High-Temperature Properties of Drain Current Variability in Scaled by hkksew3563rd

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									                                                                                                                  SS10111 29 Total pages 5
Japanese Journal of Applied Physics 50 (2011) 04DC08                                                                             REGULAR PAPER
DOI: 10.1143/JJAP.50.04DC08


High-Temperature Properties of Drain Current Variability
in Scaled Field-Effect Transistors Analyzed by Decomposition Method
Takaaki Tsunomura1 , Anil Kumar2 , Tomoko Mizutani2 , Akio Nishida1 , Kiyoshi Takeuchi1 , Satoshi Inaba1 ,
Shiro Kamohara1 , Kazuo Terada3 , Toshiro Hiramoto1;2 , and Tohru Mogami1
1
  Robust Transistor Program, NSI Project, Research Department 4, MIRAI-Selete, Tsukuba, Ibaraki 305-8569, Japan
2
  Institute of Industrial Science, The University of Tokyo, Meguro, Tokyo 153-8505, Japan
3
  Faculty of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan
Received September 21, 2010; revised December 14, 2010; accepted December 24, 2010; published online April 20, 2011

    The properties of drain current variability in field-effect transistors (FETs) at high temperature are experimentally investigated. It is found that the
    on-state drain current (ION ) at high temperature has a strong correlation with ION at room temperature and that there is no anomalous ION change
    from room temperature to high temperature. It is also found that ION variability at high temperature is smaller than that at room temperature. The
    origin of the decrease in ION variability with increasing temperature is analyzed by the decomposition method developed in our previous work. It is
    clarified that the decrease in the current–onset voltage component plays a dominant role, especially in the saturation region. Moreover, it is also
    clarified that thermal excitation of carriers suppresses current–onset voltage variability, and ultimately the current–onset voltage component of ION
    variability with increasing temperature. # 2011 The Japan Society of Applied Physics




                                                                                  NFETs and PFETs are arrayed in a matrix manner, and each
1. Introduction                                                                   FET is electrically selected by row and column decoders.
The electrical characteristic variability of field-effect                           The measurement is executed using the Agilent N9201A
transistors (FETs) is one of the difficulties in developing                         array structure parametric test system. This system can
scaled large-scale integration (LSI) devices.1–12) Among                          measure the characteristics of a device under test (DUT)
electrical characteristics, drain current (Ids ) variability is                   while controlling the decoders using addressing signals.
as important an issue as threshold voltage (VT ) variability,                        The test samples are fabricated using the 65 nm process
since the operation speed of LSI is affected by the drain                          technology with a polycrystalline silicon (poly-Si) dual gate
current of FETs.                                                                  and a silicon oxy-nitride (SiON) gate stack. The gate length
   At the same time, semiconductor devices that can be used                       (Lg ) of FETs is 60 nm and the gate width (Wg ) of FET is
at high temperature are increasingly needed, for example, in                      120 nm. The effective oxide thickness (EOT) of the gate
the automobile industry.13,14) Thus, it is very important to                      oxide layer is 1.9 nm.
investigate the property of electrical characteristics vari-                         To evaluate ION variability, the Ids –gate voltage (Vgs )
abilities at high temperature for developing high-quality LSI.                    characteristics of 8000 NFETs and PFETs are measured at
The high-temperature characteristics of VT variability have                       room (303 K) and high (393 K) temperatures. The drain bias
been analyzed in our previous studies.9,10) It was clarified                       of FETs is set to jVds j ¼ 1:2 V in the saturation region, and
that VT variability decreases with increasing temperature.                        to jVds j ¼ 50 mV in the linear region. ION is defined as Ids at
Although the origin of drain current variability has been                         jVgs j ¼ 1:2 V.
studied, most studies did not focus on the temperature
dependence of drain current variability.15–29) There are some                     3. Results and Discussion
studies on the effect of temperature variation on circuit                          3.1 ION variabilities at room and high temperatures
operation.30) However, there are few reports on drain current                     At first, the correlation between ION values at room and high
variability at high temperature.                                                  temperatures is evaluated to determine whether there is an
   In this study, on-state drain current (ION ) variability at                    anomalous ION change from room temperature to high
high temperature is evaluated and compared with ION                               temperature. Figure 1 shows the scatter plots between ION
variability at room temperature.31) It is found that ION                          values at room and high temperatures. ION values at room
variability decreases with increasing temperature. The origin                     and high temperatures have strong correlations, and there
of the ION variability decrease with increasing temperature                       are no anomalous ION changes from room temperature to
is analyzed by the decomposition method of the variability                        high temperature. These strong correlations stem from the
component that we have recently developed.26–28) It is                            temperature characteristics of physical parameters related to
clarified that the decrease in the current–onset voltage                           ION . The scatter plots of VTHC values at room and high
component of ION variability is dominant in the saturation                        temperatures are also shown in Fig. 2. Here, VTHC is the
region. In the following sections, the details of the                             threshold voltage defined by the subthreshold constant
experimental method, measured results, and origin of the                          current (10 nA Â Wg =Lg ) method. VTHC values at room
decrease in ION variability with increasing temperature are                       and high temperatures also have strong correlations.10)
explained and discussed.                                                             Next, ION variabilities at both temperatures are compared
                                                                                  using the normal probability plots shown in Fig. 3. ION
2. Experimental Methods                                                           values at both temperatures exhibit normal distributions.
To evaluate ION variability accurately, it is important to                        ION variabilities ( ION /median ION ) are also indicated.
evaluate a large number of FETs. To measure a large                               Median ION and ION decrease from room temperature to
number of FETs effectively, the device matrix array-test                           high temperature. Considering median ION and ION
element group (DMA-TEG) is used.32–34) In the DMA-TEG,                            together, ION variability decreases with increasing tempera-
                                                                         04DC08-1                            # 2011 The Japan Society of Applied Physics
Jpn. J. Appl. Phys. 50 (2011) 04DC08                                                                                                                                                                                                                                                                                  T. Tsunomura et al.


