Schrodinger-Poisson Solver Research Articles

On the role of interface states in low-voltage leakage currents of metal–oxide–semiconductor structures

This work investigates the additional gate current component with respect to the direct tunneling of electrons between the conduction bands measured in ultrathin oxide metal–oxide–semiconductor field-effect transistors at low voltages, before and after the application of a high field stress. We discuss several possible conduction mechanisms on the basis of the band diagram profiles obtained by means of a one-dimensional self-consistent Poisson–Schrodinger solver and we explain why this additional leakage current is mainly due to electron tunneling involving the native and stress-induced interface states in the silicon band gap either at the cathode or at the anode.

Two-dimensional quantum effects in nanoscale MOSFETs

In this paper, a full two-dimensional (2-D) quantum mechanical (QM) device simulator for deep submicron MOSFETs is presented. The model couples a 2-D Schrodinger-Poisson solver with a semiclassical transport model. The validity of the proposed model is first tested against a QM model for transport, developed as a benchmark. Then, QM effects on nanoscale MOSFETs performance are quantitatively addressed and discussed. It is shown that QM effects strongly influence the device performance, namely subthreshold slope drain-induced barrier lowering and short-channel effects. These results show that full QM simulations will become a mandatory issue for nanoscale MOSFETs modeling and design.

Novel low-temperature C-V technique for MOS doping profile determination near the Si/SiO/sub 2/ interface

An inverse modeling technique for doping profile extraction from MOS C-V measurements is presented. The method exploits the "kink" effect observed near flat bands in low-temperature C-V curves to accurately estimate the dopant concentration at the oxide-silicon surface. The inverse modeling approach, based on a self-consistent Schrodinger-Poisson solver, overcomes the limitations of previous analytical methods. The accuracy of the doping extraction is demonstrated by successfully reconstructing doping profiles from simulated C-V curves, including abrupt variations of doping in the vicinity of the oxide interface. When applied to experimental data from boron- and phosphorus-doped samples, the technique is shown to provide a substantial improvement in resolution with respect to room-temperature C-V measurements.

Understanding the effects of wave function penetration on the inversion layer capacitance of NMOSFETs

A comprehensive analysis of the effects of wave function penetration on the capacitance of NMOS capacitors has been performed for the first time, using a self-consistent Schrodinger-Poisson solver. The study reveals that accounting for wave function penetration into the gate dielectric causes carrier profile to be shifted closer to the gate dielectric reducing the electrical oxide thickness. This shift increases with increasing gate voltage. For example, in one simulation, the peak is shifted by about 0.2 nm at a surface field of 1.96 MV/cm and 0.33 nm at a surface field of 3.7 MV/cm. This shifting results in all increased capacitance. The increase in capacitance observed in the inversion region is relatively insignificant when a poly gate electrode with a doping of less than 1/spl times/10/sup 20/ cm/sup -3/ is used due to the poly-depletion effect. A physical picture of the effect of physical thickness on the tunneling current is also presented.

Impact of super-steep-retrograde channel doping profiles on the performance of scaled devices

Super-steep retrograded (SSR) channels were compared to uniformly doped (UD) channels as devices are scaled down from 250 nm to the 50 nm technology node, according to the scheme targeted by the National Technology Roadmap for Semiconductors (1997). The comparison was done at the same gate length L/sub gate/ and the same off-state leakage current I/sub off/, where it was found that SSR profiles always have higher threshold voltages, poorer subthreshold swings, higher linear currents, and lower saturation currents than UD profiles. Using a simulation strategy that takes into account the impact of short-channel effects on drive current, it was found that the improved short-channel effect of retrograde profiles is not enough to translate into a higher performance over the UD channels for all technologies. Hence, if the effective gate-dielectric thickness scales linearly with technology, retrograde doping will not be useful from a performance point of view. However, if the scaling of the gate-dielectric is limited to about 2 nm, SSR profiles can give higher drive current than UD channels for the end of the roadmap devices. Thus, the suitability of SSR channels over UD channels depends on the gate-dielectric scaling strategy. Simulations using a self-consistent Schrodinger-Poisson solver were also used to show that the impact of quantum mechanical (QM) effects on the long-channel characteristics of SSR and UD MOSFET's will be similar.

Reliable extraction of MOS interface traps from low-frequency CV measurements

An improved version of the low-frequency capacitance-voltage (LFCV) method for MOS interface trap extraction is presented. The rising edge of the gate-channel capacitance is used as a reliable reference for determining the surface potential, allowing a more accurate calculation of the trap energy. Also, a self-consistent Schrodinger-Poisson solver is employed to obtain a theoretical CV curve, accounting for quantization effects. It is shown that the improved method supplies better results than the conventional LFCV and high-low frequency methods.

