Channel Transit Time Research Articles

Ultrafast Electron Tunneling Devices-From Electric-Field Driven to Optical-Field Driven.

The search for ever higher frequency information processing has become an area of intense research activity within the micro, nano, and optoelectronics communities. Compared to conventional semiconductor-based diffusive transport electron devices, electron tunneling devices provide significantly faster response times due to near-instantaneous tunneling that occurs at sub-femtosecond timescales. As a result, the enhanced performance of electron tunneling devices is demonstrated, time and again, to reimagine a wide variety of traditional electronic devices with a variety of new "lightwave electronics" emerging, each capable of reducing the electron transport channel transit time down to attosecond timescales. In response to unprecedented rapid progress within this field, here the current state-of-the-art in electron tunneling devices is reviewed, current challenges and opportunities are highlighted, and possible future research directions are identified.

Enhanced High-Frequency Performance of Top-Gated Graphene FETs Due to Substrate- Induced Improvements in Charge Carrier Saturation Velocity

The high-frequency performance of top-gated graphene field-effect transistors (GFETs) depends to a large extent on the saturation velocity of the charge carriers, a velocity limited by inelastic scattering by surface optical phonons from the dielectrics surrounding the channel. In this work, we show that, by simply changing the graphene channel surrounding dielectric with a material having higher optical phonon energy, one could improve the transit frequency and maximum frequency of oscillation of GFETs. We fabricated GFETs on conventional SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Si substrates by adding a thin Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> interfacial buffer layer on top of SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /Si substrates, a material with about 30% higher optical phonon energy than that of SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and compared performance with that of GFETs fabricated without adding the interfacial layer. From S-parameter measurements, a transit frequency and a maximum frequency of oscillation of 43 and 46 GHz, respectively, were obtained for GFETs on Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> with 0.5- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> gate length. These values are approximately 30% higher than those for state-of-the-art GFETs of the same gate length on SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . For relating the improvement of GFET high-frequency performance to improvements in the charge carrier saturation velocity, we used standard methods to extract the charge carrier velocity from the channel transit time. A comparison between two sets of GFETs with and without the interfacial Al <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> layer showed that the charge carrier saturation velocity had increased from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.5\cdot 10^{{7}}$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\cdot 10^{{7}}$ </tex-math></inline-formula> cm/s.

(Invited) 2D Transport and Velocity Modulation in Black Phosphorus Field Effect Transistors

Black phosphorus (bP) is an elemental allotrope with a layered crystal structure of puckered honeycombs that can be mechanically exfoliated down to atomic layer thickness. First synthesized over a century ago, bP has been previously studied as a bulk semiconductor [1,2] and is subject to a resurgence of interest as a 2D semiconductor with properties complementary to the 2D semi-metal graphene [3]. bP is the most thermodynamically stable allotrope of phosphorus but is nonetheless subject to photo-oxidation in the presence of water, oxygen and visible light with a reaction rate that increases as bP layer thickness decreases [4]. We have fabricated bP quantum wells in both back-gated and dual-gated field effect transistor (FET) geometries with bP thicknesses ranging from 6±1 nm to 47±1 nm. Stability under ambient conditions was achieved in back-gated FETs by encapsulation with a layer of poly methyl methacrylate (PMMA), while dual-gated FETs were additionaly protected by a combination of Al2O3 deposited by atomic layer deposition and optically opaque gold metallization. Charge transport measurements reveal ambipolar conduction, field effect mobilities of up to 900 cm2/Vs for holes at low temperatures ( T< 100 K ), current saturation as expected of a bona fide semiconductor, and on/off current ratios exceeding 105 at room temperature [5]. Shubnikov-de Haas (SdH) oscillations were observed in bP FETs at 300 mK to 30 K and magnetic fields of up to 35 T. Lifshitz-Kosevich analysis of the SdH oscillations indicates the presence of a 2-D hole gas with Schrödinger fermion character in an accumulation layer at the bP surface. A simple Schrödinger-Poisson analysis predicts accumulation of holes in a single 2-D sub-band at 300 mK over the range of applied electric fields used in our experiments. Analysis of the thermal activation of SdH oscillations yields a hole effective mass of m*=0.36±0.03m0. Improvements to bP device quality by the independent Y. Zhang group has led to the observation of the quantum Hall effect [6].The top gate of dual-gate bP FETs was found to be effective at modulating both carrier mobility and contact resistance [7]. The mobility modulation effect enables operation of the dual-gate bP FET as a velocity modulated transistor (VMT), first proposed by Sakaki [8] to overcome the limitation on transistor switching frequency imposed by the channel transit time of charge carriers. The mobility of charge carriers within an assymetric bP FET structure is dependent upon the charge carrier density distribution, and is thereby dependent upon the externally applied electric field of the top gate. A two-fold mobility modulation and a two-fold contact resistance modulation leads to a four-fold modulation of transconductance at a fixed hole density. The observation of mobility modulation effects in dual-gate bP FETs demonstrates the capacity for bP to function as a room temperature VMT. Charge density distribution plays an important role in the charge transport properties of 2D atomic crystals, where the exposed surfaces of naked quantum well structures can lead to a strong spatial dependence of charge carrier scattering rates. The recent observation in angle resolved photo-emission spectroscopy of bandgap tuning and a semiconductor to semi-metal transition in K-doped bP via a giant Stark effect [9] suggests the possibility of electric field tuning of bP bandgap in bP FETs. Further work is required to improve the quality of bP/dielectric interfaces and to increase the applied electric field strength to access electric field tunable bandgap devices with bP.

