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Journal ArticleDOI

The influence of the thermal equilibrium approximation on the accuracy of classical two-dimensional numerical modeling of silicon submicrometer MOS transistors

01 May 1988-IEEE Transactions on Electron Devices (IEEE)-Vol. 35, Iss: 5, pp 689-697
TL;DR: In this article, it is shown that the classical equations are accurate for predicting drain current for devices with effective channel lengths as small as 0.3 mu m. However, accurate substrate current modeling requires a more detailed level of simulation even for devices having longer channel lengths.
Abstract: Classical semiconductor equations are based on the thermal equilibrium approximation. Limitations introduced by this approximation for the 2-D numerical modeling of n-channel silicon submicrometer MOS transistors are investigated. It is shown that the classical equations are accurate for predicting drain current for devices with effective channel lengths as small as 0.3 mu m. However, accurate substrate current modeling requires a more detailed level of simulation even for devices with longer channel lengths. The solution of the energy conservation equation is discussed. >
Citations
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Journal ArticleDOI
29 Apr 2003
TL;DR: A detailed review of various transport models proposed which account for the average carrier energy or temperature, highlighting the differences and similarities between the models, and shed some light on the critical issues associated with higher order transport models.
Abstract: 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.

259 citations


Cites background from "The influence of the thermal equili..."

  • ...Other improvements in terms of convergence are based on iteration schemes where the equations are solve in a decoupled manner [8], [117], similar...

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  • ...For a rapidly increasing electric field, however, the average energy lags behind the electric field, and the assumption of local equilibrium becomes invalid [8]....

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Journal ArticleDOI
TL;DR: An improved energy transport model for device simulation is derived from the zeroth and second moments of the Boltzmann transport equation (BTE) and from the presumed functional form of the even part of the carrier distribution in momentum space.
Abstract: An improved energy transport model for device simulation is derived from the zeroth and second moments of the Boltzmann transport equation (BTE) and from the presumed functional form of the even part of the carrier distribution in momentum space. Energy-band nonparabolicity and non-Maxwellian distribution effects are included to first order. The model is amenable to an efficient self-consistent discretization taking advantage of the similarity between current and energy flow equations. Numerical results for ballistic diodes and MOSFETs are presented. Typical spurious velocity overshoot spikes, obtained in conventional hydrodynamic (HD) simulations of ballistic diodes, are virtually eliminated. >

183 citations

Journal ArticleDOI
TL;DR: In this paper, a coupled thermal and electrical model is developed for sub-micron silicon semiconductor devices consisting of the hydrodynamic equations for electron transport and energy conservation equations for different phonon modes.
Abstract: High electric fields, that are characteristic of sub‐micron devices, produce highly energetic electrons, lack of equilibrium between electrons, optical phonons, and acoustic phonons, and high rates of heat generation. A simple coupled thermal and electrical model is developed for sub‐micron silicon semiconductor devices consisting of the hydrodynamic equations for electron transport and energy conservation equations for different phonon modes. An electron Reynolds number is proposed and used to simplify the electron momentum equation. On a case study of the metal‐oxide‐semiconductor field‐effect transistor with 0.24 μm gate length, the calculated transconductance of 0.175 1/Ω m agreed well with measured value of 0.180 1/Ω m at 2 V drain voltage. The maximum electron temperature is found to occur under the drain side of the gate where the electric field is the highest. Comparison with experimental data shows the predictions of optical and acoustic phonon temperature distributions to have the correct trend and the observed asymmetric behavior. Increase in substrate boundary temperature by 100 °C reduces the drain current by 17% and decreases the maximum electron temperature by 8%. The first effect increases device delay and the second effect decreases the possibility of device degradation by charge trapping in the gate oxide.

161 citations

Journal ArticleDOI
TL;DR: In this article, the behavior of small semiconductor devices is simulated using an advanced Monte Carlo carrier transport model, which improves upon the state of the art by including the full band structure of the semiconductor, by using scattering rates computed consistently with the band structure, and by accounting for both long and short-range interactions between carriers.
Abstract: The behavior of small semiconductor devices is simulated using an advanced Monte Carlo carrier transport model. The model improves upon the state of the art by including the full band structure of the semiconductor, by using scattering rates computed consistently with the band structure, and by accounting for both long- and short-range interactions between carriers. It is sufficiently flexible to describe both unipolar and bipolar device operation, for a variety of semiconductor materials and device structures. Various results obtained with the associated DAMOCLES program for n- and p-channel Si MOSFETs, GaAs MESFETs, and Si bipolar junction transistors are presented.

