Discrete distribution of implanted and annealed arsenic atoms in silicon nanowires and its effect on device performance
 Masashi Uematsu^{1, 3}Email author,
 Kohei M Itoh^{1, 3},
 Gennady Mil'nikov^{2, 3},
 Hideki Minari^{2, 3} and
 Nobuya Mori^{2, 3}
DOI: 10.1186/1556276X7685
© Uematsu et al.; licensee Springer. 2012
Received: 23 August 2012
Accepted: 20 November 2012
Published: 21 December 2012
Abstract
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 ntype gateallaround NW transistors. The current–voltage characteristics are calculated using the nonequilibrium 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 oncurrent fluctuation. We also found that the oncurrent fluctuation mainly originated from the randomness of interatomic distances of As atoms and hence is inherent in ultrasmall NW transistors.
Keywords
Silicon nanowires Random discrete dopant distribution Gateallaround transistors Kinetic Monte Carlo Nonequilibrium green's functionBackground
Fluctuation due to random discrete dopant (RDD) distribution is becoming a major concern for continuously scaled down metaloxide semiconductor fieldeffect transistors (MOSFETs) [1–4]. For ultrasmall 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 ntype gateallaround (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 nonequilibrium Green's function (NEGF) method. Our results demonstrate that the oncurrent fluctuation mainly originated from the randomness of the dopant location and hence is inherent in ultrasmall NW transistors.
Methods
Results and discussion
As distribution by KMC simulation
NEGF simulation
Drain current fluctuation
Summary of correlation factors of drain current
Factors  V_{g} = 0.0 V (offstate)  V_{g} = 0.5 V (onstate)  

V_{d} = 0.05 V  V_{d} = 0.5 V  V_{d} = 0.05 V  V_{d} = 0.5 V  
L _{g} ^{*}  −0.41  −0.56  −0.12  −0.11 
σ  0.00  −0.02  −0.32  −0.06 
S _{s}  −0.09  −0.11  −0.14  −0.28 
S  0.07  0.05  −0.30  −0.14 
N _{s}  0.16  0.25  0.08  −0.08 
N  0.13  0.21  0.07  −0.09 
Significant correlations between I_{d} and L_{g}^{*} are found at the offstate with V_{d} of both 0.05 and 0.5 V. Negative correlation means that I_{d} tends to decrease with increasing L_{g}^{*}. The sum of the standard deviations of interatomic distances in the S/D extensions (σ) shows a clear correlation at the onstate with V_{d} = 0.05 V. Concerning the maximum separation, a clear correlation at the onstate with V_{d} = 0.5 V and that with V_{d} = 0.05 V are found with S_{s} and S, respectively, while little correlation with S_{d} is seen at any cases. These results demonstrate that the effective gate length (L_{g}^{*}) is a main factor for the offstate, where the channel potential mainly governs the I V characteristics. We mention that the offcurrent becomes larger when active As atoms penetrate into the channel region, which is not taken into account in the present simulation. This increase in offcurrent can be explained in terms of the ioninduced barrier lowering [16], where the potential barrier in the channel is significantly lowered by attractive donor ions, which enhances the electron injection from the source. For the onstate, random As distribution in the S extension (S_{s}) is an important factor at high V_{d} due to current injection from S, and that in the S/D extensions (σ and S) is dominant at low V_{d} because the backflow current from D also contributes the current.
On the other hand, little or weak correlations between I_{d} and the number of As dopants are found. The weak positive correlations with N_{s} and N at the offstate are attributed to a tendency that a larger number of dopants lead to smaller L_{g}^{*}. In order to further investigate the effect of the number of As, I_{d}V_{g} characteristics of NWs implanted at a smaller dose of 2 × 10^{14} cm^{−2} were calculated. The average number of active As atoms in this NW is 16, which averages 1.8 × 10^{20} cm^{−3}. The average and standard deviation of the oncurrent in this NW are almost the same as those in the 1 × 10^{15} cm^{−2} NW. This is consistent with little or weak correlations between I_{d} and the number of As dopants as we mentioned above. However, a few out of 100 NW devices of 2 × 10^{14} cm^{−2} have oncurrent 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 oncurrent fluctuation is caused by the fluctuation of interatomic distances of discrete As atoms, not by the fluctuation of the number of As. The offcurrent 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 oncurrent fluctuation may be inherent in ultrasmall NW transistors because interatomic distance is determined by random atomic movement.
Conclusions
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 ntype 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 oncurrent fluctuation is not directly due to the fluctuation of the number of dopants in the S/D extensions. The oncurrent fluctuation may be caused by the randomness of As dopant positions in the S/D extensions and hence is inherent in ultrasmall NW transistors.
Abbreviations
 GAA:

gateallaround
 KMC:

kinetic Monte Carlo
 MOSFET:

metaloxide semiconductor fieldeffect transistors
 NEFG:

nonequilibrium Green's function
 NW:

nanowire
 RDD:

random discrete dopant
 S/D:

source and drain.
Declarations
Acknowledgments
We acknowledge Dr. Ignacio Martin Bragado for the fruitful discussions on KMC modeling.
Authors’ Affiliations
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