Static Phase Offset in a Multiplying Phase Detector

This article analyzes the static phase offset DeltaPhi <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> of a Gilbert cell phase detector, and attributes the majority of the offset to intrinsic channel transit time. A 6.5 GHz phase detector fabricated in a standard 0.18 mum CMOS technology is used for the study. The static phase offset is broken down into layout and intrinsic contributions, and a simple model is used to calculate the intrinsic component. The use of analytical equations for current and intrinsic phase offset results in prediction of the intrinsic static phase offset to within 12% for the current ranges considered. The use of the intrinsic model with extracted parasitics is then shown via analysis, simulation and experimental data to be useful in predicting the phase detector static phase offset. The analysis, confirmed by measurements, indicates the degree to which the static phase offset can be reduced by increasing the tail bias current.

Thermal characterization of a double-gate silicon-on-insulator MOSFET

A two-dimensional analytical model to study the behaviour of the device parameters in various temperature ranges is developed. The temperature dependences of the threshold voltage, drain current and channel transconductance are modelled using temperature-sensitive parameters. The effects of temperature on the cut-off frequency and channel-transit time are also discussed. The results so obtained are compared with the experimental data for a single-gate silicon-on-insulator MOSFET.

Measurement of blood rheology using micromachined channel array.

Arrays of microgrooves (width 6, 7, and 8 μm; depth 4.5μm; length 10, 20, 30, 40, and 100μm; number 2600 or 4704 in parallel) photofabricated in the surface of a single-crystal silicon substrate were converted to arrays of leak-proof microchannels by tightly covering them with an optically flat glass plate. Using the microchannels as a model of physiological capillaries, total flow rate of blood was determined under a constant suction while flow behavior of blood cells in each channel was microscopically observed. Erythrocyte deformability, leukocyte adhesiveness, and platelet aggregability quantified by channel transit time or channel blocking and reopening rates showed changes caused by environmental factors such as diet and exposure to bacterial cells.

On density-wave oscillations in two-phase flows

Density-wave oscillations in two-phase boiling flow systems have been studied numerically using a robust model based on two non-linear, functional, integro-differential equations. Results of several numerical simulations are used to gain insight into the physical mechanism behind density-wave oscillations. For a wide range of parameter values we find that: (1) traveling density-waves do not play an important role during the oscillations, and that oscillations may persist with very weak traveling density waves; (2) the oscillation period is between three and four times the channel transit time rather than twice as commonly reported; and (3) the variation in mixture velocity, in general, plays a more important role than the variation in mixture density in determining the channel pressure drop characteristics. A physical mechanism for these non-linear oscillations applicable to a large region of parameter space, as suggested by—and consistent with—the results of the numerical experiments, is proposed.

Analytical modeling of MOSFET conductance parameters at cryogenic temperatures

MOSFET conductance parameters: channel transit-time constant, channel resistance and inversion-layer mobility were studied using a transmission line equivalent circuit for the conductance channel in the 296-77 K temperature range. The temperature dependence of channel transit time constant is modeled using temperature-sensitive parameters such as inversion-layer mobility, the Fermi potential, intrinsic carrier concentration and threshold voltage. It is shown that the channel time constant and channel resistance are strongly sensitive to the temperature variation in the inversion region. Channel inversion layer mobilities are also calculated as a function of effective transverse electric field from the peak frequency in the conductance curve at 296 and 77 K, respectively. It is shown that the peak frequency in the a.c. conductance curve is sensitive to temperature variation due to its dependence on channel time constant.

An improved resistor shunted junction model of superconducting metal-oxide-semiconductor field effect transistors

Some preliminary experimental realizations of three terminal devices using low and high Tc electrodes and various semiconducting materials for the active channel have been reported recently. However, little progress has been made towards the theoretical modeling of these systems. We develop the resistively shunted junction model proposed by Ivanov and Claeson, but remove some of the unecessarily restrictive (and sometimes unrealistic) assumptions made by these authors. The model is based on the classic metal-oxide-semiconductor field effect transistor theory modified to take into account the superconducting current flowing between source and drain. Contrary to Ivanov and Claeson, (1) we use the Fermi–Dirac distribution of carriers in the active channel, (2) we take into account the field dependent mobility in the channel, and (3) we do not assume full ionization of the dopants. These points are essential in a highly degenerate two-dimensional electron gas at low temperature. We show that by including the effect of Coulomb and surface scattering in the electron mobility dependence on carrier concentration, the critical current expression of Likharev gives a good fit to the critical current in the superconducting metal-oxide-semiconductor field effect transistor reported by Hatano et al. For a source to drain voltage of 0.1 meV, the minimum gate channel transit time and maximum transconductance per unit width for Hatano’s device are calculated to be around 70 ps and 0.5 mS/mm, respectively.