                                           1.0                                                                                          1.5                                                                       5                                                                             5
                                                       NFET                                                                                                                                                                NFET Saturation                                                                NFET Linear
                                                                                                                                                  NFET                                                            4                                                                             4
 ION at high temp. (393 K) [×10-4 A]




                                                                                                  ION at high temp. (393 K) [×10-5 A]
                                                       Saturation                                                                                                                                                                                                                                        High Temp. (393 K)
                                                                                                                                                  Linear                                                                    High Temp. (393 K)
                                           0.8         Lg = 60 nm                                                                                                                                                 3                                                                             3        σION /Median ION
                                                                                                                                                  Lg = 60 nm                                                                σ ION /Median ION
                                                       Wg = 120 nm                                                                                                                                                                                                                                       = 7.3%
                                                                                                                                                  Wg = 120 nm                                                     2         = 8.7%                                                              2
                                                                                                                                        1.0




                                                                                                                                                                                                Normal quantile




                                                                                                                                                                                                                                                                              Normal quantile
                                           0.6                  ρ = 1.00                                                                                                                                          1                                                                             1
                                                                                                                                                                                                                  0                                                                             0
                                                                                                                                                     ρ = 1.00
                                           0.4                                                                                                                                                                    -1                                                                            -1
                                                                                                                                        0.5
                                                                                                                                                                                                                  -2                                                                            -2
                                           0.2                                                                                                                                                                    -3                             Room Temp. (303 K)                             -3                         Room Temp. (303 K)
                                                                                                                                                                                                                                                 σION /Median ION                                                          σION /Median ION
                                                                                                                                                                                                                  -4                             = 9.3%                                         -4                         = 8.0%
                                             0.0           0.2     0.4     0.6     0.8      1.0                                            0.0             0.5          1.0           1.5                         -5                                                                            -5
                                                                                                                                                                                                                       0      0.2          0.4     0.6        0.8     1.0                            0          0.5        1.0              1.5        2.0
                                                       ION at room temp. (303 K) [×10 -4 A]                                                      ION at room temp. (303 K) [×10 -5 A]                                                     ION [×10-4 A]                                                               ION [×10-5 A]
                                                                         (a)                                                                                     (b)                                                                             (a)                                                                      (b)
                                           0.5                                                                                          0.75
                                                        PFET                                                                                                                                                      5                                                                             5
                                                                                                                                                  PFET
     ION at high temp. (393 K) [×10-4 A]




                                                                                                                                                                                                                           PFET Saturation                                                               PFET Linear
                                                                                                  ION at high temp. (393 K) [×10-5 A]



                                                        Saturation                                                                                Linear                                                          4                                                                             4
                                           0.4          Lg = 60 nm                                                                                Lg = 60 nm
                                                                                                                                                                                                                            High Temp. (393 K)                                                               High Temp. (393 K)
                                                                                                                                                                                                                  3         σION /Median ION =                                                  3
                                                        Wg = 120 nm                                                                               Wg = 120 nm                                                                                                                                                σION /Median ION
                                                                                                                                        0.50                                                                      2         6.3%                                                                2            = 4.6%




