# Electrostatic Effect of Localized Charge in Dual Bit Memory Cells with DiscreteTraps

*L. Perniola(1, 2,*), S. Bernardini(3), G. Iannaccone(1,6), B. De Salvo (4),
G. Ghibaudo (2), P. Masson(3), C. Gerardi(5) *

*(1)Dipartimento di Ingegneria dell’Informazione,
Università degli Studi di Pisa, Via Caruso, 56122 Pisa, Italy, *perniola@enserg.fr
(2)IMEP-CNRS/INPG, Avenue de Martyrs 32, 38016 Grenoble, France
(3) L2MP-Polytech – IMT Technopôle de Château Gombert, 13451
Marseille Cedex 20 France
(4)CEA-LETI, Avenue de Martyrs 16, 38054 Grenoble, France
(5)STMicroelectronics, Catania, Italy
(6)IEIIT-CNR, Via Caruso, 56122 Pisa, Italy. *

The following article, presented at ESSDERC 2004 conference, illustrates the capability of ATLAS in the validation and the comprehension of complex effects of new and promising devices like non-volatile discrete trap memory devices.

**Abstract**

In this paper the electrostatic impact of Channel
Hot Electron (CHE) injection in discrete-trap memories is quantitatively addressed.
The dual bit behavior of the transfer characteristic during forward and reverse
read of a written cell is thoroughly analysed with the help of an analytical
model. Such model allows, for the first time, to estimate the effective charged
portion of the discrete storage layer, *L _{2}*, and the quantity
of electrons,

*Q*, injected in the trapping sites from the experimental parameters of the

*I*characteristics, the reverse-forward threshold voltage shift

_{d}-V_{g}*V*, and the total threshold voltage shift

_{RF}*Vtot*. The viability of this model is confirmed with tests performed on nanocrystal memories, under different bias conditions. These results are confirmed with the help of a 2D drift-diffusion commercial code (

**-SILVACO).**

*ATLAS*

**1. Introduction **

Channel Hot Electron injection is widely used as a standard writing method for non-volatile discrete-trap memory products [1]-[2]. It provides the opportunity to localise the charges injected in a small region of the trapping medium, and two-bit operation is achieved through multilevel storage [3]. The basic principle on which two-bit operation resides, is common to NROM memories and nanocrystal memories [4]-[5]. It is possible to trap charges near one junction (drain or source) with a programming stress, and read them in the reverse mode, compared to the programming, enhancing the electrostatic effect of these charges on the conductivity of the active channel (see Figure 1).

It has been shown in the literature [1]-[3]-[6]
that the threshold voltage during the forward read, V* _{th-F}*,
is lower than the threshold voltage during the reverse read,

*V*, when the cell is polarised in the saturation regime.

_{th-R}This is due to the strong two dimensional effects
near the charged junction. If the injected charge, near the drain, is completely
screened by the high *V _{ds}* applied in forward read (which
induces a long pinchoff region), the

*I*characteristic results very close to the characteristic of the fresh cell. In this case we have a low

_{d}-V_{g}*V*. On the other hand, during the reverse read the high

_{th-F}*V*applied is not able to screen the effect of electrons and the conductivity of the active channel is lowered by the “bottleneck” near the low-voltage contact. In such a case we have a high

_{ds}*V*[2]-[6].

_{th-R}
Figure 1. The concept of forward and reverse read
after Channel Hot Electron programming, considering a non zero bulk potential.
In the figure the depletion width under the charged and uncharged regions
is highlighted. |

With a simple 1D approach (Gradual Channel Approximation)
[6] it is not possible to simulate such an asymmetric behavior. In this paper,
with the help of a simple quasi 2D analytical approach, we are able to quantify
for the first time, both the length of the charged region, *L _{2}*,
and the number of injected electrons per unit area in the trapping sites,

*Q*, from the two quantities available from experiments, the total threshold voltage shift,

*V*, (i.e., the difference between the threshold voltage in the reverse read,

_{th-tot}*V*and the threshold voltage of the fresh cell,

_{th-R},*V*) and the reverse-forward threshold voltage shift,

_{th-fresh}*V*(i.e. the difference between

_{RF}*V*and

_{th-R}*V*).

_{t-F}The viability of the model is tested with 2D numerical
simulations of a commercial TCAD code (** ATLAS**-SILVACO).

Main results from the theory are widely tested, under different bias conditions, on nanocrystal memories fabricated by ST-Microelectronics [4]. The influence of the bulk potential, as well as that of the drain-to-source potential, are carefully assessed in this work.

**2. Quasi-2D Analytical Model**

With a simple 1D approach it is not possible to describe properly the 2D effects near the charged region, which are the first cause of the dual bit behavior. For the first time, to our knowledge, we present an analytical approach, which starts from quasi 2D considerations [7].

