Center for Quantum Devices - Most Downloaded Journal Articles

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1.	Band edge tunability of M-structure for heterojunction design in Sb based Type-II superlattice photodiodes B.M. Nguyen, D. Hoffman, P.Y. Delaunay, E.K. Huang, M. Razeghi, and J. Pellegrino Applied Physics Letters, Vol. 93, No. 16, p. 163502-1-- October 20, 2008 ...[Visit Journal] We present theoretically and experimentally the effect of the band discontinuity in Type-II misaligned InAs/GaSb superlattice heterodiodes. Calculations using the empirical tight binding method have shown the great flexibility in tuning the energy levels of the band edge in M-structure superlattice as compared to the standard InAs/GaSb superlattice. Through the experimental realization of several p-pi-M-n photodiodes, the band discontinuity alignment between the standard binary-binary superlattice and the M-structured superlattice was investigated via optical characterization. The agreement between the theoretical predictions and the experimental measurement confirms the capability of controlling the M-structure band edges and suggests a way to exploit this advantage for the realization of heterostructures containing an M-structured superlattice without bias dependent operation. [reprint (PDF)]
1.	III-Nitride photon counting avalanche photodiodes R. McClintock, J.L. Pau, K. Minder, C. Bayram and M. Razeghi SPIE Conference, January 20-25, 2008, San Jose, CA Proceedings – Quantum Sensing and Nanophotonic Devices V, Vol. 6900, p. 69000N-1-11.-- February 1, 2008 ...[Visit Journal] In order for solar and visible blind III-Nitride based photodetectors to effectively compete with the detective performance of PMT there is a need to develop photodetectors that take advantage of low noise avalanche gain. Furthermore, in certain applications, it is desirable to obtain UV photon counting performance. In this paper, we review the characteristics of III-nitride visible-blind avalanche photodetectors (APDs), and present the state-of-the-art results on photon counting based on the Geiger mode operation of GaN APDs. The devices are fabricated on transparent AlN templates specifically for back-illumination in order to enhance hole-initiated multiplication. The spectral response and Geiger-mode photon counting performance are analyzed under low photon fluxes, with single photon detection capabilities being demonstrated in smaller devices. Other major technical issues associated with the realization of high-quality visible-blind APDs and Geiger mode APDs are also discussed in detail and solutions to the major problems are described where available. Finally, future prospects for improving upon the performance of these devices are outlined. [reprint (PDF)]
1.	Review of high power frequency comb sources based on InP From MIR to THZ at CQD Manijeh Razeghi, Quanyong Lu, Donghai Wu, Steven Slivken Event: SPIE Optical Engineering + Applications, 2018, San Diego, California, United States-- September 14, 2018 ...[Visit Journal] We present the recent development of high performance compact frequency comb sources based on mid-infrared quantum cascade lasers. Significant performance improvements of our frequency combs with respect to the continuous wave power output, spectral bandwidth, and beatnote linewidth are achieved by systematic optimization of the device's active region, group velocity dispersion, and waveguide design. To date, we have demonstrated the most efficient, high power frequency comb operation from a free-running room temperature continuous wave (RT CW) dispersion engineered QCL at λ~5-9 μm. In terms of bandwidth, the comb covered a broad spectral range of 120 cm⁻¹ with a radio-frequency intermode beatnote spectral linewidth of 40 Hz and a total power output of 880 mW at 8 μm and 1 W at ~5.0 μm. The developing characteristics show the potential for fast detection of various gas molecules. Furthermore, THz comb sources based on difference frequency generation in a mid-IR QCL combs could be potentially developed. [reprint (PDF)]
