Discrete distribution of implanted and annealed arsenic atoms in silicon nanowires and its effect on device performance

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 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.

Figure 1

Discrete As distribution in a Si NW. Cross-sectional view (left) and entire view (right). Red dots show active As atoms in Si. Blue dots, As precipitates; light blue dots, As-V clusters; orange dots, As at the oxide/Si interface; and yellow dots, As in the oxide.

Figure 2

Schematic diagram of the n-type GAA Si NW MOSFET. Discrete distributions of the active As atoms are introduced into the S/D extensions. To mimic metal electrodes, the S/D regions are heavily doped with N_d = 5 × 10²⁰ cm⁻³ (continuously doping). The channel region is intrinsic. We simulated 100 samples using 200 different random seeds (each sample needs two random seeds for S/D extensions).

Figure 3

Histogram of the number of active As atoms in the Si NWs. Si NWs (3 nm wide, 3 nm high, and 10 nm long) with 1-nm-thick oxide are implanted with As (0.5 keV, 1 × 10¹⁵ cm⁻²) and annealed at 1,000°C with a hold time of 0 s. Two hundred different random seeds were calculated.

Figure 4

I_d-V_gcharacteristics of GAA Si NW transistors atV_d = 0.5 V. Gray lines show the I_d-V_g of 100 samples with different discrete As distributions. Open circles represent their average value 〈I_d〉. The continuously doping case with N_d = 3 × 10²⁰ cm⁻³ in the S/D extensions is shown by solid circles for comparison.

Figure 5

Carrier density profiles and location of active As atoms in NW devices. Equidensity surfaces (blue and green surfaces) and dopant positions (yellow dots) for (a) continuously doped, (b) high-current (red dashed line in Figure 4), (c) medium-current (green dashed line in Figure 4), and (d) low-current (blue dashed line in Figure 4) devices. V_d = V_g = 0.5 V.

Figure 6

Average and standard deviation of drain current in NW devices. Average current 〈I_d〉 and standard deviation σI_d vs. V_g. I₀ is the drain current of the continuously doped device.

Figure 7

One-dimensional model to analyze drain current fluctuation. Blue dots represent active As atoms. L_g^*, effective gate length; σ = σ_s + σ_d, sum of the standard deviations of interatomic distances in the S/D extensions; S_s, the maximum separation between neighboring impurities in the S extension; S_d, that in the D extension; S, that in the S/D extensions. s_i and d_i are interatomic distances in the S/D extensions. The effects of the number of As dopants in the S extension (N_s), in the D extension (N_d), and in the S/D extensions (N) are also examined.

Figure 8

Correlation coefficients between drain current and factors related to random As distributions. Blue and red circles represent correlation coefficients at V_d = 0.05 and 0.5 V, respectively. The coefficient of 0 means no correlation, and those of ±1, the strongest correlation.