Average Carrier Velocity Research Articles

Electronic transport properties and quantum localization effects monitored by selective functionalization in Bernal bilayer graphene

Monitoring electronic properties of 2D materials is an essential step to open a way for applications such as electronic devices and sensors. From this perspective, Bernal bilayer graphene (BLG) is a fairly simple system that offers great possibilities for tuning electronic gap and charge carriers' mobility by selective functionalization (adsorptions of atoms or molecules). Here, we present a detailed numerical study of BLG electronic properties when two types of adsorption site are present simultaneously. We focus on realistic cases that could be realized experimentally with adsorbate concentration c varying from 0.25% to 5%. For a given value of c, when the electronic doping is lower than c we show that quantum effects, which are ignored in usual semi-classical calculations, strongly affect the electronic structure and the transport properties. A wide range of behaviors is indeed found, such as gap opening, metallic behavior or abnormal conductivity, which depend on the adsorbate positions, the c value, the doping, and eventually the coupling between midgap states which can create a midgap band. These behaviors are understood by simple arguments based on the fact that BLG lattice is bipartite. We also analyze the conductivity at low temperature, where multiple scattering effects cannot be ignored. Moreover, when the Fermi energy lies in the band of midgap states, the average velocity of charge carriers cancels but conduction is still possible thanks to quantum fluctuations of the velocity.

Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon

Starting from a gauge-invariant Dirac Hamiltonian with noncommutativity of space sector in the presence of an external uniform magnetic field, the resulting Dirac equation has been solved for electrons and its corresponding Zitterbewegung (ZBW) phenomenon has been studied. The corresponding energy spectrum is shown to be different from previous studies wherein the non-gauge-invariant Dirac Hamiltonian has been used. The effects of noncommutativity alter the amplitude as well as the cyclotron and the ZBW frequencies of the average velocity of charge carriers. This result is contrary to previous studies wherein there was no magnetic field, and hence, neither the amplitude nor the frequency of the motion was affected. Moreover, all of the ZBW frequencies of the Landau energy levels appear in the results. Also, in weak magnetic fields, we have calculated the average velocity of charge carriers for two initially localized spin-up and spin-down cases. The plotted trajectories reveal difference between these two cases. In addition, the ZBW phenomenon has been shown that manifests itself as a circular motion whose direction is spin dependent while accompanied by the cyclotron motion.

Kinetics of Charge Carriers across a Graphene-Silicon Schottky Junction

We perform a comparative study on the transfer velocity of charge carriers across two-dimensional and (2D) three-dimensional (3D) graphene-silicon and 3D-3D $\mathrm{Au}$-silicon Schottky junctions. Within the framework of classical thermionic emission theory, the transfer velocity of carriers across the $\mathrm{Au}$-$\mathrm{Si}$ interface is determined as $\overline{v}\ensuremath{\sim}{10}^{7}$ cm/s that is thoroughly consistent with the average thermal velocity of carriers in silicon. In contrast, the graphene-$\mathrm{Si}$ interface discloses a much lower transfer velocity of $\overline{v}\ensuremath{\sim}{10}^{1}$ cm/s, i.e., nearly 6 orders of magnitude smaller than the thermal velocity of carriers in silicon. Utilizing the ${T}^{1}$ universal scaling law for vertical 2D-3D Schottky junctions, we determine the effective out-of-plane velocity of charge carriers in graphene as ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}\ensuremath{\sim}{10}^{0}$ cm/s. This indicates current flow across the graphene-$\mathrm{Si}$ contact is substantially limited by ${v}_{\ensuremath{\perp}}^{\ensuremath{\ast}}$. Moreover, by analyzing experimental activation-energy data, we uncover a general correlation between the kinetics of charge carriers and the potential barrier at the graphene-$\mathrm{Si}$ interface. It is found that the transfer velocity increases almost exponentially with the Schottky barrier height, which cannot be explained in the framework of classical theory. Considering nonconserving ${\mathbf{k}}_{\ensuremath{\parallel}}$ scattering strength as an exponential function of Schottky barrier height, ${T}^{1}$ scaling theory leads to a comprehensive interpretation of experimental data. This study sheds light on the electronic processes across 2D-3D interfaces.