1.	Characterization of InTlSb/InSb Grown by Low Pressure Metalorganic Chemical Vapor Deposition on GaAs Substrat Y.H. Choi, P. Staveteig, E. Bigan, and M. Razeghi Journal of Applied Physics 75 (6)-- March 15, 1994 ...[Visit Journal] Optical properties of InTlSb, a new long wavelength infrared material, are investigated. InTlSb/InSb epilayers grown by low‐pressure metal‐organic chemical vapor deposition on semi‐insulating GaAs substrates were characterized using Auger electron spectroscopy and Fourier transform infrared spectroscopy. Auger electron spectra confirm the presence of thallium. Transmission measurements at 77 K indicate an absorption shift from 5.5 μm for InSb up to 8 μm for InTlSb that is confirmed by photoconductivity measurements. [reprint (PDF)]
1.	Injector doping level dependent continuous-wave operation of InP-based QCLs at λ~ 7.3 µm above room temperature J.S. Yu, S. Slivken, and M. Razeghi Semiconductor Science and Technology (SST), Vol. 25, No. 12, p. 125015-- December 1, 2010 ...[Visit Journal] We report the continuous-wave (CW) operation of InGaAs/InAlAs quantum cascade lasers (QCLs) operating at λ ~ 7.3 µm above room temperature. The injector doping level–dependent CW characteristics above room temperature are investigated for doping densities between 7 × 10¹⁶ cm⁻³ and 2 × 10¹⁷ cm⁻³. The device performance, i.e. threshold current density, output power, operating temperature and characteristic temperature, depends strongly on the injector doping density. For a relatively low injector doping density of 7 × 10¹⁶ cm⁻³, a high-reflectivity-coated 10 µm wide and 4 mm long laser exhibits an improved device performance with an output power of 152 mW and a threshold current density of 1.37 kA cm⁻² at 298 K under CW mode, operating up to 343 K. The thermal characteristics are also analyzed by the estimation from the experimentally measured data for the QCLs with different injector doping densities. [reprint (PDF)]
1.	Effects of well width and growth temperature on optical and structural characteristics of AlN/GaN superlattices grown by metal-organic chemical vapor deposition C. Bayram, N. Pere-Laperne, and M. Razeghi Applied Physics Letters, Vol. 95, No. 20, p. 201906-1-- November 16, 2009 ...[Visit Journal] AlN/GaN superlattices (SLs) employing various well widths (from 1.5 to 7.0 nm) are grown by metal-organic chemical vapor deposition technique at various growth temperatures (Ts) (from 900 to 1035 °C). The photoluminescence (PL), x-ray diffraction, and intersubband (ISB) absorption characteristics of these SLs and their dependency on well width and growth temperature are investigated. Superlattices with thinner wells (grown at the same Ts) or grown at lower Ts (employing the same well width) are shown to demonstrate higher strain effects leading to a higher PL energy and ISB absorption energy. Simulations are employed to explain the experimental observations. ISB absorptions from 1.04 to 2.15 µm are demonstrated via controlling well width and growth temperature. [reprint (PDF)]
1.	Reliable High-Power Uncoated Al-free InGaAsP/GaAs Lasers for Cost-Sensitive Optical Communication and Processing Applications M. Razeghi SPIE Conference, Dallas, TX, -- November 4, 1997 ...[Visit Journal] Unlike InP-based systems for long-distance communication applications, GaAs-based optoelectronic systems mostly for local-area network, optical interconnection or optical computing are very cost-sensitive because often these optoelectronic devices constitute most of the cost for these applications and fewer users share the cost. Thus besides technical issues, the processing cost should be addressed in the selection of materials and fabrication methods. We discuss a number of major advantages of Al-free InGaAsP/GaAs lasers for these applications, such as not coating- requirement, low cost, high long-term reliability, high performance. We discuss recent preliminary results of Al- free lasers as a first step toward these optoelectronic applications. [reprint (PDF)]
