Metal-Semiconductor-Metal Photodetector (MSM)

1. Theory

• Definition: A metal-semiconductor-metal (MSM) photodetector is a planar device with two interdigitated metal electrodes, each forming a Schottky barrier with an undoped or lightly doped absorbing layer, so that the two barriers face back to back and one of them is always reverse-biased.
• Structure: Typical devices have fingers 1 μm to 2 μm wide separated by 2 μm to 2.5 μm on a semi-insulating substrate, a circular active area of 50 μm to 150 μm diameter, a layer of about 1 μm of $\mathrm{I}{\mathrm{n}}_{0.53}\mathrm{G}{\mathrm{a}}_{0.47}\mathrm{As}$ on InP, and a wider-gap AlInAs buffer and graded InAlAs Schottky enhancement layer.
• Materials: GaAs, InGaAs, Si, SiC, AlGaAs, GaN, AlGaN and other semiconductors with Ti/Au, Ni/Au, Al or Pt/Au electrodes; GaN devices with semitransparent Ni/Au (15 nm) fingers give visible-blind ultraviolet detection.
• Low capacitance: The capacitance is set by the geometry of the fingers, $C={\epsilon }_0({\epsilon }_r+1)(N-1)LK(k)/K(k^{\prime })$, is independent of the bias after depletion, and is intrinsically lower than that of a vertical PIN diode of the same size.
• Speed: The photocurrent is collected laterally across the spacing $s$, so the transit time is ${\tau }_{tr}\approx s/v_{sat}$ and bandwidths of 6 GHz to more than 8 GHz were measured for 50 μm devices, with a slower tail from the holes.
• Shadowing: The fingers cover a fraction $S_h=w/(w+s)$ of the area (38% for 1.5 μm and 2.5 μm), which lowers the responsivity of the top-illuminated device, e.g. 0.64 A/W corrected for the shadowing, about 0.40 A/W measured, at 1.55 μm.
• Dark current: It is set by the barrier heights, $J_S\propto e^{-q\Phi /k_{B}T}$, which is why a large-gap enhancement layer is used with InGaAs; it is about 1 nA to 41 nA at 5 V in the InGaAs devices of the sources.
• No gain: The photocurrent saturates at a bias below 1 V, when the layer is depleted, and the device has no internal gain.

2. Working Principle

• Back-to-back barriers: Under any bias polarity one Schottky contact is forward-biased and the other reverse-biased, so the dark current is limited by the reverse-biased barrier, as in $J(V)$ of the double-barrier model.
• Depletion: At a small bias (below 5 V in a 1 μm layer) the absorber is depleted between the fingers, and the field is highest near the edges of the fingers.
• Absorption: Light enters from the top between the fingers, or from the back through a thinned substrate, and photons with $h\nu \ge E_g$ create electron-hole pairs in the layer, $\eta =(1-S_h)(1-R_f)(1-e^{-\alpha d})$.
• Collection: The field sweeps the electrons and holes sideways to the fingers; the electrons reach the saturated velocity above about 2 V and give the fast peak, while the holes, which move more slowly in the low-field regions, give a tail.
• Illumination direction: Top illumination makes the carriers near the fingers, so it is faster; back illumination avoids the shadowing but makes the carriers farther away, below the fingers, and reduces the bandwidth by about 50% in the quoted device.
• Bias dependence: The bandwidth of the top-illuminated device falls above about 11 V, when the average field exceeds the field of peak electron velocity, while that of the back-illuminated one keeps rising with bias.
• Readout: The small capacitance permits a high-impedance receiver with a transimpedance amplifier or FET preamplifier, with the pad capacitance as the main limit.