Surface Potential Modeling of Graded-Channel Gate-Stack (GCGS) High-K Dielectric Dual-Material Double-Gate (DMDG) MOSFET and Analog/RF Performance Study

In each complementary metal-oxide-semiconductor (CMOS) technology generation, design of new device architectures at nanoscale regime becomes quite challenging task due to increased short channel effects (SCEs) and leakage current. A double-gate (DG) MOSFET is an alternative structure. To enhance the performance of DG MOSFET, gate stack (GS) and dual-material gate (DMG) with graded-channel (GC) concepts are amalgamated. Analytical surface potential modeling of GCGS DMDG MOSFET has been done by solving the two-dimensional (2D) Poisson’s equation with suitable boundary conditions. The surface potential profile of GCGS DMDG MOSFET shows a step variation at the interface of two materials. The electrical parameters drain induced barrier lowering (DIBL), sub-threshold swing (SS) and on-current to off-current $\left (\frac {I_{on}}{I_{off}}\right )$ ratio reveals that, DMDG shows a better performance over single-material (SM) DG MOSFET with all (Si3N4, HfO2 and Ta2O5) GS high-k dielectric configurations. An enhanced performance in GCGS DMDG is due to the fact of increased average carrier velocity, reduced drain field effect and leakage current. Further, analog/RF performance parameters such as transconductance (gm), transconductance generation factor (TGF), cut-off frequency (fT), transconductance generation frequency product (TGFP), gain frequency product (GFP) and gain transconductance frequency product (GTFP) are extracted and compared for both SMDG and DMDG MOSFET with HfO2 GS configuration. The efficacy of analytically modeled results is compared with numerically simulated results obtained from 2D ATLAS device simulator.

Hopping charge transport in amorphous semiconductors with the spatially correlated exponential density of states.

Hopping charge transport in amorphous semiconductors having spatially correlated exponential density of states has been considered. Average carrier velocity is exactly calculated for the quasi-equilibrium (nondispersive) transport regime. We suggest also a heuristic approach for the consideration of the carrier velocity for the non-equilibrium dispersive regime.

A two-dimensional (2D) analytical subthreshold swing and transconductance model of underlap dual-material double-gate (DMDG) MOSFET for analog/RF applications

The double-gate (DG) metal-oxide-semiconductor field effect transistors (MOSFETs) are the choice of technology in sub -100 nm regime of leading microelectronics industry. To enhance the analog and RF performance of DG MOSFET, an underlap dual-material (DM) DG MOSFET device structure has been considered because, it has the advantages of both underlap as well as that of dual-material gate (DMG). A 2D analytical surface potential, subthreshold current, subthreshold swing as well as transconductance modelling of underlap DMDG MOSFET has been done by solving the Poisson's equation. It has also been found that, numerically simulated data approves the analytically modelled data with commendable accuracy. As underlap length (Lun) increases, a substantial reduction of subthreshold current due to enhanced gate control over channel regime is observed. DMG structure facilitates to improve the average velocity of carriers which leads to superior drive current of the device. The underlap DMDG MOSFET device structure demonstrates an ameliorated subthreshold characteristic. The analog figure of merits (FOMs) such as transconductance (gm), transconductance generation factor (TGF), output conductance (gd), early voltage (VEA), intrinsic gain (AV) and RF FOMs namely cut-off frequency (fT), gain frequency product (GFP), transconductance frequency product (TFP) and gain transconductance frequency product (GTFP) have been evaluated. The aforesaid analysis revels that, the device is best suited for communication related Analog/RF applications.