1.	Near bulk-limited R0A of long-wavelength infrared type-II InAs/GaSb superlattice photodiodes with polyimide surface passivation Andrew Hood, Pierre-Yves Delaunay, Darin Hoffman, Binh-Minh Nguyen, Yajun Wei, Manijeh Razeghi, and Vaidya Nathan Applied Physics Letters 90, 233513-- June 4, 2007 ...[Visit Journal] Effective surface passivation of Type-II InAs/GaSb superlattice photodiodes with cutoff wavelengths in the long-wavelength infrared is presented. A stable passivation layer, the electrical properties of which do not change as a function of the ambient environment nor time, has been prepared by a solvent-based surface preparation, vacuum desorption, and the application of an insulating polyimide layer. Passivated photodiodes, with dimensions ranging from 400×400 to 25×25 µm², with a cutoff wavelength of ~11 µm, exhibited near bulk-limited R₀A values of ~12 Ω·cm², surface resistivities in excess of 10⁴ Ω·cm, and very uniform current-voltage behavior at 77 K. [reprint (PDF)]
1.	Room-temperature continuous-wave operation of quantum-cascade lasers at λ ~ 4 µm J.S. Yu, S.R. Darvish, A. Evans, J. Nguyen, S. Slivken, and M. Razeghi Applied Physics Letters 88 (4)-- January 23, 2006 ...[Visit Journal] High-power cw λ~4 μm quantum-cascade lasers (QCLs) are demonstrated. The effect of different cavity length and laser die bonding is also investigated. For a high-reflectivity-coated 11-μm-wide and 4-mm-long epilayer-down bonded QCL, cw output powers as high as 1.6 W at 80 K and 160 mW at 298 K are obtained, and the cw operation is achieved up to 313 K with 12 mW. [reprint (PDF)]
1.	8.5 μm Room Temperature Quantum Cascade Lasers Grown by Gas-Source Molecular Beam Epitaxy S. Slivken and M. Razeghi SPIE Conference, San Jose, CA, -- January 28, 1998 ...[Visit Journal] We report room-temperature pulsed-mode operation of 8.5 μm quantum cascade lasers grown by gas-source molecular beam epitaxy. The theory necessary to understand the operation of the laser is presented and current problems are analyzed. Very good agreement is shown to exist between theoretical and experimental emission wavelengths. The high- temperature operation is achieved with 1 μs pulses at a repetition rate of 200 Hz. Peak output power in these conditions is in excess of 700 mW per 2 facets at 79 K and 25 mW at 300 K. Threshold current as a function of temperature shows an exponential dependence with T₀ equals 188 K for a 1.5 mm cavity. [reprint (PDF)]
1.	Novel Sb-based Alloys for Uncooled Infrared Photodetector Applications M. Razeghi SPIE Conference, San Jose, CA, -- January 22, 2001 ...[Visit Journal] We report on the growth and characterization of InSbBi, InTlSb, InTlP, and the quaternary alloys for uncooled long- wavelength infrared photodetector applications. The layers were grown on InSb and GaAs substrates by low-pressure metalorganic chemical vapor deposition. The incorporation of Bi and Tl in InSb was investigated with high-resolution x-ray diffraction, energy dispersive x-ray analysis, and optical photoresponse measurements. We also demonstrate the photodetectors fabricated from the grown InSbBi and InTlSb alloys. InSb_0.96Bi_0.04 photoconductive detectors exhibited a responsivity of 3.2 V/W at 77 K. The estimated Johnson noise limited detectivityat 7 micrometers was 1.7 X 10⁸ cm·Hz^½/W at 77 K. A room temperature operating InSb_0.95Bi_0.05 photodetector was also demonstrated.Photoresponse up to 12 micrometers was achieved at 300 K. The responsivity and Johnson noise-limited detectivity at 10.6 μm were 1.9 mV/W and 1.2 X 10⁶ cm·Hz^½/W, respectively. Photoresponse up to 15 μm was achieved at 300 K from quaternary InTlAsSb and InBiAsSb alloys. [reprint (PDF)]
1.	320x256 infrared focal plane array based on type-II InAs/GaSb superlattice with a 12 μm cutoff wavelength P.Y. Delaunay, B.M. Nguyen, D. Hoffman, and M. Razeghi SPIE Porceedings, Vol. 6542, Orlando, FL 2007, p. 654204-- April 9, 2007 ...[Visit Journal] In the past few years, significant progress has been made in the structure design, growth and processing of Type-II InAs/GaSb superlattice photodetectors. Type-II superlattice demonstrated its ability to perform imaging in the middle and long infra-red range, becoming a potential competitor for technologies such as QWIP and HgCdTe. Using an empirical tight-binding model, we developed a superlattice design that matches the lattice parameter of GaSb substrates and presents a cutoff wavelength of 12 μm. Electrical and optical measurements performed on single element detectors at 77 K showed an R₀A averaging 13 Ω·cm² and a quantum efficiency as high as 54%. We demonstrated high quality material growth with x-ray FWHM below 30 arcsec and an AFM rms roughness of 1.5 Å over an area of 20x20 μm². A 320x256 array of 25x25μm² pixels, hybridized to an Indigo Read Out Integrated Circuit, performed thermal imaging up to 185 K with an operability close to 97%. The noise equivalent temperature difference at 81 K presented a peak at 270 mK, corresponding to a mean value of 340 mK. [reprint (PDF)]