3. Applications

• Optical receivers: InGaAs MSM detectors in multichannel receivers, such as a four-channel receiver of 100 μm devices with 1.5 GHz amplifiers that ran at 1.4 Gb/s, and a sensitivity of $-26\mathrm{dBm}$ at a bit-error rate of $10^{-9}$ and 1 Gb/s.
• Visible detection: GaAsP MSM detectors with gold fingers, studied at 632 nm, with nanoampere dark currents at 8 V.
• Ultraviolet detection: Visible-blind GaN and AlGaN MSM detectors with semitransparent Ni/Au electrodes, most sensitive at 350 nm to 360 nm.
• Infrared detection: InGaAs MSM detectors for 1.0 μm to 1.6 μm, with nanocrystal or plasmonic enhancements studied for higher efficiency.
• Laser radar: Spiral and concentric-ring MSM electrodes are used in ladar detectors for their lower capacitance, dark current and ringing.

Name	Formula	Related Formulae	Variables/Constants
Finger geometry and shadowing factor	$S_h=\frac{w}{w+s}$	$p=w+s$ $N-1\approx \frac{D}{w+s}$	$\begin{array}{r}{S}_h:fractionoftheactiveareacoveredby\\ themetalfingers(thefillfactor),which\\ blocksthelightinthetop-illuminated\\ device\end{array}$ $w:fingerwidth$ $s:spacingbetweenneighbouringfingers$ $p:pitchofthefingers$ $N:numberoffingers$ $\begin{array}{r}D:diameterofacircularactivearea\\ (w=1.5\mu \mathrm{m}ands=2.5\mu \mathrm{m}give{S}_h=38\%in\\ onedevice)\end{array}$
Responsivity of the top-illuminated device	$\mathcal{R}=\frac{\eta \lambda }{1.24}A/W,\eta =\left(1-S_h\right)\left(1-R_f\right)\left(1-e^{-\alpha d}\right)$	${\mathcal{R}}_{int}=\frac{\mathcal{R}}{1-S_h}$ ${\eta }_{EQE}=\frac{\mathcal{R}hc}{q\lambda }$	$\begin{array}{r}d:thicknessoftheabsorbinglayer(about\\ 1\mu \mathrm{m}ofI{n}_{0.53}G{a}_{0.47}Asinthedevicesofthe\\ sources)\end{array}$ $\begin{array}{r}{R}_f:reflectanceofthesurfacebetweenthe\\ fingers(reducedbyaSi{N}_{x}antireflection\\ coating)\end{array}$ $\begin{array}{r}{\mathcal{R}}_{int}:responsivitycorrectedforthe\\ shadowing(0.64A/Wat1.55\mu \mathrm{m}for{S}_h=\\ 38\%gives\mathcal{R}\approx 0.40A/W,computed)\end{array}$ $\begin{array}{r}\lambda :wavelengthinmicrometresinthe\\ numericalform\end{array}$ $\begin{array}{r}(thephotocurrentsaturatesatabias\\ below1V,whichindicatesthatthelayer\\ isdepletedandthatthereisnointernal\\ gain)\end{array}$
Capacitance of the interdigitated electrodes (conformal mapping)	$C={\epsilon }_0\left({\epsilon }_r+1\right)\left(N-1\right)L\frac{K\left(k\right)}{K\left(k^{\prime }\right)}$	$k={\tan }^2\left(\frac{\pi w}{4\left(w+s\right)}\right),k^{\prime }=\sqrt{1-k^2}$ $C\approx {\epsilon }_0\left({\epsilon }_r+1\right)\frac{A}{w+s}\frac{K\left(k\right)}{K\left(k^{\prime }\right)}$	$L:lengthofthefingers$ $\begin{array}{r}K:completeellipticintegralofthefirst\\ kind(K(k)/K(k^{\prime })=0.5forw=s)\end{array}$ $\begin{array}{r}{\epsilon }_r:relativepermittivityofthe\\ semiconductor,thefieldlinesbeingtaken\\ tofillthesemiconductorhalf-spaceand\\ theairaboveit\end{array}$ $\begin{array}{r}A:activearea(thesecondformtakesthe\\ totallengthofthegapsasA/(w+s));for\\ {\epsilon }_r=13.9(assumed)itgives32fFforD=50\\ \mu \mathrm{m},w=s=2\mu \mathrm{m}and155fFforD=120\mu \mathrm{m},\\ w=1.5\mu \mathrm{m},s=2.5\mu \mathrm{m}(computed)\end{array}$ $\begin{array}{r}(thecapacitanceisindependentofthe\\ biasoncethelayerisdepleted,andis\\ lowerthanthatofaverticalPINdiodeof\\ thesamearea,about240fFfora1\mu \mathrm{m}\\ layerunder50\mu \mathrm{m}diameter(computed))\end{array}$
