Type-II Superlattice and Barrier Photodetector (T2SL, nBn, XBn)

1. Theory

• Definition (T2SL): A type-II superlattice is a stack of layers a few nanometres thick, usually InAs/GaSb or the Ga-free InAs/InAsSb, in which the electrons sit mainly in the InAs and the holes mainly in the GaSb or InAsSb, and the coupled states form minibands whose effective gap $E_g^{eff}=E_{C1}-E_{V1}$ is set by the layer thicknesses.
• Cutoff tuning: The thicknesses tune the cutoff wavelength from about 3 μm to 30 μm, so that the same material system covers the mid and long wavelength atmospheric windows.
• Absorption: The absorption between the minibands rises above the gap as $\alpha \propto (E-E_g{)}^{1/2}$, and the gap narrows on heating, by about $-0.22$ meV/K for one n-B-p device (computed).
• Competition with HgCdTe: The electron effective mass depends weakly on the gap, which should lower the tunnelling current, and the spatial separation of electrons and holes is predicted to suppress the Auger recombination, whereas the measured minority-carrier lifetime of InAs/GaSb is short (below 20 ns above 150 K).
• Barrier detector (nBn, XBn): A thin wide-gap barrier between a contact and the narrow-gap absorber blocks the majority carriers (a large conduction band offset) and passes the minority carriers (a valence band offset near zero), so that the depletion region lies in the barrier and the dark current is diffusion-limited.
• Unipolar operation: A barrier detector has no p-n junction in the absorber, its photoconductive gain is unity, and it blocks the surface leakage of the majority carriers.
• Device variants: The nBn and XBn have an n-type absorber, the XBp (and pBp) a p-type absorber, the XBp barrier is an InAs/AlSb superlattice and the n-B-p structure has a p-type absorber; the absorber is several micrometres thick.
• Figures of merit: The 50% cutoff, the quantum efficiency, the dark current density against temperature, the resistance-area product $R_{0}A$, $D^{\ast }$ and the comparison with the empirical benchmark of HgCdTe known as Rule 07.

2. Working Principle

• Absorption and collection: A photon absorbed in the absorber creates a pair, the minority carrier diffuses to the barrier over the diffusion length $L_D$, crosses it because the band offset for the minority carrier is near zero, and is collected at the contact.
• Barrier action: The wide-gap barrier takes the applied voltage in its depletion region, so that the narrow-gap absorber is neutral, and the thermal generation in the barrier is small because its intrinsic density is low.
• Dark current: The diffusion current dominates at high temperature and the generation-recombination current and the surface leakage at low temperature, with a crossover near 130 K to 180 K in the devices cited here.
• Bias: A small reverse bias, about $-0.1$ V to $-0.2$ V, removes the residual valence band offset; at a larger bias the depletion region reaches the absorber, about $-300$ mV in an InAs/GaSb XBp, and the generation-recombination current returns.
• Lifetime limits: The collection is limited by the diffusion length, which is set by the lifetime of the minority carriers; the electrons of the InAs/GaSb superlattice have a high mobility and a short lifetime, and the holes of the Ga-free superlattice a long Auger-limited lifetime and a low mobility.
• Temperature: Heating shifts the cutoff to longer wavelength and lowers the responsivity as the diffusion length shrinks.

3. Applications

• Mid-wave and long-wave focal plane arrays: Ga-free InAs/InAsSb XBn arrays have been operated close to 130 K in the mid wave, and InAs/GaSb XBp arrays at 77 K in the long wave, with a dark current limited by diffusion.

Type-II Superlattice Photodiode (T2SL)