Simulation Study of Quasi-Ballistic Transport in Asymmetric DG-MOSFET by Directly Solving Boltzmann Transport Equation

In this study, we simulate double-gate MOSFET using a 2-D direct Boltzmann transport equation solver. Simulation results are interpreted by quasi-ballistic theory. It is found that the relation between average carrier velocity at virtual source and back-scattering coefficient needs to be modified due to the oversimplified approximations of the original model. A 1-D potential profile model also needs to be extended to better determine the kT-layer length. The key expression for back-scattering coefficient is still valid, but a field-dependent mean free path is needed to be taken into account.

A Microscopically Accurate Model of Partially Ballistic NanoMOSFETs in Saturation Based on Channel Backscattering

We propose a model for partially ballistic MOSFETs and for channel backscattering that is alternative to the well known Lundstrom model and is more accurate from the point of view of the actual energy distribution of carriers. The key point is that we do not use the concept of "virtual source". Our model differs from the Lundstrom model in two assumptions: i) the reflection coefficients from the top of the energy barrier to the drain and from top of the barrier to the source are approximately equal (whereas in the Lundstrom model the latter is zero), and ii) inelastic scattering is assumed through a ratio of the average velocity of forward-going carriers to that of backward-going carriers at the top of the barrier kv > 1 (=1 in the Lundstrom model). We support our assumptions with 2D full band Monte Carlo (MC) simulations including quantum corrections in nMOSFETs. We show that our model allows to extract from the electrical characteristics a backscattering coefficient very close to that obtained from the solution of the Boltzmann transport equation, whereas the Lundstrom model overestimates backscattering by up to 40%.

Carrier velocity in InAlN/AlN/GaN heterostructure field effect transistors on Fe-doped bulk GaN substrates

We report microwave characteristics of field effect transistors employing InAlN/AlN/GaN heterostructures grown on low-defect-density bulk Fe-doped GaN substrates. We achieved unity current gain cutoff frequencies of 14.3 and 23.7 GHz for devices with gate lengths of 1 and 0.65 μm, respectively. Measurements as a function of applied bias allow us to estimate the average carrier velocity in the channel to be ∼1.0×107 cm/sec for a 1 μm device. Additionally, we found nearly no gate lag in the devices, which is considered a precondition for good performance under large signal operation.

Impact of the self-generated heat on the scalability of HEMTs

This work is aimed at studying the influence of the self-heating effect on the scalability of HEMTs from an experimental point of view. To accomplish that, we analyze the DC and microwave performance of devices having scaled gate widths. Our experimental results show that the DC transconductance does not scale linearly with the gate periphery under high power dissipation condition. The observed degradation of the transconductance in larger devices can be explained by a reduction of the average carrier velocity due to the occurrence of self-heating. Thermal phenomena even affect the RF small signal performance of the devices under test as they influence the DC operating point. Therefore, the RF transconductance and the forward transmission coefficient are degraded when the dissipated power increases so that all the self-generated heat cannot be completely removed.

Hot carrier quasi-ballistic transport in semiconductor devices

A physically transparent and computationally efficient model of hot carrier transport is described based on an asymptotic solution of the Boltzmann Transport Equation. The model provides the first qualitative and quantitative explanation of certain hot carrier phenomena observed with Monte Carlo simulations. For devices to which a finite voltage is applied such as metal-oxide-semiconductor field-effect-transistors (MOSFET’s) and n-i-n structures the effects explained include the ‘knee effect’ observed in the quasi-ballistic regime; the asymptotic limit of the high energy tail; the phonon absorption/emission ratio above and below the supply energy; the influence of boundary conditions and temperature. The hot carrier distributions obtained with the model are shown, with the exception of a scaling factor, to be independent of field, in keeping with the results of Monte Carlo simulations. Recent research on avalanche photodiodes (APD’s) has shown that the average velocity of charge carriers involved in impact ionization processes can be higher than the saturation velocity, in keeping with quasi-ballistic transport. The model should therefore prove useful as a tool for modelling secondary impact ionization phenomena in MOSFETs and impact ionization in APD’s.

