The Position Dependence of Strain in Different Regions in Performance of Devices

The Position Dependence of Strain in Different Regions in Performance of Devices

Yasenjan Ghupur1, 2, Mamtimin Geni1, Mamatrishat Mamat2

1School of Mechanical Engineering, 2School of Physics Science and Technology, Xinjiang University

1Yanan Road 1234, 2Shengli Road 14, Urumqi, China

Abudukelimu Abudureheman3

3UMC Japan Tateyama 294-8502, Japan

Abstract–We investigated the position dependence of strain on velocity, current, heat generation rate and resistance in the drain regions for the Si-devices by Monte Carlo simulation method. In this work, we selected ballistic channel Si-diodes with strain in the channel, in the drain and both in the drain and channel regions. The strain treated as a function of Ge contents (x) respectively. The simulation results show the enhancement of the drain current for the case of both strained channel and drain regions is a higher than for strained drain regions, due to the higher in ratio of the velocity of electrons in the drain regions. Moreover, our results show lower in ratios of heat generation rate and resistance in the drain for the both strained channel and drain regions compared to the case of strained drain regions. Our results indicate that the position of strain in the different regions of devices could affect the performance of devices.

Keywords – Strain, Si-Diode, Ballistic channel, Monte Carlo simulation

. INTRODUCTION

Further improving the performance of the current semiconductor devices by scaling down the device dimensions brings extremely difficult and technologically challenging problems [1]. Strained-Si (substrate induced strained silicon) recognized as an important method by the International Technology Roadmap for Semiconductors (ITRS) [2], because of its superior transport properties. Recent theoretical research works shown a qualitative agreement with most of the experimental data on strained-Si devices [3, 4]. These studies indicated that applying relaxed Si1-xGex (SiGe, mole fraction x represents the Ge content) as a substrate layer in metal-oxide-semiconductor field-effect

transistors (MOSFETs) is one of the most effective ways to introduce larger biaxial tensile strain. The lattice constant of Si being smaller than SiGe creates biaxial tensile strain in the Si [5]. The use of strained-Si channel pseudomorphically grown on a SiGe virtual substrate is becoming a promising way to accelerate the improvement of CMOS performance [6]. About 96% of electrons transporting with small effective mass (mt, transverse effective mass) are kept in the lowered valleys X2 (lower in energy), when Ge content (x) in the Si1-xGex reaches 0.15 [6]. When strain causes band splitting, splitting energy between the lowered valleys X2 (lower in energy) and the raised valleys X4 (higher in energy) becomes comparable or larger than the optical phonon energy, and this will reduce intervalley scattering [7]. Band splitting results in electrons repopulating from the X4 valley to the X2 valley. The repopulation into X2 causes the average effective mass to decrease and carrier mobility to increase [8]. Using strained-Si for channel and for source and drain have improved p-MOS performance by 20% and 35%, respectively [4, 9].

For short-channel devices, the time for a carrier staying

in the channel is greatly reduced and the probability of scattering is decreased [7]. At the room temperature, if channel length is reduced to less than or comparable to the mean free path of carriers [10], the device operation is essentially governed by ballistic transport. Using a novel step/edge technique, the research group in IBM fabricated Si MOSFET with a 20 nm channel length [11]. Simulations also show that as device dimensions shrink to around 30 nm, the carrier transport will become near ballistic [12]. In the case of ballistic transport, electrons injected from source

and flowed into drain become hot electrons. The drain current are significantly reduced by the rebound of hot electrons, because of the effects of the scatterings resulted from the hot electrons [13]. Elastic scattering causes the backward scattering of hot electrons from the drain and substantially degrades the peak of mean velocity of the electrons and the current [14, 15].

Using the self-consistent Monte-Carlo approach to solve the semi classical Boltzmann transport equation is very well suited for getting accurate information for ballistic carrier transport in nanoscale devices at least gate length down to 10 nm [16, 17].

The position dependence of strain in the channel [6-8, 18] or in the drain [19] on the performance of devices were investigated. The dependence of strain in both channel and drain regions on performance of devices have not been studied in detailed. Thus, in this study, we have

undergo any scattering in the channel, thus, the channel region is intrinsic and ballistic.

