Bernd Meinerzhagen

Hydrodynamic equations for semiconductors with nonparabolic band structure

A system of generalized hydrodynamic equations is derived from Boltzmanns transport equation for semiconductors without the assumption of a parabolic band structure. After some simplifications these equations can be arranged in such a way that their structure is similar to that of the well-known conventional ones. For this purpose the quantity carrier temperature is redefined and five relaxation times have to be introduced instead of the two in use so far, in order to take nonparabolicity into account. For all quantities of interest results from Monte Carlo simulation are presented for silicon with an impurity concentration of up to 10/sup 18/ cm/sup -3/ and an electric field of up to 200 kV/cm. They show that two of the five relaxation times are not distinguishable; hence, for silicon at room temperature the number of relaxation times can be reduced to four. Considerable deviations from results derived under the assumption of a parabolic band structure demonstrate the necessity of this generalized hydrodynamic model. The new hydrodynamic model is applied to a n-channel LDD MOSFET with a 0.5- mu m channel length. The results agree well with the results of Monte Carlo device simulation. >

Physics-Based Modeling of Hole Inversion-Layer Mobility in Strained-SiGe-on-Insulator

The hole inversion-layer mobility of strained-SiGe homo- and heterostructure-on-insulator in ultrathin-body MOSFETs is modeled by a microscopic approach. The subband structure of the quasi-2-D hole gas is calculated by solving the 6times6koarrldrpoarr Schrodinger equation self-consistently with the electrostatic potential. The model includes four important scattering mechanisms: optical phonon scattering, acoustic phonon scattering, alloy scattering, and surface-roughness scattering. The model parameters are calibrated by matching the measured low-field mobility of two particularly selected long-channel pMOSFET cases. The calibrated model reproduces available channel-mobility measurements for many different strained-SiGe-on-insulator structures. For the silicon-on-insulator MOS structures with unstrained-Si channels, the silicon-thickness dependence resulting from our model for the low-field channel mobility agrees with previous publications.

Comparison of (001), (110) and (111) uniaxial- and biaxial- strained-Ge and strained-Si PMOS DGFETs for all channel orientations: Mobility enhancement, drive current, delay and off-state leakage

Using the non-local empirical pseudopotential method (bandstructure), full-band Monte-Carlo simulations (transport), self-consistent Poisson-Schrodinger (electrostatics) and detailed band-to-band-tunneling (BTBT) (including bandstructure and quantum effects) simulations, the effect of surface/channel orientation, uniaxial- and biaxial-strain, band-structure, mobility, and high-field transport on the drive current, off-state leakage and switching delay in nano-scale, strained-Si and strained-Ge, p-MOS DGFETs have been presented and the optimum strain and channel/surface orientations for highest drive-lowest delay-lowest leakage have been obtained.

Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices II. Results

For pt. I see ibid., vol. 49, pp. 1250-1257 (2002). Terminal current noise is investigated with Langevin-type drift-diffusion (DD) and hydrodynamic (HD) noise models for one-dimensional (1-D) N/sup +/ NN/sup +/ and P/sup +/ PP/sup +/ structures and a realistic two-dimensional (2-D) SiGe NPN HBT. The new noise models, which are suitable for technology computer aided design (TCAD), are validated by comparison with Monte Carlo (MC) device simulations for the 1-D structures including noise due to particle scattering and generation of secondary particles by impact ionization (II). It is shown that the accuracy of the usual approach based on the DD model in conjunction with the Einstein relation degrades under nonequilibrium conditions. 2-D MC noise simulations are found to be feasible only if the current correlation functions decay on a subpicosecond scale, what is not always the case.

Failure of moments-based transport models in nanoscale devices near equilibrium

It is shown that the conductance in nanoscale devices near equilibrium strongly depends on the choice of the transport model. Errors larger than a factor of two can be encountered, if the drift-diffusion (DD) model is used instead of a model based on the full Boltzmann equation. This effect is due to a fundamental difference in carrier heating between bulk systems and devices. Although carrier heating is included in hydrodynamic models, this effect is captured only partially by these models due to the model inherent approximations. A direct consequence of the failure of the DD approximation is that the usual method for inversion layer mobility extraction from measurements in the linear regime becomes inaccurate for short gate lengths and the extracted mobilities might be too small. This error has also an impact on the modeling accuracy at strong nonequilibrium. In the case of the DD model, the overestimation of the conductivity in the linear regime can partly compensate the underestimation of the current at high bias, and the model accidentally appears to be more accurate than expected.