Monte Carlo simulations of double-gate MOSFETs

A fullband Monte Carlo simulator has been used to analyze the performance of scaled n-channel double-gate (DG) MOSFETs. Size quantization in the channel is accounted for by using a quantum correction based on Schrodinger equation. Scattering induced by the oxide interface is included with a model calibrated with measurements for bulk devices. The detailed self-consistent treatment of quantum effects leads to several interesting observations. We observe that the sheet charge in DG devices does not decrease as much as expected in bulk devices when quantum-mechanical effects are included. The average carrier velocity in the channel is also somewhat reduced by quantum effects, as a second-order effect. In the test cases studied here, application of quantum effects causes a reduction in simulated current not exceeding 15%. In a DG structure, quantum effects tend to concentrate the charge density in the center of the channel, where transverse fields are lower. Because of this, interface scattering appears to be less pronounced when quantum effects are included.

Investigation of impact ionization using the balance-equation approach for multivalley nonparabolic semiconductors

We study the effect of impact ionization (II) on high-field electron transport in bulk Si with a conduction band composed of ellipsoidal X and L valleys, using the nonparabolic multivalley balance-equation method. The impact ionization process is described by the II-induced effective acceleration A ii , the II-induced energy-loss rate W ii , and the II rate g ii , which are determined self-consistently during the process of the calculation. The calculated results such as average carrier velocity and the II coefficient show good agreement with experimental data and with MC simulation, thus confirming the validity of the model. An empirical relation of the field- and lattice temperature-dependence of the II coefficient is suggested, which may be useful in device simulation with the balance-equation theory.

Plasmon excitations and accumulation layers in heavily doped InAs(001).

High-resolution electron-energy-loss spectroscopy (HREELS) has been used to study the (001) surface of degenerate n-type InAs grown by molecular-beam epitaxy and prepared either by As decapping or ion bombardment and annealing (IBA). The effects of temperature on the conduction-band electron plasmon excitation have been monitored with HREELS, and analyzed using dielectric theory in the framework of a three-layer model consisting of the bulk, an accumulation layer, and a carrier-free layer at the surface. Specific emphasis has been placed on the importance of the individual layer thicknesses, spatial dispersion, and plasmon lifetime in obtaining good theoretical agreement with the experimental spectra. The measured plasmon spatial dispersion coefficient for the decapped samples was found to agree with the predictions of the Thomas-Fermi model, but was significantly reduced for samples prepared by IBA. This is interpreted as a reduction in the average carrier velocity due to additional defect scattering. Samples prepared by both methods showed a sharp increase in plasmon damping at short wavelengths which is attributed to Landau damping. Ohmic damping of the plasmon at long wavelengths was found to be greater in the ion-bombarded samples, again due to additional defect scattering. IBA was also shown to increase the carrier concentration through the creation of donorlike defects. Neither the surface-state energy nor the surface-state density were found to be significantly affected by the IBA treatment. \textcopyright{} 1996 The American Physical Society.

Correct and rigorous single-electron-gas hydrodynamic transport model for multi-valley semiconductors

A rigorous full hydrodynamic transport model accurately applicable to multi-valley semiconductors is developed based on the single-electron-gas approximation. In the new development, two additional terms appear. One term accounts for local changes of average carrier velocity due to local spatial variations of average carrier effective mass to conserve momentum. The other term accounts for carrier thermal kinetic energy reductions as intervalley carrier transfer takes place. In the model, several newly defined hot-electron correction factors are incorporated which can be accurately quantified as a function of average carrier energy by Monte Carlo simulations. In the single-electron-gas approximation, the carrier temperature for energy conservation is different from that for momentum conservation. This effect is also taken into account in the model.

