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Collective Tunneling Model in Charge-Trap-Type Nonvolatile Memory Cell

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					                                                                                                                 SS10201 47 Total pages 4
Japanese Journal of Applied Physics 50 (2011) 04DD04                                                                            REGULAR PAPER
DOI: 10.1143/JJAP.50.04DD04


Collective Tunneling Model in Charge-Trap-Type Nonvolatile Memory Cell
Masakazu Muraguchi, Yoko Sakurai1 , Yukihiro Takada1 , Yasuteru Shigeta2 , Mitsuhisa Ikeda3 , Katsunori Makihara4 ,
Seiichi Miyazaki4 , Shintaro Nomura1 , Kenji Shiraishi1 , and Tetsuo EndohÃ
Center for Interdisciplinary Research, Tohoku University, Sendai 980-8578, Japan
1
  Graduate School of Pure and Applied Science, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
2
  Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
3
  Graduate School of Advanced Sciences of Matter, Hiroshima University, Higashihiroshima, Hiroshima 739-8530, Japan
4
  Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan
Received September 22, 2010; accepted November 29, 2010; published online April 20, 2011

    A new tunneling model between an inversion layer and the trap sites for the charge-trap-type (CT-) nonvolatile memory (NVM) cell is proposed. By
    considering the geometrical mismatch between the inversion layer and the trap site of the CT-NVM cell, we can conclude that electron tunneling is
    induced by a rare event, which causes the localization of electrons in the inversion layer near the trap sites. In addition, we also reveal that the
    successive tunneling of electrons is triggered by this rare event tunneling by focusing on the temporal fluctuation of the electronic state in the
    inversion layer. On the basis of these phenomena, we propose the collective tunneling model in the charge injection of the CT-NVM cell, where the
    electrons tunnel to the trap sites collectively with a long waiting time. This insight is important in designing the CT-NVM cell. By using collective
    tunneling, the amount of injection charge can be controlled discretely by adjusting the charge injection time. This enables us to realize a multilevel
    charge trap cell. # 2011 The Japan Society of Applied Physics




1. Introduction                                                                                                            Blocking
Recently, it has been difficult for the floating gate type                                                                    Oxide
                                                                                                        Gate                Charge
nonvolatile-memory (NVM) to maintain its program speed
because of the floating gate interference effect.1) To                                                                        Trap Layer
overcome this drawback, many types of cell structure and
architecture have been studied.2–4) One of the most                                                                       Tunnel
                                                                                                      Substrate           Oxide
promising candidates is CT-cells such as the silicon–
oxide–nitride–oxide–silicon (SONOS)-type NVM, because                                                          Inversion Layer
CT-NVM cells can scale the charge trap layer and reduce
this interference effect (Fig. 1). On the other hand, the                            Fig. 1. Schematic illustration of SONOS-type NVM cell structure.
mechanism of the program/erase (P/E) operation of CT-
NVM is still unclear. Many studies have been devoted to                          electron dynamics in the inversion layer in the channel.
revealing the mechanism of P/E operation. However, most                          Then, we propose a collective tunneling model in the CT-
studies focused on the physical properties of traps, such as                     NVM cell. In x3, we evaluate our model by our developed
the spatial position and the energy level distributions, in                      numerical calculation, which emulates the proposed tunnel-
relation to the retention characteristics.5–11) In this study,                   ing model with the experimental conditions taken into
we point out that a more basic and important problem in                          account. In x4, we summarize our results.
the CT-NVM cell exists in the charge injection from the
inversion layer in the channel to the trap sites: the mismatch                   2. Collective Tunneling Model
in the size and dimension between the inversion layer in the                     2.1 Importance of the transiently localized state
channel and the trap sites. We investigated the importance of                    First, we consider the dimensional mismatch between a
the electronic state of the inversion layer for the electron                     trap site and the inversion layer of the channel in charge
injection process of direct tunneling for a similar system                       injection, where the inversion layer is spread two-
in our previous studies.12,13) We reveal that this mismatch                      dimensionally, whereas the trap site covers only a part of
results in a significant change of the charge injection feature                   the inversion layer (Fig. 2). Therefore, the electrons are
in the CT-cell from the conventional floating-gate-type cells.                    inevitably injected from a large area to a small area in this
   In this study, we theoretically investigate the electron                      system. This means that the geometrical matching between
injection process to the trap sites of the CT-NVM cell                           the electronic state in the inversion layer and those in the
structure and propose a new collective electron tunneling                        trap site is necessary in addition to energy matching, since
model between the inversion layer state and trap sites for the                   the overlap between two states is one of the key factors for
scaled CT-NVM cell. This tunneling determines the P/E                            quantum tunneling. This aspect is neglected in the conven-
features of the CT-memory cell. By using this tunneling                          tional one-dimensional tunneling model for tunneling from
mode, the amount of injection charge can be controlled                           the inversion layer to the trap site. On the basis of this
discretely with time. This is useful for realizing the                           viewpoint, we proposed that a sufficient overlap of electron
multilevel charge trap cell.                                                     density is necessary between the electronic states in the
   The structure of this paper is as follows. In x2, we identify                 inversion layer and the trap site, as shown Fig. 2(a). As
the role of the electronic state of the inversion layer in the                   shown in Figs. 2(b) and 2(c), the tunneling probability from
charge injection of the CT-NVM cell by focusing on the                           the inversion layer to the trap site is very small owing to the
                                                                                 small overlap between the electronic state in the inversion
Ã
 E-mail address: endoh@riec.tohoku.ac.jp                                         layer and the trap sites. This new insight indicates that the
                                                                        04DD04-1                           # 2011 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 50 (2011) 04DD04                                                                                                                          M. Muraguchi et al.