1.	InAs/InAs_1-xSb_x type-II superlattices for high performance long wavelength infrared detection M. Razeghi, A. Haddadi, A. M. Hoang, R. Chevallier, S. Adhikary, A. Dehzangi Proc. SPIE 9819, Infrared Technology and Applications XLII, 981909-- May 20, 2016 ...[Visit Journal] We report InAs/InAs1-xSbx type-II superlattice base photodetector as high performance long-wavelength infrared nBn device grown on GaSb substrate. The device has 6 μm-thick absorption region, and shows optical performance with a peak responsivity of 4.47 A/W at 7.9 μm, which is corresponding to the quantum efficiency of 54% at a bias voltage of negative 90 mV, where no anti-reflection coating was used for front-side illumination. At 77K, the photodetector’s 50% cut-off wavelength was ~10 μm. The device shows the detectivity of 2.8x10¹¹ cm•Hz^½/W at 77 K, where RxA and dark current density were 119 Ω•cm² and 4.4x10^-4 A/cm² , respectively, under -90 mV applied bias voltage [reprint (PDF)]
1.	Growth and characterization of InAs/GaSb photoconductors for long wavelength infrared range H. Mohseni, E. Michel, J. Sandven, M. Razeghi, W. Mitchel, and G. Brown Applied Physics Letters 71 (10)-- September 8, 1997 ...[Visit Journal] In this letter we report the molecular beam epitaxial growth and characterization of InAs/GaSb superlattices grown on semi-insulating GaAs substrates for long wavelength infrared detectors. Photoconductive detectors fabricated from the superlattices showed photoresponse up to 12 µm and peak responsivity of 5.5 V/W with Johnson noise limited detectivity of 1.33 × 10⁹ cm·Hz^½/W at 10.3 µm at 78 K. [reprint (PDF)]
1.	Broad area photonic crystal distributed feedback quantum cascade lasers emitting 34 W at λ ~ 4.36 μm B. Gokden, Y. Bai, N. Bandyopadhyay, S. Slivken and M. Razeghi Applied Physics Letters, Vol. 97, No. 13, p. 131112-1-- September 27, 2010 ...[Visit Journal] We demonstrate room temperature, high power, single mode, and diffraction limited operation of a two dimensional photonic crystal distributed feedback quantum cascade laser emitting at 4.36 μm. Total peak power up to 34 W is observed from a 3 mm long laser with 400 μm cavity width at room temperature. Far-field profiles have M2 figure of merit as low as 2.5. This device represents a significant step toward realization of spatially and spectrally pure broad area high power quantum cascade lasers. [reprint (PDF)]
1.	GaN nanostructured p-i-n photodiodes J.L. Pau, C. Bayram, P. Giedraitis, R. McClintock, and M. Razeghi Applied Physics Letters, Vol. 93, No. 22, p. 221104-1-- December 1, 2008 ...[Visit Journal] We report the fabrication of nanostructured p-i-n photodiodes based on GaN. Each device comprises arrays of ~200 nm diameter and 520 nm tall nanopillars on a 1 µm period, fabricated by e-beam lithography. Strong rectifying behavior was obtained with an average reverse current per nanopillar of 5 fA at −5 V. In contrast to conventional GaN diodes, nanostructured devices reproducibly show ideality factors lower than 2. Enhanced tunneling through sidewall surface states is proposed as the responsible mechanism for this behavior. Under backillumination, the quantum efficiency in nanostructured devices is partly limited by the collection efficiency of holes into the nanopillars. [reprint (PDF)]