                                                                                                                                                                                               Normal quantile




                                                                                                                                                                                                                                                                              Normal quantile
                                           0.3
                                                                                                                                                                                                                  1                                                                             1
                                                                                                                                                                          ρ = 0.98
                                                                               ρ = 0.99                                                                                                                           0                                                                             0           Room Temp. (303 K)
                                           0.2
                                                                                                                                        0.25                                                                      -1                                                                            -1          σION /Median ION
                                                                                                                                                                                                                                                                                                            = 5.0%
                                                                                                                                                                                                                  -2                                                                            -2
                                           0.1                                                                                                                                                                                                         Room Temp.
                                                                                                                                                                                                                  -3                                   (303 K)                                  -3
                                                                                                                                                                                                                  -4                                   σION /Median ION                         -4
                                                                                                                                                                                                                                                       = 6.6%
                                                 0.0       0.1     0.2     0.3     0.4      0.5                                            0.0            0.25         0.50           0.75                        -5                                                                            -5
                                                       ION at room temp. (303 K) [×10 -4 A]                                                      ION at room temp. (303 K) [×10 -5 A]                                  0        1            2       3         4          5                          0       0.1       0.2     0.3               0.4   0.5
                                                                                                                                                                                                                                          ION [×10-5 A]                                                               ION [×10-5 A]
                                                                         (c)                                                                                     (d)
                                                                                                                                                                                                                                                 (c)                                                                      (d)
Fig. 1. Scatter plot between ION values at room and high temperatures of
(a) NFETs in the saturation region, (b) NFETs in the linear region,                                                                                                                          Fig. 3. (Color online) Normal probability plots of ION of (a) NFETs in
(c) PFETs in the saturation region, and (d) PFETs in the linear region. There                                                                                                                the saturation region, (b) NFETs in the linear region, (c) PFETs in the
are strong correlations between ION values at room and high temperatures in                                                                                                                  saturation region, and (d) PFETs in the linear region at both room and high
both NFETs and PFETs.                                                                                                                                                                        temperatures. ION variabilities (ION /median ION ) are also shown. ION
                                                                                                                                                                                             variability decreases from room temperature to high temperature.

                                           0.6                                                                                          0.6
                                                       NFET                                                                                       NFET
                                                       Saturation                                                                                 Linear                                                                                         VTHC         VTHEX
         VTHC at high temp. (393 K) [V]




                                                                                                       VTHC at high temp. (393 K) [V]




                                           0.5                                                                                          0.5
                                                       Lg = 60 nm                                                                                 Lg = 60 nm
                                           0.4
                                                       Wg = 120 nm
                                                                                                                                        0.4
                                                                                                                                                  Wg = 120 nm                                                                           10-3                                                                               1.5

                                                                                                                                                          ρ = 0.99
                                                                                                                                                                                                                                          -4                         ΔVTH
                                           0.3                                                                                          0.3                                                                                             10
                                                                 ρ = 0.99
                                           0.2                                                                                          0.2
                                                                                                                                                                                                                                        10-5                                                                               1.0




                                                                                                                                                                                                                                                                                                                                 Ids [×10-4 A]
                                                                                                                                                                                                                              Ids [A]




                                           0.1                                                                                          0.1
                                                                                                                                                                                                                                        10-6
                                             0.0         0.1    0.2    0.3   0.4    0.5    0.6                                             0.0     0.1    0.2    0.3   0.4    0.5     0.6
                                                         VTHC at room temp. (303 K) [V]                                                            VTHC at room temp. (303 K) [V]                                                       10-7                                                                               0.5
                                                                         (a)                                                                                    (b)
                                           0.6                                                                                          0.6                                                                                             10-8
                                                       PFET                                                                                       PFET
                                                       Saturation                                                                                 Linear                                                                                10-9                                                                              0
         VTHC at high temp. (393 K) [V]




                                                                                                       VTHC at high temp. (393 K) [V]




                                           0.5                                                                                          0.5
                                                       Lg = 60 nm
                                                       Wg = 120 nm
                                                                                                                                                  Lg = 60 nm                                                                               0.0              0.5        1.0                                1.5          2.0
                                                                                                                                                  Wg = 120 nm
                                           0.4                                                                                          0.4                                                                                                                          Vgs [V]
                                           0.3                ρ = 0.99                                                                  0.3

                                                                                                                                                                       ρ = 0.99
                                                                                                                                                                                             Fig. 4. Ids –Vgs characteristic of NFET in the saturation region. VTHEX is
                                           0.2                                                                                          0.2
                                                                                                                                                                                             the threshold voltage defined by the extrapolation method. ÁVTH can be
                                           0.1                                                                                          0.1                                                  expressed by ÁVTH  VTHEX À VTHC .