Intravalley acoustic phonon scattering can be treated as elastic scattering at room temperature. Phonon coupling constants, phonon energies and the longitudinal/transverse effective masses of the electrons were assumed to be same as in unstrained Si in scattering rate calculations [23]. For intervalley phonon and intravalley acoustic phonon scatterings, we used the parameters in the references of [24] and [20]. Nonparabolic band provides a reasonable approximation to the density of states (DOS) for the conduction bands of bulk silicon. The approximated DOS determines the scattering rates of ionized impurity and the phonon scattering when electron energy less than 2 eV [13].

Impact ionization is important in the strained-Si because of the band gap reduction. The scattering rate Wimpact(k) is modeled by using a modified threshold expression [25]:

comparatively investigated the dependence of strain in both

channel and drain regions on performance of the ballistic

Eimpact

1. P[E(k) Eth

   (x)]2

   (1)

   channel device implementing a modified ensemble Monte Carlo (MC) simulation method self-consistently coupled with Poissons equation [20, 21].

   . SIMULATION METHOD

   In this work the considered length of the source, channel and drain are 100, 20 and 100 nm, respectively, and the diode width is 40 nm for silicon n+-i-n+ diode along [100] direction. The temperature is 300 K and doping concentrations of the source and drain are ND = 1018 cm3. It is assumed that the strained-Si in the channel and drain is grown on a relaxed Si1-xGex substrate and is a function of Ge content x. Energy bands were modeled by an analytical non parabolic band with respect to six equivalent X-valleys of bulk silicon [20]. Electrons deal with preferentially occupying the lower energy levels (X2), when the six-fold degenerate X6 valleys in Si are split into X2 valleys and X4 valleys that resulted by in-plane biaxial-tensile strain [22]. In order to minimize complexity for better isolation and better understanding of the effects of strained-Si, we only considered the ionized impurity scattering, intravalley acoustic phonon scattering, intervalley phonon scattering and impact ionization in the source and drain regions. The formulae of the scattering rates for the ionized impurity, intravalley acoustic, and intervalley phonon scattering are same as given in reference [21]. Assumed electrons do not

   Where Eth is empirical threshold energy, E(k) is the carriers energy and P is a prefactor which determine the softness of the threshold. The threshold energy is 1.11 eV for unstrained-Si.

   Moreover, nonparabolic band is a good approximation for electron transport when the voltage of the devices is near orless than the band gap [26]. The nonparabolicity parameter is inversely proportional to the band gap Eg(x) for the biaxial strain, and Eg(x) = 1.110.4x. The splitting energy between the lowered and the raised valleys is empirically represented by E = 0.67x [27]. .

   The threshold energy is assumed to be proportional to the band gap Eth(x) = 1.18Eg(x)/Eg(0) for the strained-Si.

   Fig.1 Values of E(x), Eg(x) and Eth(x) with x.

   Figure 1 shows the values of the band valley splitting E(x),

   the band gap Eg(x) and the threshold energy Eth(x) for the strained silicon. The result show that E(x) linearly increased, whereas Eg(x) and Eth(x) linearly decreased with the increasing of the Ge content (x).

   For nanoscaled devices, it is necessary to include quantum effects such as in the simulation. In this work, we use this effective potential approach for the modeling of these quantum effects. Since for correcting the quantum effects, an effective potential approach has the advantages of easy numerical implementation and almost guaranteed convergence [28]

   The presence of heat generation in the drain extension region is inevitable, and the heat generation has crucial effects on the hot electron transport and the characteristics of nanoscale devices. The drain resistances does not decrease proportional to the channel length [29], but can be estimated using the heat generation [30]. Heat generation rate Q [31] and drain resistance Rd [30] are estimated using:

   voltage (i = 0.2 ~ 1V), j represents Ge content (x), i.e., j = 0.2~0.8, sub index d represents the values of A in the drain region. Acij represents the case of with strain in the channel (ch). The ratios v/v, Id/Id, Hd/Hd, Rd/Rd represent (vij-vcij)/ vcij, (Idij Idcij)/ Idcij, (Hdij -Hdcij)/ Hdcij, and (Rdij- Rdcij)/ Rdcij.

