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Quantum Mechanical Mixing Model for Hot Electron Bolometers

Harald Merkel, P. Khosropanah, T. L. van den Berg, Serguei Cherednichenko, E. Kollberg

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

In recent experiments, quantum effects have become visible in the device noise of hot electron bolometers. Modelling attempts have been made to asses this additional noise [1] Here a model is presented, where the bolometer is associated with a photon counting operator. Since the local oscillator and the radio frequency signal are treated as photon flows, a stochastic fluctuation of the absorbed power in time is caused by the graininess of the incoming radiation. Applying counting operators to the downconverted signal and using a simple Poisson distribution for the presence or absence of a photon, a closed form expression for the quantum noise of the HEB is found that is similar to the relations given in [1]. Quantum noise is a substantial part in the mixer noise at larger THz frequencies and dominates the mixer noise of NbN phonon cooled HEB at frequencies around 8THz and above. Quantum noise contributions are found to be subject to the same electrothermal feedback process as fluctuation and thermal noise are. A way to minimize quantum noise contribution is one is achieved by a correct matching of the active part of the bolometer to the antenna. On the other side, for frequencies above the quasiparticle bandgap, the whole HEB must be matched to the antenna for optimum performance so the best mixer performance lies in between these extrema.

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Rigorous Analysis of a Superconducting Hot-Electron Bolometer Mixer: Theory and Comparison with Experiment

Rainer S. Nebosis, Alexei D. Semenov, Yu. P. Gousev +1 more

We present theoretical analysis of the performance of a superconducting hot-electron bolometer mixer with electron cooling due to electron phonon interaction. The analysis is based on a complete set of thermal balance equations for phonons and electrons. A non-thermal action of a dc current has been considered phenomenologically using an analytical fit of isothermal current-voltage characteristics of the mixer. The operation point of the mixer has been determined as a result of the heating by both the power of a local oscillator and the power dissipated by the current. Electron temperature fluctuations, Nyquist noise, and shot noise have been supposed to only contribute to the mixer noise. The conversion gain and the noise temperature of the mixer have been evaluated taking into account an electro-thermal feedback between the mixer and an intermediate frequency circuit with an arbitrary impedance. We have obtained general expressions for the conversion gain, noise temperature and impedance which enabled us to estimate ultimate performance of a superconducting hot-electron bolometer mixer. Theoretical predictions are in good agreement with experimental results obtained for a NbN hot-electron bolometer mixer at a radiation frequency of 2.5 THz.

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Quantum noise contribution to NbN hot electron bolometer receiver

E. Kollberg, P. Khosropanah, Wen Zhang +4 more

Abstract— Superconducting NbN hot electron bolometer (HEB) mixers are so far the most sensitive detectors for\nheterodyne spectroscopy in the frequency range between 1.5 THz and 5 THz. To reach the ultimate receiver noise\ntemperatures in the high end of the THz range (3-6 THz), it is crucial to understand their fundamental noise contribution\nfrom different origins. With increasing frequency, the classical output noise contribution should remain unchanged, but\nthe quantum noise contribution is expected to play an increasing role [1].\nThis paper reports the first dedicated experiment using a single NbN HEB mixer at a number of local oscillator\nfrequencies between 1.6 to 4.3 THz to address and quantify the contribution of the quantum noise to the receiver noise\ntemperature.\nWe used a spiral antenna coupled NbN HEB mixer with a bolometer size of 2 μm×0.2 μm. In order to minimize\nuncertainties in the corrections of the optical losses, we use a vacuum hot/cold load setup [2] to eliminate the air loss, and\nan uncoated elliptical Si lens. Although other components, a 3 μm Mylar beam splitter and a QMC heat filter, also\nintroduce frequency dependent optical losses, they can be accurately calibrated. Furthermore, to reduce uncertainties in\nthe data, we measure Y-factors responding to the hot/cold load by fixing the voltage, but varying the LO power [2]. As\nLO, we use a FIR gas laser.\nWe measure the Y-factor at the optimal point at different frequencies by only varying LO frequencies, but keeping\nthe rest exactly the same. We obtain DSB receiver noise temperatures, which are 842 K (at 1.6 THz), 845 K (1.9 THz), 974\nK (2.5 THz) and 1372 K (4.3 THz). After the correction for the losses of the QMC filter and the beam splitter, the noise\ndata show a linear increase with increasing frequency.\nUsing a quantum noise model [1] for HEB mixers and using a criterion for which the classical output noise must be\nconstant at different frequencies, we analyze the results and find the excess quantum noise factor β to be around 2 and\nthat 24 % of the total receiver noise temperature at 4.3 THz (at the input of the entire receiver) can be ascribed to\nquantum noise. Clearly the quantum noise has a small but measurable effect on the receiver noise temperature at this\nfrequency.\nWe are still analyzing different alternatives of interpretation for the mismatch loss between the bolometer and\nthe spiral antenna.\n[1] E. L. Kollberg and K. S. Yngvesson, “Quantum-noise theory for terahertz hot electron bolometer mixers,” IEEE Trans.\nMicrowave Theory and Techniques, 54, 2077, 2006.\n[2] P. Khosropanah, J.R. Gao, W.M. Laauwen, M. Hajenius and T.M. Klapwijk, “Low noise NbN hot-electron bolometer mixer\nat 4.3 THz,” Appl. Phys. Lett., 91, 221111, 2007.\n