Time-resolved studies of electronic transport in Si and Ge backbone polymers

Time-resolved transport studies in alkyl- and aryl-substituted Si and Ge polymers, together with xerographic discharge measurements, clearly demonstrate the ability of a wide variety of these polymers to transmit holes, photogenerated (or photoinjected) at one surface under an applied field, through the film bulk to the opposite surface with negligible loss of these carriers to deep traps. The average carrier velocity per unit field (i.e., the drift mobility μ) is measured by the small-signal current-mode time-of-flight technique (TOF). Two key results are discussed in detail: (1) the mechanism of electronic transport in the glassy state, which is established to be hopping among energetically inequivalent sites on the polymer main chain (rather than band motion); and (2) elucidation of the mechanism by which drift mobility in a given polymer can be modified by chemical doping.

Split-gate field-effect transistor

We propose a new field-effect transistor (FET) where the gate voltage swing (i.e., the difference between the gate voltage and the threshold voltage) is varied along the channel in such a way that charge carriers are accelerated more rapidly and the average carrier velocity in the channel is increased. This can be achieved either by making the threshold voltage to be a function of position or by using a new device structure—split-gate FET (SFET). In both cases a smaller gate voltage swing close to the source leads to a higher electric field in this portion of the channel and, hence, to a more rapid increase of the carrier drift velocity with distance. Calculations of the device transconductances for a heterostructure SFET using a charge-control model show that the performance in the split-gate device is considerably improved compared to a conventional device. The improved electric field and potential distributions in a SFET should make it possible to utilize ballistic effects in this lateral device.

Monte Carlo modeling of electron transport in repeated overshoot structures

Repeated velocity overshoot has been proposed as a way of obtaining high average velocities over significant distances in semiconductor devices. The potential of this concept is examined using a fully-self-consistent particle-field Monte Carlo simulation. Numerical results are presented for realistic periodic overshoot structures for a range of bias conditions and operating temperatures of 77 and 300 K. Local velocity overshoot peaks are observed in the simulated structures, but the average carrier velocity and current at each bias point are in all cases less than those associated with transport in bulk material at the same bias point. The physical mechanisms underlying this result are analyzed. It is found that ensemble (diffusion) effects, which were neglected in the original proposal of the repeated overshoot concept, strongly influence the results that are achievable in practice.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Self-consistent theory including nonstationary phenomena for carrier transport in the AlGaAs/GaAs high electron mobility transistor

An analytical formulation is developed for carrier transport in the two-dimensional conducting channel of the AlGaAs/GaAs high electron mobility transistor (HEMT). The problem related to current saturation is also addressed, and a simple model for the pinchoff region is proposed. The present description is based on a self-consistent treatment of electric field, carrier velocity, and carrier density in the potential well. It has previously been shown that important nonstationary effects such as velocity overshoot are reasonably well described within the framework of the relaxation time approximation of the Boltzmann transport equation. Justified by the same approximation, it is shown here that a simple and manageable theory for nonuniform transport in the HEMT can be formulated on the basis of the transient behavior of the average carrier velocity in the homogeneous case. The required homogeneous transient responses to step changes in the electric field can readily be obtained from the space invariant Boltzmann equation, and can be calculated once and for all by advanced methods, such as the Monte Carlo technique. Specific calculations of stationary current-voltage characteristics and of associated transport variables for a HEMT are presented.

Analytical formulation of nonstationary electron dynamics in submicron field effect transistors

A self-consistent and analytical formulation is developed for carrier transport in the conducting channel of submicron FET's, such as AlGaAs/GaAs HEMT's and GaAs MESFET's, where high-field velocity overshoot is expected to be of significance. It is known that important nonstationary phenomena can be described reasonably well in the relaxation time approximation of the Boltzmann transport equation. Justified by the same approximation, it is here shown that a theory for nonuniform transport, applicable to submicron FET's, can be formulated on the basis of the transient behaviour of the average carrier velocity in the homogeneous case. Specific calculations are presented for the HEMT.