# Responsivity

Last updated

Responsivity measures the input–output gain of a detector system. In the specific case of a photodetector, responsivity measures the electrical output per optical input.

In electronics, gain is a measure of the ability of a two-port circuit to increase the power or amplitude of a signal from the input to the output port by adding energy converted from some power supply to the signal. It is usually defined as the mean ratio of the signal amplitude or power at the output port to the amplitude or power at the input port. It is often expressed using the logarithmic decibel (dB) units. A gain greater than one, that is amplification, is the defining property of an active component or circuit, while a passive circuit will have a gain of less than one.

Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation. A photo detector has a p–n junction that converts light photons into current. The absorbed photons make electron–hole pairs in the depletion region. Photodiodes and photo transistors are a few examples of photo detectors. Solar cells convert some of the light energy absorbed into electrical energy.

The responsivity of a photodetector is usually expressed in units of either amperes or volts per watt of incident radiant power. For a system that responds linearly to its input, there is a unique responsivity. For nonlinear systems, the responsivity is the local slope. Many common photodetectors respond linearly as a function of the incident power.

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

The watt is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by .

Responsivity is a function of the wavelength of the incident radiation and of the sensor properties, such as the bandgap of the material of which the photodetector is made. [1] One simple expression for the responsivity R of a photodetector in which an optical signal is converted into an electric current (known as a photocurrent) is

In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is thus the inverse of the spatial frequency. Wavelength is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ). The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating (radiating) through space, carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays.

Photocurrent is the electric current through a photosensitive device, such as a photodiode, as the result of exposure to radiant power.

${\displaystyle R=\eta {\frac {q}{hf}}\approx \eta {\frac {\lambda _{(\mu m)}}{1.23985(\mu m\times W/A)}}}$

where ${\displaystyle \eta }$ is the quantum efficiency (the conversion efficiency of photons to electrons) of the detector for a given wavelength, ${\displaystyle q}$ is the electron charge, ${\displaystyle f}$ is the frequency of the optical signal, and ${\displaystyle h}$ is Planck's constant. [2] This expression is also given in terms of ${\displaystyle \lambda }$, the wavelength of the optical signal, and has units of amperes per watt (A/W).

The term quantum efficiency (QE) may apply to incident photon to converted electron (IPCE) ratio, of a photosensitive device or it may refer to the TMR effect of a Magnetic Tunnel Junction.

The term responsivity is also used to summarize input–output relationship in non-electrical systems. For example, a neuroscientist may measure how neurons in the visual pathway respond to light. In this case, responsivity summarizes the change in the neural response per unit signal strength. The responsivity in these applications can have a variety of units. The signal strength typically is controlled by varying either intensity (intensity-response function) or contrast (contrast-response function). The neural response measure depends on the part of the nervous system under study. For example, at the level of the retinal cones, the response might be in photocurrent. In the central nervous system the response is usually spikes per second. In functional neuroimaging, the response measure is usually BOLD contrast. The responsivity units reflect the relevant stimulus and physiological units.

When describing an amplifier, the more common term is gain.

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal. It is a two-port electronic circuit that uses electric power from a power supply to increase the amplitude of a signal applied to its input terminals, producing a proportionally greater amplitude signal at its output. The amount of amplification provided by an amplifier is measured by its gain: the ratio of output voltage, current, or power to input. An amplifier is a circuit that has a power gain greater than one.

Deprecated synonym sensitivity. A system's sensitivity is the inverse of the stimulus level required to produce a threshold response, with the threshold typically chosen just above the noise level.

The sensitivity of an electronic device, such as a communications system receiver, or detection device, such as a PIN diode, is the minimum magnitude of input signal required to produce a specified output signal having a specified signal-to-noise ratio, or other specified criteria.

## Related Research Articles

In mathematics convolution is a mathematical operation on two functions to produce a third function that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, it differs from cross-correlation only in that either f (x) or g(x) is reflected about the y-axis; thus it is a cross-correlation of f (x) and g(−x), or f (−x) and g(x). For continuous functions, the cross-correlation operator is the adjoint of the convolution operator.

In engineering, a transfer function of an electronic or control system component is a mathematical function which theoretically models the device's output for each possible input. In its simplest form, this function is a two-dimensional graph of an independent scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory.

Noise-equivalent power (NEP) is a measure of the sensitivity of a photodetector or detector system. It is defined as the signal power that gives a signal-to-noise ratio of one in a one hertz output bandwidth. An output bandwidth of one hertz is equivalent to half a second of integration time. The units of NEP are watts per square root hertz. The NEP is equal to the noise spectral density divided by the responsivity.

