Spontaneous emission - Wikipedia, the free encyclopedia
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Semiconductor Lasers, Radiative Transitions
Britney Spears get electrons into excited states, allowing recombination to occur resulting in stimulated emission. Sometimes the emission is spontaneous. In other ...
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Solar Radiative Recombination Spectrum
Results of Numerical Computations ... Solar Radiative Recombination Spectrum. Research Fig.14: ... densities due to recombination (thick solid curve, displaced ...
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Radiative and three-body recombination in the Alcator C-Mod divertor
tinuum radiation due to the combined effects of radiative. recombination and bremsstrahlung. ... recombination means that each radiative decay from those ...
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Recombination data
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Discrimination of local radiative and nonradiative recombination ...
Precise identification of recombination dynamics based on local, radiative, and nonradiative recombination has been achieved at room temperature in a blue-light ...
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Mechanism for radiative recombination in ZnCdO alloys-[Applied Physics ...
Temperature dependent cw- and time-resolved photoluminescence combined with absorption measurements are employed to evaluate the origin of radiative recombination in ...
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Energy Citations Database (ECD) - - Document #4184019
We have investigated the electron-ion three-body collisional-radiative recombination for electron temperatures below 4000 degreeK using the Mansbach-Keck rates of ...
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Tokamak Plasma Spectroscopy at LLNL
... ionization and recombination rate coefficients, and impurity radiative cooling. ... and radiative recombination and bremsstrahlung continuum emission have ...
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Excitation-dependent transition between defect-related and radiative ...
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Spontaneous emission is the process by which a light source such as an atom, molecule, nanocrystal or atomic nucleus in an excited state undergoes a transition to the ground state and emits a photon. Spontaneous emission of light or luminescence is a fundamental process that plays an essential role in many phenomena in nature and forms the basis of many applications, such as fluorescent tubes, television screens, plasma display panels, lasers and light emitting diodes.

Introduction If a light source ('the atom') is in the excited state with energy E_2, it may spontaneously decay to the ground state, with energy E_1, releasing the difference in energie between the two states as a photon. The photon will have frequency \omega and energy \hbar \omega:

E_2 - E_1 = \hbar \omega,

where \hbar is Dirac's constant. The phase (waves) of the photon in spontaneous emission is random as is the direction the photon propagates in. This is not true for stimulated emission. An energy level diagram illustrating the process of spontaneous emission is shown below:



If the number of light sources in the excited state is given by N, the rate at which N decays is:

\frac{\partial N}{\partial t} = -A_{21} N,

where A_{21} is the rate of spontaneous emission. In the rate-equation it is a proportionality constant for this particular transition in this particular light source. The constant is referred to as the Einstein A coefficient, and has units s^{-1}R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University Press Inc.,New York, 2001)..The above equation can be solved to give:

N(t) =N(0) e^{ - A_{21}t }= N(0) e^{ - \Gamma_{rad}t } ,

where N(0) is the initial number of light sources in the excited state, t is the time and \Gamma_{rad} is the radiative decay rate of the transition. The number of excited states N thus decays exponentially with time, similar to radioactive decay. After one lifetime, the number of excited states decays to 36,8% of its original value (\frac{1}{e}-time). The radiative decay rate \Gamma_{rad} is inversly proportional to the lifetime \tau_{12}: A_{21}=\Gamma_{12}=\frac{1}{\tau_{21-->.

Theory Quantum mechanics explicitly prohibits spontaneous transitions. That is, using the machinery of ordinary first-quantized quantum mechanics and one computes the probability of spontaneous transitions from one stationary state to another, one finds that it is zero. In order to explain spontaneous transitions, quantum mechanics must be extended to a second-quantized theory, wherein the electromagnetic field is quantized at every point in space. Such a theory is known as a quantum field theory; the quantum field theory of electrons and electromagnetic fields is known as quantum electrodynamics.

