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Development of an analytical mobility
model for the simulation of ultra thin SOI
MOSFETs.
M.Alessandrini, *D.Esseni, C.Fiegna
Department of Engineering - University of Ferrara, Italy
*DEGM, University of Udine, Italy
Introduction
The scaling of the conventional bulk CMOS technology requires high
doping concentration to counteract short channel effects (SCE).
Problem:
the increase of doping concentration leads to a significant
degradation of the low field mobility (black curves in figure):
SOI devices with
almost undoped ultrathin silicon layer
represent a possible
solution for mobility
degradation
Dependence of effective mobility on Tsi
Recent works reported a dependence of effective mobility in SOI
MOSFETs on the thickness of the silicon layer (TSI ) which is
particularly evident at low inversion densities
Conventional
mobility models
overestimate
experimental
mobility and are not
able to qualitatively
reproduce the
dependence of
mobility on Tsi
This work
In this work we developed analytical models for
electron mobility limited by two scattering
processes that lead to the mobility modulation by
TSI in SOI MOSFETs:
●
●
Surface optical phonos scattering
Coulomb scattering with interface states
Scattering with surface optical
phonons
The model for mobility limited by surface optical phonons has been
developed starting from the general formulation of M. Fischetti and
S.Laux (''Monte Carlo study of electron transport in silicon inversion
layers'' Phys.Rev. B Vol 48, 1993)* under the following approximations:
single parabolic umprimed subband,
● one constant effective value for the exchanged wave
vector with no angular dependence (qe ).
●
Under these approximations we obtained the following scattering rate:
* This formulation has been used in D. Esseni et al. ''Study of low field electron transport in
ultra-thin single and double gate SOI MOSFETs'' IEDM 2002
Scattering with surface optical
phonons
●
The wave function is approximated as follow*:
Normalized concentration:
n(z)/Ninv
We empirically relate the parameter b to the
effective field Eeff as follows:
●
Fitting parameter
*According to F.Stern and W. Howard ''Properties of Semiconductor Sueface Inversion Layer in the
Electric Quantum Limit'' Phis.Rev. Vol.163 1997
Determination of the parameter a.
We determined the value of the parameter a by comparing the calculated g(z) with
the normalized charge density obtained from Schroedinger-Poisson calculations:
Bulk MOSFET
Schroedinger Poisson simulations
g(z) approximation
SOI MOSFET
(TSI=5.2 nm)
Schroedinger Poisson simulations
g(z) approximation
Scattering with surface optical
phonons
Scattering rate for the case of two Si-SiO2 interfaces:
Mobility in the relaxation-time approximation:
Scattering with surface optical
phonons
Parameter values used in this model:
The effective exchanged wave vector is obtained
by fitting the results of rigorous numerical
calculation :
D.Esseni et al. ''Study of low field electron transport
in ultra-thin single and double gate SOI MOSFETs''
IEDM 2002
Scattering with surface optical
phonons
Simulation Results : fitting of rigorous numerical calculation
Numerical model
Analytical model applied to electric field obtained
by Schrodinger/Poisson calculation
Scattering with surface optical
phonons
Calculation of total effective mobility
We performed a drift diffusion simulation of long MOSFETs using
a mobility model for bulk MOSFETs and accounting for quantization
by the density gradient model.
● We evaluated the mobility limited by SO phonons scattering by postprocessing the electric-field distribution with equation:
●
We calculated the total electron mobility composing, by the Mathiessen
rule, the mobility evaluated at discretization points within the inversion
layer with mobility limited by SO phonons scattering.
• The effective mobility in the inversion layer is then obtained as an
average weigthed by carrier concentration according to:
•
Scattering with surface optical
phonons
Effective mobility in ultra-thin SOI SG MOSFETs including surface
optical phonons scattering (symbols) and experimental data for lowdoped Bulk MOSFETs (line)
(qualitative agreement with Koga et al. IEEE TED June 2002).
Scattering with surface optical
phonons
Simulation Results: effective mobility versus Eeff for bulk structures
Simulations including the
effects of SO phonons
Experimental data
Coulomb scattering with interface states
Following the same procedure we described for SO phonons scattering, we
obtained the following scattering rate with unscreened interface charge:
Areal density of
interface states
Where Mf and Mb are the same used for SO phonons
scattering and
Coulomb scattering with interface states
Screening
The screening by inversion carrier is accounted for by a modified
Where
is the Debye length.
:
Coulomb scattering with interface states
Left: experimental mobility versus Ninv
Right: simulations including SO phonons scattering and interface
states scattering.
Conclusions
In this work, analytical models for the mobility limited by
surface optical phonons and by interface states has been
developed and applied to the calculation of electron
effective mobility in MOSFETs.
●The proposed models can be adopted in conjunction with
conventional mobility models developed for bulk devices,
and allow to reproduce the main feature of recently-reported
mobility data for ultra-thin SOI MOSFETs.
●The model for SO-phonons-limited mobility has been
recently implemented in DESSIS using the physical-model
software interface.
●