View source for Resonant-cavity-enhanced photo detector

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{{Technical|date=August 2022}}
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{{Use dmy dates|date=March 2018}}
'''Resonant-cavity-enhanced photodetectors''', also known as '''RCE photodetectors''', are sensors designed to detect light or other forms of electromagnetic radiation. They achieve this by utilizing an [[optical cavity]]—a configuration of [[mirror]]s or other optical elements that forms a [[cavity resonator]] for [[light wave]]s, allowing for more efficient targeting of specific wavelengths.

In RCE photodetectors, the active device structure of a photodetector is placed inside a [[Fabry–Pérot interferometer]]. This interferometer has two parallel surfaces between which a selected wavelength of light can resonate, amplifying the [[Electromagnetic field|optical field]]. While the active device structure of RCE detectors is similar to that of conventional photodetectors, the amplification effect of the optical cavity allows RCE photodetectors to be made thinner and therefore faster, while simultaneously increasing the [[quantum efficiency]] at the resonant [[wavelength]]s.

==Advantages==
The [[quantum efficiency]] of conventional [[detectors]] is dominated by the optical [[absorption (electromagnetic radiation)]] of the [[semiconductor]] material. For semiconductors with low [[absorption coefficient]]s, a thicker absorption region is required to achieve adequate [[quantum efficiency]], but at the cost of the [[bandwidth (signal processing)|signal-processing bandwidth]] of the photodetector.

An RCE detector can have significantly higher bandwidth than a conventional detector. The constructive [[Interference (wave propagation)|interference]] of a Fabry–Pérot cavity enhances the [[optical field]] inside the photodetector at the [[resonance]] wavelengths to achieve a [[quantum efficiency]] of close to unity. Moreover, the [[optical cavity]] makes the RCE detectors wavelength selective, making RCE photodetectors a viable option for low [[crosstalk]] wavelength [[demultiplexing]].{{Technical inline|date=August 2022}} Improved quantum efficiency reduces power consumption, while higher bandwidth translates to faster operation.

The RCE photodetectors have both wavelength selectivity and high-speed response making them ideal for [[wavelength division multiplexing]] applications. [[Optical modulator]]s situated in an [[optical cavity]] require fewer [[quantum well]]s to absorb the same fraction of the incident light and can therefore operate at lower voltages. In the case of emitters, the cavity modifies the [[spontaneous emission]] of [[light-emitting diode]]s (LED) improving their [[spectral purity]] and [[directivity]].

[[Optical communication]] systems can perform much faster, with more bandwidth and can become more reliable. [[Camera sensor]]s could give more resolutions, better [[contrast ratio]]s and less distortion. For these reasons, RCE devices can be expected to play a growing role in [[optoelectronics|optical electronics]] over the coming years.{{citation needed|date=December 2011}}

==Theory of RCE photo detectors==

Compared to a conventional [[photodiode]], RCE photo detectors can provide higher [[quantum efficiency]], a higher detection speed and can also provide wavelength selective detection.

===Quantum efficiency of RCE photo detectors===

The RCE photodetectors are expected to have higher quantum efficiency η than compared to conventional [[photodiode]]s. The formulation of η for RCE devices gives insight to the design criteria.

A generalized RCE photodetector can give the required theoretical model of [[photodetection]]. A thin absorption region of thickness d is sandwiched between two relatively less absorbing regions, substrate, of thickness L<sub>1</sub> and L<sub>2</sub>. The [[optical cavity]] is formed by a period of λ/4 [[distributed Bragg reflector]] (DBR), made of non-absorbing larger bandgap materials, at the end of the substrate. The front mirror has a [[transmittance]] of t<sub>1</sub> and generally has lower [[reflectivity]] than compared to the mirror at back (R<sub>1</sub> < R<sub>2</sub> ). Transmittance t<sub>1</sub> allows light to enter into the cavity, and reflectivity R<sub>1</sub> (=r<sub>1</sub><sup>2</sup>) and R<sub>2</sub> (=r<sub>2</sub><sup>2</sup>) provides the optical confinement in the cavity.