                                             0.0         0.1    0.2    0.3   0.4    0.5    0.6                                             0.0     0.1    0.2    0.3   0.4    0.5     0.6
                                                         VTHC at room temp. (303 K) [V]                                                            VTHC at room temp. (303 K) [V]
                                                                         (c)                                                                                    (d)                          ION variability, which was developed in our previous study,
                                                                                                                                                                                             is performed.26–29) In this method, it is assumed that ION
Fig. 2. Scatter plot between VTHC values at room and high temperatures                                                                                                                       variability can be decomposed into three components
of (a) NFETs in the saturation region, (b) NFETs in the linear region,                                                                                                                       originating from VTHC , Gm,max , and ÁVTH variabilities.
(c) PFETs in the saturation region, and (d) PFETs in the linear region. There                                                                                                                Gm,max is the maximum slope of the tangent to the Ids –Vgs
are also strong correlations between VTHC values at room and high
                                                                                                                                                                                             characteristic. ÁVTH is the current–onset voltage, which
temperatures.
                                                                                                                                                                                             indicates the sharpness of increasing Ids with increasing Vgs .
                                                                                                                                                                                             The definition of ÁVTH is explained by the measured Ids –Vgs
ture. In the following subsections, the origin of the ION                                                                                                                                    characteristic of NFET shown in Fig. 4. First, the threshold
variability change is investigated.                                                                                                                                                          voltage defined by the extrapolation method (VTHEX ) is
                                                                                                                                                                                             introduced. VTHEX is defined as the Vgs intercept of the
3.2 Origin of decrease in ION variability with increasing                                                                                                                                    tangent to the Ids –Vgs characteristic that shows the highest
    temperature                                                                                                                                                                              slope among all Vgs points. The current–onset voltage ÁVTH
To investigate the origin of the decrease in ION variability                                                                                                                                 can be expressed by ÁVTH  VTHEX À VTHC . When Ids rises
with increasing temperature, the decomposition method of                                                                                                                                     sharply, ÁVTH decreases.
                                                                                                                                                                                      04DC08-2                                                            # 2011 The Japan Society of Applied Physics

                                                                                                                                                                                                                                                                                                                                                  SS10111
Jpn. J. Appl. Phys. 50 (2011) 04DC08                                                                                                                                                                               T. Tsunomura et al.


                               1.0                                                                                                           1.0
                                                        Measured NFET,                                                                                                                              Measured NFET,
                                                        Saturation                                                                                                                                  Saturation
                               0.8                                                                                                           0.8
                                                                                                                                                                                                                 ΔION
               ION [×10-4 A]




                                                                                                                             ION [×10-4 A]
                               0.6                                                                                                           0.6


                               0.4                                                                                                           0.4


                               0.2                                                                                                           0.2


                               0.0                                                                                                           0.0
                                        0.1   0.2     0.3    0.4   0.5   0.6                                                                    0.4          0.5    0.6      0.7    0.8                            0.9      1.0
                                                    VTHC [V]                                                                                                              VTHEX [V]


Fig. 5. (Color online) Scatter plot of measured ION and VTHC of NFETs                Fig. 7. (Color online) Scatter plot of measured ION and VTHEX of NFETs
in the saturation region.                                                            in the saturation region. Difference between the measured ION and expected
                                                                                     ION from the regression line at the same VTHEX is defined as ÁION . Since
                                                                                     Gm,max variability is dominant in the ION variability of FETs that have the
                               1.0                                                   same VTHEX , ÁION stems from Gm,max variability.
                                                Measured NFET,
                                                Saturation
                               0.8
                                                                                                                10                                                                                  10
                                                                                                                                    NFET Saturation                                                                NFET Linear
              ION [×10-4 A]




                               0.6                                                                              8                                                                                   8
                                                                                        σION / Median ION [%]                                  Room temp. (303 K)




                                                                                                                                                                            σION / Median ION [%]
                                                                                                                                                                                                                           Room temp. (303 K)
                                                                                                                6                                  High temp. (393 K)                               6                       High temp. (393 K)
                               0.4
                                                                                                                 4                                                                                   4
                               0.2
                                                                                                                 2                                                                                   2

                               0.0                                                                              0                                                                                   0
                                       0.1    0.2     0.3 0.4      0.5   0.6                                         Total              VTHC          ΔVTH         Gm                                    Total      VTHC         ΔVTH     Gm
                                                    ΔVTH [V]                                                                                    (a)                                                                        (b)
                                                                                                           10                                                                                       10
                                                                                                                                  PFET Saturation                                                                 PFET Linear
Fig. 6. (Color online) Scatter plot of measured ION and ÁVTH of NFETs                                           8                                                                                   8
that have the same VTHC in the saturation region. It is clearly shown that ION                                               Room temp. (303 K)
                                                                                        σION / Median ION [%]




