Drift-diffusion Transport Research Articles

Experimental and Simulation Analysis of Program/Retention Transients in Silicon Nitride-Based NVM Cells

A new characterization technique and an improved model for charge injection and transport through ONO gate stacks are used to investigate the program/retention sequence of silicon nitride-based (SONOS/TANOS) nonvolatile memories. The model accounts for drift-diffusion transport in the conduction band of silicon nitride (SiN). A priori assumptions on the spatial distribution of the charge at the beginning of the program/retention operations are not needed. We show that the carrier transport in the SiN layer impacts the spatial distribution of the trapped charge and, consequently, several aspects of program and retention transients. A few model improvements allow us to reconcile the apparent discrepancy between the values of silicon nitride trap energies extracted from program and retention experiments, thus reducing the number of model parameters.

High frequency and noise model of gate-all-around metal-oxide-semiconductor field-effect transistors

The surrounding gate (SGT) metal-oxide-semiconductor field-effect transistor is one of the most promising candidates for the downscaling of complementary metal-oxide-semiconductor technology toward the sub-50-nm channel length range since the SGT architecture allows excellent control of the channel charge in the silicon film, thus reducing short channel effects. However, at these dimensions, quantum effects must be considered in order to develop accurate compact models useful for circuit simulations. In this paper we study the influence of quantum effects on dc, radio frequency (rf), and microwave noise for nanoscale SGT transistors including nonstationary effects. We present an analytical charge model for adjusting the charge control computed from the self-consistent solution of the two-dimensional Schrödinger and Poisson equations. rf and noise performances are calculated using the active transmission line method. We compared, on the one hand, classical and quantum charge control models and, on the other, drift-diffusion and hydrodynamic transport models.

Program efficiency and high temperature retention of SiN/high- K based memories

This paper presents an experimental and simulation study of the program efficiency and retention of SANOS memory cells. We analyzed the experimental curves of the available cells by a physics based model that includes drift-diffusion transport of carriers in the nitride conduction band. We evidenced how the gate stack dimensions impact the program efficiency; in particular, thicker Si 3N 4 layers allow for faster programming. However, the Si 3N 4 thickness hardly influence the high temperature retention, since charge loss due to thermal emission dominates. Good agreement of the model with a wide set of experiments makes us confident on the validity of the interpretation of data which is suggested by the modeling results.

Spin drift–diffusion transport and its applications in semiconductors

We study theoretically the propagation and distribution of electron spin density in semiconductors within the drift–diffusion model in an external electric field. From the solution of the spin drift–diffusion equation, we derive the expressions for spin currents in the down-stream ( DS) and up-stream ( US) directions. We find that drift and diffusion currents contribute to the spin current and there is an electric field, called the drift–diffusion crossover field, where the drift and diffusion mechanisms contribute equally to the spin current in the DS direction, and that the spin current in the US direction vanishes when the electric field is very large. We calculate the drift–diffusion crossover field and show that the intrinsic spin diffusion length in a semiconductor can be determined directly from it if the temperature, electron density and both the temperature and electron density, respectively, are known for nondegenerate, highly degenerate and degenerate systems. The results will be useful in obtaining transport properties of the electron’s spin in semiconductors, the essential information for spintronic technology.

Simulation Analysis of Quantum Confinement and Short-Channel Effects in Independent Double-Gate Metal–Oxide–Semiconductor Field-Effect Transistors

A two-dimensional (2D) numerical simulation code of drain current including self-consistent solving of the Schrödinger and Poisson equations coupled with the drift-diffusion transport equation in double-gate (DG) metal–oxide–semiconductor field-effect transistor (MOSFET) devices has been developed. This code has been used to investigate the operation of independent DG (IDG) MOSFETs compared with classical DG MOSFETs in terms of short-channel effects (SCEs) and carrier quantum confinement. Simulations show that IDG MOSFET operation is different from that of DG MOSFETs due to the presence of a transverse electric field in the first structure that induces significant enhancement of quantum mechanical confinement. This leads to subthreshold performance degradation and to SCE enhancement in IDG MOSFETs compared with DG MOSFETs. We show that, in contrast to DG MOSFETs, quantum confinement effects must be taken into account in IDG MOSFET operation even for thick silicon films (>10–15 nm).