Name	Formula	Related Formulae	Variables/Constants
Effective gap, cutoff and absorption	$E_g^{eff}=E_{C1}-E_{V1},{\lambda }_c\left(\mu m\right)=\frac{1.2398}{E_g^{eff}\left(\mathrm{eV}\right)}$	$\alpha \left(\lambda \right)\propto {\left[E\left(\lambda \right)-E_g\left(T\right)\right]}^{1/2}$ $\frac{d{E}_g}{dT}\approx \frac{E_g\left(T_2\right)-E_g\left(T_1\right)}{T_2-T_1}$	$\begin{array}{r}{E}_{C1},E_{V1}:lowestconductionminiband\\ (electronsmainlyinInAs)andhighest\\ valenceminiband(holesmainlyinGaSb),\\ theeffectivegapissetbythelayer\\ thicknesses\end{array}$ $\begin{array}{r}{\lambda }_c:cutoffwavelength(about3\mu \mathrm{m}to30\mu \mathrm{m}\\ bydesign)\end{array}$ $E:photonenergy$ $\begin{array}{r}(E_g=184meVat77Kand159meVat190K\\ correspondto6.7\mu \mathrm{m}and7.8\mu \mathrm{m}andto\\ d{E}_g/dT=-0.22meV/K,computed;the50\%\\ cutoffswere6.4\mu \mathrm{m}and7.3\mu \mathrm{m})\end{array}$
Quantum efficiency and responsivity	$\mathfrak{R}=\frac{\eta q\lambda }{hc},\eta =\left(1-R\right)\left(1-e^{-\alpha d}\right){\eta }_c$	$\eta \left(\lambda \right)=\frac{1.24\mathfrak{R}}{\lambda \left(\mu m\right)}$ ${\eta }_c\approx 1-e^{-d_c/L_D}$	$\eta :externalquantumefficiency$ $R:reflectance$ $\alpha :absorptioncoefficient$ $d:absorberthickness$ ${\eta }_c:collectionefficiencyofthephotocarriers$ $d_c:distancetothejunctionorbarrier$ $\begin{array}{r}{L}_D:minority-carrierdiffusionlength(the\\ formof{\eta }_{c}isanestimate)\end{array}$ $\begin{array}{r}(\mathfrak{R}=0.56A/Wat77Kandapeaknear6\\ \mu \mathrm{m}(assumed)give\eta =12\%,computed;the\\ measuredefficiencywas10\%to15\%)\end{array}$
Lifetime and diffusion length	$\frac{1}{\tau }=\frac{1}{{\tau }_{SRH}}+\frac{1}{{\tau }_{Auger}}+\frac{1}{{\tau }_{rad}},L_D=\sqrt{D\tau }$	$D=\frac{k_{B}T}{q}\mu$ $L_D=\sqrt{3\times 10^{-2}\mathrm{c}{\mathrm{m}}^2/s\times 200\mathrm{ns}}$	$\begin{array}{r}{\tau }_{SRH},{\tau }_{Auger},{\tau }_{rad}:lifetimesby\\ trap-assisted,Augerandradiative\\ recombination\end{array}$ $D:diffusivity$ $\mu :mobility$ $\begin{array}{r}{L}_D:diffusionlength,theAugerlifetime\\ ofann-B-pdevicewasabout20nsabove\\ 150KandtheSRHlifetimebelow20nsfor\\ InAs/GaSb\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(anInAs/InAsSbnBndevicegave\tau =200\\ ns,averticaldiffusivityof3\times 10^{-2}\mathrm{c}{\mathrm{m}}^2/s\\ and{L}_D=750nmatliquid-helium\\ temperature;theformulagives0.77\mu \mathrm{m},\\ computed)\end{array}$
Dark current of the absorber	$J_{diff}\propto T^3\exp \left(-\frac{E_g}{k_{B}T}\right),J_{GR}\propto T^{3/2}\exp \left(-\frac{E_g}{2k_{B}T}\right)$	$J_{dark}=J_{diff}+J_{GR}+J_{other}$ $J_{diff}=J_{GR}\mathrm{at}T=T_C$	$J_{diff}:diffusioncurrent$ $\begin{array}{r}{J}_{GR}:generation-recombinationcurrentof\\ thedepletionregion\end{array}$ $J_{other}:tunnellingandsurfaceleakage$ $\begin{array}{r}{T}_C:temperatureofthecrossover\\ (diffusionaboveit)\end{array}$ $k_B:Boltzmannconstant$ $\begin{array}{r}(theactivationenergyofthediffusion\\ currentis{E}_{g}andthatoftheG-Rcurrent\\ E_g/2,whichis92meVfor184meV,\\ computed;ann-B-pdevicegave61.6meV\\ below130Kand159.9meVabove)\end{array}$
Resistance-area product and detectivity	$D^{\ast }=\mathfrak{R}\sqrt{\frac{R_{0}A}{4k_{B}T}}$	$i_n^2=\left(\frac{4k_{B}T}{R_0}+2q{I}_{dark}\right)\Delta f$ $D^{\ast }=\frac{\mathfrak{R}\sqrt{A\Delta f}}{i_n}$	$R_{0}A:zero-biasresistance-areaproduct$ $A:area$ $\begin{array}{r}T:temperature,thefirstformholdsfor\\ theJohnson-noiselimit\end{array}$ $i_n:noisecurrent$ $I_{dark}:darkcurrent$ $\Delta f:bandwidth$ $k_B:Boltzmannconstant$ $\begin{array}{r}(\mathfrak{R}=0.56A/W,R_{0}A=8\times 10^3\Omega \mathrm{c}{\mathrm{m}}^{2}andT=\\ 77Kgive7.7\times 10^{11}\mathrm{cm}\mathrm{H}{\mathrm{z}}^{1/2}/W,computed,\\ against7.6\times 10^{11}measured)\end{array}$