   1. Bias voltage dependence of the electron velocity,

      current, heat generation rate and resistance

      In gure 2(a)-(d), the ratio of v, Id, Hd and Rd in the range of the bias voltage Vd = 0.2~1V for dr and ch&dr were compared to ch for x = 0.4. The figures show ratios of both velocity and current for ch&dr are higher, and the ratios of heat generation rate and resistance for ch&dr are smaller than the ratios for dr.

      In the range of Vd = 0.2-0.4 V, the ratios of velocity and current are ~23% and ~20%, the ratios of heat generation rate and resistance change from ~-55% to ~-56% and from

      ~-65% to ~-69% for ch&dr, respectively. In the range of Vd

      = 0.4-0.6 V, the ratios of velocity and current change from

      N

      ~24% to ~20% and from ~21% to ~16%, the ratios of heat

      Q'''

      N t V

      h ems

      h abs

      (2)

      generation rate and resistance change from ~-60% to ~-50%

      Rd

      sup sim

      Q'''

      I

      2

      d

      (3)

      and from ~-73% to ~-63% for ch&dr, respectively. In the range of Vd = 0.6-1 V, the ratios of velocity and current are

      ~20% and ~16%, the ratios of heat generation rate and resistance ratios are ~-50% and ~-63% for ch&dr,

      Where N is the total number of mobile charges in the device, Nsup is the number of super particles used in the simulation. (N/Nsup) is the scaling ratio of the real Q and the simulated Q. V is the volume element at each grid node, tsim is the total simulation time, ems, abs are the emitted and absorbed phonon energy respectively, and Id is the drain current.

      III. RESULTS AND DISCUSSIONS

      We selected the range of Ge contents x varying from 0.2 to 0.8 by step 0.05 and the range of drain voltage Vd from

      0.2 to 1V by step 0.1, in this work.

      The symbols used in the figures such as ch, dr and ch&dr represent a diode with strained channel, with strained drain (sold line) and with simultaneous strained channel and drain (dashed line). The vertical axes of figures are

      A/A = (Aij-Acij)/Acij, where A represents a value for mean electron velocity (v), current (Id), heat generation rate (Hd) and resistance (Rd) in the drain regions, respectively. The sub index i represents the value of applied drain bias

      respectively. When Vd = ~ 0.5 ~ 1V, the ratio of velocity for ch&dr is smaller than for dr, and the effect of strain in the channel becomes smaller with the increase of bias voltage

      Fig.2 The ratios of velocity (a), current (b), heat generation rate (c) and resistance(d) in the drain region in the range of Vd from 0.2 to 1 V for x

      = 0.4.

      as shown in fig.2 (a) .

   2. Strain dependence of the mean velocity, current, heat generation rate and resistance

Fig.3(a)-(d) show ratios of v, Id, Hd and Rd as a function of x (from 0.2 to 0.8) when Vd= 0.4 V and for dr and ch&dr. The figures show ratios of both velocity and current for ch&dr are higher and the ratios of heat generation rate and resistance for ch&dr are smaller than the ratios for dr. In the range of x = 0.2-0.3, the ratios of velocity and current are

~24% and the ratios of heat generation rate and resistance change from~-65% to ~-60% and from ~-75% to ~-73% for ch&dr, respectively. In the range of x = 0.3 ~ 0.6, the ratios of velocity and current change from ~24% to ~20% and from ~21% to ~16%, the ratios of heat generation rate and resistance change from ~-60% to ~-50% and from ~-73% to

~-63% for ch&dr, respectively. In the range of x = 0.6-0.8, the ratios of velocity and current are ~20% and ~16%, the ratios of heat generation rate and resistance ratios are ~-50% and ~-63% for ch&dr, respectively.