        (a) Electron Localized   (b) Electron Localized   (c) Electron Spread               (a)         Trap Site          (b)              Trap Site        (c)
                                                                                                        (Unoccupied)                        (Occupied)
            below trap site          far from trap site       around trap site                                            Tunneling Event                    Collective Motion of Electron




    0

                 Position                 Position                  Position                  x                              x                           x

                                                                                                      Potential on INVL
Fig. 2. Schematic illustration of tunneling conditions. Transient localized                       x

electrons induce tunneling from inversion layer to the trap site.
                                                                                      Fig. 3. Potential profiles in the proposed collective tunneling model:
                                                                                      (a) Unoccupied state. (b) Rare trigger electron tunneling. (c) Successive
transiently localized state would be a main contribution to                           tunneling.
tunneling between the inversion layer and the trap site. We
propose a new tunneling model, where the tunneling is
induced by a rare event. This indicates that we must include
                                                                                                            (a)
a long waiting time in order to model the electron injection
in a CT-NVM cell in the charge injection time. Con-
ventionally, the electronic state in the inversion layer is
assumed to be spatially distributed uniformly (eigenstate of
inversion layer) and the tunneling probability is calculated
on the basis of these states. However, the transiently
localized electron model is quite intuitive, because, in the                                                                        Time
inversion layer, the electronic state should fluctuate owing to
the several types of scattering. Thus, the electronic state of                                             (b)
the inversion layer is a transient state, and the spatial                                                                              Succesive
distributions of electrons should fluctuate with time. We                                                                               Tunneling
called this tunneling rare trigger tunneling.
                                                                                                                       Waiting Time for
                                                                                                                       Next Rare Event
2.2 Collective motion of electron tunneling
The rare trigger tunneling event also introduces another
important phenomenon, successive electron tunneling. We                                                                          Time           Rare Event
again focus on the electronic state of the inversion layer.
During the first tunneling event to the trap site, a dip in                            Fig. 4. Overview of the dependence of tunneling current on charge
potential is induced in the inversion layer just below the trap                       injection time: (a) Conventional tunneling model and (b) proposed tunneling
site, and it becomes deeper and wider during tunneling.                               model.
We reported this phenomenon in our previous study.13) This
dip induces electron localization (rare event) around the
occupied trap site, and it triggers the next tunneling. The                              As shown in Fig. 4, the electron tunneling current in
number of induced localized electrons would exponentially                             charge injection to trap sites depends on the charge injection
increase and the electrons would successively tunnel to the                           time. The fast electron tunneling (successive tunneling)
trap sites. The resulting tunneling time should be very fast,                         should occur after a long waiting time. We experimentally
which is why we call the first tunneling rare trigger                                  observe this type of tunneling in a similar structure.14,15) In
tunneling.                                                                            device design, this feature is useful for developing a stable
                                                                                      multilevel CT-NVM cell. By controlling the period of one
2.3 Collective tunneling model in CT-NVM cell                                         trial of collective electron tunneling, we obtain discrete
On the basis of the results above, we propose a new                                   charge injection to the memory cell.
tunneling model for charge injection of a CT-cell. Figure 3
shows our new tunneling model. Once the electron in the                               3. Theoretical Analysis with Collective Tunneling
inversion layer matches the tunneling condition, the electron                            Scheme
localization occurs successively owing to the fluctuation of                           3.1 Calculation model and its flowchart
the potential field of the inversion layer, and electrons tunnel                       In order to investigate the suggested tunneling model, we
to the trap sites successively. This successive tunneling                             emulate the experiment by numerical simulation, where we
should stop when it reaches the dilute trap region or no                              assume that the main contribution to the electron tunneling
longer satisfies the energy-matching condition. Then, the                              was induced by the wave-packet-like state below the trap
next rare event is awaited. Note that a concrete mechanism                            site. Figure 5 indicates the overview of our calculation
of stopping successive tunneling is still under consideration.                        model. In the calculation, we introduce the idea that once