145 citations

Journal ArticleDOI
R. Thoma1, A. Emunds1, B. Meinerzhagen1, H.J. Peifer1, W.L. Engl1 
TL;DR: In this paper, a generalized hydrodynamic model for semiconductors without the assumption of a parabolic band structure is presented, where the quantity carrier temperature is defined and five relaxation times have to be introduced instead of the two in use so far, in order to take nonparabolicity into account.
Abstract: A system of generalized hydrodynamic equations is derived from Boltzmann's 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. >

133 citations

References
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Journal ArticleDOI
D.L. Scharfetter1, H.K. Gummel1
TL;DR: In this article, the authors presented theoretical calculations of the large-signal admittance and efficiency achievable in a silicon p-n-v-ns Read IMPATT diode.
Abstract: This paper presents theoretical calculations of the large-signal admittance and efficiency achievable in a silicon p-n-v-ns Read IMPATT diode. A simplified theory is employed to obtain a starting design. This design is then modified to achieve higher efficiency operation as specific device limitations are reached in large-signal (computer) operation. Self-consistent numerical solutions are obtained for equations describing carrier transport, carrier generation, and space-charge balance. The solutions describe the evolution in time of the diode and its associated resonant circuit. Detailed solutions are presented of the hole and electron concentrations, electric field, and terminal current and voltage at various points in time during a cycle of oscillation. Large-signal values of the diode's negative conductance, susceptance, average voltage, and power-generating efficiency are presented as a function of oscillation amplitude for a fixed average current density. For the structure studied, the largest microwave power-generating efficiency (18 percent at 9.6 GHz) has been obtained at a current density of 200 A/cm2, but efficiencies near 10 percent were obtained over a range of current density from 100 to 1000 A/cm2.

2,042 citations

Journal ArticleDOI
TL;DR: In this article, a simplified model of secondary ionization, avalanche breakdown and microplasma phenomena in p-n junctions was proposed, in which holes and electrons have identical properties described by four constants: generation of highest energy or Raman phonons, energy E R and mean-free-path L R ; ionization or electron-hole pair production, threshold carrier energy E i and mean free path L i.
Abstract: The phenomena of secondary ionization, avalanche breakdown and microplasma phenomena in p - n junctions are analyzed using a simplified model in which holes and electrons have identical properties described by four constants. Only two scattering processes for carriers are considered, each having two constants: generation of highest energy or Raman phonons, energy E R and mean-free-path L R ; ionization or electron-hole pair production, threshold carrier energy E i and mean-free-path L i . E R is determined from neutron scattering data; E R = 0·063 eV for Si and 0·037 eV for Ge. The other three constants are adjustable. E i and L i / L R = r are chosen to fit data on quantum yield for photons with 1 hv Q = 3−2 exp (E g +2E i −hv) 2rE R . For silicon this gives E i = 1·1 eV (which is equal to the energy gap E g ) and r = 17·5. For germanium E i is also about 1·1 eV and r = 57. The simple model predicts that the ionization coefficient α ( F ) varies with field F as (qF rE R ) exp − (E i qL R F ) which is in good agreement with data for electrons in silicon if L R is set equal to 50 A. The model predicts an energy per pair for ionization by high-energy particles of about 2·2 E i + rE R which is in good agreement with measured values. It also predicts a hot-carrier random energy of about 0·2 eV for F = 400,000 V/cm, which agrees with the spectra of hole-electron recombination in microplasmas. Thus the three adjustable constants permit fitting six pieces of experimental data in four independent experiments in spite of the fact that the intricacies of the band structure are disregarded. The effects of statistical spatial fluctuations of donor and acceptor ions are considered and it is concluded that these will be randomly distributed according to a Poisson distribution. This randomness leads to a characteristic fluctuation voltage (qF B K) 1 2 − 0·3 V for silicon where F B is the breakdown field, and the dielectric constant K = 1·04 × 10 −12 F/cm for silicon. The effect of these fluctuations is to produce local regions in a p - n junction with breakdown about 0·7 V lower than the average in uncompensated material. The fluctuations of voltage are larger by [(N d +N a ) (N d −N a )] 1 2 in compensated material. The fluctuations can increase the apparent ionization coefficient substantially. Microplasma effects are considered and it is shown that in a junction with only the Poisson fluctuations the microplasma should be stabilized by an apparent series resistance due to space charge of magnitude 1 υ max K − 10 5 Ω where υ max = (E R m ∗ ) 1 2 is the limiting drift velocity. This is much larger than the spreading resistance term of magnitude 1 μF B K − 2000 Ω . It is concluded that typical noisy microplasma phenomena are probably associated with localized structural defects probably having two characteristics: (1) they increase the effect ionization coefficient to a value greater than 10 5 cm −1 over a region less than 10 −5 cm long; (2) they have a mechanism for capturing charge which increases the field once the microplasma has formed. Small SiO 2 precipitates and dense arrays of dislocations appear to have the requisite properties. Metal precipitates in the space-charge layer produce “soft” reverse characteristics with localized currents of the form V 6±1 .