                                                                                                                                                                            σION / Median ION [%]

fluctuates with ÁVTH .                                                                                           6                 High temp. (393 K)                                                6             Room temp. (303 K)
                                                                                                                                                                                                                    High temp. (393 K)
                                                                                                                4                                                                                   4
   The decomposition method is explained as follows.
The decomposition is based on scatter plots. The VTHC                                                           2                                                                                   2

component is extracted from the scatter plot of ION and VTHC                                                    0                                                                                   0
                                                                                                                     Total              VTHC          ΔVTH         Gm                                    Total      VTHC         ΔVTH     Gm
shown in Fig. 5. Here, the slope of the regression line is                                                                                      (c)                                                                        (d)
termed ‘‘SlopeðVTHC Þ’’. The VTHC component [ION ðVTHC Þ]
is calculated as                                                                     Fig. 8. (Color online) Measured and decomposed ION variabilities at
                                                                                     room and high temperatures. (a) NFETs in the saturation region, (b) NFETs
              ION ðVTHC Þ ¼ SlopeðVTHC Þ Â VTHC :                            ð1Þ   in the linear region, (c) PFETs in the saturation region, and (d) PFETs in the
                                                                                     linear region. In the saturation region, the ÁVTH component has the largest
The ÁVTH component is extracted from the scatter plot of                             contribution to the decrease in measured ION variability with increasing
ION and ÁVTH of FETs that have the same VTHC shown                                   temperature. In the linear region, the ÁVTH component has a partial
in Fig. 6. It is clearly shown that ION fluctuates with                               contribution.
ÁVTH . Here, the slope of the regression line is termed
‘‘SlopeðÁVTH Þ’’. The ÁVTH component [ION ðÁVTH Þ] is
calculated as                                                                        abilities at both temperatures. From the decomposition, it is
           ION ðÁVTH Þ ¼ SlopeðÁVTH Þ Â ðÁVTH Þ:                             ð2Þ   clarified that the decrease in ÁVTH component is larger than
                                                                                     the decrease in the other components in the saturation
Next, the method of decomposing the Gm component is                                  region. In the linear region, both ÁVTH and Gm components
explained. The scatter plot of ION and VTHEX is shown in                             mainly contribute to the decrease in ION variability with
Fig. 7. Here, the difference between the measured ION and                             increasing temperature.
expected ION from the regression line at the same VTHEX is                              Since the ÁVTH component contributes to the decrease
defined as ÁION . This ÁION stems from Gm,max variability.                            in ION variability dominantly in the saturation region, and
On the bases of this relationship between ÁION and Gm,max ,                          partially in the linear region, the mechanism of the decrease
the Gm component [ION ðGm Þ] is calculated as                                       in the ÁVTH component is analyzed.
                                     ION ðGm Þ ¼ ðÁION Þ:                    ð3Þ      Since the ÁVTH component is proportional to ðÁVTH Þ, as
                                                                                     shown in eq. (2), the temperature dependence of ðÁVTH Þ is
  Using the above method, ION variability is decomposed.                             evaluated. In Fig. 9, ðÁVTH Þ and the normal probability
Figure 8 shows the measured and decomposed ION vari-                                 plots of ÁVTH both at room and high temperatures are
                                                                               04DC08-3                                                                  # 2011 The Japan Society of Applied Physics

                                                                                                                                                                                                                                         SS10111
Jpn. J. Appl. Phys. 50 (2011) 04DC08                                                                                                                                                                                                             T. Tsunomura et al.

                   5                                                                      5                                                                                                                  0.15




                                                                                                                                                           (The origin is the average potential.)
                   4       NFET Saturation                                                4       NFET Linear
                                                                                                                                                                                                                                       High temp.




                                                                                                                                                             Potential along divided line [V]
                          Room temp. (303 K)                                                      Room temp. (303 K)
                   3                                                                      3
                          σ(ΔVTH )                                                                σ(ΔVTH )                                                                                                   0.10
                   2      = 23.3 mV                                                       2       = 19.3 mV                                                                                                                            Room temp.
 Normal quantile




                                                                        Normal quantile
                   1                                                                      1
                                                                                                                                                                                                             0.05
                   0                                                                      0
                   -1                                                                     -1
                   -2                                                                     -2
                                                                                                                                                                                                                  0
                   -3                          High temp. (393 K)                         -3                           High temp. (393 K)
                                               σ(ΔVTH ) = 22.4 mV                                                      σ(ΔVTH ) = 16.6 mV                                                                   -0.05
                   -4                                                                     -4
                   -5                                                                     -5
                    0.2         0.3      0.4           0.5        0.6                      0.0         0.1           0.2      0.3          0.4
                                                                                                                                                                                                            -0.10
                                       ΔVTH [V]                                                                  ΔV TH [V]

