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Laser Photonics Rev. 8, No. 2, 297–302 (2014) / DOI 10.1002/lpor.201300147

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Abstract With the modern development of infrared lasersources such as broadly tunable quantum cascade lasers andfrequency combs, applications of infrared laser spectroscopyare expected to become widespread. Consequently, convenientinfrared detectors are needed, having properties such as fast re-sponse, high efficiency, and room-temperature operation. Thiswork investigated conditions to achieve near-room-temperaturephoton-noise-limited performance of quantum well infrared pho-todetectors (QWIPs), in particular the laser power requirement.Both model simulation and experimental verification were car-ried out. At 300 K, it is shown that the ideal performance can bereached for typical QWIP designs up to a detection wavelengthof 10 μm. At 250 K, which is easily reachable with a thermo-electric Peltier cooler, the ideal performance can be reachedup to 12 μm. QWIPs are therefore suitable for detection andsensing applications with devices operating up to or near roomtemperature.

Near-room-temperature photon-noise-limited quantum wellinfrared photodetector

Ming Rui Hao1,∗, Yao Yang1, Shuai Zhang1, Wen Zhong Shen1,∗, Harald Schneider1,2,∗,and Hui Chun Liu1

1. Introduction

Quantum well infrared photodetectors (QWIPs) [1] havebeen applied to focal plane arrays (FPAs) for thermal imag-ing [2, 3] and high-speed and high-frequency detectorsin the mid- and long-wavelength infrared spectral ranges[4,5]. New applications, such as trace-gas sensing based onquantum cascade lasers (QCLs) have drawn wide attention[6, 7].

Infrared photodetectors generally work at low tem-peratures to minimize the dark current and dark currentnoise. Some new designs, such as photovoltaic [8] or quan-tum cascade detectors [9], are investigated to improve thesignal-to-noise ratio. For weak signals, it is usually desir-able that photodetectors operate under background-limitedperformance (BLIP) condition. The BLIP temperature ofmid-infrared photodetectors is around the liquid nitrogentemperature range, which is also reached by using closed-cycle coolers. One way to optimize the detectors for high-temperature operation is using efficient resonant cavities[10]. However, for some applications (e.g., gas sensing[11–13] and heterodyne detection [14, 15]) involving astrong light source, the photocurrent can be made larger

1 Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physics and Astronomy, Shanghai Jiao TongUniversity, Shanghai 200240, China2 Institute of Ion-Beam Physics and Materials Research, Helmholtz-Zentrum Dresden-Rossendorf 01314, Dresden, Germany∗Corresponding authors: e-mail: mrhao@sjtu.edu.cn; wzshen@sjtu.edu.cn; h.schneider@hzdr.de

than the dark current, such that the photodetector wouldthen still have a good signal-to-noise ratio (SNR) at highoperating temperatures. State-of-the-art QCLs for 4–14 μmwavelength coverage provide single-mode light emissionwith high power up to hundreds of milliwatts [16]. Illu-minated by such a QCL, the signal photocurrent can behigher than the dark current, as well as the backgroundphotocurrent, even for room- or near-room-temperatureoperation.

In this work, we use the three-dimensional carrier driftmodel to simulate the dark current of QWIPs at high oper-ating temperatures. The temperature effect on Fermi energyis taken into consideration, which is essential in this high-temperature region. Based on simulation results, we predictthe laser power requirement to reach photon-noise-limitedperformance for QWIPs peaked at different wavelengthsfor near-room-temperature operation. At 250 K, ideal per-formance can be reached for typical QWIPs up to a detec-tion wavelength of 12 μm, under a laser power density of0.1 mW/μm2. To validate the predictions, we measured thedark currents of QWIP samples at high operating temper-atures. Theoretical results are in good agreement with theexperimental data.

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298 M. R. Hao et al.: Near-room-temperature photon-noise-limited quantum well infrared photodetector

Figure 1 The schematic shows the photon-noise-limited performance of the QWIP. Un-der laser light illumination, the current flow-ing above the barrier is dominated by thephotocurrent.

2. Discussion

QWIP noise is caused by carrier density fluctuations orig-inating from random thermal and photon excitation. Ac-cording to the origins, it is normally categorized into threetypes, device noise from dark current, background noisefrom background radiation, and signal noise from incidentsignal light. Signal noise is typically much smaller thanthe other two for usual applications such as infrared ther-mal imaging. To achieve high performance, infrared pho-todetectors are typically cryogenically cooled to suppressthermal generation and thus dark current noise. When theoperating temperature is low enough, background noisedominates over the device noise, and background-limitedperformance is achieved.