1.	Advances in UV sensitive visible blind GaN-based APDs M. Ulmer, R. McClintock and M. Razeghi SPIE Proceedings, San Francisco, CA (January 22-27, 2011), Vol. 7945, p. 79451G-- January 23, 2011 ...[Visit Journal] In this paper, we describe our current state-of-the-art process of making visible-blind APDs based on GaN. We have grown our material on both conventional sapphire and low dislocation density free-standing c- and m-plane GaN substrates. Leakage current, gain, and single photon detection efficiency (SPDE) of these APDs are compared. The spectral response and Geiger-mode photon counting performance of UV APDs are studied under low photon fluxes. Single photon detection capabilities with over 30% are demonstrated. We show how with pulse height discrimination the Geiger-mode operation conditions can be optimized for enhanced SPDE versus dark counts. [reprint (PDF)]
1.	Kinetics of photoconductivity in n-type GaN photodetector P. Kung, X. Zhang, D. Walker, A. Saxler, J. Piotrowski, A. Rogalski, and M. Razeghi Applied Physics Letters 67 (25)-- December 18, 1995 ...[Visit Journal] High-quality ultraviolet photoconductive detectors have been fabricated using GaN layers grown by low-pressure metalorganic chemical vapor deposition on (11⋅0) sapphire substrates. The spectral responsivity remained nearly constant for wavelengths from 200 to 365 nm and dropped sharply by almost three orders of magnitude for wavelengths longer than 365 nm. The kinetics of the photoconductivity have been studied by the measurements of the frequency‐dependent photoresponse and photoconductivity decay. Strongly sublinear response and excitation‐dependent response time have been observed even at relatively low excitation levels. This can be attributed to redistribution of the charge carriers with increased excitation level. [reprint (PDF)]
1.	Type-II InAs/GaSb Superlattices and Detectors with Cutoff Wavelength Greater Than 18 μm M. Razeghi, Y. Wei, A. Gin, G.J. Brown and D. Johnstone Proceedings of the SPIE, San Jose, CA, Vol. 4650, 111 (2002)-- January 25, 2002 ...[Visit Journal] The authors report the most recent advances in Type-II InAs/GaSb superlattice materials and photovoltaic detectors. Lattice mismatch between the substrate and the superlattice has been routinely achieved below 0.1%, and less than 0.0043% as the record. The FWHM of the zeroth order peak from x-ray diffraction has been decreased below 50 arcsec and a record of less than 44arcsec has been achieved. High performance detectors with 50% cutoff beyond 18 micrometers up to 26 micrometers have been successfully demonstrated. The detectors with a 50% cut-off wavelength of 18.8 micrometers showed a peak current responsivity of 4 A/W at 80K, and a peak detectivity of 4.5¹⁰ cm·Hz^½·W^-1 was achieved at 80K at a reverse bias of 110 mV under 300 K 2(pi) FOV background. Some detectors showed a projected 0% cutoff wavelength up to 28~30 micrometers . The peak responsivity of 3Amp/Watt and detectivity of 4.25¹⁰ cm·Hz^½·W^-1 was achieved under -40mV reverse bias at 34K for these detectors. [reprint (PDF)]
1.	Growth of In_1-xTl_xSb, a New Infrared Material, by Low-Pressure Metalorganic Chemical Vapor Deposition Y.H. Choi, R. Sudharsanan, C, Besikci, and M. Razeghi Applied Physics Letters 63 (3)-- July 19, 1993 ...[Visit Journal] We report the growth of In_1-xTl_xSb, a new III-V alloy for long-wavelength infrared detector applications, by low-pressure metalorganic chemical vapor deposition. In_1-xTl_xSb with good surface morphology was obtained on both GaAs and InSb substrates at a growth temperature of 455 °C. X-ray diffraction measurements showed resolved peaks of In_1-xTl_xSb and InSb films. Infrared absorption spectrum of In_1-xTl_xSb showed a shift toward lower energies compared to InSb spectrum. Hall mobility data on In_1-xTl_xSb/InSb/GaAs structure showed enhanced mobility at low temperatures compared to InSb/GaAs structure. [reprint (PDF)]