Specific detectivity, or D*, for a photodetector is a figure of merit used to characterize performance, equal to the reciprocal of noise-equivalent power (NEP), normalized per square root of the sensor's area and frequency bandwidth.

A photodiode is a semiconductor device that converts light into an electrical current. The current is generated when photons are absorbed in the photodiode. Photodiodes may contain optical filters, built-in lenses, and may have large or small surface areas. Photodiodes usually have a slower response time as their surface area increases. The common, traditional solar cell used to generate electric solar power is a large area photodiode.

Fourier optics is the study of classical optics using Fourier transforms (FTs), in which the waveform being considered is regarded as made up of a combination, or superposition, of plane waves. It has some parallels to the Huygens–Fresnel principle, in which the wavefront is regarded as being made up of a combination of spherical wavefronts whose sum is the wavefront being studied. A key difference is that Fourier optics considers the plane waves to be natural modes of the propagation medium, as opposed to Huygens–Fresnel, where the spherical waves originate in the physical medium.

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

In radiometry, photometry and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.

Spectroradiometers are devices designed to measure the spectral power distribution of a source. From the spectral power distribution, the radiometric, photometric, and colorimetric quantities of light can be determined in order to measure, characterize, and calibrate light sources for various applications.

An optical medium is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by

Optical resolution describes the ability of an imaging system to resolve detail in the object that is being imaged.

In mathematics, the spectral theory of ordinary differential equations is the part of spectral theory concerned with the determination of the spectrum and eigenfunction expansion associated with a linear ordinary differential equation. In his dissertation Hermann Weyl generalized the classical Sturm–Liouville theory on a finite closed interval to second order differential operators with singularities at the endpoints of the interval, possibly semi-infinite or infinite. Unlike the classical case, the spectrum may no longer consist of just a countable set of eigenvalues, but may also contain a continuous part. In this case the eigenfunction expansion involves an integral over the continuous part with respect to a spectral measure, given by the Titchmarsh–Kodaira formula. The theory was put in its final simplified form for singular differential equations of even degree by Kodaira and others, using von Neumann's spectral theorem. It has had important applications in quantum mechanics, operator theory and harmonic analysis on semisimple Lie groups.

Spectral sensitivity is the relative efficiency of detection, of light or other signal, as a function of the frequency or wavelength of the signal.

A Quantum Well Infrared Photodetector (QWIP) is an infrared photodetector, which uses electronic intersubband transitions in quantum wells to absorb photons. In order to be used for infrared detection, the parameters of the quantum wells in the quantum well infrared photodetector are adjusted so that the energy difference between its first and second quantized states match the incoming infrared photon energy. QWIPs are typically made of gallium arsenide, a material commonly found in smartphones and high-speed communications equipment. Depending on the material and the design of the quantum wells, the energy levels of the QWIP can be tailored to absorb radiation in the infrared region from 3 to 20 µm.

Resonant-cavity-enhanced photo detectors enable improved performance over their predecessors by placing the active device structure inside a Fabry–Pérot resonant cavity. Though the active device structure of the RCE detectors remains close to other conventional photodetectors, the effect of the optical cavity, which allows wavelength selectivity and an enhancement of the optical field due to resonance, allows the photo detectors to be made thinner and therefore faster, while simultaneously increasing the quantum efficiency at the resonant wavelengths.

In mathematics, an ambit field is a d-dimensional random field describing the stochastic properties of a given system. The input is in general a d-dimensional vector assigning a real value to each of the points in the field. In its most general form, the ambit field, , is defined by a constant plus a stochastic integral, where the integration is done with respect to a Lévy basis, plus a smooth term given by an ordinary Lebesgue integral. The integrations are done over so-called ambit sets, which is used to model the sphere of influence which affect a given point.

Impedance control is an approach to dynamic control relating force and position. It is often used in applications where a manipulator interacts with its environment and the force position relation is of concern. Examples of such applications include humans interacting with robots, where the force produced by the human relates to how fast the robot should move/stop.

## References

1. Paschotta, Dr. Rüdiger. "Encyclopedia of Laser Physics and Technology - responsivity, photodetectors, photodiodes, sensitivity". www.rp-photonics.com. Retrieved 2018-08-21.
2. Kenneth W. Busch, Marianna A. Busch (1990). Multielement Detection Systems for Spectrochemical Analysis. Wiley-Interscience. ISBN   0-471-81974-3.

This article incorporates  public domain material from the General Services Administration document "Federal Standard 1037C" (in support of MIL-STD-188 ).