   This tunneling model indicates several important features                          tunneling occurs, the potential field of the inversion layer
for the device operation of the CT-NVM cell. One of them                              fluctuates and the electron tends to localize around the trap
is the asymmetry of the time scale between the electron                               site. Our model calculation of the electron injection process
tunneling time and the waiting time. Here, the time scale of                          for the CT-Cell consists of three main parts: (i) the
tunneling is very fast because of the collective tunneling;                           calculation of one-dimensional tunneling, (ii) the calculation
however, on the other hand, a tunneling event is very rare.                           of the point tunneling, and (iii) the calculation of successive
                                                                                 04DD04-2                                  # 2011 The Japan Society of Applied Physics

                                                                                                                                                                                   SS10201
Jpn. J. Appl. Phys. 50 (2011) 04DD04                                                                                                                         M. Muraguchi et al.


              Rare Event Collective                                                           accordance with this situation, the rare event distribution is
              Tunneling Motion V2                                                             enhanced under the trap site compared with the other part of
         V1
                                                                                              the 2DEG, where the rare event has a Gaussian distribution
    V0
                     Vacant                              Occupied                             for the center of the trap site. We assume that this
                                                                                              enhancement effect exponentially increases with increasing
                                                                                              gate bias.
                t0       Measurement Time           t1          Measurement Time
                                                                                                 If the trial electron density distribution satisfies the
     time                                                                                     tunneling conditions, electrons tunnel to a trap site, and
                                                                                              jump to the successive tunneling stage. If it does not satisfy
                                                                                              the tunneling condition, return to the first procedure of this
                                                                                              stage. This stage continues until the number of iterations
                                                                                              time becomes L.
                                                                                                 In the successive tunneling stage, the spatial distribution
                                                                                              of the generation of rare events is emphasized in the
         Fig. 5. Schematic illustration of our calculation model.
                                                                                              neighborhood of the occupied trap. Then, the same
                                                                                              procedure of point tunneling is iterated, and the tunneling
tunneling probabilities. The main flow of our calculation and                                  event is checked. We assume that the transient fluctuation of
the detailed flowchart of both the point tunneling and                                         the 2DEG is relaxed when the number of trials is over N.
successive tunneling stages are shown in Fig. 6.                                              In this case, the calculation returns to the point tunneling
   After setting the initial parameters, we calculate the                                     stage. These calculations are iterated until the occupied dot
tunneling probability in the z-direction, where we employ                                     reaches M.
the WKB formalism with the standard triangle potential.                                          We also include several conditions so that our calculation
This calculation is done in each trial. Then, we move to the                                  emulates the experimental conditions, where the gate bias is
rare triggered tunneling stage. In this stage, the electron                                   set to a certain value during the finite measurement time,
density distribution in the inversion layer with the given                                    then it is stepped up to the next bias voltage (Fig. 5), after a
probability distribution of the generation of a rare event is                                 certain duration. We assume that the electron localizations
calculated, where we represent the trial spatial electron                                     increase exponentially with increasing gate bias owing to the
density distribution as a wave-packet-like state. The rare                                    concentration of electric field. The size and density of the
event distribution includes the effect of electric field due to                                 trap site are 1.3 nm2 and 3 Â 1011 /cm2 , respectively. In this
gate bias. In the flat band condition, the rare event occurs at                                calculation, we imposed a uniform distribution of the energy
random in the 2DEG. With increasing gate bias, the electric                                   distribution of trap sites, assuming they have a continuous
field in the 2DEG concentrates below the trap site. In                                         energy level. The spatial position of trap sites was set at