Dark current of two back-to-back Schottky contacts	$J\left(V\right)=\frac{2J_S\left({\Phi }_1\right)J_S\left({\Phi }_2\right)\sinh \left(\beta V/2n\right)}{J_S\left({\Phi }_1\right)e^{\beta V/2n}+J_S\left({\Phi }_2\right)e^{-\beta V/2n}}$	$J_S\left(\Phi \right)=A^{\ast }{T}^2{e}^{-\beta \Phi },\beta =\frac{q}{k_{B}T}$	$\begin{array}{r}{\Phi }_1,{\Phi }_2:barrierheightsofthetwo\\ contacts,oneofwhichisreverse-biased\\ whateverthepolarityofthebias\end{array}$ $\begin{array}{r}n:idealityfactor(afittingparameterof\\ themodel)\end{array}$ $\begin{array}{r}{A}^{\ast }:Richardsonconstant(1.01\times 10^{5}A{m}^{-2}{K}^{-2}\\ inthesource);thefitoftwoInGaAs\\ devicesgavebarriersof0.49to0.54eV\\ against0.7eVexpectedforTionInAlAs\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(alargerbarrierlowersthedarkcurrent\\ by{e}^{\Delta \Phi /k_{B}T},afactorofabout2300for0.2\\ eVat300K,computed,whichisthe\\ purposeofthewider-gapenhancement\\ layer)\end{array}$
Specific detectivity limited by the dark-current shot noise	$D^{\ast }=\sqrt{\frac{A}{2q{I}_{dark}}}\mathcal{R}\left(\lambda \right)$	$\mathrm{NEP}=\frac{\sqrt{2q{I}_{dark}}}{\mathcal{R}}$	$D^{\ast }:specificdetectivityincmH{z}^{1/2}/W(Jones)$ $I_{dark}:darkcurrentattheoperatingbias$ $A:activearea$ $\begin{array}{r}(thedarkcurrentofanMSMdetectoris\\ largerthanthatofaPINdiodeofthe\\ samearea,so{D}^{\ast }islower;twoInGaAs\\ deviceshadpeak{D}^{\ast }ofabout10^{9}and10^{10}\\ Jones)\end{array}$
Transit-time-limited bandwidth	$f_{tr}\approx \frac{0.44}{{\tau }_{tr}}=\frac{0.44v_{sat}}{s}$	${\tau }_{tr}\approx \frac{s}{v_{sat}}$ $\bar{E}\approx \frac{V}{s}$	$\begin{array}{r}{\tau }_{tr}:timeforthefastercarriertocross\\ thespacingsatthesaturatedvelocity\\ v_{sat},thecarriersoftheslowertype\\ givingatailonthepulseresponse\end{array}$ $\begin{array}{r}\bar{E}:averagefieldbetweenthefingersfor\\ abiasV,thebandwidthofthe\\ top-illuminateddevicefallingwhenit\\ exceedsthefieldofpeakelectron\\ velocity\end{array}$ $\begin{array}{r}(derivedherebyanalogywiththePIN\\ photodiode;fors=2\mu \mathrm{m}and{v}_{sat}=6\times 10^{6}cm/s\\ itgives33psand13GHz,computed,while\\ measuredbandwidthsof50\mu \mathrm{m}devicesare6\\ tomorethan8GHz)\end{array}$
RC-limited bandwidth and overall bandwidth	$f_{RC}=\frac{1}{2\pi R_{L}C}$	$\frac{1}{f_{3dB}^2}\approx \frac{1}{f_{tr}^2}+\frac{1}{f_{RC}^2}$	$R_L:loadresistance(50\Omega )$ $\begin{array}{r}C:capacitanceoftheelectrodesplusthe\\ padcapacitance(about200fFfor200\mu \mathrm{m}\\ padsinonedevice,soithastobe\\ correctedfor)\end{array}$ $\begin{array}{r}(forC=35fFtheRClimitis91GHz\\ (computed),farabovethemeasured\\ bandwidths,sosmalldevicesarelimited\\ bythetransittime)\end{array}$