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The performance of a NbN based phonon-cooled Hot Electron Bolometric (HEB) quasioptical mixer is investigated in the 0.65-3.12 THz frequency range. The device is made from a 3 nm thick NbN film on high resistivity Si and integrated with a planar spiral antenna on the same substrate. The in-plane dimensions of the bolometer strip are 0.2/spl times/2 /spl mu/m. The best results of the DSB noise temperature at 1.5 GHz IF frequency obtained with one device are: 1300 K at 650 GHz, 4700 K at 2.5 THz and 10000 K at 3.12 THz. The measurements were performed at 4.5 K ambient temperature. The amount of local oscillator (LO) power absorbed in the bolometer is about 100 nW. The mixer is linear to within 1 dB compression up to the signal level 10 dB below that of the LO. The intrinsic single sideband conversion gain measured at 650 GHz is -9 dB, the total conversion gain is -14 dB.

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Noise temperature and local oscillator power requirement of NbN phonon-cooled hot electron bolometric mixers at terahertz frequencies

Pavel A. Yagoubov, M. Kroug, H. Merkel +4 more

In this letter, the noise performance of NbN-based phonon-cooled hot electron bolometric quasioptical mixers is investigated in the 0.55–1.1 THz frequency range. The best results of the double-sideband (DSB) noise temperature are: 500 K at 640 GHz, 600 K at 750 GHz, 850 K at 910 GHz, and 1250 K at 1.1 THz. The water vapor in the signal path causes significant contribution to the measured receiver noise temperature around 1.1 THz. The devices are made from 3-nm-thick NbN film on high-resistivity Si and integrated with a planar spiral antenna on the same substrate. The in-plane dimensions of the bolometer strip are typically 0.2×2 μm. The amount of local oscillator power absorbed in the bolometer is less than 100 nW.

