Discrete distribution of implanted and annealed arsenic atoms in silicon nanowires and its effect on device performance
© Uematsu et al.; licensee Springer. 2012
Received: 23 August 2012
Accepted: 20 November 2012
Published: 21 December 2012
We have theoretically investigated the effects of random discrete distribution of implanted and annealed arsenic (As) atoms on device characteristics of silicon nanowire (Si NW) transistors. Kinetic Monte Carlo simulation is used for generating realistic random distribution of active As atoms in Si NWs. The active As distributions obtained through the kinetic Monte Carlo simulation are introduced into the source and drain extensions of n-type gate-all-around NW transistors. The current–voltage characteristics are calculated using the non-equilibrium Green's function method. The calculated results show significant fluctuation of the drain current. We examine the correlation between the drain current fluctuation and the factors related to random As distributions. We found that the fluctuation of the number of dopants in the source and drain extensions has little effect on the on-current fluctuation. We also found that the on-current fluctuation mainly originated from the randomness of interatomic distances of As atoms and hence is inherent in ultra-small NW transistors.
KeywordsSilicon nanowires Random discrete dopant distribution Gate-all-around transistors Kinetic Monte Carlo Non-equilibrium green's function
Fluctuation due to random discrete dopant (RDD) distribution is becoming a major concern for continuously scaled down metal-oxide semiconductor field-effect transistors (MOSFETs) [1–4]. For ultra-small MOSFETs, not only random location of individual dopant atoms but also fluctuation of the number of active impurities is expected to have significant impacts on the device performance. Effects of the RDD distribution are usually analyzed with a randomly generated RDD distribution. The actual RDD distribution, however, should be correlated with the process condition and can be different from a mathematically generated one. In the present study, we investigate the effects of random discrete distribution of implanted and annealed arsenic (As) atoms in source and drain (S/D) extensions on the characteristics of n-type gate-all-around (GAA) silicon nanowire (Si NW) transistors. We investigate a GAA Si NW transistor since it is considered as a promising structure for ultimately scaled CMOS because of its excellent gate control [2, 5–7]. Kinetic Monte Carlo (KMC) simulation is used for generating realistic random distribution of active As atoms in Si NWs. The current–voltage characteristics are then calculated using the non-equilibrium Green's function (NEGF) method. Our results demonstrate that the on-current fluctuation mainly originated from the randomness of the dopant location and hence is inherent in ultra-small NW transistors.
Results and discussion
As distribution by KMC simulation
Drain current fluctuation
Summary of correlation factors of drain current
Vg = 0.0 V (off-state)
Vg = 0.5 V (on-state)
Vd = 0.05 V
Vd = 0.5 V
Vd = 0.05 V
Vd = 0.5 V
L g *
Significant correlations between Id and Lg* are found at the off-state with Vd of both 0.05 and 0.5 V. Negative correlation means that Id tends to decrease with increasing Lg*. The sum of the standard deviations of interatomic distances in the S/D extensions (σ) shows a clear correlation at the on-state with Vd = 0.05 V. Concerning the maximum separation, a clear correlation at the on-state with Vd = 0.5 V and that with Vd = 0.05 V are found with Ss and S, respectively, while little correlation with Sd is seen at any cases. These results demonstrate that the effective gate length (Lg*) is a main factor for the off-state, where the channel potential mainly governs the I V characteristics. We mention that the off-current becomes larger when active As atoms penetrate into the channel region, which is not taken into account in the present simulation. This increase in off-current can be explained in terms of the ion-induced barrier lowering , where the potential barrier in the channel is significantly lowered by attractive donor ions, which enhances the electron injection from the source. For the on-state, random As distribution in the S extension (Ss) is an important factor at high Vd due to current injection from S, and that in the S/D extensions (σ and S) is dominant at low Vd because the back-flow current from D also contributes the current.
On the other hand, little or weak correlations between Id and the number of As dopants are found. The weak positive correlations with Ns and N at the off-state are attributed to a tendency that a larger number of dopants lead to smaller Lg*. In order to further investigate the effect of the number of As, Id-Vg characteristics of NWs implanted at a smaller dose of 2 × 1014 cm−2 were calculated. The average number of active As atoms in this NW is 16, which averages 1.8 × 1020 cm−3. The average and standard deviation of the on-current in this NW are almost the same as those in the 1 × 1015 cm−2 NW. This is consistent with little or weak correlations between Id and the number of As dopants as we mentioned above. However, a few out of 100 NW devices of 2 × 1014 cm−2 have on-current which is only about one half its average. This is attributable to the large interatomic distances of discrete As atoms in these devices. These results indicate that the on-current fluctuation is caused by the fluctuation of interatomic distances of discrete As atoms, not by the fluctuation of the number of As. The off-current fluctuation can be reduced by a process in which dopants in the S/D extensions are likely to exist near the channel region. In contrast, the on-current fluctuation may be inherent in ultra-small NW transistors because interatomic distance is determined by random atomic movement.