Barrier Photodetector (nBn, XBn)

Name	Formula	Related Formulae	Variables/Constants
Band alignment of the barrier	$\Delta E_V\approx 0,\Delta E_C\gg k_{B}T\left(\mathrm{nBn},\mathrm{XBn}\right)$	$\Delta E_C\approx 0,\Delta E_V\gg k_{B}T\left(\mathrm{pBp},\mathrm{XBp}\right)$ $V_{on}=\frac{\Delta E_{V,res}}{q}$	$\begin{array}{r}\Delta E_V,\Delta E_C:valenceandconductionband\\ offsetsbetweentheabsorberandthe\\ barrier,inannBntheelectronsarethe\\ blockedmajoritycarriersandtheholes\\ theminoritycarriersthatcarrythe\\ photocurrent,inanXBptherolesare\\ exchanged\end{array}$ $\begin{array}{r}{V}_{on}:turn-onvoltageneededtoremovea\\ residualoffset(simulatedforMWIR\\ HgCdTe:350mVfornBnwith\Delta E_V\approx 100\\ meV,and200mVforpBn)\end{array}$ $k_B:Boltzmannconstant$
Dark current with a barrier	$J_{dark}=J_{diff}+J_{GR,b}+J_{other},J_{GR,b}=\frac{q{n}_{i,b}{W}_b}{2{\tau }_b}$	$\frac{n_{i,b}}{n_{i,a}}=\exp \left(-\frac{E_{g,b}-E_{g,a}}{2k_{B}T}\right)$ $V_{GR}\approx -300\mathrm{mV}$	$\begin{array}{r}{J}_{GR,b}:generation-recombinationcurrentof\\ thedepletionregioninthebarrier\\ (derived)\end{array}$ $\begin{array}{r}{n}_{i,b},n_{i,a}:intrinsicdensitiesofthe\\ barrierandtheabsorber\end{array}$ $W_b:widthofthedepletedregioninthebarrier$ ${\tau }_b:lifetimeinthebarrier$ $\begin{array}{r}{V}_{GR}:biasatwhichthedepletionregion\\ reachestheabsorberofanInAs/GaSbXBp\\ detector,(agapdifferenceof0.5eV\\ (assumed)at150Klowers{n}_{i}by4\times 10^{-9},\\ computed)\end{array}$ $k_B:Boltzmannconstant$
Diffusion-limited current and unity gain	$J_{diff}=\frac{q{n}_i^2{L}_D}{N_A\tau }\left(\mathrm{n}-\mathrm{type}\mathrm{contact},\mathrm{p}-\mathrm{type}\mathrm{absorber}\right)$	$n_i^2=N_C{N}_V\exp \left(-\frac{E_g}{k_{B}T}\right)$ $g=1$	$N_A:dopingoftheabsorber$ $n_i:intrinsicdensityoftheabsorber$ $N_C,N_V:effectivedensitiesofstates$ $\begin{array}{r}{L}_D:diffusionlengthoftheminority\\ carriers,theexpressionisthestandard\\ ideal-diodeform(derived)\end{array}$ $\begin{array}{r}g:gainoftheunipolardetector,thedark\\ currentofabarrierdetectoris\\ diffusion-limitedanditsphotoconductive\\ gainisunity\end{array}$ $k_B:Boltzmannconstant$
Operating bias window	$\left|V_{on}\right|<\left|V_{op}\right|<\left|V_{GR}\right|$	$V_{op}\approx -0.2\mathrm{V}\left(\mathrm{XBn}\right)$ $V_{op}\approx -0.1\mathrm{V}\left(\mathrm{XBp}\right)$	$\begin{array}{r}{V}_{on}:turn-onvoltagethatremovesthe\\ residualvalencebandoffset(thequantum\\ efficiencyofanLWIRInAs/InAsSbnBn\\ saturatedaboveabout0.1Vofreverse\\ bias)\end{array}$ $\begin{array}{r}{V}_{op}:operatingbiasoftheInAs/InAsSbXBn\\ andtheInAs/GaSbXBp\end{array}$ $\begin{array}{r}{V}_{GR}:biasatwhichthedepletionregion\\ reachestheabsorberandtheG-Rcurrent\\ returns,(ashort-cutoffInAs/GaSbbarrier\\ detectorhadaquantumefficiencyof43\%\\ at2.8\mu \mathrm{m}and200K,double-passwithout\\ anantireflectioncoating,limitedbya\\ diffusionlengthof1.8\mu \mathrm{m})\end{array}$