Drain Current Model Including Velocity Saturation for Symmetric Double-Gate MOSFETs

A drain current model is developed for a symmetrically driven undoped (or lightly doped) symmetric double-gate MOSFET (SDGFET) under the drift-diffusion transport mechanism, with velocity saturation effects being included as an integral part of the model derivation. Velocity saturation effects are modeled by using the Caughey-Thomas engineering model with exponent n = 2. Id-Vd, Id-Vg, gm -Vg, and gDS-Vd comparisons are made with 2-D device simulation results, and a very good match is found all the way from subthreshold to strong inversion. Gummel symmetry compliance is also shown.

Two-Dimensional Tunneling Effects on the Leakage Current of MOSFETs With Single Dielectric and High-$\kappa$ Gate Stacks

The gate leakage currents of single-gate silicon-on- insulator (SOI) n-type MOSFETs are investigated, assuming direct tunneling as the leakage mechanism and using either a 1-D Schrodinger-Poisson-based approach coupled to the conventional drift-diffusion transport model or a full quantum mechanical treatment. The first approach consists of calculating the transmission probability through the dielectric material along straight lines connecting the transistor channel to the gate. The second method is based on a 2-D Schrodinger-Poisson solver, where carriers are injected into the device from the source, drain, and gate contacts. The simulated structures have a physical gate length of 32 nm. The channel is isolated from the gate contact by a dielectric layer with an equivalent oxide thickness of 1.2 nm. This layer is composed of either pure SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> or a high-kappa SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stack. Irrespective of the dielectric material, the leakage currents calculated with the 1-D approach are about one order of magnitude smaller at low gate voltages and converge toward the same value as the channel potential barrier decreases. The difference is caused by the diffraction of the electron waves at both edges of the gate contact. This peculiar 2-D behavior of the gate leakage currents, as well as the limit of the 1-D model, is discussed in this paper for various dielectric configurations.

RF and noise model of gate-all-around MOSFETs

Silicon-on-insulator (SOI) devices are excellent candidates to become an alternative to conventional bulk CMOS. The most promising SOI devices for the nanoscale range are based on multiple gate structures such as surrounding gate (SGT) or gate-all-around (GAA). These devices could be used for high-frequency application due to a significant increase in the transition frequency fit for these devices. We present a new analytical model for cylindrical undoped (lightly doped) GAA or SGT MOSFETs for dc, RF and noise analyses. The model is based on a surface potential formulation for charge control and a drift-diffusion transport model. Short-channel effects, velocity saturation effects and quantum effects have been incorporated in the model. The dc model has been extended to ac and noise using the active transmission line method. Using this model, GAA RF and noise performances are studied.

Theoretical foundations of the quantum drift-diffusion and density-gradient models

In this paper, we examine the theoretical foundations of the quantum drift-diffusion and density-gradient transport models for the simulation of fully-depleted silicon-on-insulator and silicon nanowire FETs. In doing so, we highlight the strengths and limitations of both approaches. In the former case, the harmonization of the classical and quantum-mechanical perspectives is pursued by means of Bohm’s theory of quantum potential and by solving, in addition to the coupled Schrödinger–Poisson equations, as many drift-diffusion equations as the number of populated subbands. The latter approach is affected instead by more serious conceptual problems, as it basically replaces the Schrödinger equation with a simplified non-linear equation in the electron-charge concentration, by which energy quantization, multiple subbands, and multiple effective-masses are neglected. Despite these limitations, the density-gradient model turns out to be remarkably successful in predicting the device I– V characteristics. Simulation examples are discussed and the model predictions are compared. In our implementation, the simulation efficiency of the QDD is superior to that of the DG model.