A physically-based model for quantization effects in hole inversion layers

As MOS devices have been successfully scaled to smaller feature sizes, thinner gate oxides and higher levels of channel doping have been used in order to simultaneously satisfy the need for high drive currents and minimal short-channel effects. With the onset and development of deep submicron (/spl les/0.25 /spl mu/m gate length) technology, the combination of the extremely thin gate oxides (t/sub ox//spl les/10 nm) and high channel doping levels (/spl ges/10/sup 17/ cm/sup -3/) results in transverse electric fields at the Si/SiO/sub 2/ interface that are sufficiently large, even near threshold, to quantize the motion of inversion layer carriers near the interface. The effects of quantization are well known and begin to impact the electrical characteristics of the deep submicron devices at room temperature when compared to the traditional classical predictions which do not take into account these quantum mechanical (QM) effects. For accurate device simulations, quantization effects must be properly accounted for in today's widely used moment-based device simulators. This paper describes a new computationally efficient three-subband model that predicts the effects of quantization on the terminal characteristics in addition to the spatial distribution of holes within the inversion layer. The predictions of this newly developed model agree very well with both the predictions of a self-consistent Schrodinger-Poisson solver and experimental measurements of QM effects in MOS devices.

Quantum effects upon drain current in a biased MOSFET

In the past, classical device simulators have been modified to incorporate quantum effects using a quantum mechanical (QM) threshold-shift correction. In this way, it is hoped to retain accuracy without greatly complicating the simulation by incorporation of a coupled Schrodinger equation solver. In this work, the accuracy of this approach is checked for some specific examples. The drain current of heavily doped MOSFETs is found using a one-dimensional (1-D) Schrodinger-Poisson solver combined with a gradual channel model. Numerical results are compared to classical calculations augmented by the commonly proposed channel-current invariant QM threshold correction. Comparison of the two /spl radic/I/sub d(sat)/ versus V/sub GS/ curves shows the same threshold shifts, but different slopes. The slope discrepancies are independent of substrate doping, and are largest for thin oxides. These differences are shown to be due to QM effects upon the surface potential gradient, a variation neglected in previous studies. To simplify device simulations, two simple quantum-effect corrections are proposed that show a great improvement in accuracy when compared to the earlier QM correction based on a channel-current invariant V/sub G/-shift.

A simple model for quantum mechanical effects in hole inversion layers in silicon PMOS devices

The effects of quantization of the inversion layer of MOSFET devices is an area of increasing importance as technology is aggressively scaled below 0.25 /spl mu/m. Although electron inversion layers have attracted considerable interest, very little work has been reported for holes. This paper describes the implementation and results of a simple, computationally efficient model, appropriate for device simulators, for predicting the effects of hole inversion layer quantization. This model compares very favorably with experimental results and the predictions of a full-band, self-consistent Schrodinger-Poisson solver.

Conduction band offset of strained InGaP by quantum well capacitance-voltage profiling

The conduction band alignment of compressively strained In1−xGaxP relative to lattice matched InGaP/GaAs has been determined by capacitance-voltage profil-ing. A modified version of Kroemer’s capacitance-voltage profiling method is developed wherein a quantum well is profiled instead of a single heterojunction. A one-dimensional Poisson-Schrodinger solver was used to fit the reconstructed carrier profiles corresponding to a value of ΔEc at varying temperatures. Schottky barrier diode structures containing a single strained InGaP quantum well were grown by low pressure metalorganic chemical vapor deposition. The two strained compositions studied contained 35 and 31% gallium. Conduction band offsets of 101 and 131 meV were found for the 35 and 31% samples, respectively, with an estimated accuracy of ±5 meV. These results agreed closely with values predicted by empirical calculations.

Auger recombination in long-wavelength strained-layer quantum-well structures

A model calculation of Auger recombination in strained-layer InGaAs-InGaAlAs and InGaAs-InGaAsP quantum-well structures is presented as an extension of an empirical Auger theory based on the effective mass approximation. The valence band effective masses around k/sub /spl par//=0 are calculated by using a six-band Luttinger-Kohn Hamiltonian and the quasi-Fermi levels are determined with a self-consistent Poisson-Schrodinger solver under the effective mass approximation. Three basic Auger processes are considered with the excited carrier being in a bound state of the quantum well, as well as an unbound state. The empirical model includes Fermi statistics as well as a revaluation of the Coulomb interaction overlap integral in the Auger recombination rate. Bound-unbound Auger transitions are proved to be an important nonradiative recombination mechanism in strained-layer quantum-well systems. Our calculations of Auger coefficient are in reasonable agreement with the experimental data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modeling of the optical properties of a barrier, reservoir, and quantum-well electron transfer structure

We present a novel numerical simulator, OPCONS, for the analysis of the optical properties of In/sub x/Ga/sub 1-x/As/In/sub 1-y/Al/sub y/As multiple-quantum-well heterostructures with tunable charge density. The influence of carriers and dopant ion charges on the electronic properties are simulated with a self-consistent Poisson-Schrodinger solver. The calculated optical constants of the quantum well reproduce well the experimental electrooptic characteristics. The code implements the drift-diffusion and thermionic emission currents to calculate the I-V characteristics and shows a good agreement with the experimental data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Simulation of the refractive index properties of a tunable-electron-density quantum well and reservoir structure

A numerical simulation of the optical properties of a novel In/sub x/Ga/sub 1-x/As/In/sub 1-y/Al/sub y/As multiple quantum well heterostructure with tunable charge density is presented. The influence of carriers and dopant ion charges on the electronic properties is simulated by a self-consistent Poisson-Schrodinger solver. The calculated optical constants of the quantum well reproduce well the experimental data. It appears that this model can easily be implemented to include current injection and used as a design tool to optimize the performance of optical modulator quantum well devices.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>