However, the signal photocurrent can become muchlarger than the dark current and the background photocur-rent when the photodetector is illuminated by a strong in-frared laser source (e.g., a QCL or a CO2 laser), and thesignal noise becomes the major noise source. In such acase, the performance of the device is determined by thesignal radiation and we call this photon-noise-limited per-formance (PLIP). Under this condition, the signal-to-noiseratio of the detector is optimum in the sense that it cannot beimproved any more by reducing the operating temperature.Figure 1 shows the principal processes of the PLIP regimein a QW structure. Within this model for QWIPs, the totalcurrent Itot is composed of three parts, dark current Idarkgenerated from thermal activation, background current IBfrom background radiation in the detector field of view, andsignal current IS from signal photon flux. The total currentcan therefore be expressed as

Itot = Idark + R PB + R PS. (1)

Here, R is the detector responsivity. PB and PS are theincident powers of background radiation and signal, respec-tively.

We consider a typical QWIP with a bound-to-quasibound intersubband transition scheme. Here, electronsare photoexcited from a confined state with energy E1, intoan excited state E2, which is in resonance with the barrierVb (E2 ≈ Vb). The barriers are assumed to be sufficientlythick and the number of quantum well (QW) repeats suf-ficiently large to allow us to neglect interwell tunnelingand contact effects. All carriers in the QW structure origi-nate from doping assuming complete ionization. Electronsdistribute according to Fermi–Dirac statistics involving atwo-dimensional (2D) density of states ρ2D in the well andan unbound three-dimensional (3D) density of states ρ3Dabove the barrier. Thus, the Fermi level dependence of thesheet doping level and temperature is determined by

Nd =∫ ∞

0ρ2D(ε) f (ε) dε+Lp

∫ ∞Vb−E1

ρ3D(ε) f (ε) dε,

(2)

where Nd is the sheet doping density in each quantum well,Lp is the quantum well period (sum of well width Lw andbarrier width Lb). The energy distribution f(ε) is givenby the Fermi–Dirac distribution f (ε) = 1/1+ exp( ε−EFkBT ),where EF is the Fermi level referenced to the ground-stateenergy E1, kB is the Boltzmann constant and T is the tem-perature.

For QWIPs operated close to room temperature, only asmall bias voltage is required. Thermionic emission currentis the major dark current component, neglecting resonant,interwell and thermally assisted tunnelings. The dark cur-rent density Jdark is estimated using the 3D carrier drift

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Laser Photonics Rev. 8, No. 2 (2014) 299

model [1] by accounting for the carriers thermally excitedout of the well and flowing above the barriers. Therefore,Jdark is given by

Jdark = eN3DVdrift(F), (3)

where e is electron charge and Vdrift(F) is the average driftvelocity in the barrier as a function of electric field F. Ne-glecting diffusion processes, the average drift velocity takesthe usual form Vdrift(F) = μF/[1+(μF/vsat)2]1/2, where μis the low-field mobility and υsat is the saturated drift veloc-ity. The 3D mobile electron density on top of the barriersN3D is calculated by

N3D = 2(

m∗bkBT2π�2

) 32

exp

(− Eact

kBT

), (4)

where ћ is the reduced Planck constant, mb* is the bar-rier effective mass, Eact is the thermal activation energythat equals the energy difference between the barrier heightand the Fermi level in the well. Neglecting the bias-field-induced barrier lowering effect, we have Eact = Vb − EF.

The signal current density Jphoto is given by the standardexpression

Jphoto = eηg�s, (5)

where η is the absorption quantum efficiency, �s is photonnumber flux density of the signal, g is photoconductive gainthat equals the ratio of the photoelectron capture lifetimeto the transit time across the device. The transit time canbe estimated by τ trans ≈ NLp/Vdrift(F). The photoconductivegain is then given by

g = τcapVdrift(F)N Lp

, (6)

where τ cap is the electron capture time into the well, and Nis the number of QWs.

