# Integrated Photodetectors Based on Group IV and Colloidal Semiconductors: Current State of Affairs
## 2 Figure of Merits for Characterizing Photodetectors  
In order to characterize the performance of photodetectors and compare different kinds of PD, some key figure-of-merit parameters are typically used. The main ones are summarized below [25; 26]:  
Figure 1: Composition and wavelength diagram of semiconductor material systems (Reprinted from [[PERSON]; [PERSON]; [PERSON] Third-generation infrared photodetector arrays. _J. Appl. Phys._**2009**, _105_, 091101, doi:10.1063/1.3099572], with the permission of AIP Publishing). * _Quantum efficiency (QE)_: is the number of carriers (electrons or holes) generated per photon of a given energy. There are two types of QE: Internal quantum efficiency (IQE) that represents the number of charge carriers collected by the PD to the number of absorbed photons of a given energy, and external quantum efficiency (EQE) that is the number of charge carriers collected by the PD to the number of incident photons of a given energy. * _Responsivity (R)_: The ratio of photogenerated current \(I_{ph}\) to input light power \(P_{in}\), indicating the electrical response of an optical signal in units of A W\({}^{-1}\), \[R=\frac{I_{ph}}{P_{in}}\] (1)
* _Spectral response_: Describes the responsivity of a PD as a function of photon frequency. * _Specific detectivity (D*)_: Represents the ability to detect weak optical signals. \(D^{*}\) depends on the specific measurement conditions comprising the bias voltage, operating temperature, wavelength and modulation frequency. It is expressed in units of cm Hz\({}^{1/2}\) W\({}^{-1}\) (Jones), \[D^{*}=\frac{R(A\Delta f)^{1/2}}{i_{n}}\] (2) where \(A\) is the effective area of the device, \(\Delta f\) is the electrical bandwidth and \(i_{n}\) is the noise current that includes the shot noise from the dark current, Johnson noise and flicker noise. However, \(D^{*}\) is generally considered in the shot noise limit, thus the Johnson noise and flicker noise can be neglected. Thus, Equation (2) can be simplified as \(D^{*}=RA^{1/2}/(2 el_{dark})^{1/2}\), where \(e\) is the electron charge, and \(I_{dark}\) is the dark current. * _Response time_: The time needed for a PD to rise or fall (\(\tau_{t}\)/\(\tau_{f}\)) from 10% to 90% or 90% to 10% of the final output. * _Noise-equivalent power (NEP)_: Indicates the lowest amount of light power needed to generate a signal comparable to the noise of the device (i.e., a signal-to-noise ratio of \(\approx\)1) when the electrical bandwidth of the noise measurement is equal to 1 Hz. The NEP (W Hz\({}^{-1/2}\)) is proportional to the reciprocal of \(D^{*}\), \[NEP=\frac{(A\Delta f)^{1/2}}{D^{*}}=\frac{i_{n}}{R}\] (3)
* \(-3\)_dB bandwidth (f\({}_{3 dB}\))_: Defined by the incident light modulation frequency at which the output signal is half-attenuated respect to its value under continuous wave illumination. * _Linear dynamic range (LDR)_: The range of incident light for which the detector responds linearly. * _Fill factor_: The ratio of a light sensitive area of a pixel to its total area, typically it characterizes an image sensor array. The effective fill factor can be increased, often to nearly 100%, by using microlenses. In an ideal photodiode, each photon of an input optical signal is immediately converted into a free electron and the generated current is linearly proportional to the input optical power. However, in real photodiodes, a lower absorption of photons and a leakage in carrier collection into the semiconductor material cause a non-perfect conversion in electrons of incoming photons. Moreover, the electric structures show an equivalent parasitic RC and the carrier transient effect limits the photodetection speed. Thus, the detection speed and the responsivity of a photodiode depend on the material quality, the bandgap structure of the semiconductor, the design of the device photonic and the electrodes [13].