic requirements for a PD are:
1) It possesses sufficiently high responsivity at the system's operating wavelength, meaning it can output the largest possible photocurrent for a given incident light power.
2) It has a sufficiently fast response speed, suitable for high-speed or broadband systems.
3) It has the lowest possible noise to minimize the device's influence on the signal.
4) They feature small size and long operating life.
Currently, there are two commonly used semiconductor photodetectors: PIN photodiodes (PIN-PDs) and avalanche photodiodes (APDs). This section mainly introduces the principles, performance indicators, and two commonly used types of photodetectors.
Principle of photodetectors
Photodetectors utilize the photoelectric effect of semiconductor materials to achieve photoelectric conversion. The photoelectric effect of semiconductor materials is shown in the figure below.
When the energy hv of the incident photon is less than the band gap E, the photoelectric effect will not occur regardless of the intensity of the incident light. That is, the following condition must be met for the photoelectric effect to occur:
In other words, incident light with a frequency v < E/h cannot produce the photoelectric effect. Converting v to wavelength, λc = hc/E. That is, only incident light with a wavelength λ < λc can generate photogenerated carriers in this material. Therefore, λc is the maximum wavelength of incident light required to produce the photoelectric effect, also known as the cutoff wavelength, and the corresponding v is called the cutoff frequency. Each photon absorbed by a semiconductor material will generate an electron-hole pair. If an electric field is applied to the semiconductor material, the electron-hole pair will travel through the semiconductor material, forming a photocurrent.
Besides having a cutoff wavelength, the photodiode's conversion efficiency decreases when the incident light wavelength is too short. In a photodiode, incident photons are absorbed, generating electron-hole pairs. When the distance x = 0, the optical power is P(0). After a distance x, the absorbed optical power is：
In the formula, α(λ) is the absorption coefficient of the material, which is a function of wavelength.
When the incident light wavelength is very short, the absorption coefficient of the material is very large. As a result, a large number of photons are absorbed at the surface of the photodiode, creating a zero-electric-field region. Electron-hole pairs generated here must first diffuse to the depletion layer before being collected by the external circuit. However, in this region, minority carriers have very short lifetimes and diffuse very slowly, often recombinating before being collected. This reduces the efficiency of the photodetector. Therefore, photodiodes made of certain materials have a specific wavelength response range. For example, the wavelength response range of Si photodiodes is 0.5–10 μm, and that of InGaAs photodiodes is 1.1–1.6 μm.
Characteristics of photodetectors
quantum efficiency
Incident light (power P) contains a large number of photons. The ratio of the number of photons that can be converted into photocurrent to the total number of incident photons is called the quantum efficiency, which is calculated by the following formula:
In the formula, α is the electron charge, α = 1.6 × 10⁻¹℃; I is the generated photocurrent; h is Planck's constant; and v is the frequency of the photon. The quantum efficiency ranges from 50% to 90%.
If the reflectivity of the incident surface is r, and the electron-hole pairs generated in the zero-electric-field surface layer cannot be effectively converted into photocurrent, and the incident light power is P(0), then the photocurrent is：
In the formula, α is the absorption coefficient of the zero-field region and the depletion layer, is the thickness of the zero-field region, and is the width of the depletion layer. The efficiency is then：
responsiveness
The ratio of photocurrent to incident light power in a photodetector is called responsivity (measured in A/W).
This characteristic indicates the efficiency of the photodetector in converting optical signals into electrical signals. Typical values for R range from 0.5 to 1.0 A/W. For example, the R value for a Si photodetector is 0.65 A/W at a wavelength of 900 nm; the R value for a Ge photodetector is 0.45 A/W (at 1300 nm); and the responsivity of InGaAs is 0.9 A/W at 1300 nm and 1.0 A/W at 1550 nm.
For a given wavelength, the responsivity is a constant, but it is not constant when considering a large wavelength range. As the wavelength of the incident light increases, the energy of the incident photons decreases, and when it is less than the bandgap, the responsivity drops rapidly at the cutoff wavelength.
Response spectrum
In order to generate photogenerated carriers, the energy of the incident photon must be greater than the bandgap of the photodetector material. This condition can be expressed as follows:
In the formula, λ is the cutoff wavelength.
In other words, for a given semiconductor detection material, only light with wavelengths shorter than the cutoff wavelength can be detected, and the quantum efficiency of the detector varies with wavelength; this characteristic is called the response spectrum. Therefore, photodetectors are not universal, and the response spectra of different materials differ. Commonly used photoelectric semiconductor materials include Si, Ge, InGaAs, InGaAsP, and GaAsP, and their response spectra are shown in Figure x.
Response time
The rate at which the photocurrent generated by a photodiode follows the incident light signal is typically expressed as response time. Response time is a parameter reflecting the photodetector's ability to respond to transient or high-speed modulated light signals. It is mainly affected by the following three factors:
1) The transit time of photocarriers in the depletion region.
2) The diffusion time of photocarriers generated outside the depletion region.
3) The RC time constant of the photodiode and its associated circuitry.
Response time can be expressed as the rise time and fall time of the output pulse of a photodetector. When the junction capacitance of the photodiode is relatively small, the rise time and fall time are short and relatively consistent; when the junction capacitance of the photodiode is relatively large, the response time is limited by the RC time constant formed by the load resistance and junction capacitance, resulting in longer rise and fall times.
Generally, the technical specifications of photodetectors provide the rise time. For PIN photodiodes, the rise time t0 is typically <1 ns; for APDs, this value is less than 0.5 ns.
Dark current
Dark current refers to the current in a photodetector when there is no incident light. Although there is no incident light, at a certain temperature, external heat energy can generate some free charges in the depletion region. These charges flow under the influence of a reverse bias voltage, forming a dark current. Obviously, the higher the temperature, the more electrons are excited by temperature, and the larger the dark current. For a PIN photodiode, let the dark current at temperature T be I(T). When the temperature rises to T, then:
In the formula, C is an empirical constant, and C=8 for Si photodiode.
The dark current ultimately determines the minimum detectable optical power, which is the sensitivity of the photodiode.
Depending on the semiconductor material used, the dark current varies between 0.1 and 500 nA.
