Erratum: “Theory of electron transport in small semiconductor devicesusing the Pauli master equation” [J. Appl. Phys. 83, 270 (1998)]Massimo V. Fischetti Citation: J. Appl. Phys. 83, 6202 (1998); doi: 10.1063/1.367504 View online: http://dx.doi.org/10.1063/1.367504 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v83/i11 Published by the American Institute of Physics. Related ArticlesAtomistic simulations of heat transport in real-scale silicon nanowire devices Appl. Phys. Lett. 100, 223107 (2012) Full-band Monte Carlo simulation of high-energy carrier transport in single photon avalanche diodes withmultiplication layers made of InP, InAlAs, and GaAs J. Appl. Phys. 111, 104508 (2012) A ultra-high-vacuum wafer-fusion-bonding system Rev. Sci. Instrum. 83, 055108 (2012) Multiple-trapping in pentacene field-effect transistors with a nanoparticles self-assembled monolayer AIP Advances 2, 022128 (2012) Device model for electronic processes at organic/organic interfaces J. Appl. Phys. 111, 094507 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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JOURNAL OF APPLIED PHYSICS VOLUME 83, NUMBER 11 1 JUNE 1998

ERRATA

Erratum: ‘‘Theory of electron transport in small semiconductor devicesusing the Pauli master equation’’ †J. Appl. Phys. 83, 270 „1998…‡

Massimo V. FischettiIBM Research Division, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights,New York 10598

@S0021-8979~98!01111-6#

1. Equation~2! on page 272 should read:

]r

]t5

i

\@r,H2Hres#1S ]r

]t Dres

, ~2!

since evidently the termHres present in the right-hand side of Eq.~1! has already been absorbed into the last term onright-hand side.

2. The equation after Eq.~8! on page 273 should read:

zm~z!5Am@exp~1 ikm1z!1exp~2 ikm

1z2 ifm!# ,

in general, although only states withfm50 have been considered.3. Equation~30! on page 278 should read:

D2D~E!5m*

p\2 (m

u~E2Em!uAms u2

2

11ur ms u2 . ~30!

4. Page 280, the fourth line from the top, left column, should read:

‘‘...stateor modifying the ‘‘reservoir’’ term in Eqs.~15!, ...’’.

5. Equations~39!, ~41!, and~42! on page 280 should read:

O~z!51

r~z,z! (mKs

rmKs^mKsuz&^zuOumKs&, ~39!

Ekin~z!51

r~z,z! (mKs

rmKs@Em~K !1eV~z!#uzms~z!u2, ~41!

vdri f t~z!51

r~z,z!

\

m* ~z! (ms

rms ImFzm*s~z!

dzms~z!

dz G , ~42!

for consistency with the average quantitiesper particleactually plotted in Figs. 3 and 5.6. Page 285, the fourth line in the caption of Fig. 8 should read:

‘‘...processes. The various curves are parametrized by the applied bias from 0.05...’’ since there is no curve correspa bias of 0 V.

7. Page 290, footnote 40 should read:

‘‘The smallness of the dimensionless electron-phonon coupling constanta follows from van Hove’s argument. Since thermphonons act incoherently~i.e., with random phases!, the root mean square displacement^x2&1/2 of the ions associated to ththermal phonons is proportional to the square root of the number of phonons,Nq , and it takes a very small value. So, foacoustic phononsx2&1/2 is of the order of@\Nq /(2Mccsq)#1/2, whereMc is the mass of the unit cell andNq the number ofphonons of wave vectorq. In the high temperature limit,x2&1/2'@kBT/(2Mc)#1/2/(csq), so that the shift of the conductioband edge caused by the strain induced by this displacement is^DEc&'Dacq^x2&1/25Dac@kBT/(2Mccs

2)#1/2, about 25Dac

meV in Si at 300 K, where the acoustic deformation potential is measured in eV. For optical phonons,^x2&1/2

'@\Nop /(2Mcvop)#1/2. For Si, \vop560 meV, and^x2&1/2'8.2310211 cm, so that^DEc&'(DK)op^x2&1/2'8(DK)op

meV, where the optical deformation potential is measured in units of 108 eV/cm. In both cases the perturbation causedphonons is at most of the order of hundreds of meV. Thus,a'^DEc&/E0 , whereE0'e/(4pe0a0), e0 being the vacuumpermittivity anda0 the Bohr radius, is the energy-scale of the unperturbed Hamiltonian of an electron in the crystal,H0 . Thus,a is of the order of 1022 or less, and terms of the ordera2 represent small corrections.’’

62020021-8979/98/83(11)/6202/1/$15.00 © 1998 American Institute of Physics

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