Low temperature behaviour of channel transit time constant in MOS transistor

The channel transient response time constant of a MOS transistor is studied through the transmission line network of the conductance channel in the 296–77°K temperature range. The temperature dependence of the channel transit time constant is modelled through the temperature sensitive parameters such as inversion layer mobility, the Fermi potential, intrinsic carrier concentration and threshold voltage. It is shown that the channel time constant is strongly sensitive to the temperature variation in the inversion region and results in the MOS transistor channel resistance having zero, negative and positive temperature coefficients depending upon the gate bias voltage.

A nonquasi-static MOSFET model for SPICE-transient analysis

The long-channel MOSFET model is based on an approximate solution to the nonlinear current-continuity equation in the channel. The model includes the large-signal transient and the small-signal AC analyses, although only the transient model is reported here. Comparisons have been made between this model and the 1-D numerical solution to the current-continuity equation, 2-D device simulation (PISCES), and the quasistatic (QS) results. The channel-charge partitioning scheme in the charge-based QS models is shown to be inadequate for the fast transient. This model does not use a charge-partitioning scheme and the currents are dependent on the history of the terminal voltages, not just the instantaneous voltages and their derivatives. For the slow signals (compared to the channel transit time), the nonquasistatic (NQS) model is reduced to the quasistatic 40/60 channel-charge partitioning scheme. The CPU time required for this model is about two to three times longer than that of conventional MOSFET models in SPICE.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear high-frequency response of GaAs metal-semiconductor field-effect transistors

Calculations show that phase nonlinearity in 1 μm gate length power GaAs metal-semiconductor field-effect transistors (MESFET’s) can be accounted for by the variation of gate-channel capacitance with gate bias voltage. Buried-layer GaAs MESFET’s having constant gate-channel capacitance have been fabricated and their high-frequency linearity measured. The devices display dramatic reductions of phase nonlinearity to 0.15°/W output power at 6 GHz for powers below saturation in 8 mm gate-width devices confirming that nonlinear capacitance causes nonlinearity observed in conventional GaAs MESFET’s. Channel transit time, estimated at 3–6 ps, is not significant as a cause of nonlinearity and varies less than 100 fs with signal level.

Transient analysis of long-channel MOS devices using the finite-element method

The turn-on and turn-off characteristics of long-channel MOS devices are studied using the finite-element method, for both large and small signal inputs. This method can accurately predict the channel transit-time delays regardless of. device type, channel length, width, doping and effective mobility.

Large- and small-signal channel transit time delays in long-channel MOS transistors

Turn-on and turn-off delay times (intrinsic channel transit times) of long-channel MOST's are studied for both large-and small-signal inputs. By developing large-signal dynamic equations in normalized form it is evident that the normalized channel current and voltage distributions are unique and independent of device parameters and applied voltages. Channel transit time delays for both large and small signal are found to be given by a simple analytical expression containing a constant, undefined for large signal but defined explicitly for small signal. Values for the constant are found for large- signal operation in several modes by computer simulation representing the channel as a series of cascaded CCD elements. Those for small signal are found by representing the channel as an RC transmission line. With the values of the constant determined, the simple analytical expression is shown to accurately predict channel transit time delays regardless of device type, channel length, width, substrate doping, crystal orientation, or effective mobility. It is concluded that the data presented can be used in designing delay lines or low-pass filters employing long-channel devices.

Theoretical transducer properties of piezoelectric insulator FET transducers

An oriented piezoelectric film incorporated in the insulator region of a silicon insulated-gated field-effect transistor (FET) results in a sensitive high-frequency strain transducer. Theory governing the transducer properties of the piezoelectric insulator FET transducer is presented. Equations are developed which relate the drain current of the device to induced polarizations of the piezoelectric layer. The highest frequency of surface strains to which the FET transducer can respond is determined by the FET frequency response—ultimately by the channel transit time. This frequency can extend to the GHz range. The low-frequency response to applied strain is determined by the dielectric relaxation frequency of the piezoelectric layer.

Switching characteristics of m.o.s. and junction-gate field-effect transistors

The nonlinear differential equations describing the large-signal switching behaviour of field-effect transistors (f.e.t.s) are derived. They are shown to be analogous to those of an RC transmission line having uniform linear resistance but nonlinear capacitance per unit length. Solutions of these equations, based on an effective linear-capacitance approximation, are obtained and applied to the cases of metal-oxide-semiconductor transistors (m.o.s.t.s) and junction-gate field-effect transistors. It is experimentally established that there is little difference between the response characteristics of an exact nonlinear RC distributed line, and these of a corresponding effective linear RC distributed line. Under switching conditions, the rise time associated with the short-circuit current response is shown to be smaller than the rise time associated with the open-circuit voltage response. The latter is found to be approximately equal to the small-signal channel transit time in both the m.o.s.t. and junction-gate f.e.t.