Applied Physics Letters•Nov 9, 1998•33 citations
In recent experiments, quantum effects have become visible in the device noise of hot electron bolometers. Modelling attempts have been made to asses this additional noise [1] Here a model is presented, where the bolometer is associated with a photon counting operator. Since the local oscillator and the radio frequency signal are treated as photon flows, a stochastic fluctuation of the absorbed power in time is caused by the graininess of the incoming radiation. Applying counting operators to the downconverted signal and using a simple Poisson distribution for the presence or absence of a photon, a closed form expression for the quantum noise of the HEB is found that is similar to the relations given in [1]. Quantum noise is a substantial part in the mixer noise at larger THz frequencies and dominates the mixer noise of NbN phonon cooled HEB at frequencies around 8THz and above. Quantum noise contributions are found to be subject to the same electrothermal feedback process as fluctuation and thermal noise are. A way to minimize quantum noise contribution is one is achieved by a correct matching of the active part of the bolometer to the antenna. On the other side, for frequencies above the quasiparticle bandgap, the whole HEB must be matched to the antenna for optimum performance so the best mixer performance lies in between these extrema.
We present theoretical analysis of the performance of a superconducting hot-electron bolometer mixer with electron cooling due to electron phonon interaction. The analysis is based on a complete set of thermal balance equations for phonons and electrons. A non-thermal action of a dc current has been considered phenomenologically using an analytical fit of isothermal current-voltage characteristics of the mixer. The operation point of the mixer has been determined as a result of the heating by both the power of a local oscillator and the power dissipated by the current. Electron temperature fluctuations, Nyquist noise, and shot noise have been supposed to only contribute to the mixer noise. The conversion gain and the noise temperature of the mixer have been evaluated taking into account an electro-thermal feedback between the mixer and an intermediate frequency circuit with an arbitrary impedance. We have obtained general expressions for the conversion gain, noise temperature and impedance which enabled us to estimate ultimate performance of a superconducting hot-electron bolometer mixer. Theoretical predictions are in good agreement with experimental results obtained for a NbN hot-electron bolometer mixer at a radiation frequency of 2.5 THz.
Abstract— Superconducting NbN hot electron bolometer (HEB) mixers are so far the most sensitive detectors for\nheterodyne spectroscopy in the frequency range between 1.5 THz and 5 THz. To reach the ultimate receiver noise\ntemperatures in the high end of the THz range (3-6 THz), it is crucial to understand their fundamental noise contribution\nfrom different origins. With increasing frequency, the classical output noise contribution should remain unchanged, but\nthe quantum noise contribution is expected to play an increasing role [1].\nThis paper reports the first dedicated experiment using a single NbN HEB mixer at a number of local oscillator\nfrequencies between 1.6 to 4.3 THz to address and quantify the contribution of the quantum noise to the receiver noise\ntemperature.\nWe used a spiral antenna coupled NbN HEB mixer with a bolometer size of 2 μm×0.2 μm. In order to minimize\nuncertainties in the corrections of the optical losses, we use a vacuum hot/cold load setup [2] to eliminate the air loss, and\nan uncoated elliptical Si lens. Although other components, a 3 μm Mylar beam splitter and a QMC heat filter, also\nintroduce frequency dependent optical losses, they can be accurately calibrated. Furthermore, to reduce uncertainties in\nthe data, we measure Y-factors responding to the hot/cold load by fixing the voltage, but varying the LO power [2]. As\nLO, we use a FIR gas laser.\nWe measure the Y-factor at the optimal point at different frequencies by only varying LO frequencies, but keeping\nthe rest exactly the same. We obtain DSB receiver noise temperatures, which are 842 K (at 1.6 THz), 845 K (1.9 THz), 974\nK (2.5 THz) and 1372 K (4.3 THz). After the correction for the losses of the QMC filter and the beam splitter, the noise\ndata show a linear increase with increasing frequency.\nUsing a quantum noise model [1] for HEB mixers and using a criterion for which the classical output noise must be\nconstant at different frequencies, we analyze the results and find the excess quantum noise factor β to be around 2 and\nthat 24 % of the total receiver noise temperature at 4.3 THz (at the input of the entire receiver) can be ascribed to\nquantum noise. Clearly the quantum noise has a small but measurable effect on the receiver noise temperature at this\nfrequency.\nWe are still analyzing different alternatives of interpretation for the mismatch loss between the bolometer and\nthe spiral antenna.\n[1] E. L. Kollberg and K. S. Yngvesson, “Quantum-noise theory for terahertz hot electron bolometer mixers,” IEEE Trans.\nMicrowave Theory and Techniques, 54, 2077, 2006.\n[2] P. Khosropanah, J.R. Gao, W.M. Laauwen, M. Hajenius and T.M. Klapwijk, “Low noise NbN hot-electron bolometer mixer\nat 4.3 THz,” Appl. Phys. Lett., 91, 221111, 2007.\n
We present recent results of the development of phonon cooled hot-electron bolometric (HEB) mixers for airborne and balloon borne terahertz heterodyne receivers. Three iomportant issues have been addresses: the quality of NbN films the HEB mixers were made from, the spectral properties of the HEB mixers and the local oscillator power required for optical operation. Studies with an atomic force microscope indicate, that the performance of the HEB mixer might have been effected by the microstructure of the NbN film. Antenna gain and noise temperature were investigated at terahertz frequencies for a HEB embedded in either log-spiral or twin-slot feed antenna. Comparison suggests that at frequencies above 3 THz the spiral feed provides better overall performance. At 1.6 THz, a power of 2.5 µW was required from the local oscillator for optimal operation of the HEB mixer.
Phonon cooled hot electron bolometers (HEB) show smaller noise temperatures in mixer applications above 1THz compared to Schottky diodes or SIS devices. To determine the optimal bias point for maximum IF bandwidth and lowest noise of a FEB detailed understandin g of the current-voltage characteristic is indispensable. A complete nonlinear model for a hot electron bolometric (HEB) mixer is derived. The dynamic resistance of a superconducting film is calculated under stron g demagnetization conditions. The resistance is modeled due to vortex flow and phase slip lines. Self heating gives rise to normal domains in the film. In addition the resistance due to thermally activated flux creep and thermal fluctuations is taken into account. All these relations form a large si gnal model for the iv-characteristics and the bias points of the device. A small signal linearization yields then conversion gain and noise temperatures. Furthermore a quality measure for HEB devices is set up by deriving the thermal coupling of the film to the substrate and the achieved critical current density from measured current-voltage characteristics.
The performance of a NbN based phonon-cooled Hot Electron Bolometric (HEB) quasioptical mixer is investigated in the 0.65-3.12 THz frequency range. The device is made from a 3 nm thick NbN film on high resistivity Si and integrated with a planar spiral antenna on the same substrate. The in-plane dimensions of the bolometer strip are 0.2/spl times/2 /spl mu/m. The best results of the DSB noise temperature at 1.5 GHz IF frequency obtained with one device are: 1300 K at 650 GHz, 4700 K at 2.5 THz and 10000 K at 3.12 THz. The measurements were performed at 4.5 K ambient temperature. The amount of local oscillator (LO) power absorbed in the bolometer is about 100 nW. The mixer is linear to within 1 dB compression up to the signal level 10 dB below that of the LO. The intrinsic single sideband conversion gain measured at 650 GHz is -9 dB, the total conversion gain is -14 dB.
In this letter, the noise performance of NbN-based phonon-cooled hot electron bolometric quasioptical mixers is investigated in the 0.55–1.1 THz frequency range. The best results of the double-sideband (DSB) noise temperature are: 500 K at 640 GHz, 600 K at 750 GHz, 850 K at 910 GHz, and 1250 K at 1.1 THz. The water vapor in the signal path causes significant contribution to the measured receiver noise temperature around 1.1 THz. The devices are made from 3-nm-thick NbN film on high-resistivity Si and integrated with a planar spiral antenna on the same substrate. The in-plane dimensions of the bolometer strip are typically 0.2×2 μm. The amount of local oscillator power absorbed in the bolometer is less than 100 nW.