The electron capture time at liquid-nitrogen tempera-ture is determined by the LO phonon scattering and anexpression has been given in Ref. [17],

τcap = 4hεp EcLpe2 Ephonon I1

, (7)

where Ec is the cutoff energy, Ephonon is the optical phononenergy, εp−1 = ε(∞)−1 − ε(0) −1, ε(0) and ε(∞) is the staticand high-frequency dielectric permittivity, respectively. I1is a dimensionless integral whose value is close to 2 in the3–19 μm cutoff wavelength range. The temperature depen-dence of the LO phonon scattering rate is predicted by thephonon occupation number factor. In the range close toroom temperature, a good approximation for the capturetime is

τcap(T )−1 = τ−1cap

[1 + 2

exp(Ephonon/

kBT ) − 1

]. (8)

1/f noise, is observed in the low-frequency range for mostdetector technologies, but it is especially weak for QWIPsand does not play any role in practical systems. There-fore, we neglected the influence of 1/f noise here. Thegeneration–recombination noise is described as i2noise,dark =4egJdarkAf, where f is the measurement bandwidth andA is detector area. The noise-equivalent power (NEP) is thesignal power needed to produce the same signal strengthas produced by a noise source. According to the aboveanalysis, the dark current noise-limited (NEP)dark is

(NEP)dark =2hc

λsη(1)(T )

√N3DLp

τcap(T )N

√A f , (9)

where λs is the signal wavelength and η(1)(T) is thetemperature-dependent peak absorption quantum efficiencyfor one well. The dark current noise-limited detectivity is

D∗dark =λsη

(1)(T )

2hc

√τcap(T )N

N3DLp. (10)

Close to room temperature, PLIP operation requiresthat Jphoto is larger than Jdark, such that the minimum signalpower PPLIP is given by

PPLIP = hcλs

N3Dτcap(T )

Lpη(1)(T )

A, (11)

For PLIP operation, the total noise is i2noise =i2noise,dark + i2noise,photon, where the photocurrent noisei2noise, photon = 4egJphotoAf. Assuming Jphoto = nJdark, n ≥1, the near-PLIP detectivity is given by

D∗near−PLIP =λsη

(1)(T )

2√

1 + n2hc

√τcap(T )N

N3D Lp. (12)

If the photocurrent is much larger than the dark current,the total noise is dominated by the photon noise so that thesquare noise level is (4egf) times the signal power. So,the NEPPLIP = 4hc f /λsη as a figure of merit is not appli-cable. Therefore, SNR is preferred to describe the detectorperformance and is given by

S

N= Jphoto A√

A f (4eg Jdark + 4eg Jphoto)

=√

n

n + 1

√η(T )φs A

4 f. (13)

If the signal power satisfies Eq. (11), i.e. Jphoto = Jdark,the corresponding SNR is

√η(T )φs A/8 f . If Jphoto � Jdark,

the SNR is√

η(T )φs A/4 f . For the ideal case η(T) = 1,the SNR is limited to a value of

√φs A/4 f , which is

determined by the signal flux density, detector area and themeasurement bandwidth.

The temperature-dependent absorption of a single QWis proportional to the occupation density of the ground state,

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300 M. R. Hao et al.: Near-room-temperature photon-noise-limited quantum well infrared photodetector

Figure 2 Calculated minimum signal power density for QWIPswith different peak wavelengths achieve photon-noise limited per-formance at 200, 250 and 300 K.

taking into account the impact of the spectral broadening[18]

η(1)(T ) = κδE

m∗bkBTπ�2

ln

[exp

(EF

kBT

)+ 1

], (14)

where κ represents the proportionality coefficient that isrelated to the QW structure parameters, δE is the half-width at half-maximum of the absorption lineshape. Com-bining Eq. (14) with Eqs. (4) and (11), the doping-density-dependent minimum signal power PPLIP is a function ofEF/kBT and proportional to

PPLIP ∝exp

(EF

kBT

)ln

[exp

(EF

kBT

)+ 1

] . (15)This expression shows that the way of obtaining low

PLIP signal power is to reduce EF/kBT. However, low dop-ing will also degrade the absorption and signal-to-noiseratio. If we replace the signal radiation by background ra-diation, the derivation of the minimum PPLIP is essentiallyequivalent to the maximum ratio of photocurrent to darkcurrent, which is similar to the discussion on the maximumBLIP temperature in Ref. [19]. The optimal doping was notpredicted from our calculation if the photons are efficientlyabsorbed. Therefore, we face a trade-off between the PLIPsignal power and signal-to-noise ratio. The doping densityshould be low enough to get a moderate PLIP signal power,but high enough to get a good signal-to-noise ratio.

Following Refs. [1] and [20], we take the room-temperature absorption per quantum well per pass to beabout 0.54% for polarized light for a 2D electron den-sity of 5 × 1011 cm−2. Considering typical QWIP designswith different peak response wavelengths, the minimumsignal power for near-room-temperature operation is ob-tained from Eq. (11). Figure 2 shows the calculated signalpower densities for detection peak wavelength in the 3–16 μm band.