                   5                                                                      5                                                                                                                 -0.15
                   4      PFETs Saturation                                                4       PFETs Linear                                                                                                        0     20    40    60    80 100 120
                   3
                          Room temp. (303 K)
                                                                                          3                                                                                                                           Position (Channel width direction) [nm]
                   2      σ(ΔVTH )                                                        2
 Normal quantile




                                                                        Normal quantile




                   1      = 18.4 mV                                                       1
                                                                                                                                                 Fig. 11. (Color online) Simulated channel potentials at room and high
                   0                                                                      0
                                                                                                                                                 temperatures are compared along the divided line. The potential fluctuation
                   -1                                                                     -1
                                                                                                                      High temp. (393 K)         at room temperature is in good agreement with the potential fluctuation at
                   -2                                                                     -2                          σ(ΔVTH ) = 9.7 mV
                                                                                                                                                 high temperature.
                   -3                                                                     -3
                   -4                        High temp. (393 K)                           -4 Room temp. (303 K)
                                             σ(ΔVTH ) = 16.4 mV                              σ(ΔVTH ) = 12.1 mV
                   -5                                                                     -5
                    0.2         0.3        0.4         0.5        0.6                      0.0          0.1        0.2        0.3          0.4
                                      |ΔV TH | [V]                                                            |ΔV TH | [V]
                                                                                                                                                                                                            1.0




                                                                                                                                                                         Fermi distribution function (E )
Fig. 9. (Color online) Normal probability plots of ÁVTH values at room
                                                                                                                                                                                                            0.8
and high temperatures. (a) NFETs in the saturation region, (b) NFETs in the
linear region, (c) PFETs in the saturation region, and (d) PFETs in the linear
region. In this graph, ðÁVTH Þ is also shown. Both ðÁVTH Þ values of                                                                                                                                      0.6
NFETs and PFETs decrease with increasing temperature.
                                                                                                                                                                                                            0.4
                                                                                                                                                                                                                                             High temp.

                                                                                                      Divided                                                                                               0.2
                                 120 nm
                                                                                                       line                                                                                                            Room temp.
                                                                                                                                                                                                            0.0
                                                                                                                                                                                                               -0.2       -0.1        μ      + 0.1    + 0.2
                                                                                                                                                                                                                                    E [eV]
                                                     Source




                                                                                                                                                 Fig. 12. (Color online) Fermi–Dirac distribution functions calculated at
                                                                                          Drain




                                      Wg                                                                                                         room and high temperatures.



                                                                                                                                                    At first, the potential fluctuation change with temperature
                                                                                                                                                 is investigated as one of the possible origins of the decrease
                                      0 nm                                                                                                       in ðÁVTH Þ with increasing temperature. The simulated
                                               0 nm           Lg                               60 nm
                                                                                                                                                 potentials along the potential divided lines at room and high
                                                                                                                                                 temperatures are compared in Fig. 11.27) In this graph, the
Fig. 10. (Color online) Two-dimensional potential profile at the channel
                                                                                                                                                 origin of the y-axis (channel potential) is the average
surface calculated by the device simulation. The broken line represents the                                                                      potential along the divided line. To compare the potential
divided line of the potential.                                                                                                                   fluctuations at room and high temperatures, the potentials
                                                                                                                                                 are shifted so that the average potentials are zero. This is
                                                                                                                                                 because the average potentials at room and high tempera-
shown. It is clarified that ðÁVTH Þ decreases with increasing                                                                                    tures are different. It is found that the potential fluctuation at
temperature. This reduction in ðÁVTH Þ causes the reduction                                                                                     room temperature is in good agreement with that at high
in the ÁVTH component with increasing temperature.                                                                                               temperature. Therefore, the decrease in ðÁVTH Þ with
   The possible origins of the decrease in ðÁVTH Þ with                                                                                         increasing temperature cannot be explained by the potential
increasing temperature are considered on the basis of the                                                                                        fluctuation.
origin of ÁVTH . From the device simulation, it was proved                                                                                          Another possible origin is the thermal excitation of
that the dominant origin of ÁVTH variability is the channel                                                                                      carriers. Carriers that show a higher kinetic energy increase
potential fluctuation along the potential divided line,                                                                                           in number with increasing temperature by the thermal
which originates from random channel dopant fluctuation                                                                                           excitation, as shown in the Fermi-Dirac distribution function
(RDF).26,27) Figure 10 shows a two-dimensional potential                                                                                         in Fig. 12. The effect of thermal excitation is evaluated
profile of the channel surface calculated by the device                                                                                           using the current density. The simulated current density
simulation. The difference between the average potential and                                                                                      diagrams of the channel surface are shown in Fig. 13. The
the minimum potential along the divided line shows good                                                                                          current density fluctuation is smaller at high temperature
correlation with ÁVTH .                                                                                                                          than at room temperature, although the potential fluctuations
                                                                                                                                           04DC08-4                                                                     # 2011 The Japan Society of Applied Physics

                                                                                                                                                                                                                                                                SS10111
Jpn. J. Appl. Phys. 50 (2011) 04DC08                                                                                                                            T. Tsunomura et al.