The analytical approach describes the behavior
of the surface potential * _{S}*
along the channel of a MOSFET with non-uniform threshold voltage. The distribution
of trapped charge may be in general a complicate function of the spatial coordinates.
We assume that the charge distribution along the channel can be described by
a step function which represents an “effective” distribution. As
a result, we can distinguish two regions: one close to the source with a length

*L*, where storage nodes are not charged (uncharged region); and the second one close to the drain with a length

_{1}*L*which is uniformly charged by

_{2}*Q*electrons per unit area. In Figure 2 it can be seen how the written memory is divided in the two regions. The trapped charge raises the flat band voltage,

*V*, of the charged region

_{fb-2}*L*. In particular the flat band voltage difference between the charged and the uncharged region is:

_{2}Where *q* is the electron charge, *C _{2}*
is the top oxide capacitance per unit area.

Figure 2. Sketch of the charged and uncharged regions.
Equation (2) and (3) come from the Gauss’ law applied to the two
slices of thickness dy. Boundary conditions are shown (Vis the built-in potential), considering the presence of a bulk
voltage _{bi
}V. The potential reference value is the Fermi
level of the bulk. _{b} |

In the following model, we do not consider charges
over the drain junction, but, as already noted by [6], from Figure 3 it appears
that they do not influence* I _{d}-V_{g}* characteristics.

Figure 3. simulations
to assess the influence of charge over drain junction. It is clear that
a charged region over the junction of length comparable to ATLASL,
has negligible effects on channel conductivity. _{2} |

The model solves separately, in the two regions, the differential equations
(2) and (3). Gauss’ law is applied to a transversal slice of thickness
dy along y and cross section equal to the average depletion width *X _{dep1}*(

*i*=1,2) (see Figure 2), and allows us to write the flux of the electric field through the faces perpendicular to y in terms of the surface potential as (

*X*, where is a fitting parameter. During the gate voltage sweep, frequently the uncharged region goes in strong inversion, while the charged region is still pinched-off. The presence of both inversion charge

_{dep1}/h)d_{s}/dy*Q*and depletion charge at inversion

_{inv}*Q*, are carefully considered in Equation (3):

_{dep1}

where _{si} (_{ox})
is the silicon (oxide) electric permittivity, *V _{g}* the gate
voltage, tox is the equivalent oxide thickness,

*N*is the doping level of the bulk. If a bulk voltage,

_{sub}*V*, is applied, as sketched in Figure 2, the drain, source and gate potentials must be raised of

_{b}*V*, setting at zero the potential of the bulk. The space charge and the inversion charge have the following expression:

_{b}Where *i=1,2, _{L-i}*
is the surface potential in the case the influence of drain and source junctions
is completely neglected,

*U*is the quasi-Fermi potential referred to the source of the uncharged equivalent transistor.

_{cs}The solution to Equation (2) is a linear combination of hyperbolic sins:

where * _{r-1}*
(

*) is the right-hand (left-hand) boundary condition shown in Figure 2.*

_{l-1}*is referred to the value of the potential in the bulk. The solution to Equation (3) is of similar form of Equation (6).*

_{s-1}The parameter describes
the *short channel effects*, as it provides a clue on how strong is the
influence of the junction potential on * _{s}*
under the gate. The higher the value of l,
the smoother appears the

*curve along the channel, the weaker is the control effect of the gate on the channel.*

_{s}From the description of the surface potential, the drain current
can be calculated. As in the subthreshold region the current is a *diffusion*
dominated process, the following expression can be derived [8]:

where *µ _{eff}* is the effective mobility
of electrons in the channel,

*KT*is the thermal energy,

*ni*is the intrinsic electron concentration in silicon and

*is the minimum of the surface potential in the channel.*

_{Smin}

**3. Comparison Between the Analytical Model and ATLAS
Results **

From Equation (2), the importance of h is apparent.

To determine the proper value of this parameter, we have used
the commercial TCAD tool ** ATLAS** from SILVACO. We have
simulated a class of nanocrystal memories, fabricated from STMicroelectronics.
Parameters of the memory cell are

*L*=0.28 µm,

*W*=0.16 µm, tunnelling oxide thickness

*t*=5.5 nm, control oxide thickness

_{tun-ox}*t*=8 nm. The charged nanocrystals have been considered as a uniform charged oxide region, of thickness

_{2}*t*=2 nm, sandwiched between the tunnelling oxide and the control gate oxide.