The active region and the substrate region have absorption coefficient α and α<sub>ex</sub> respectively. The field [[reflection coefficient]]s of the front and the back mirrors are <math>r_1 e^{-j\phi_1}</math> and <math>r_2e^{-j\phi_2}</math> respectively, where ф<sub>1</sub> and ф<sub>2</sub> are the [[phase shifts]] due to the light penetration (see [[Penetration Depth]]) into the mirrors.

The [[optical microcavity]] allows building up an [[optical field]] inside the [[optical cavity]]. In compared to conventional detector, where light is absorbed in a single pass through the absorption region, for RCE detectors trapped light is absorbed each time it traverses through the absorption region.

The Quantum efficiency <math>\eta</math> for a RCE detector is given by:

::::<math>\eta=(1-R_1)(1-e^{-\alpha d} ) \left[ \frac {( e^{-\alpha_{ex} L_1} +r_2^2 e^{-\alpha_{ex} L_2 - \alpha_c L} )}{1 - 2 r_1 r_2 e^{- \alpha_c L}\cos(2\beta L+ \phi_1 + \phi_2) + (r_1r_2)^2 e^{- \alpha_c L}} \right]  </math>

Here <math>\alpha_c=\frac{\alpha_{\text{ex}}L_1+\alpha_{\text{ex}}L_2+\alpha d}{L}</math>. In practical detector design α<sub>ex</sub> << α, so α<sub>ex</sub> can be neglected and <math>\eta</math> can be given as:

::::<math>\eta=(1-R_1)(1-e^{-\alpha d} ) \left[ \frac {( 1 +R_2 e^{-\alpha d} )}{1 - 2 \sqrt{R_1 R_2} e^{- \alpha_c d}\cos(2\beta L+ \phi_1 + \phi_2) + (R_1 R_2) e^{- \alpha_c d}} \right]  </math>

The term inside the brackets represents the cavity enhancement effect. This is a periodic function of <math>2\beta L+\phi_1+\phi_2</math>, which has minima at <math>2\beta L+\phi_1+\phi_2=2m\pi</math>. And η enhanced periodically at [[resonance]] wavelength that meets this condition.  The spacing of the resonant wavelength is given by the [[Free Spectral Range]] of the cavity.

The peak value of η at resonant wavelength is given as:

::::<math>\eta=(1-R_1)(1-e^{-\alpha d} ) \left[ \frac {( 1 +R_2 e^{-\alpha d} )}{(1 -  \sqrt{R_1 R_2} e^{- \alpha_c d})^2} \right] </math>

for a thin active layer as αd<<1, η becomes:

::::<math>\eta=(1-R_1)\alpha d \left[ \frac {( 1 +R_2 e^{-\alpha d} )}{(1 -  \sqrt{R_1 R_2} e^{- \alpha_c d})^2} \right] </math>

This is a significant improvement from the quantum efficiency of a conventional photodetector which is given by:

::::<math>\eta=(1-R) \alpha L</math>.

This shows that higher quantum efficiency can be achieved for smaller absorption regions.

The critical design requirements are a very high back mirror reflectivity and a moderate absorption layer thickness. At optical frequencies, metal mirrors have low reflectivity (94%) when used on materials like GaAs. This makes metal mirrors inefficient for RCE detection. Whereas [[distributed Bragg reflector]] (DBR) can provide reflectivity near unity and are ideal choice for RCE structures.

For an R<sub>1</sub>=0.2, R<sub>2</sub>=0.99, and α=10<sup>4</sup> cm<sup>−1</sup>, an η of 0.99 or more can be achievable for d=0.7–0.95&nbsp;μm. Similarly, for different values of R<sub>1,</sub> very high η is possible to achieve. However, R<sub>1</sub>=0 limits the length of the thickness region. d>5&nbsp;μm can achieve 0.99 η, but at the cost of bandwidth.

