Phonon noise

Phonon noise, also known as thermal fluctuation noise, arises from the random exchange of <a href="/facts/Energy/wd8PrQM7">energy</a> between a thermal mass and its surrounding environment. This energy is quantized in the form of <a href="/facts/Phonons/tflWW6vw">phonons</a>. Each phonon has an energy of order 
 
 
 
 
 k
 
 B
 
 
 T
 
 
 {\displaystyle k_{\text{B}}T}
 
, where 
 
 
 
 
 k
 
 B
 
 
 
 
 {\displaystyle k_{\text{B}}}
 
 is the <a href="/facts/Boltzmann_constant/5DIejyR3">Boltzmann constant</a> and 
 
 
 
 T
 
 
 {\displaystyle T}
 
 is the <a href="/facts/Temperature/QyGe4gmj">temperature</a>. The random exchange of energy leads to fluctuations in temperature. This occurs even when the thermal mass and the environment are in <a href="/facts/Thermal_equilibrium/wHqArIwx">thermal equilibrium</a>, i.e. at the same time-average temperature. If a device has a temperature-dependent <a href="/facts/Electrical_resistance/hxSt0UAj">electrical resistance</a>, then these fluctuations in temperature lead to fluctuations in resistance. Examples of devices where phonon noise is important include <a href="/facts/Bolometers/5YlzCoe8">bolometers</a> and <a href="/facts/Calorimeter_(particle_physics)/FCA2evfS">calorimeters</a>. The <a href="/facts/Superconducting/pqQAlSzJ">superconducting</a> <a href="/facts/Transition_edge_sensor/Uw95W6y9">transition edge sensor</a> (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 <a href="/facts/Johnson%E2%80%93Nyquist_noise/ur238TgX">Johnson–Nyquist noise</a> shares many similarities with phonon noise (e.g. the <a href="/facts/Noise_spectral_density/WAGesbqr">noise spectral density</a> depends on the temperature and is <a href="/facts/White_noise/wJ0SR21n">white</a> at low frequencies), these two noise sources are distinct. Johnson–Nyquist noise arises from the random thermal motion of <a href="/facts/Electron/L0KBo5cW">electrons</a>, whereas phonon noise arises from the random exchange of phonons. Johnson–Nyquist noise is easily modeled at <a href="/facts/Thermal_equilibrium/wHqArIwx">thermal equilibrium</a>, 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 <a href="/facts/Time_invariant/NpWUk0YG">time invariant</a>, as in the occasional energy deposition from particles incident on a detector. The <a href="/facts/Transition_edge_sensor/Uw95W6y9">transition edge sensor</a> typically maintains the temperature through negative <a href="/facts/Electrothermal_feedback/5qRcIWFn">electrothermal feedback</a> associated with changes in internal electrical power.
An approximate formula for the <a href="/facts/Noise-equivalent_power/7KSh6FSu">noise-equivalent power</a> (NEP) due to phonon noise in a bolometer when all components are very close to a temperature T is

N
        E
        P
        =
        
          
            4
            
              k
              
                B
              
            
            
              T
              
                2
              
            
            G
          
        
        ,
      
    
    {\displaystyle \ NEP={\sqrt {4k_{\text{B}}T^{2}G}},}

where G is the <a href="/facts/Thermal_conductivity/qWnSG3nQ">thermal conductance</a> and the NEP is measured in 
 
 
 
 
 W
 
 /
 
 
 
 H
 z
 
 
 
 
 
 {\displaystyle \mathrm {W/{\sqrt {Hz}}} }
 
. In calorimetric detectors, the <a href="/facts/Root_mean_square/Cfmg7dws">rms</a> energy resolution 
 
 
 
 δ
 E
 
 
 {\displaystyle \delta E}
 
 due to phonon noise near quasi-equilibrium is described using a similar formula,

δ
        E
        =
        
          
            
              k
              
                B
              
            
            
              T
              
                2
              
            
            C
          
        
        ,
      
    
    {\displaystyle \ \delta E={\sqrt {k_{\text{B}}T^{2}C}},}

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 <a href="/facts/Power_law/DhAjYwwz">power law</a> across this temperature range.

Phonon noise open-in-new

Phonon noise