We have theoretically investigated the effects of random discrete distribution of implanted and annealed As atoms in the S/D extensions on the device characteristics of n-type GAA Si NW transistors. KMC simulation is used for generating realistic random distribution of active As atoms in Si NWs, and the current–voltage characteristics are calculated using the NEGF method. The fluctuation of drain current is observed with the normalized standard deviation of approximately 0.2. The correlation between the drain current and the factors related to random As distribution is examined. The results indicate that the on-current fluctuation is not directly due to the fluctuation of the number of dopants in the S/D extensions. The on-current fluctuation may be caused by the randomness of As dopant positions in the S/D extensions and hence is inherent in ultra-small NW transistors.
kinetic Monte Carlo
metal-oxide semiconductor field-effect transistors
non-equilibrium Green's function
random discrete dopant
source and drain.
We acknowledge Dr. Ignacio Martin Bragado for the fruitful discussions on KMC modeling.
- Roy S, Asenov A: Where do the dopants go? Science 2005, 309: 388–390.
- Martinez A, Aldegunde M, Seoane N, Brown AR, Barker JR, Asenov A: Quantum-transport study on the impact of channel length and cross sections on variability induced by random discrete dopants in narrow gate-all-around silicon nanowire transistors. Electron Devices, IEEE Transactions 2011, 58: 2209–2217.View Article
- Wang X, Brown AR, Cheng B, Asenov A Electron Devices Meeting (IEDM), 2011 IEEE International: December 5–7 2011. In Statistical variability and reliability in nanoscale FinFETs. Washington, DC. New York: IEEE; 2011:103–106.
- Li Y, Cheng H-W, Chiu Y-Y, Yiu C-Y, Su H-W Electron Devices Meeting (IEDM), IEEE International 2011;December 5–7 2011. In A unified 3D device simulation of random dopant, interface trap and work function fluctuations on high-κ/metal gate device. Washington, DC. New York: IEEE; 2011:107–110.
- Yang B, Buddharaju K, Teo S, Singh N, Lo G, Kwong D: Vertical silicon-nanowire formation and gate-all-around MOSFET. Electron Device Letters, IEEE 2008, 29: 791–794.View Article
- Numata T, Uno S, Kamakura Y, Mori N, Nakazato K Simulation of Semiconductor Processes and Devices (SISPAD), 2011 International Conference; September 8–10 2011. In Fully analytic compact model of ballistic gate-all-around MOSFET with rectangular cross section. Osaka. New York: sIEEE; 2011:39–42.
- Singh P, Singh N, Miao J, Park W-T, Kwong D-L: Gate-all-around junctionless nanowire MOSFET with improved low-frequency noise behavior. Electron Device Letters, IEEE 2011, 32: 1752–1754.View Article
- Synopsys, Inc: Sentaurus Process User Guide, Version F-2011.09. Mountain View; 2011.
- Martin-Bragado I Doctoral thesis. In Process atomistic simulation for microelectronics. University of Valladolid; 2004.
- Help UVAS: University of Valladolid Atomistic Simulator. Spain: University of Valladolid; 2006.
- Takeda H, Mori N: Three-dimensional quantum transport simulation of ultra-small FinFETs. J Comput Electron 2005, 4: 31–34. 10.1007/s10825-005-7102-0View Article
- Mil'nikov G, Mori N, Kamakura Y, Ezaki T: Dopant-induced intrinsic bistability in a biased nanowire. Phys Rev Lett 2009, 102: 036801.1–4.
- Asenov A, Jaraiz M, Roy S, Roy G, Adamu-Lema F, Brown AR, Moroz V, Gafiteanu R Simulation of Semiconductor Processes and Devices (SISPAD), 2002 International Conference: September 4–6 2002. In Integrated atomistic process and device simulation of decananometre MOSFETs. Kobe, Japan. New York: IEEE; 2002:6.2.1–4.
- Solmi S, Nobili D: High concentration diffusivity and clustering of arsenic and phosphorus in silicon. J Appl Phys 1998, 83: 2484–2490. 10.1063/1.367008View Article
- Uematsu M: Transient enhanced diffusion and deactivation of high-dose implanted arsenic in silicon. Jpn J Appl Phys (Part 1) 2000, 39: 1006–1012. 10.1143/JJAP.39.1006View Article
- Kamakura Y, Mil'nikov G, Mori N, Taniguchi K: Impact of attractive ion in undoped channel on characteristics of nanoscale multigate field effect transistors: a three-dimensional nonequilibrium Green's function study. Jpn J Appl Phys 2010, 49: 04DC19.1–5.View Article
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.