Important Questions

Ques: Why does a barrier suppress the generation-recombination current without blocking the photocurrent?

In an nBn structure the barrier has a large conduction band offset, which blocks the majority electrons, and a valence band offset near zero, so the minority holes of the photocurrent pass. The applied voltage drops across the barrier, the absorber stays neutral, and the depletion region lies in the wide-gap barrier, where the intrinsic density is lower by $\exp [-(E_{g,b}-E_{g,a})/2k_{B}T]$, i.e. $4\times 10^{-9}$ for a gap difference of 0.5 eV at 150 K (assumed, computed). The current is then diffusion-limited, with unity gain. In a simulation of mid-wave HgCdTe a unipolar barrier in the p-region of a p-n diode lowered the dark current by about two orders and in the n-region by up to four, and the surface leakage of the majority carriers is blocked as well. Reference: Martyniuk and Gawron, Barrier Detectors Versus Homojunction Photodiode, Metrol. Meas. Syst. 21, 675 (2014); P. C. Klipstein, Perspective on III-V barrier detectors (2022).

Ques: Is the lifetime of the InAs/GaSb superlattice limited by the Auger or by the SRH recombination?

The n-B-p paper cites an Auger-limited minority lifetime of about 20 ns and a diffusion length below 5 μm above 150 K, and says that Auger recombination may limit the transport at high temperature, whereas the barrier-detector review states that the SRH recombination through deep centres dominates in InAs/GaSb, with lifetimes below 20 ns for $T>150$ K, and that the Auger recombination is predicted to be suppressed by the separation of electrons and holes. The XBn/XBp review adds that the short lifetime is the main obstacle of the InAs/GaSb material. The SRH limit is the more likely, because the Auger suppression is a prediction of the band structure and the lifetime is attributed to defects, so that both statements give the same 20 ns for different reasons. Reference: InAs/GaSb type-II superlattice n-B-p infrared photodetector on GaAs (JQE manuscript, discovery-pp.ucl.ac.uk; the fetch gave no title or authors); Martyniuk and Gawron, Barrier Detectors Versus Homojunction Photodiode, Metrol. Meas. Syst. 21, 675 (2014); XBn and XBp detectors based on type II superlattices (cris.biu.ac.il, abstract).

Ques: Why does the activation energy of 61.6 meV not match the generation-recombination current, which should be $E_g/2$?

The n-B-p device had an effective gap of 184 meV at 77 K. The generation-recombination current from midgap traps has the activation energy $E_g/2=92$ meV, and the diffusion current $E_g$ (computed). The Arrhenius fit at -0.1 V gave 61.6 meV between 77 K and 130 K, which the authors equate with $E_g/3$ and with G-R, and 159.9 meV between 130 K and 300 K, which equals the gap of 159 meV at 190 K and identifies the diffusion. A value near $E_g/3$ lies below the G-R value, which suggests a mixture of the G-R current with trap-assisted tunnelling or surface leakage (an interpretation, not stated by the source), so that the low-temperature current is not a pure G-R current. Reference: InAs/GaSb type-II superlattice n-B-p infrared photodetector on GaAs (JQE manuscript, discovery-pp.ucl.ac.uk; the fetch gave no title or authors).