                 (a) Main Flow
                                                                                                                           Calculation of
                                                                                         Rare Trigger                      Tunneling Probability for
                        Start                                    Set Gate Bias
                                                                                         Tunneling Stage                   One-dimensional Direction

                        Set the initial parameters                Set Gate Bias
                        (Oxide Thickness,                                                Successive Tunneling
                                                                                                                                                End
                        Barrier Height, Temperature)                                     Stage
                                                                  Set Gate Bias
                     (b) Rare Trigger Tunneling Stage                                       (c) Successive Tunneling Stage

                        From the One-Dimensional
                             Tunneling Stage                                                  From the Point Tunneling Stage


                                                                                              Give Rare Event Distribution in INVL
                       Give Rare Event Distribution in INVL
                                                                                              Reflecting the Position of Occupied Trap Site ,
                       Reflecting the Bias Voltage and Temperature
                                                                                              Bias Voltage, and Temperature



                       Give the Position and Width                                            Give the Position and Width
                                                                      Yes
                       of Trial Wave Function (Rare Event)                                    of Trial Wave Function (Rare Event)
                                                                                                                                          Yes
                                                                Number of
                                                             Trial Times <L ?
                                                                                    No                                                                       No
                                                    No                                                                      No            Number of
                           Check Tunneling                                                        Check Tunneling                      Trial Times <N ?
                                                                             Set the Next
                             Yes                                                                     Yes
                                                                             Gate Bias                                                            Back to Point
                                                                                                                                                  Tunneling Stage
                              Number of             No
                                                                 Go to Successive                   Number of                 No
                       Occupied Trap Sites >M ?
                                                                 Tunneling Stage              Occupied Trap Sites >M ?                 Reset Trial Time




                                   End                                                                     End



                                Fig. 6. Flowchart of the numerical calculation for the collective tunneling model in CT-NVM.

                                                                                     04DD04-3                                  # 2011 The Japan Society of Applied Physics

                                                                                                                                                                        SS10201
Jpn. J. Appl. Phys. 50 (2011) 04DD04                                                                                               M. Muraguchi et al.