Fig.2-3 show the ratios of the drain current and mean velocity in the drain regions for ch&dr are higher than the ratios for dr as a function of selected Ge content x and bias voltages, respectively. Because the number of electrons occupying in the lower energy valleys X2 is increasing. About 96% of electrons transporting with small effective mass (mt, transverse effective mass) are kept in the lowered valleys X2 (lower in energy), when Ge content (x) in the Si1-xGex reaches 0.15 [6]. This is due to the effects of simultaneously applied strain in both channel and drain regions is larger than the other cases. For the biaxial tensile strain, when strain causes band splitting, the splitting energy becomes comparable or larger than the optical phonon energy, and this will reduce inter-valley scattering [7]. The reduced intervalley scattering can lower backward scattering of electrons from the drain and reduce the number of hot electrons. Hot electrons readily cause impact ionization and intervalley scattering. If hot electrons experience impact ionization, they will lose their energy and become low energy electrons in the drain. Band splitting results in electrons repopulating from the X4 (higher in energy) to the X2 (lower in energy) and thereby most of electrons will locate in the lower X2 valleys with small mt. The two effects of strained-Si, the electron transporting with small mt and the suppressed intervalley scatterings of the electrons can

increase the drain current and the mean velocity of electrons. Band splitting results in electrons repopulating from the X4 valley to the X2 valley. The repopulation into X2 causes the average effective mass to decrease and carrier mobility to increase [8].

For strained ballistic channel, the strained-Si results in the increasing of the mean velocity of electrons and the current in the drain region, but could not suppress the intervalley scattering. However, for the strained drain both the electrons transporting with small mtand the suppressed intervalley scattering are play major role. For the strained drain, the strained-Si results in the large increasing of mean velocity of electrons and the current in the drain region due to the two effects of strained-Si. Our study, applying strained-Si both in the channel and drain simultaneously, show a larger increase of the mean velocity and the current in the drain region compared to the case of strained-Si in channelor in drain alone.

Fig.3 (a) – (d) show in the range of x = 0.2-0.3, the ratios of velocity and current are higher, the ratios of heat generation rate and resistance changes are lower than the value of ratios at x>0.3 for ch&dr, respectively. Figure 1 also show the band splitting energy is less than the threshold energy and band gap in the range of 0.2<x<0.8. The difference between the splitting energy and the threshold energy and band gap become smaller as a function of x. If hot electrons experience impact ionization, they will release

Fig. 3 The ratios of velocity (a), current (b), heat generation rate (c) and resistance (d) in the drain region for ballistic channel diodes with dr and ch&dr, respectively. The range of the Ge content x is 0.2~0.8, when Vd=

0.4 V

their energy and become low energy electrons within drain.

V. CONCLUSION

We investigated the position dependence of strain on velocity, current, heat generation rate, and resistance in the drain regions for the Si-devices by Monte Carlo simulation method. In this work, we selected ballistic channel Si-diodes with strain in the channel, in the drain and both in the drain and channel regions, as a function of Ge contents (x) respectively. Our results show that the position of strain in the different regions of devices could affect the performance of devices. The enhancement of performance of devices with both strained channel and drain regions is higher than with strained drain or with strained channel regions. The enhancements of performance of devices in the range of x from 0.2 to 0.3 are higher than x greater than 0.3 as figure 3 (a)-(e). The enhancement of the electron velocity and current can be understood as following facts: the electrons transporting with small effective mass (mt) will locate in the lower X2-band valleys (lower in energy). The energy of valley splitting which causes the suppressed intervalley scattering is larger than most of the electrons energy. The backward scattering of electrons from drain was lower, thereby increase the mean velocity and drain current in the drain region, because of suppressed intervalley scatterings of electrons. For the strained ballistic channel, the electrons of only those transporting with small effective mass play major role for the increment of electron velocity. In contrast, for the strained-Si in both channel and drain regions, the electrons transporting with small effective mass and the suppressed intervalley scattering play major role for the increment of electron velocity. The results tallies with the report that strain could effectively suppress the inter-valley scatterings of electrons and make electron transporting with small transverse mass [6-8].

ACKNOWLEDGMENT

This work was supported in part by the National Natural Science Foundation of China (Grant No.: 61366001), in part by the National Basic Research Program of China (Grant No.: 2011CB706601), in part by Doctoral fellowship Funding (Grant No.: 208-61344) and in part by New Energy and Industrial Technology Development Organization (NEDO), Japan. Authors are grateful the support and help of Prof. Hiroshi Iwai, Kenji Natori, and associate Prof. Parhat

Ahmet at the Tokyo Institute of Technology, Japan. Special thanks to High Performance Computing Platform of Xinjiang University, China.

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