Numerical and experimental indication of thermally activated tunneling transport in CIS monograin layer solar cells

The purpose of this work was to build a numerical model of thermally activated tunneling transport by upgrading the drift-diffusion transport model in one-dimensional semiconductor simulator ASPIN, and to identify the current limiting mechanisms of the CIS monograin layer solar cells. The superposition of the classical drift-diffusion transport and the semi-classical thermionic-field transport is applied across the whole solar cell structure. The implemented model correctly predicts the shapes of temperature dependent current density–voltage characteristics and the temperature dependence of the photogenerated current density at the short-circuit condition in the range from 320 K down to 160 K.

An Analytical Compact Circuit Model for Nanowire FET

In this paper, we propose a quasi-analytical device model of nanowire FET (NWFET) for both ballistic and drift-diffusion current transport, which can be used in any conventional circuit simulator like SPICE. The closed form expressions for current-voltage (I-V) and capacitance-voltage characteristics are obtained by analytically solving device equations with appropriate approximations. The developed model was further verified with the measured I-V characteristics of an NWFET device. Results show a close match of the model with measured data.

Bias current effects on the magnetoresistance of a ferromagnetic-semiconductor-ferromagnetic trilayer

The authors apply a self-consistent ballistic-diffusive theoretical model to study the bias current j effect on the magnetoresistance of a ferromagnet (FM)-semiconductor (SC)-FM trilayer, with SC highly doped (n++). The interfacial resistance becomes a dynamic parameter and its decrease with increasing j would be responsible for the decrease of magnetoresistance (MR) with j. The underlying physics of this model is based on a self-consistent treatment between the spin drift diffusion transport of electrons in the bulk and ballistic transmission at the interfaces. This model applies qualitatively to the more common FM-nonmagnetic-FM, metal-based current-perpendicular-to-plane spin valve, which has shown experimentally observed decline of MR with j.

Enhancement of ballistic transport in an AlGaAs∕InGaAs high electron mobility transistor at low temperatures

The authors investigated the current-voltage characteristics of a 100nm AlGaAs∕InGaAs pseudomorphic high electron mobility transistor as a function of temperature. The drain current in the linear region showed a dramatic increase when the temperature was lowered below a critical value (TB) and the drain voltage is increased. A quantitative analysis based on self-consistent Schrödinger-Poisson and simple electrostatic band potential profile calculations was performed to model the transmission coefficient. The modeled results are consistent with the measured data, confirming that the main transport mechanism switches from a classical drift-diffusion transport into a quasiballistic transport when decreasing temperature below TB and increasing drain voltage.

Investigation of the impact of band offset perturbations on the performance of abrupt HBT with heavily doped base

Heavy impurity doping leads to bandgap narrowing (BGN) and this causes perturbations to the value of the band offsets at the hetero-interface. As a result, the form and height of energy barriers in abrupt HBT is disturbed, which changes the value of the current flowing through its interfaces. The analysis is based on the thermionic field-diffusion model which combines the drift-diffusion transport in the bulk of the transistor with the thermionic emission and tunneling at the base-emitter interface. The calculations reveal a more important role to the transport of carriers played by the modification of the built-in potential than that of the range of barrier energies available for tunneling because the impact of the built-in potential on the current is exponential. Therefore, it is important for a better description of the currents to use an accurate dopant-dependent BGN distribution model between bands.

Nonequilibrium drift-diffusion transport in semiconductors in presence of strong inhomogeneous electric fields

The self-consistent analysis of drift-diffusion transport in strong inhomogeneous electric fields shows that the local mobility is determined by the “field parameter” f(r)=∇rEc(r)∙∇rEF(r), rather than the electric field ∇rEc(r)∕e or the quasi-Fermi potential gradient ∇rEF(r)∕e, as is usually assumed. This takes place at both high and low carrier densities. The methods for derivation of μ(f) in both cases are presented. The analysis is applied to numerical simulation of a p-i-n photodiode, and it is shown that the use of μ(F) with F(r)=∣∇rEc(r)∕e∣ results in grossly exaggerated carrier drift velocities. The implications for drift-diffusion models used in commercial device simulators are discussed.