                       Room Temp.                                       High Temp.                            S. Miyano, T. Sakurai, and T. Hiramoto: Symp. VLSI Technology Dig.,
             120                                             120                                              2010, p. 191.
                                                                                                         4)   K. J. Kuhn: IEDM Tech. Dig., 2007, p. 471.
                                                                                                         5)   A. T. Putra, A. Nishida, S. Kamohara, and T. Hiramoto: Appl. Phys.
                                                                                                              Express 2 (2009) 024501.
                                                                                                         6)   A. T. Putra, A. Nishida, S. Kamohara, T. Tsunomura, and T. Hiramoto:




                                                   Wg [nm]
   Wg [nm]




                                                                                                              Jpn. J. Appl. Phys. 48 (2009) 044502.
                   Source




                                                                   Source
                                      Drain




                                                                                      Drain
              60                                              60                                         7)   A. T. Putra, T. Tsunomura, A. Nishida, S. Kamohara, K. Takeuchi, and T.
                                                                                                              Hiramoto: Jpn. J. Appl. Phys. 48 (2009) 064504.
                                                                                                         8)   T. Tsunomura, A. Nishida, and T. Hiramoto: IEEE Trans. Electron Devices
                                                                                                              56 (2009) 2073.
                                                                                                         9)   T. Tsunomura, A. Nishida, K. Takeuchi, S. Inaba, A. T. Putra, S.
                                                                                                              Kamohara, K. Terada, T. Hiramoto, and T. Mogami: Ext. Abstr. Solid State
                                                                                                              Devices and Materials, 2008, p. 860.
              0               30              60              0                30             60        10)   T. Tsunomura, A. Nishida, and T. Hiramoto: Jpn. J. Appl. Phys. 49 (2010)
                            Lg [nm]                                         Lg [nm]                           054101.
                                               Vgs = VTHC                                               11)   T. Tsunomura, F. Yano, A. Nishida, and T. Hiramoto: Jpn. J. Appl. Phys.
                                                                                                              49 (2010) 074104.
Fig. 13. (Color online) Simulated current density diagrams of the channel                               12)   T. Tsunomura, A. Nishida, and T. Hiramoto: IEEE Trans. Electron Devices
surface both at room and high temperatures. Here, Vgs is set to VTHC at each                                  58 (2011) 364.
                                                                                                        13)   T. Abo: Symp. VLSI Technology Dig., 2007, p. 2.
temperature. Clearly, the current density fluctuation at high temperature is
                                                                                                        14)   C. Schmidt: IEDM Tech. Dig., 2007, p. 3.
smaller than that at room temperature.
                                                                                                        15)   F. Forti and M. E. Wright: IEEE J. Solid-State Circuits 29 (1994) 138.
                                                                                                        16)   T. Mizuno, M. Iwase, H. Niiyama, T. Shibata, K. Fujisaki, T. Nakasugi, A.
                                                                                                              Toriumi, and Y. Ushiku: Symp. VLSI Technology Dig., 1994, p. 13.
                                                                                                        17)   P. G. Drennan and C. C. McAndrew: IEDM Tech. Dig., 1999, p. 167.
along the divided lines are the same. This result shows that                                            18)   T. Linton, M. Chandhok, B. J. Rice, and G. Schrom: IEDM Tech. Dig.,
carrier motion is less affected by the potential fluctuation at                                                 2002, p. 303.
high temperature owing to the thermal excitation of carriers.                                           19)   P. G. Drennan and C. C. McAndrew: IEEE J. Solid-State Circuits 38
This reduced effect of the potential fluctuation should reduce                                                  (2003) 450.
                                                                                                        20)   H. Yang, V. Macary, J. L. Huber, W. G. Min, B. Baird, and J. Zuo: IEEE
ðÁVTH Þ with increasing temperature, and as a result, should                                                 Trans. Electron Devices 50 (2003) 2248.
also reduce the ÁVTH component of ION variability.                                                      21)   P. Dollfus, A. Bournel, S. Galdin, S. Barraud, and P. Hesto: IEEE Trans.
                                                                                                              Electron Devices 51 (2004) 749.