Consistent gate and substrate current modeling based on energy transport and the lucky electron concept

A numerical model for electron gate and substrate currents in n-channel silicon MOS devices is presented. The model accurately describes hot electron injection into the gate oxide triggered by substrate voltage, drain voltage, and substrate current over a large range of bias conditions and channel lengths. In all three cases the electrons with energies higher than the respective threshold energy are modeled identically. Differences due to different physical mechanisms involved in the three cases are taken into account by means of three different constant leading factors.<<ETX>>

Comparative study of electron transit times evaluated by DD, HD, and MC device simulation for a SiGe HBT

Transit times of a silicon/germanium heterojunction bipolar transistor (HBT) with a base width of 24 nm are investigated in the quasi-stationary limit for the first time by consistent drift-diffusion (DD), hydrodynamic (HD), and fullband Monte Carlo (MC) simulations. The quasi-ballistic transport in the base and collector leading to a strong velocity overshoot is well described by the HD model and corresponding transit times are in good agreement with the MC results. On the other hand, the DD model fails in this region and substantially overestimates the base transit time bearing the possibility of wrong guidelines for transistor design optimization. However, since the base transit time is no longer dominating the cutoff frequency of high-speed HBTs, the failure of the DD model leads to an underestimation of the peak cutoff frequency by only 10%. Close to high injection differences in the emitter transit times of the HD and MC model are observed which are mainly related to small differences in the Gummel plot.

Full-band Monte Carlo simulation of a 0.12 /spl mu/m-Si-PMOSFET with and without a strained SiGe-channel

Si-PMOSFETs with and without a strained Si/sub 0.7/Ge/sub 0.3/-layer in the channel region are investigated by full-band Monte Carlo simulation for the first time. The low-field effective channel mobility is considerably enhanced due to the strained SiGe-layer. However, the resultant performance improvement in the case of a 0.12 /spl mu/m-PMOSFET with a drain and gate bias of 1.5 V is less than 10%. This is due to the saturation velocity, which in contrast to the low-field mobility is not enhanced but reduced compared to relaxed Si.

Evaluation of impact ionization modeling in the framework of hydrodynamic equations

Using consistent Monte Carlo (MC) and hydrodynamic (HD) MOS device models the validity of the three impact ionization modeling approaches which are most frequently used in the framework of hydrodynamic equation is examined with the MC model as physical reference. Good agreement with the MC reference for substrate currents as well as spatial impact ionization distributions is observed for the HD model in combination with an improved version of the nonlocal field line based lucky electron model reported by B. Meinerzhagen (1988). The agreement of impact ionization distributions is poor if the HD model is combined with either a local field or local carrier temperature model. But substrate current results are still satisfactory for the carrier temperature model of R.K. Mains et al. (1983).<<ETX>>

Investigation of compact models for RF noise in SiGe HBTs by hydrodynamic device simulation

A comprehensive investigation of the SPICE and unified compact noise models is performed by comparison with the more fundamental hierarchical hydrodynamic device model. It is shown that the rather simple SPICE and unified compact noise models yield good results for frequencies up to 10 GHz for state-of-the-art SiGe HBTs with a low base resistance. The base noise resistance, a key parameter of the compact noise models turns out to be independent of frequency and bias. It can be well estimated based on the sheet resistance of the intrinsic and extrinsic base or with the modified circle-fit method. The unified model, which in comparison to the SPICE model considers in addition the finite transit time of shot noise, is found to be somewhat more accurate than the SPICE model, especially at higher frequencies and collector currents. But this is achieved at the expense of a transit time parameter which cannot be determined without accurate and detailed noise measurements or physics-based numerical simulations.