In quantum electrodynamics (or QED), the electromagnetic field has a ground state, the vacuum state, which can mix with the excited stationary states of the atom (for more information, see Ref. ). As a result of this interaction, the "stationary state" of the atom is no longer a true eigenstate of the combined system of the atom plus electromagnetic field. In particular, the electron transition from the excited state to the electronic ground state mixes with the transition of the electromagnetic field from the ground state to an excited state, a field state with one photon in it.

Although there is only one electronic transition from the excited state to ground state, there are many ways in which the electromagnetic field may go from the ground state to a one-photon state. That is, the electromagnetic field has infinitely more degrees of freedom, corresponding to the directions in which the photon can be emitted. Equivalently, one might say that the phase space offered by the electromagnetic field is infinitely larger than that offered by the atom. Since one must consider probabilities that occupy all of phase space equally, the combined system of atom plus electromagnetic field must undergo a transition from electronic excitation to a photonic excitation; the atom must decay by spontaneous emission. The time the light source remains in the excited state thus depends on light source it self as well as its environment.

Rate of spontaneous emission The rate of spontaneous emission (i.e., the radiative rate) can be described by Fermi's golden ruleB. Henderson and G. Imbusch, Optical Spectroscopy of Inorganic Solids (Clarendon Press, Oxford, UK, 1989).. The rate of emission depends on two factors: an 'atomic part', which describesthe internal structure of the light source and a 'field part', which describes the density of electromagnetic modes of the environment. The atomic part describes the strength of a transition between two states in terms of transition moments. In a homogenous medium, such as free space, the rate of spontaneous emission is given by:

\Gamma_{rad}(\omega)= \frac{\omega^3n|\mu_{12}|^2} {3\pi\varepsilon_{0}\hbar c^3}

where \omega is the emission frequency, n is the index of refraction, \mu_{12} is the transition dipole moment, \varepsilon_0 is the vacuum permitivity, \hbar is Planck's constant and c is the vacuum speed of light. Clearly, the rate of spontaneous emission in free space increases with \omega^3. In contrast with atoms, which have a discrete emission spectrum, quantum dots form an ideal model system to probe the frequency dependence: the emission frequency of quantum dots can be tuned continuously by their size. In fact, it was confirmed that the the rate of spontaneous emission of quantum dots follows the \omega^3-frequency dependence as described by Fermi's golden ruleA. F. van Driel, G. Allan, C. Delerue, P. Lodahl,W. L. Vos and D. Vanmaekelbergh,Frequency-dependent spontaneous emission rate from CdSeand CdTe nanocrystals: Influence of dark states, Physical Review Letters,95, 236804 (2005).http://cops.tnw.utwente.nl/pdf/05/PHYSICAL%20REVIEW%20LETTERS%2095%20236804%20(2005).pdf.

Radiative and nonradiative decay: the quantum efficiency In the rate-equation above, it is assumed that decay of N only occurs under emission of light. In this case one speaks of full radiative decay and this means that the quantum efficiency is 100%. Besides radiative decay, which occurs under the emission of light, there is a second decay mechanism; nonradiative decay. To determine the total decay rate \Gamma_{tot}, radiative and nonradiative rates should be summed:

\Gamma_{tot}=\Gamma_{rad} + \Gamma_{nrad}

where \Gamma_{tot} is the total decay rate, \Gamma_{rad} is the radiative decay rate and \Gamma_{nrad} the nonradiative decay rate. The quantum efficiency (QE) is defined as the fraction of emission processes in which emission of light is involved:

QE=\frac{\Gamma_{rad-->{\Gamma_{nrad} + \Gamma_{rad-->

In nonradiative relaxation, the energy is released as phonons, more commonly known as heat. Nonradiative relaxation occurs when the energy difference between the levels is very small, and these typically occur on a much faster time scale than radiative transitions. For many materials (for instance, semiconductors), electrons move quickly from a high energy level to a meta-stable level via small nonradiative transitions and then make the final move down to the bottom level via an optical or radiative transition. This final transition is the transition over the bandgap in semiconductors. Large nonradiative transitions do not occur frequently because the crystal structure generally can not support large vibrations without destroying bonds (which generally doesn't happen for relaxation). Meta-stable states form a very important feature that is exploited in the construction of lasers. Specifically, since electrons decay slowly from them, they can be piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal.