4. Conclusions                                                                                          22)   C. Alexander, G. Roy, and A. Asenov: IEEE Trans. Electron Devices 55
                                                                                                              (2008) 3251.
The characteristic of ION variability at high temperature and                                           23)         ´
                                                                                                              T. Merelle, G. Curatola, A. Nackaerts, N. Collaerta, M. J. H. van Dal, G.
the origin of the temperature dependence of ION variability                                                   Doornbos, T. S. Doornb, P. Christie, G. Vellianitis, B. Duriez, R. Duffy,
are investigated. By evaluating 8000 NFETs and PFETs, it is                                                   B. J. Pawlak, F. C. Voogtb, R. Rooyackersa, L. Wittersa, M. Jurczaka, and
found that there is no anomalous ION change from room                                                         R. J. P. Lander: IEDM Tech. Dig., 2008, p. 241.
                                                                                                        24)   W. Lee, J. J.-Y. Kuo, W. P.-N. Chen, P. Su, and M.-C. Jeng: Symp. VLSI
temperature to high temperature, and that ION variability                                                     Technology Dig., 2009, p. 112.
decreases with increasing temperature. By the decomposi-                                                25)   M. Saitoh, N. Yasutake, Y. Nakabayashi, K. Uchida, and T. Numata:
tion method of ION variability, it is clarified that the                                                       Symp. VLSI Technology Dig., 2009, p. 114.
                                                                                                        26)   T. Tsunomura, A. Kumar, T. Mizutani, C. Lee, A. Nishida, K. Takeuchi, S.
contribution of ÁVTH component to the decrease in
                                                                                                              Inaba, S. Kamohara, K. Terada, T. Hiramoto, and T. Mogami: Symp. VLSI
measured ION variability with increasing temperature is                                                       Technology Dig., 2010, p. 97.
dominant rather than those of the other components in the                                               27)   A. Kumar, T. Mizutani, K. Shimizu, T. Tsunomura, A. Nishida, K.
saturation region. In the linear region, both the ÁVTH and                                                    Takeuchi, S. Inaba, S. Kamohara, K. Terada, and T. Hiramoto: Silicon
                                                                                                              Nanoelectronics Workshop Abstr., 2010, p. 7.
Gm components contribute to the decrease in measured ION                                                28)   T. Mizutani, A. Kumar, T. Tsunomura, A. Nishida, K. Takeuchi, S. Inaba,
variability with increasing temperature. Moreover, it is also                                                 S. Kamohara, K. Terada, and T. Hiramoto: Silicon Nanoelectronics
clarified that the ÁVTH component decreases with increasing                                                    Workshop Abstr., 2010, p. 81.
temperature owing to the thermal excitation of carriers.                                                29)   T. Tsunomura, A. Kumar, T. Mizutani, A. Nishida, K. Takeuchi, S. Inaba,
                                                                                                              S. Kamohara, K. Terada, T. Hiramoto, and T. Mogami: Appl. Phys.
                                                                                                              Express 3 (2010) 114201.
Acknowledgement
                                                                                                        30)   S. Nassif, K. Bernstein, D. J. Frank, A. Gattiker, W. Haensch, B. L. Ji, E.
This work is supported by the New Energy and Industrial                                                       Nowak, D. Pearson, and N. J. Rohrer: IEDM Tech. Dig., 2007, p. 569.
Technology Development Organization (NEDO).                                                             31)   T. Tsunomura, A. Kumar, T. Mizutani, A. Nishida, K. Takeuchi, S. Inaba,
                                                                                                              S. Kamohara, K. Terada, T. Hiramoto, and T. Mogami: Ext. Abstr. Solid
                                                                                                              State Devices and Materials, 2010, p. 699.
                                                                                                        32)   S. Ohkawa, M. Aoki, and H. Masuda: IEEE Trans. Semicond. Manuf. 17
                                                                                                              (2004) 155.
 1) A. J. Bhavnagarwala, X. Tang, and J. D. Meindl: IEEE J. Solid-State                                 33)   M. Aoki, S. Ohkawa, and H. Masuda: Proc. 17th IEEE Int. Conf.
    Circuits 36 (2001) 658.                                                                                   Microelectronic Test Structures, 2004, p. 201.
 2) F. Tachibana and T. Hiramoto: Jpn. J. Appl. Phys. 44 (2005) 2147.                                   34)   T. Tsunomura, A. Nishida, and T. Hiramoto: Jpn. J. Appl. Phys. 48 (2009)
 3) M. Suzuki, T. Saraya, K. Shimizu, A. Nishida, S. Kamohara, K. Takeuchi,                                   124505.




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                                                                                                                                                                              SS10111

								
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