===Detection speed of RCE photodiodes===
The detection speed depends upon the drift velocities of the electrons and holes. And between these two holes have slower [[drift velocity]] than the electrons. The transit time limited bandwidth of conventional p-i-n photodiode is given by:

:<math>f_{\text{transit}} =0.45\frac{v_h}{L}</math>

However, the quantum efficiency is a function of L as:

:<math>\eta=(1-R) \alpha L</math>.

For a high-speed detector for a small value of L, as α is very small, η becomes very small (η<<1). This shows for an optimum value of quantum efficiency the bandwidth has to sacrifice.

A p-i-n RCE photodetector can reduce the absorption region to a much smaller scale. In this case the carriers need to traverse a smaller distance as well, L<sub>1</sub> (< L) and L<sub>2</sub> (< L) for electrons and holes respectively.

The length of L1 and L2 can also be optimized to match the delay between the hole and electron drift. Afterwards, the transition bandwidth is given by:

:<math>f_{\text{transit}} =0.45\frac{v_h + v_e}{L+d}</math>

As in most of semiconductors <math>v_e</math> is more than <math>v_h</math> the bandwidth increases drastically.

It has been reported that for a large device of L=0.5&nbsp;μm 64&nbsp;GHz of bandwidth can be achieved and a small device of L=0.25&nbsp;μm can give 120&nbsp;GHz bandwidth, whereas conventional photodetectors have a bandwidth of 10–30&nbsp;GHz.

===Wavelength selectivity of RCE photo detectors===
An RCE structure can make the detector wavelength selective to an extent due to the resonance properties of the cavity. The resonance condition of the cavity is given as <math>2\beta L+\phi_1+\phi_2=2m\pi</math>. For any other value the efficiency η reduces from its maximum value, and vanishes when <math>2\beta L+\phi_1+\phi_2=(2m+1)\pi</math>. The wavelength spacing of the maxima of η is separated by the [[Free Spectral Range|free spectral range]] of the cavity, given as:

:<math>FSR=\frac {\lambda^2}  {2 n_{\text{eff}} (L + L_{\text{eff},1} + L_{\text{eff},2})}</math>

Where n<sub>eff</sub> is the effective [[refractive index]] and L<sub>eff,i</sub> {{clarify|date=September 2012}} are the effective [[optical path length]]s of the mirrors.

Finesse, the ratio of the FSR to the FWHM at the resonant wavelength, gives the wavelength selectivity of the cavity.

:<math>\text{Finesse} = \frac{\pi(R_1R_2)^{1/4} e^{-\frac{\alpha d}{2}}} {(1 -  \sqrt{R_1 R_2} e^{- \alpha_c d})^2} </math>

This shows that the wavelength selectivity increases with higher [[reflectivity]] and smaller values of L.

==Material requirements for RCE devices==
The estimated superior performance of the RCE devices critically depends on the realization of a very low loss active region. This enforces the conditions that: the mirror and the cavity materials must be non-absorbing at the detection wavelength, and the mirror should have very high reflectivity so that it gives the highest optical confinement inside the cavity.

The absorption in the cavity can be limited by making the [[bandgap]] of the active region smaller than the cavity and the mirror. But a large difference in the bandgap would be a blockage in the extraction of photo-generated carriers from a [[heterojunction]]. Usually, a moderate offset is kept within the absorption spectrum.

Different material combinations satisfy all of the above criteria and are therefore used in the RCE scheme. Some material combinations used for RCE detection are:

:1.GaAs(M,C) / AlGaAs(M) / InGaAs(A) near 830-920nm.
:2.InP(C) / In<sub>0.53</sub>Ga<sub>0.47</sub>As(M) / In<sub>0.52</sub>Al<sub>0.48</sub>As(M) / In<sub>0.53–0.7</sub>GaAs(A) near 1550nm.
:3.GaAs(M,C) / AlAs(M) / Ge(A) near 830-920nm.
:4.Si(M,C) / SiGe(M) / Ge(A) near 1550nm.
:5.GaP(M) / AlP(M) / Si(A,S) near [[visible region]].