Important Questions

Ques: Why is the capacitance of an MSM photodetector lower than that of a PIN diode of the same area?

The two electrodes lie in the same plane, and the field lines between neighbouring fingers pass through the semiconductor and the air over a lateral spacing $s$ of 2 μm, so the capacitance per gap is set by $K(k)/K(k^{\prime })$ and by the finger length, not by the area divided by the thickness. For $D=50$ μm, $w=s=2$ μm and an assumed ${\epsilon }_r=13.9$, $C={\epsilon }_0({\epsilon }_r+1)(A/(w+s))K(k)/K(k^{\prime })=32$ fF (computed), compared with 35 fF measured after the pad correction, whereas a vertical PIN diode with a 1 μm layer under the same area has ${\epsilon }_{s}A/W_i\approx 240$ fF (computed). The source states that planar MSM devices have an intrinsically lower capacitance than vertical PIN diodes. The formula is the standard conformal-mapping result and was not readable in the fetched sources, so the agreement (8% low here and 16% low for the 120 μm device, 155 fF against 185 fF, computed) is only a consistency check. Reference: Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996); InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559); NECTEC Technical Journal No. 11, short paper on a GaAsP MSM photodetector.

Ques: What limits the responsivity of the top-illuminated MSM detector, and how is it improved?

The fingers block the light, so the external efficiency contains the factor $1-S_h=s/(w+s)$, 62% for $w=1.5$ μm and $s=2.5$ μm. The measured responsivity of 0.40 A/W corresponds to the intrinsic 0.64 A/W at 1.55 μm that the source gives after the correction (computed), and the intrinsic value is ${\eta }_{int}=0.64\times 1.24/1.55=0.51$, which for a 1 μm layer without reflection gives $\alpha \approx 7\times 10^3\mathrm{c}{\mathrm{m}}^{-1}$ (computed), between the $5000\mathrm{c}{\mathrm{m}}^{-1}$ and $10^4\mathrm{c}{\mathrm{m}}^{-1}$ discussed on the PIN Photodiode page. The remedies are a smaller finger width or a larger spacing (the second lengthens the transit time), a silicon-nitride antireflection coating tuned to 1.3 μm (about 5% more is expected from a better one), transparent electrodes, or back illumination, whose bandwidth was about half that of the top one. Reference: InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559); Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996).

Ques: Why does an MSM detector have a fast peak followed by a slow tail?

The electrons reach the saturated velocity above about 2 V and cross the spacing $s$ in ${\tau }_{tr}\approx s/v_{sat}$, about 33 ps for 2 μm at $6\times 10^6$ cm/s (computed), whereas the holes, which are slower and sit in low-field regions near the fingers, arrive later and form the tail, which the source attributes to the holes. Top illumination creates the carriers close to the fingers, where the field is highest and the path short, and back illumination creates them below the fingers, which lengthens the path and enhances the tail beyond 50 ps. The tail lowers the bandwidth below the electron estimate of $0.44v_{sat}/s\approx 13$ GHz (computed), and the measured values are 6 GHz to more than 8 GHz. The velocity formula is derived by analogy with the PIN photodiode, not taken from a source. Reference: Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996); InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559).

Ques: How fast are 50 μm MSM detectors: 6 GHz or more than 8 GHz?