_{ch}Figure 4 (a) Comparison of the
transfer characteristics from (solid lines)
and analytical model (circles) to extract the value of the fitting parameter
. In the case of ATLASL=_{2}L/4,
the best value is =4. (b)
Comparison of V versus _{th}Q obtained with
(solid lines) and the analytical model
(circles) shows that is
weakly dependent on the density of electrons injected in dots. In the
inset of Figure 4(b) the dependence of
on L2 is provided. ATLAS |

Figure 5. Reverse-forward threshold
voltage shift V
as a function of the charged length _{RF}L obtained from
_{2} (circles) and the analytical model (solid
line). Parameters are dot density 10ATLAS^{12} cm^{-2}, 6 el./dot
and according to the inset
of Figure 4(b). |

As specified before, we simply assumed that the charge distribution
in the oxide is a step function where the charged length can be varied and the
density of charge has been chosen to fit different flat band voltages *V _{fb}’*s.

In Figure 4(a) a sample comparison between ** ATLAS**
results and the analytical model for

*L*/4 is shown. The parameter h to fit

_{2}=L*I*numerical characteristics has shown a weaker dependence on the density of electrons trapped in dots,

_{d}-V_{g}*Q*, than on the charged length

*L*. This property is shown in Figure 4(b), where, provided one value of

_{2}*L*, it is possible to fairly fit different values of

_{2}*Q*, with one value of . In the inset, on the other hand, the dependence of on

*L*is provided (strong dependence of on

_{2}*L*).

_{2}Figure 6 . Reverse-forward threshold
voltage shift V
as a function of the density of electrons Q obtained from _{RF}
results (circles) and the analytical model (solid line). Parameters are
ATLASL (35 nm) =3
and _{2}=L/8L=_{2}L/4 (70 nm) =4
(according to the inset of Figure 4(b)). |

Already the plot of Figure 4(a) shows that the forward and
reverse bits are not clearly detached for *L _{2}*=

*L*/4 (

*L*=70 nm), and cannot be easily sensed as

_{2}*V*and

_{th-F}*V*are similar. From Figure 5, it is clear that one-bit operation appears for

_{th-R}*L*>70 nm (

_{2}*V*0V). It is not required that the whole region of the channel is uniformly charged to have

_{RF}*V*

_{th-F}*V*.

_{th-R}Another interesting property is the* charge density*
insensitivity of *V _{RF}*,
once a saturation limit is achieved.

In Figure 6 such a behavior is shown for *L _{2}*=

*L*/8 (L2=35 nm) and for

*L*=

_{2}*L*/4 (

*L*=70 nm). In the case of

_{2}*L*=

_{2}*L*/4, for

*Q*>2x10

^{12}el./cm

^{2}the window between the forward and reverse threshold voltage is almost constant; while in the case of

*L*=

_{2}*L*/8, this property appears for

*Q*>5x10

^{12}el./cm

^{2}. Therefore

*V*can be used as an

_{RF}*absolute*indicator of the charged region dimension.

**4. Comparison Between the Analytical Model and Experiments
**

Figure 7. Analytical model vs data
obtained from nanocrystal memories as a function of drain-to-source Vds
reading voltage. |

Experiments performed on STMicroelectronics nanocrystal memory cells [4] confirm both the validity of the analytical model and suggest how to perform a reading procedure which allows to enhance the asymmetry between forward and reverse read.

Figure 8. Analytical model versus experiments
obtained from nanocrystal memories with V=1.5V and
different bias condition for _{ds}V. _{d} |

From Figure 7, it is clear that raising *V _{ds}*
enhances the electrostatic effect of trapped electrons, and decreases

*V*to the value of the fresh cell threshold voltage,

_{th-F}*V*. In experiments the maximum reading

_{th-fresh}*V*has been put at 1.5V. In Figure 8, the viability of this analytical model with different bulk voltages,

_{ds}*V*has been tested. The most relevant conclusion of this work is presented in Figure 9. As an example it is shown a contour plot of

_{b}*V*and

_{tot}(L_{2},Q)*V*that can be calculated from this model. From the two experimental parameters

_{RF}(L_{2},Q)*V*(blu line) and

_{tot}*V*(red line) is possible to find in the contour plot the crossing point and then deduce the values of

_{RF}*V*and the density of electrons

_{2}*Q*injected in the trapping medium.

**5. Conclusions **

A detailed model concerning Channel Hot Electron (CHE) electrostatic
impact on forward/reverse reading has been provided. Both numerical simulations
and experiments on nanocrystal memories, performed under different bias conditions
confirm the viability of the model. At our knowledge, for the first time in
literature, a contour plot is provided (Figure 9) where, from the experimental
results at hand (*V _{tot}*
and

*V*), it is possible to assess the effective charged length, L2 and the density of injected electrons,

_{RF}*Q*. Support from EU projects ADAMANT (IST-2001-34234), SINANO (IST-506844) and from the CNR through the FIRB project is gratefully acknowledged.

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