835 citations

Journal ArticleDOI
TL;DR: In this paper, the authors derived transport equations for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs.
Abstract: Transport equations are derived for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs. Care is taken to state and discuss the assumptions which are made in the derivation. The collision processes are expressed in terms of relaxation times. The accuracy is improved by considering these to depend on the average kinetic energy rather than the electron temperature. Other transport equations used in the literature are discussed, and shown to be incomplete and inaccurate in many cases. In particular, the usual assumption that the mobility and diffusion constant depend locally on the electric field strength is shown to be incorrect. Rather, these quantities should be taken as functions of the local average velocity of electrons in the lower valley.

765 citations

Journal ArticleDOI
TL;DR: In this paper, an improved method is presented for calculating the ionization rates αn and αp from charge multiplication measurements on diffused silicon p-n junctions, where the real impurity profile is approximated by an exponential function whose parameters are calculated from capacitance measurements; the ratio αp/αn as a function of the electric field is calculated from multiplication measurements.
Abstract: An improved method is presented for calculating the ionization rates αn and αp from charge multiplication measurements on diffused silicon p-n junctions. The main features of this method are: The real impurity profile is approximated by an exponential function whose parameters are calculated from capacitance measurements; the ratio γ = αp/αn as a function of the electric field is calculated from multiplication measurements; the ionization rates are solved from the ionization integral for pure electron injection, taking the influence of the threshold energy into account. Measurements on narrow junctions agree with measurements on wide junctions by assuming a threshold energy of 1.8 eV for electrons, in agreement with the results of M oll and van O verstraeten .(1) The ionization rates differ from those of M oll and van O verstraeten (1) and of L ee , L ogan et al.(2) mainly because these authors neglect the influence of the threshold energy. The electron and hole data satisfy Chynoweth's law α(E) = α ∞ exp (−b/¦E¦), cm −1 with: for electrons α∞ = 7.03 × 105 cm−1 b = 1.231 × 106 V cm−1 for 1.75 × 105 ⩽ E ⩽ 6.0 × 105 V cm−1 for holes α∞ = 1.582 × 106 cm−1b = 2.036 × 106 V cm−1 for 1.75 × 105 ⩽ E ⩽ 4.0 × 105 V cm−1 and α∞ = 6.71 × 105 cm−1b = 1.693 × 106 V cm−1 for 4.0 × 105 ⩽ E ⩽ 6.0 × 105 V cm−1 Breakdown voltages are computed for high voltage p-n and p-i-n diodes. These are in good agreement with experiments, indicating the reliability of the ionization rates.

723 citations

Journal ArticleDOI
A. G. Chynoweth1
TL;DR: In this article, the ionization rates for holes and electrons in silicon have been determined over the following ranges of field: for holes, (2.5-6.0)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ volts
Abstract: The ionization rates for holes and electrons in silicon have been determined over the following ranges of field: for holes, (2.5-6.0)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ volts ${\mathrm{cm}}^{\ensuremath{-}1}$; for electrons, (2.0-5.0)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ volts ${\mathrm{cm}}^{\ensuremath{-}1}$. The ionization rate for electrons is higher than that for holes. The results suggest that the field dependence of the ionization rate for holes and, probably, for electrons also, can be expressed by $a\mathrm{exp}(\ensuremath{-}\frac{b}{E})$, where $E$ is the field. The constants $a$ and $b$ are different for electrons and holes.

526 citations