One source reports a bandwidth of about 6 GHz from the pulse fall time of its InGaAs detectors (the bit-error-rate device had $D=50$ μm and $w=s=2$ μm), and another reports more than 8 GHz for 50 μm devices, with a Fourier-derived FWHM of 17 to 19 ps. The two differ in the finger geometry (the second is quoted as 1 μm and 2 μm but the extraction was garbled), the bias, the buffer and the way the bandwidth is derived. A pulse width of 18 ps would suggest $0.44/18\mathrm{ps}\approx 24$ GHz for a time-bandwidth product of 0.44 (computed), which is larger than 8 GHz, probably because the tail narrows the bandwidth. Both are below the transit estimate of 13 GHz, and the lower figure is the safer for a receiver design, though the sources do not show which is more representative. Reference: InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559); Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996).

Ques: Why does an MSM detector use a wide-gap enhancement layer, and why is the barrier lower than expected?

The Schottky barrier of a metal on narrow-gap InGaAs is low, so the thermionic dark current $J_S=A^{\ast }{T}^2{e}^{-q\Phi /k_{B}T}$ is large; a graded InAlAs layer of larger gap on top raises the barrier, and each 0.2 eV lowers the dark current by about 2300 at 300 K (computed). Dark currents of about 1 nA at 5 V and 8 nA at 10 V (one device) and 41 nA at 300 K and 5 V (another) were reported. A fit with the double-barrier model of two InGaAs devices gave barriers of 0.49 to 0.54 eV against 0.7 eV expected for Ti on InAlAs, with ideality factors of 12 to 19, the source attributing the low barriers to pitting defects of about $10^6\mathrm{c}{\mathrm{m}}^{-2}$. The expected 0.7 eV is for an ideal interface and the measured 0.5 eV is more likely for those defective devices. Reference: Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996); InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559); arXiv:2408.10389, InGaAs MSM infrared photodetectors with nanocrystals (Eqs. 1 to 4).

Ques: Why does the specific detectivity of an MSM detector depend on the dark current?

When the shot noise of the dark current is the dominant noise, $D^{\ast }=R\sqrt{A/(2q{I}_{dark})}$, so a detector of area $A$ and responsivity $R$ has a detectivity that falls as $1/\sqrt{I_{dark}}$. Two InGaAs MSM devices with finger width 10 μm, spacing 3 μm and an area of $500\times 540\mu {\mathrm{m}}^2$ had peak $D^{\ast }$ of about $10^9$ and $10^{10}$ Jones, and the source calls their dark currents relatively large without giving a value. With an assumed responsivity of 0.28 A/W at the peak, $D^{\ast }=10^{10}$ Jones implies $I_{dark}\approx 6.6$ μA (computed), a rough estimate. The large area and the low barriers (0.5 eV) raise $I_{dark}$, so the figure improves with a smaller area, a higher barrier and a higher responsivity. Reference: arXiv:2408.10389, InGaAs MSM infrared photodetectors with nanocrystals (Eqs. 1 to 4).

Ques: Why does the MSM detector have no internal gain even though it looks like two Schottky diodes?

Carriers cross the structure once, from the point of generation to a finger, and there is no mechanism that multiplies them: the photocurrent saturates at a bias below 1 V, when the field has depleted the layer and collected every carrier, and the responsivity then stays constant with bias. The source concludes that this indicates depletion and no internal gain. Nothing in the sources suggests a gain mechanism. The ac responsivity of the top-illuminated device (0.2 A/W) was lower than its dc responsivity (0.35 A/W) in another source, which the source does not explain. Reference: InGaAs MSM photodetector paper (lightweb.ie.cuhk.edu.hk, publication BF00430559); Hargis et al., InGaAs MSM photodetector study (research.engineering.ucdavis.edu/woodall, 1996).

Related pages in this vault: PIN Photodiode, PN Photodiode, Schottky-Barrier Photodiode, Ultraviolet Photodetector (AlGaN, SiC, Ga2O3, Diamond), Waveguide Photodiode, Photodetectors (PIN and Avalanche Photodiodes), Diodes (PN, PIN, Schottky, Zener).