==Future of RCE photodiodes==
There are many examples of RCE devices such as the [[PIN diode|p-i-n]] photodiode, [[Avalanche photodiode]] and [[Schottky diode]] that verifies the theory successfully. Some of them are already in use today, while there are future use cases such as modulators, and optical logics in [[wavelength division multiplexing]] (WDM) systems which could enhance the quantum efficiency, operating bandwidth, and wavelength selectivity.

RCE detectors are preferable in potential price and performance in commercial WDM systems. RCE detectors have potential for implementation in WDM systems and improve performance significantly. There are various implementations of RCE modulators are made and room for further improvement in the performance of those. Other than the photodetectors the RCE structures have many other implementations and a very high potential for improved performance. A [[Light Emitting Diode]] (LED) can be made to have narrower [[spectrum]] and higher [[directivity]] to allow more coupling to [[optical fibre]] and better utilization of the Fiber bandwidth. [[Optical amplifier]]s can be made to have a more compact, thus lower power required to pump and also at a lower cost. [[Photonic logic]]s will also work more efficiently than they do. There will be much less crosstalk and more speed, with simple design.

==See also==
*[[PIN diode]]
*[[Schottky diode]]
*[[Avalanche photodiode]]
*[[Wavelength selective switching]]
*[[Photonic integrated circuit]]
*[[Semiconductor material]]
*[[Fabry–Pérot interferometer]]
*[[Fresnel equations]]
*[[Resonance]]
*[[Optical cavity]]
*[[Photoelectric effect]]

==References==
:[1] Goedbloed and Joosten; " Thin Silicon Film p-i-n Photodiodes with Internal Reflection";  IEEE Journal of Solid-State Circuits,  173 – 179, Volume: 13 Issue: 1, Feb (1978).

:[2] R G Hunsperger, Integrated Optics: Theory and Technology ispringer, New York, (1991).

:[3] M. Selim Unlu, Samuel Strite; "Resonant cavity enhanced photonic devices"; J. Appl. Phys. 78, 607 (1995).

:[4] K. Kishino. M. S. Unlu, J. I. Chyi, J. Reed, L. Arsenault, and H. Morkoc; " Resonant Cavity Enhanced Photodetectors", IEEE J. Quantum Electron. 27, 2025 (1991).

:[5] A. G. Dentai, R. Kuchibohlta, I. C. Campbell, C. Tsai, C. Lei; "HIGH QUANTUM EFFICIENCY, LONG WAVELENGTH InP/lnGaAs MICROCAVITY PHOTODIODE", 7 November 1991 Vol. 27 No 23.

:[6] Ravi Kuchibhotla, Joe C. Campbell, John C. Bean, Larry Peticolas, and Robert Hull; "Si0.8Ge0.2 /Si Bragg-reflector mirrors :for optoelectronic device applications"; Appl. Phys. Lett. 62 (18), 3 May 1993.

:[7] F. Y. Huangja, A. Salvador, X. Gui, N. Teraguchi, and H. Morkoq; "Resonant-cavity GaAs/lnGaAs/AIAs photodiodes with a:periodic absorber structure"; Appi. Phys. L&t. 63 (2), 12 July 1993.

:[8] R. Kuchibhotla;   A. Srinivasan;   J.C. Campbell;   C. Lei;   D.G. Deppe;   Y.S. He;   B.G. Streetman;   "Low-voltage high-gain resonant-cavity avalanche photodiode"; 354 – 356, Volume: 3 Issue: 4,  IEEE Photonics Technology Letters, April 1991.

:[9] Li, Z.-M. Landheer, D. Veilleux, M. Conn, D.R. Surridge, R. Xu, J.M. McDonald; "Analysis of a resonant-cavity enhanced GaAs/AlGaAs MSM photodetector"; 473 – 476, Volume: 4 Issue: 5, IEEE Photonics Technology Letters, May 1992.

:[10]S. Unlu, K. Kishino, J. I. Chyi, L. Arsenault, J. Reed, and H. Morkoc; "Wavelength demultiplexing heterojunction phototransistor"; Electron. Lett. 26, 1857 (1990).

[[Category:Photodetectors]]