                                                                            considering the geometrical mismatch between the inversion
                                                                            layer in the channels and the trap sites of the CT-NVM cell.
                                                                            On the basis of this rare trigger tunneling, we proposed the
                                                                            collective tunneling model in the CT-NVM cell, where the
                                                                            electron tunnels to the trap sites successively with a long
                                                                            waiting time. This insight is very important in designing the
                                                                            CT-NVM cell. This tunneling phenomenon will play an
                                                                            essential role in the future CT-NVM cell, since by using this
                                                                            tunneling, the amount of injection charge can be controlled
                                                                            discretely by adjusting the charge injection time. This
                                                                            tunneling mode is useful for realizing the multilevel charge
                                                                            trap cell.
Fig. 7. Dependence of tunneling current on the charge injection time with   Acknowledgements
proposed collective tunneling model.
                                                                            This work was supported by Grants-in-Aid for Scientific
                                                                            Research Nos. 18063003, 19206037, and 20760019 from
3.5 nm from the substrate, where the trap sites are spatially               the Ministry of Education, Culture, Sports, Science and
distributed over a distance of 20 nm.                                       Technology, Japan.
   Calculations are performed until 5000 trial rare events
appear in the rare event tunneling stage with the constant
gate voltage of 4 V.                                                         1) J.-D. Lee, S.-H. Hur, and J.-D. Choi: IEEE Electron Device Lett. 23 (2002)
                                                                                  264.
3.2 Results and discussion                                                   2) D. Kang, H. Shin, S. Chang, J. An, K. Lee, and J. Kim: Non-Volatile
                                                                                  Semiconductor Memory Workshop Tech. Dig., 2006, p. 36.
Figure 7 shows a typical result of tunneling current with                    3) K.-T. Park, M. Kang, D. Kim, S. Hwang, Y.-T. Lee, C. Kim, and K. Kim:
time from our calculation. As shown in this figure, three                          VLSI Symp. Circuits Tech. Dig., 2007, p. 188.
main features of the electron injection current appear in the                4) M.-S. Seo, S.-K. Prak, and T. Endoh: International Memory Workshop
time domain. This current structure in the time domain                            (IMW) Tech. Dig., 2010, p. 146.
                                                                             5) Y.-Y. Liao, S.-F. Horng, Y.-W. Chang, T.-C. Lu, K.-C. Chen, T. Wang,
corresponds to our proposed collective tunneling phenom-                          and C.-Y. Lu: IEEE Electron Device Lett. 28 (2007) 828.
ena. Each tunnel current peak is a result of collective                      6) H.-T. Lue, P.-Y. Du, S.-Y. Wang, K.-Y. Hsieh, R. Liu, and C.-Y. Lu: IEEE
tunneling, where the higher peak means that many electrons                        Trans. Electron Device 55 (2008) 2218.
are injected, successively triggered by the rare event                       7) Y. Yang and M. H. White: Solid-State Electron. 44 (2000) 949.
                                                                             8) S. Choi, H. Yang, M. Chang, S. Baek, H. Hwang, S. Jeon, J. Kim, and C.
tunneling. Thus, we successfully reproduced the proposed                          Kim: Appl. Phys. Lett. 86 (2005) 251901.
collective tunneling model for CT-NVM.                                       9) K. Yamaguchi, A. Otake, K. Kobayashi, and K. Shiraishi: IEDM Tech.
   This tunneling mode has a significant effect on future                           Dig., 2009, p. 275.
scaled CT-NVM cells, because, it determines the P/E                         10) A. Arreghini, N. Akil, F. Driussi, D. Esseni, L. Selmi, and M. J. van
                                                                                  Duuren: Proc. European Solid State Device Research Conf. (ESSDERC),
features of the CT-memory cell. By this tunneling mode, the                       2007, p. 406.
amount of injection charge can be controlled discretely by                  11)   M. L. French and M. H. White: Solid-State Electron. 37 (1994) 1913.
adjusting the charge injection time. This phenomenon is                     12)   Y. Sakurai, J. I. Iwata, M. Muraguchi, Y. Shigeta, Y. Takada, S. Nomura,
                                                                                  T. Endoh, S. Saito, K. Shiraishi, M. Ikeda, K. Makihara, and S. Miyazaki:
useful for realizing the multilevel charge trap cell for future
                                                                                  Jpn. J. Appl. Phys. 49 (2010) 014001.
scaled NVM-cells.                                                           13)   M. Muraguchi, Y. Takada, S. Nomura, and K. Shiraishi: Jpn. J. Appl. Phys.
                                                                                  47 (2008) 7807.
4. Conclusions                                                              14)   M. Ikeda, Y. Shimizu, H. Murakami, and S. Miyazaki: Jpn. J. Appl. Phys.
                                                                                  42 (2003) 4134.
We studied the electron injection process from the inversion
                                                                            15)   M. Muraguchi, Y. Sakurai, Y. Takada, S. Nomura, K. Shiraishi, M. Ikeda,
layer to the trap site in the CT-NVM cell. We proposed that                       K. Makihara, S. Miyazaki, Y. Shigeta, and T. Endoh: Tech. Dig. Int. Meet.
electron tunneling would be induced by a rare event, by                           Future of Electron Devices, Kansai (IMFEDK), 2010, p. 48.




                                                                     04DD04-4                           # 2011 The Japan Society of Applied Physics

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