Ques: Which diffusion length is right for the InAs/InAsSb absorber: 750 nm or 5 μm to 10 μm?

The electron-beam-induced-current and time-resolved photoluminescence study of an InAs/InAsSb nBn device gave a lifetime of 200 ns, a vertical diffusivity of $3\times 10^{-2}\mathrm{c}{\mathrm{m}}^2/s$ and a diffusion length of 750 nm at liquid-helium temperature, which the formula $\sqrt{D\tau }$ reproduces (0.77 μm, computed). The perspective on barrier detectors quotes 5 μm to 10 μm for T2SL devices, and a short-cutoff barrier detector had a diffusion length of 1.8 μm at 200 K. The values refer to different structures, temperatures and directions. For vertical transport in the Ga-free superlattice 1 μm to 2 μm is the more likely, since the 1.8 μm value comes from a measured efficiency at an operating temperature, and 5 μm to 10 μm is an optimistic figure. Reference: Zuo et al., Direct minority carrier transport characterization of InAs/InAsSb superlattice nBn photodetectors (2015, abstract); P. C. Klipstein, Perspective on III-V barrier detectors (2022); High performance type-II InAs/GaSb superlattice infrared photodetectors with a short cut-off wavelength, Opto-Electron. Rev. (abstract).

Ques: Why do barrier detectors still have a dark current above the Rule 07 benchmark?

Rule 07 is the empirical dark current of HgCdTe against cutoff and temperature. A Ga-free InAs/InAsSb XBn had $2\times 10^{-6}A/c{\mathrm{m}}^2$ at 150 K and -200 mV, called about two decades above it by the authors (G-R current); an InAs/GaSb XBp had $8\times 10^{-4}A/c{\mathrm{m}}^2$ at 80 K and -100 mV, a decade above (diffusion, short lifetime); an LWIR nBn had about $1A/c{\mathrm{m}}^2$ at 80 K and -1 V, two orders above. The published expression gives $1.0\times 10^{-7}$ for 4.2 μm at 150 K and $1.9\times 10^{-5}$ for 10.5 μm at 80 K (computed), so the first two are 20 and 42 times above it, 1.3 and 1.6 decades, not 2 and 1. A cutoff of 4.6 μm would give 6 times, so the convention matters; my values are the more likely for the stated cutoffs. T2SL is predicted to exceed HgCdTe, but has not reached it. Reference: Zavala-Moran et al., Antimonide-based Superlattice Infrared Barrier Photodetectors, PHOTOPTICS 2020; Kopytko et al., LWIR InAs/InAsSb Superlattice Detector for Cooled FPA, Proceedings 129, 28 (2025); High performance type-II InAs/GaSb superlattice infrared photodetectors with a short cut-off wavelength, Opto-Electron. Rev. (abstract); D. R. Rhiger, Performance Comparison of Long-Wavelength Infrared Type II Superlattice Devices with HgCdTe, J. Electron. Mater. 40, 1815 (2011) (abstract).

Ques: Why does a barrier detector need a bias, and what happens if the bias is too large?

If the valence band offset of the barrier is not exactly zero, the minority carriers are blocked until the bias bends the bands: in simulated MWIR HgCdTe devices the offset of 100 meV gave a turn-on of 350 mV for the nBn and 200 mV for the pBn, and in an LWIR InAs/InAsSb nBn the quantum efficiency rose with negative bias and saturated above about -0.1 V. At a larger bias the depletion region reaches the absorber and the G-R current returns, at about -300 mV in the InAs/GaSb XBp, which was diffusion-limited at the operating point of -100 mV. The operating bias is therefore a compromise: large enough to remove the offset, small enough to keep the depletion region in the barrier. The Ga-free XBn was operated at about -200 mV. Reference: Martyniuk and Gawron, Barrier Detectors Versus Homojunction Photodiode, Metrol. Meas. Syst. 21, 675 (2014); Kopytko et al., LWIR InAs/InAsSb Superlattice Detector for Cooled FPA, Proceedings 129, 28 (2025); Zavala-Moran et al., Antimonide-based Superlattice Infrared Barrier Photodetectors, PHOTOPTICS 2020.

