Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.

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A review of hydrodynamic and energy-transport models for semiconductor device simulation

A new programming disturbance phenomenon in the NAND flash cell operation is introduced, which we have modeled and named as "source/drain hot-carrier injection disturbance" (abbr. "hot-carrier disturbance"). The source/drain hot electrons are supplied from gate-induced drain leakage current at the GSL (ground-select line) transistor gate edge and are accelerated in the source/drain region of GSL-WLO (word line 0) cell, then are injected to the WLO cell. The simulation results show that the space of GSL-WLO cell should be kept over 110 nm to suppress the hot-carrier disturbance, which is also verified by experiment

A New Programming Disturbance Phenomenon in NAND Flash Memory By Source/Drain Hot-Electrons Generated By GIDL Current

It has been reported in the literature that in deep-submicron nMOSFETs, the worst channel hot carrier (CHC) degradation is not near the peak substrate current (as predicted by the lucky electron model), but at the V/sub GS/=V/sub DS/ bias condition. We propose a new CHC model based on an electron-electron scattering-induced hot carrier (HC) mechanism, that explains the worsening of the HC damage at high VGs and agrees well with the HC lifetime measured over the moderate to high gate voltage range and a wide L/sub EFF/ range. The predicted quadratic source current dependence of HC lifetime at mid V/sub GS//V/sub DS/, evolving into a cubic dependence at high V/sub GS//V/sub DS/, matches well the observed behavior.

Role of E-E scattering in the enhancement of channel hot carrier degradation of deep-submicron NMOSFETs at high V/sub GS/ conditions

An energy parameterized pseudo-lucky electron model for simulation of gate current in submicron MOSFET's is presented in this paper. The model uses hydrodynamic equations to describe more correctly the carrier energy dependence of the gate injection phenomenon. The proposed model is based on the exponential form of the conventional lucky electron gate current model. Unlike the conventional lucky electron model, which is based on the local electric fields in the device, the proposed model accounts for nonlocal effects resulting from the large variations in the electric field in submicron MOSFET's. This is achieved by formulating the lucky electron model in terms of an effective-electric field that is obtained by using the computed average carrier energy in the device and the energy versus field relation obtained from uniform-field Monte Carlo simulations. Good agreement with gate currents over a wide range of bias conditions for three sets of devices is demonstrated.

A pseudo-lucky electron model for simulation of electron gate current in submicron NMOSFET's

As has been frequently pointed out the distribution function of hot carriers in state-of-the-art devices is insufficiently described using just the average carrier energy. In this work the distribution function is characterized by six moments to obtain a more accurate description of hot carrier phenomena. A transport model based on six moments is derived and compared to a previously published model. A detailed comparison of results obtained from the model with Monte-Carlo data shows excellent agreement provided proper models for the relaxation times are used.

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Using six moments of Boltzmann’s transport equation for device simulation

A thermionic emission model based on a non-Maxwellian electron energy distribution function for the electron gate current in NMOSFET's is described. The model uses hydrodynamic equations to describe more correctly the electron transport and gate injection phenomena in submicron devices. A generalized analytical function is used to describe the high-energy tail of the electron energy distribution function. Coefficients of this generalized function are determined by comparing simulated gate currents with the experimental data. This model also includes the self-consistent calculation of the tunneling component of the gate current by using the WKB approximation, and by using a more accurate representation of the oxide barrier by including the image potential. Good agreement with gate currents over a wide range of bias conditions for three different technological sets of devices are demonstrated by using a single set of coefficients.

Thermionic emission model of electron gate current in submicron NMOSFETs

Two-dimensional energy-dependent substrate current models are described for NMOS and PMOS devices that have been developed using a multi-contour approach. The new models offer a significant improvement in the calculation of substrate current due to a more accurate calculation of the average energy as compared to the local-field model. The models are implemented in a post-processing manner by applying a one-dimensional energy conservation equation to each of many current contours in order to generate a two-dimensional representation of average energy and impact ionization rate, that is then integrated to calculate the substrate current. The new models have been compared to substrate current characteristics of a variety of NMOS and PMOS devices for a wide range of bias conditions and channel lengths, and very good agreement has been obtained with a single set of model parameters. An additional significance of this work is the enhancement of the standard multi-contour model by an energy-sink term that results in an improved prediction of the impact ionization process in PMOSFET's. >

Two-dimensional energy-dependent models for the simulation of substrate current in submicron MOSFET's

The control over the random variations in manufacturing processes and equipment has become increasingly critical for deep submicron MOS IC technology. This analysis involves correlating the sensitivity of eight key device electrical characteristics (responses) of a 0.18 micrometers NMOSFET to the anticipated manufacturing variations in its structural and doping parameters (inputs). Using TCAD software, a 0.18 micrometers NMOSFET has been designed and optimized to be as representative as possible of a device intended for use by industry, and has then been used as the nominal structure for the sensitivity analysis. Nine input parameters such as gate length, gate oxide, etc. were varied in accordance with a three-level Box-Behnken design, and model equations were generated. A Monte Carlo simulator was also developed to extract the statistical distribution of each response and compare it to a normal distribution that best fit the data. These models allow a quick assessment of the sensitivity of the key device electrical parameters to manufacturing variations in the NMOSFET structural and doping parameters.

Manufacturing sensitivity analysis of a 0.18-micron NMOSFET

As MOSFET dimensions are scaled, innovative techniques are required to overcome many problems specific to short-channel devices, while retaining the performance enhancement that justifies scaling to smaller dimensions. We present a design methodology and an analysis investigating the design approaches and the trade-offs for simultaneously obtaining high performance, reliable, and manufacturable 0.18 micron n-channel MOSFETs. The results of two-dimensional numerical device simulations of three candidate structural approaches that have been selected based on scalability, reliability, manufacturability, and performance considerations are discussed. The influence of effects such as velocity overshoot and inversion layer quantization on the device behavior and the trends and trade-offs are described.© (1994) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Khaled Hasnat

Papers

A pseudo-lucky electron model for simulation of electron gate current in submicron NMOSFET's

Thermionic emission model of electron gate current in submicron NMOSFETs

Two-dimensional energy-dependent models for the simulation of substrate current in submicron MOSFET's

Manufacturing sensitivity analysis of a 0.18-micron NMOSFET

Analysis and design considerations for manufacturable and reliable 0.18-micron N-MOSFETs