In practice, and according to our previous experiments,QWIPs can easily withstand a cw laser power of 10 mW[20]. The smallest device in our past experiments had anarea of 10 μm × 10 μm (for ultrahigh-speed operation)[20]. However, in practice the detector size does not needto be that small for other wavelengths. As long as the sig-nal radiation power density reaches the threshold value,the PLIP condition will be satisfied. Using a high-powerquantum cascade laser (QCL) as the source, in a limit-ing case of having 10 mW power coupled to a 10 μm ×10 μm-area QWIP, the signal power density is 0.1 mW/μm2.A sensing system as described here works in pulsedmode or with infrared signals modulated at relatively highfrequencies, for which the bolometric response can be ne-glected [15].

Figure 2 therefore predicts that up to a peak wavelengthof 10 μm QWIPs can work at signal-limited performance at300 K, which is consistent with our previous experiments[20]. At 250 K, a temperature easily reachable with a ther-moelectric Peltier cooler (TEC), this ideal performance canbe achieved for QWIPs below 12 μm peak wavelength. At200 K, the lowest temperature a TEC can reach, QWIPscan operate in the PLIP regime for the whole 3–15 μmpeak wavelength band. From our calculation the minimumsignal power density decreases rapidly when the detectionwavelength becomes shorter, since an increase in activationenergy exponentially decreases the dark current. At 250 K,the signal power density to achieve PLIP is two orders ofmagnitude larger for QWIPs with 10 μm detection wave-length than for QWIPs operating at 5 μm. PLIP is mucheasier to achieve for peak wavelengths in the 3–5 μm rangethan in the 8–14 μm range.

QWIPs have advantages in their wide dynamic rangeand stability, as compared to other types of mid-infraredphotodetectors [21]. The saturation signal intensity is esti-mated to be over 300 kW/cm2 [22], and nonlinearity can bedecreased or completely suppressed in QWIPs with a largenumber of QWs [23].

3. Experimental

We use the 3D carrier drift model to estimate the dark-current level in QWIPs, assuming that thermionic emis-sion is the major dark-current contribution. In the calcu-lation, the Fermi level is a function of both temperatureand doping density instead of simply being proportional tothe 2D doping density of the well. To validate our anal-ysis, we have measured the dark currents of a series ofQWIPs at different temperatures ranging from 150 K toroom temperature, and compared the results with modelcalculations.

The QWIPs under study were fabricated by molecu-lar beam epitaxy on semi-insulating GaAs substrates. AllQWIPs have the same structural parameters except for theSi doping densities in the quantum wells. The QWIPs withbound-to-quasibound design are peaked at a wavelength of9 μm. The QWIPs consist of 100 periods of 54 Å thick GaAs

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Laser Photonics Rev. 8, No. 2 (2014) 301

Figure 3 Calculated Fermi energy versus temperature for vari-ous QWIP samples. The sample structure parameters were se-lected for a peak absorption wavelength near 9 μm. The 2D dop-ing densities are 2 × 1011, 4 × 1011, 6 × 1011 and 8 × 1011cm−2 for samples S1, S2, S3 and S4, respectively. The Fermienergy value is referenced to the ground-state energy in thewell.

wells and 300 Å thick Al0.24Ga0.76As barriers sandwichedbetween an 8000-Å thick GaAs bottom contact and a4000-Å thick GaAs top contact, Samples S1, S2, S3, andS4 were delta doped in the GaAs well with Si to 2D concen-trations of 2 × 1011, 4 × 1011, 6 × 1011 and 8 × 1011 cm−2,respectively. The experiments were performed on 240 μm ×240 μm mesas formed by standard photolithography withwet chemical etching and ohmic contact metallization.Temperature-dependent dark-current measurements werecarried out in a closed-cycle refrigerator using a Keithley2400 source meter. More details about other measurementscan be found in Ref. [24].

Here, we analyze the temperature dependence of thedark currents for samples with different doping densities tovalidate our dark-current model close to room temperature.The number of electrons above the barriers is determined bythermally generated carriers and depends exponentially onthe distance above the Fermi energy. According to Eq. (2)we numerically calculate the Fermi energy for our sam-ples with different 2D doping densities. Figure 3 showsthe temperature dependence of the Fermi energy for Sam-ples S1, S2, S3 and S4. It is seen that the Fermi energyremains nearly unchanged at low temperature (

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302 M. R. Hao et al.: Near-room-temperature photon-noise-limited quantum well infrared photodetector

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