Ques: Why does the cutoff of a T2SL move to longer wavelength and the responsivity fall when it is heated?

The effective gap of the n-B-p device fell from 184 meV at 77 K to 159 meV at 190 K, i.e. $-0.22$ meV/K (computed), so the 50% cutoff moved from 6.4 μm to 7.3 μm, and the absorption $\alpha \propto (E-E_g{)}^{1/2}$ grows at a fixed photon energy as the gap shrinks. The peak responsivity nevertheless fell from 0.56 A/W to 0.35 A/W, a factor of 0.63 (computed). The paper notes that Auger recombination, with a lifetime of about 20 ns and a diffusion length below 5 μm above 150 K, may limit the transport at high temperature, so that fewer photocarriers reach the barrier. The change of the gap is thus a property of the miniband structure, and the loss of efficiency a property of the lifetime. Reference: InAs/GaSb type-II superlattice n-B-p infrared photodetector on GaAs (JQE manuscript, discovery-pp.ucl.ac.uk; the fetch gave no title or authors).

Ques: Why is the zero-bias detectivity of the n-B-p detector limited by the resistance-area product?

At zero bias there is no net current, so the shot noise of the dark current is absent and the noise is the Johnson noise of the differential resistance, $i_n^2=4k_{B}T\Delta f/R_0$, which gives $D^{\ast }=\mathfrak{R}\sqrt{R_{0}A/(4k_{B}T)}$ (derived). With $\mathfrak{R}=0.56$ A/W, $R_{0}A=8\times 10^3\Omega \mathrm{c}{\mathrm{m}}^2$ and $T=77$ K, the expression gives $7.7\times 10^{11}\mathrm{cm}\mathrm{H}{\mathrm{z}}^{1/2}/W$ (computed), against $7.6\times 10^{11}$ measured, so the Johnson limit describes the device. The peak $R_{0}A$ was larger, $1.8\times 10^4\Omega \mathrm{c}{\mathrm{m}}^2$ at -0.1 V; the design places the depletion field in the barrier to keep the G-R current of the absorber low. At a nonzero bias the full expression $i_n^2=(4k_{B}T/R_0+2q{I}_{dark})\Delta f$ applies, since the shot noise of the dark current is then added to the Johnson noise. Reference: InAs/GaSb type-II superlattice n-B-p infrared photodetector on GaAs (JQE manuscript, discovery-pp.ucl.ac.uk; the fetch gave no title or authors).

Ques: Why do the Ga-free and the Ga-containing superlattices have opposite transport properties?

In the InAs/GaSb superlattice of an XBp detector the minority carriers are electrons, which have a high mobility but a short lifetime, below 20 ns above 150 K because of SRH recombination at defects. In the Ga-free InAs/InAsSb superlattice of an XBn detector the minority carriers are holes, which have a long lifetime, 200 ns at liquid-helium temperature, but a low mobility, because the hole conduction is non-metallic (a vertical diffusivity of only $3\times 10^{-2}\mathrm{c}{\mathrm{m}}^2/s$). The perspective explains the contrast by the competition of G-R and Auger recombination and by the transition between metallic and non-metallic conduction, and the XBn/XBp review reaches the long Auger-limited hole lifetime at a doping below $10^{15}\mathrm{c}{\mathrm{m}}^{-3}$. Both materials thus have a diffusion length of the order of a micrometre, from opposite combinations of mobility and lifetime. Reference: P. C. Klipstein, Perspective on III-V barrier detectors (2022); XBn and XBp detectors based on type II superlattices (cris.biu.ac.il, abstract); Zuo et al., Direct minority carrier transport characterization of InAs/InAsSb superlattice nBn photodetectors (2015, abstract).

Related pages in this vault: Interband Cascade Infrared Photodetector (ICIP), HgCdTe Photodiode, Quantum-Dot Infrared Photodetector (QDIP), PN Photodiode, Ultraviolet Photodetector (AlGaN, SiC, Ga2O3, Diamond), Inter-band Cascade Laser (ICL).