Controlling spontaneous emission: Purcell Effect The rate of spontaneous emission depends in part on its environment. This means that by placing the light source in a special environment, the rate of spontaneous emission can be modified. In the 1950s Edward Mills Purcell discovered the enhancement of spontaneous emission rates of atoms when they are matched in a resonant cavity (the Purcell Effect)E. M. Purcell, Phys. Rev. 69, 681 (1946).. It has been predicted theoreticallyV. P. Bykov, Spontaneous emission from a medium with a band spectrum, Soviet Journal of Quantum Electronics 4, 861 (1975).E. Yablonovitch, Inhibited spontaneous emission in solid-state physics and electronics, Physical Review Letters 58, 2059(1987).http://www.ee.ucla.edu/faculty/papers/eliy1987PhysRevLett.pdf that a 'photonic' material environment can control the rate of radiative recombination of an embedded light source. A main research goal is the achievement of a material with a complete photonic bandgap: a range of frequencies in which no electromagnetic modes exist and all propagation directions are forbidden. At the frequencies of the photonic bandgap, spontaneous emission of light is completely inhibited. Fabrication of a material with a complete photonic bandgap is a huge scientific challenge. For this reason photonic materials are being extensively studied. Many different kind of systems in which the rate of spontaneous emission is modified by the environment are reported, including cavities, two-A. Kress, F. Hofbauer, N. Reinelt, M. Kaniber, H. J. Krenner, R. Meyer, G. Bohm, and J. J. Finley, Manipulation of the spontaneous emission dynamics of quantum dots in two-dimensional photonic crystals, Physical Review B 71, 241304 (2005)., and three-dimensionalP. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh andW. L. Vos, Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals, Nature, 430, 654 (2004).http://cops.tnw.utwente.nl/pdf/04/nature02772.pdf photonic materials.

See also

• absorption (optics)
• stimulated emission
• photonic crystal
• laser science
• emission spectrum
• spectral line
• Atomic spectral line

References

External links

• Britney's Guide to Semiconductor Physics

Radiative Recombination Cross Section for Rydberg States
Results from Consistent Numerical Calculations ... Research Fig.1: Radiative recombination cross section as a function of electron energy for some (effective) atomic levels and ...

Solar Radiative Recombination Spectrum
Results of Numerical Computations ... Research Fig.14: Theoretical flux densities due to recombination (thick solid curve, displaced upwards by 8 orders of magnitude) and cascading ...

Strathprints - Radiative recombination data for modeling dynamic ...
We have calculated partial final-state resolved radiative recombination (RR) rate coefficients from the initial ground and metastable levels of all elements up to and including Zn ...

Strathprints - Dielectronic recombination (via N = 2→N = 2 core ...
... overestimate the strength of the DR process unless they include the effects of radiation damping. We also find that the coupling between the DR and radiative recombination (RR ...

Extracing Radiative Recombination
Extracing Radiative Recombination. The radiative recombination currents extracted from single (SQW) and double-quantum well (DQW) samples have ideality n = 1 as expected.

Extracing Radiative Recombination
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Radiative and Auger recombination in 1.3 µm InGaAsP and 1.5 µm ...
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MIJ-NSR Vol. 4, Art. 16, B. Monemar et al.
Radiative recombination in In 0.15 Ga 0.85 N/GaN multiple quantum well structures. B. Monemar, J. P. Bergman, J. Dalfors, G. Pozina, B.E. Sernelius, P.O.

Radiative recombination with highly charged Si6+ and Si11+ ions
Radiative recombination with highly charged Si 6+ and Si 11+ ions. L H Andersen et al 1992 J. Phys. B: At. Mol. Opt. Phys. 25 277-283 doi: 10.1088/0953-4075/25/1/029

Spontaneous emission - Wikipedia, the free encyclopedia
It has been predicted theoretically [9] [10] that a 'photonic' material environment can control the rate of radiative recombination of an embedded light source.