Phonon noise
Encyclopedia
Phonon noise, also known as thermal fluctuation noise, arises from the random exchange of energy
between a thermal mass and its surrounding environment. This energy is quantized in the form of phonons. Each phonon has an energy of order
, where 
is Boltzmann's constant and 
is the temperature
. The random exchange of energy leads to fluctuations in temperature. This occurs even when the thermal mass and the environment are in thermal equilibrium
, i.e. at the same time-average temperature. If a device has a temperature-dependent electrical resistance
, then these fluctuations in temperature lead to fluctuations in resistance. Examples of devices where phonon noise is important include bolometers and calorimeters
. The superconducting transition edge sensor
(TES), which can be operated either as a bolometer or a calorimeter, is an example of a device for which phonon noise can significantly contribute to the total noise.
Although Johnson–Nyquist noise
shares many similarities with phonon noise (e.g. the noise spectral density
depends on the temperature and is white
at low frequencies), these two noise sources are distinct. Johnson-Nyquist noise arises from the random thermal motion of electron
s, whereas phonon noise arises from the random exchange of phonons. Johnson-Nyquist noise is easily modeled at thermal equilibrium
, where all components of the circuit are held at the same temperature. A general equilibrium model for phonon noise is usually impossible because different components of the thermal circuit are nonuniform in temperature and also often not time invariant, as in the occasional energy deposition from particles incident on a detector. The transition edge sensor
typically maintains the temperature through negative electrothermal feedback
associated with changes in internal electrical power.
An approximate formula for the noise-equivalent power
(NEP) due to phonon noise in a bolometer when all components are very close to a temperature T is
where G is the thermal conductance. In calorimetric detectors, the rms
energy resolution
due to phonon noise near quasi-equilibrium is described using a similar formula
where C is the heat capacity.
A real bolometer or calorimeter is not at equilibrium because of a temperature gradient between the absorber and the bath. Since G and C are generally nonlinear functions of temperature, a more advanced model may include the temperature of both the absorber and the bath and treat G or C as a power law
across this temperature range.
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
between a thermal mass and its surrounding environment. This energy is quantized in the form of phonons. Each phonon has an energy of order
, where is Boltzmann's constant and is the temperatureTemperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
. The random exchange of energy leads to fluctuations in temperature. This occurs even when the thermal mass and the environment are in thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
, i.e. at the same time-average temperature. If a device has a temperature-dependent electrical resistance
Electrical resistance
The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...
, then these fluctuations in temperature lead to fluctuations in resistance. Examples of devices where phonon noise is important include bolometers and calorimeters
Calorimeter (particle physics)
In particle physics, a calorimeter is an experimental apparatus that measures the energy of particles. Most particles enter the calorimeter and initiate a particle shower and the particles' energy is deposited in the calorimeter, collected, and measured. The energy may be measured in its...
. The superconducting transition edge sensor
Transition edge sensor
A transition edge sensor or TES is a type of cryogenic particle detector that exploits the strongly temperature-dependent resistance of the superconducting phase transition.-Principle of operation:...
(TES), which can be operated either as a bolometer or a calorimeter, is an example of a device for which phonon noise can significantly contribute to the total noise.
Although Johnson–Nyquist noise
Johnson–Nyquist noise
Johnson–Nyquist noise is the electronic noise generated by the thermal agitation of the charge carriers inside an electrical conductor at equilibrium, which happens regardless of any applied voltage...
shares many similarities with phonon noise (e.g. the noise spectral density
Noise spectral density
In communications, noise spectral density No is the noise power per unit of bandwidth; that is, it is the power spectral density of the noise. It has dimension of power/frequency , whose SI coherent unit is watts per hertz, which is equivalent to watt-seconds or joules...
depends on the temperature and is white
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...
at low frequencies), these two noise sources are distinct. Johnson-Nyquist noise arises from the random thermal motion of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s, whereas phonon noise arises from the random exchange of phonons. Johnson-Nyquist noise is easily modeled at thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
, where all components of the circuit are held at the same temperature. A general equilibrium model for phonon noise is usually impossible because different components of the thermal circuit are nonuniform in temperature and also often not time invariant, as in the occasional energy deposition from particles incident on a detector. The transition edge sensor
Transition edge sensor
A transition edge sensor or TES is a type of cryogenic particle detector that exploits the strongly temperature-dependent resistance of the superconducting phase transition.-Principle of operation:...
typically maintains the temperature through negative electrothermal feedback
Electrothermal feedback
Electrothermal feedback is a concept in electronics that describes the interaction of the electric current and the temperature in a device with a temperature-dependent electrical resistance. This interaction arises from Joule heating....
associated with changes in internal electrical power.
An approximate formula for the noise-equivalent power
Noise-equivalent power
Noise-equivalent power 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...
(NEP) due to phonon noise in a bolometer when all components are very close to a temperature T is
where G is the thermal conductance. In calorimetric detectors, the rms
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
energy resolution
due to phonon noise near quasi-equilibrium is described using a similar formulawhere C is the heat capacity.
A real bolometer or calorimeter is not at equilibrium because of a temperature gradient between the absorber and the bath. Since G and C are generally nonlinear functions of temperature, a more advanced model may include the temperature of both the absorber and the bath and treat G or C as a power law
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
across this temperature range.