1-D simulation of a novel nonvolatile resistive random access memory device

The operation of a novel, nonvolatile memory device based on a conductive ferroelectric/semiconductor thin film multilayer stack is simulated numerically. The simulation involves the self-consistent steady-state solution of the transport equation for electrons assuming a drift-diffusion transport mechanism and the Poisson equation. Special emphasis is put on the screening of the spontaneous polarization by conduction electrons as a function of the applied voltage. Depending on the orientation of the polarization in the ferroelectric layer, a high and a low resistive state are found, giving rise to a hysteretic I-V characteristic. The switching ratio, ranging from > 50% to several orders of magnitude, is calculated as a function of the dopant content. The suggested model provides one possible physical explanation of the I-V hysteresis observed for single-layer ferroelectric devices, if interfacial layers are taken into consideration. The approach will allow one to develop guidelines to improve the performance of these devices.

A compact nonquasi-static MOSFET model based on the equivalent nonlinear transmission line

A compact physics-based nonquasi-static (NQS) metal-oxide-semiconductor field-effect transistor (MOSFET) model with the equivalent nonlinear transmission line (TL) representing channel carriers drift-diffusion transport is developed and implemented in the simulation program with integrated circuit emphasis (SPICE) program. An auxiliary subcircuit is described, which efficiently solves the channel surface boundary potentials without the need for employing separate iterative algorithms. The short-channel effects and the quantum effects are efficiently included owning to a surface-potential-based modeling approach. In comparison with other Berkeley short-channel IGFET model 3 (BSIM3)-based NQS MOSFET models, it is shown that the new NQS TL model has the advantages in higher accuracy and substantially fewer number of model parameters. From comparison with a two-dimensional device simulator, it is demonstrated that the new NQS TL model can accurately predict dc, ac, and transient behavior of long- and short-channel n-type MOSFETs in all operational regions and for the input signal frequencies up to 10 f/sub T/ values, using only one set of model parameters.

Simulation of nanoscale MOSFETs using modified drift-diffusion and hydrodynamic models and comparison with Monte Carlo results

The dc behavior of single-gate and double-gate MOSFETs with gate lengths ranging from 5 to 100 nm is simulated using drift-diffusion, hydrodynamic, and Monte Carlo approaches. It is shown that by simple adjustments of the drift-diffusion and hydrodynamic transport model parameters the Monte Carlo currents can be reproduced in the entire gate length range. The suitability of the different simulation methods for the simulation of nanometer MOSFETs is briefly discussed.

Spin-injection efficiency and magnetoresistance in a ferromagnet-semiconductor-ferromagnet trilayer

We present a drift-diffusion transport model to evaluate the spin-injection efficiency η and magnetoresistance (MR) ratio in a ferromagnetic (FM) metal-semiconductor (SC)-FM metal trilayer structure. This model takes into account the differential interfacial resistances (IR) for spin-up and spin-down electrons and spin relaxation within the SC layer. The electrochemical potential μ for both spin directions is analytically solved and expressions for η, spin polarization of current P, and the MR ratio are derived. The presence of IR at the FM-SC boundary is crucial for generating a large spin splitting of μ, and consequently a high injection efficiency η. The IR needs to fulfill the requirements of (i) of a large magnitude comparable to the resistance of the SC layer and (ii) high asymmetry with respect to the two spin directions. To increase η from 1% to 30%, we require a large IR of 10−5Ωcm2 and a spin asymmetry of 10:1. There are more stringent requirements for achieving a high MR ratio. An IR of 10−5Ωcm2 and FM contact polarization Pc of 80% will only yield an MR ratio of 10%. We require a much larger IR ⩾10−4Ωcm2 or virtually half-metallic contacts, i.e., Pc of ∼100% to achieve high MR ratio exceeding 50%.

Code for the 3D Simulation of Nanoscale Semiconductor Devices, Including Drift-Diffusion and Ballistic Transport in 1D and 2D Subbands, and 3D Tunneling

We present a three-dimensional device simulator, suitable for the study of a wide range of nanoscale devices, in which quantum confinement and carrier transport are taken into account. In particular, depending on the confinement, the 1D, 2D or 3D Schrodinger equation with density functional theory in the local density approximation is coupled with the Poisson equation in the three-dimensional domain. Continuity equation in the ballistic and in the drift-diffusion regime are also solved assuming separation of the subbands.