1.	Comparison of PLD-Grown p-NiO/n-Ga2O3 Heterojunctions on Bulk Single Crystal β-Ga2O3 and r-plane Sapphire Substrates D. J. Rogers , V. E. Sandana, F. Hosseini Teherani and M. Razeghi Proc. of SPIE Vol. 12895, Quantum Sensing and Nano Electronics and Photonics XX, 128870J (28 January - 1 February 2024 San Francisco)doi: 10.1117/12.3012511 ...[Visit Journal] p-NiO/n-Ga2O3 heterostructures were formed on single crystal (-201) β (monoclinic) Ga2O3 and r-sapphire substrates by Pulsed Laser Deposition. Ring mesa layer stacks were created using a shadow mask during growth. X-Ray diffraction studies were consistent with the formation of (111) oriented fcc NiO on the bulk Ga2O3 and randomly oriented fcc NiO on (102) oriented β-Ga2O3 /r-sapphire. RT optical transmission studies revealed bandgap energy values of ~3.65 eV and ~5.28 eV for the NiO and Ga2O3 on r-sapphire. p-n junction devices were formed by depositing gold contacts on the layer stacks using shadow masks in a thermal evaporator. Both heterojunctions showed rectifying I/V characteristics. On bulk Ga2O, the junction showed a current density over 16mA/cm2 at +20V forward bias and a reverse bias leakage current over 3 orders of magnitude lower at -20V (1 pA). On Ga2O3/r-sapphire the forward bias current density at +15V was about an order of magnitude lower than for the p-NiO/bulk n-Ga2O3 heterojunction while the reverse bias leakage current at -15V (~ 20 pA) was an order of magnitude higher. Hence the NiO/bulk Ga2O3 junction was more rectifying. Upon illumination with a Xenon lamp a distinct increase in current was observed for the IV curves in both devices (four orders of magnitude for -15V reverse bias in the case of the p-NiO/bulk n-Ga2O3 heterojunction). The p-NiO/n-Ga2O3/rsapphire junction gave a spectral responsivity with a FWHM value of 80nm and two distinct response peaks (with maxima at 230 and 270nm) which were attributed to carriers being photogenerated in the Ga2O3 underlayer. For both devices time response studies showed a 10%/90% rise and fall of the photo generated current upon shutter open and closing which was relatively abrupt (millisecond range), and there was no evidence of significant persistent photoconductivity.
1.	Gain and recombination dynamics of quantum-dot infrared photodetecto H. Lim, B. Movaghar, S. Tsao, M. Taguchi, W. Zhang, A.A. Quivy, and M. Razeghi Virtual Journal of Nanoscale Science & Technology-- December 4, 2006 ...[Visit Journal][reprint (PDF)]
1.	Very high quantum efficiency in type-II InAs/GaSb superlattice photodiode with cutoff of 12 µm B.M. Nguyen, D. Hoffman, Y. Wei, P.Y. Delaunay, A. Hood and M. Razeghi Applied Physics Letters, Vol. 90, No. 23, p. 231108-1-- June 4, 2007 ...[Visit Journal] The authors report the dependence of the quantum efficiency on device thickness of Type-II InAs/GaSb superlattice photodetectors with a cutoff wavelength around 12 µm. The quantum efficiency and responsivity show a clear delineation in comparison to the device thickness. An external single-pass quantum efficiency of 54% is obtained for a 12 µm cutoff wavelength photodiodes with a -region thickness of 6.0 µm. The R₀A value is kept stable for the range of structure thicknesses allowing for a specific detectivity (2.2×10¹¹ cm·Hz^½/W). [reprint (PDF)]
1.	High differential resistance type-II InAs/GaSb superlattice photodiodes for the long-wavelength infrared A. Hood, D. Hoffman, B.M. Nguyen, P.Y. Delaunay, E. Michel and M. Razeghi Applied Physics Letters, 89 (9)-- August 28, 2006 ...[Visit Journal] Type-II InAs/GaSb superlattice photodiodes with a 50% cutoff wavelength ranging from 11 to 13 μm are presented. Optimization of diffusion limited photodiodes provided superlattice structures for improved injection efficiency in direct injection hybrid focal plane array applications. [reprint (PDF)]
1.	High quantum efficiency two color type-II InAs/GaSb n-i-p-p-i-n photodiodes P.Y. Delaunay, B.M. Nguyen, D. Hoffman, A. Hood, E.K. Huang, M. Razeghi, and M.Z. Tidrow Applied Physics Letters, Vol. 92, No. 11, p. 111112-1-- March 17, 2008 ...[Visit Journal] A n-i-p-p-i-n photodiode based on type-II InAs/GaSb superlattice was grown on a GaSb substrate. The two channels, with respective 50% of responsivity cutoff wavelengths at 7.7 and 10 µm, presented quantum efficiencies (QEs) of 47% and 39% at 77 K. The devices can be operated as two diodes for simultaneous detection or as a single n-i-p-p-i-n detector for sequential detection. In the latter configuration, the QEs at 5.3 and 8.5 µm were measured as high as 40% and 39% at 77 K. The optical cross-talk between the two channels could be reduced from 0.36 to 0.08 by applying a 50 mV bias. [reprint (PDF)]

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