I. INTRODUCTION

Owing to its strong control capability over a channel, a metal-oxide-semiconductor field-effect transistor (MOSFET) with multiple gate structures is advantageous for alleviating technical problems posed by aggressive down scaling of the device dimensions, such as short-channel effects (SCEs) ^(1-5). This advantage is attributed to the solution form of the drain electrical potential from Poisson’s equation, where λ is defined as the natural length. A small λ implies that the drain electrical potential decreases rapidly such that the impact of the drain on the channel will be suppressed, which will enable the gate to control the switching of the device ^(3,6-8). Compared to other multiple gate structures, the gate-all-around (GAA) nanowire metal-oxide-semiconductor field-effect transistor (NWFET) has the smallest natural length in the same technology node; hence, it has excellent gate control capability for alleviating SCEs ⁽⁶⁾. Therefore, according to the International Technology Roadmap for Semiconductors, high-performance integrated circuits are witnessing development in the direction of GAA NWFETs ⁽⁹⁾.

A suitable dual-metal gate (DMG) structure can effectively improve the device performance. Selecting a low work function (WF) metal near the drain adjusts the channel potential and electric field distributions to suppress the drain-induced barrier, thereby improving the carrier transport efficiency in DMG devices ^(10-12). Process variations such as random discrete doping, line-edge roughness and work-function variation (WFV) have been recognized as primary causes in advanced MOSFETs. At present, the commonly used high-k/metal gate technique induces metal WFV, which has been reported as a major random source that adversely affects the device performance, which is further degraded with the scaling of the device dimensions ^(3,13-17).This is because the WF of the gate metal depends on its grain orientation, which is extremely difficult to control during fabrication by existing technologies. Although the impact of WFV on a single metal gate (SMG) structure has been reported from different aspects, the WFV-induced variability in DMG structures remains to be addressed. In addition, compared with the conventional inversion-mode (IM) transistor, junctionless (JL) devices show considerable potential for future technology nodes owing to their stronger immunity to SCEs, simpler fabrication process, lower electric field in the “on”- state, etc. ^{(11,15,16,18-20)}. Thus, we investigate and compare the effects of WFV- induced performance variability in IM and JL DMG GAA NWFETs.

II. DEVICE STRUCTURE AND SIMULATION

Fig. 1. (a) WFV and structure of JL and IM DMG GAA NWFETs, (b) Cross section along the x-axis at x = 0. M1 is the control gate and M2 is the screen gate.

Fig. 1 shows a schematic of the JL or IM DMG GAA NWFETs used in this study. The JL and IM DMG GAA NWFETs have the same size, and the device dimensions are summarized in Table 1. DMG devices have two different gate metals (M1 and M2). In this study, TiN and TaN are used as M1 and M2, respectively. The physical properties of TiN and TaN are summarized in Table 2 ^(13,14), where ‘Probability’ refers to the possibility of the occurrence of grains with different orientations. It is worth noting that TiN can be used alone as the metal gate in an SMG n-channel device (i.e., $L_{1}$/$L$ = 1), whereas TaN (i.e., $L_{1}$/$L$ = 0) cannot be used alone.

In addition, we explore the effects of the ratio of $L_{1}$ to $L$ on the performance variability caused by WFV by setting $L_{1}$/$L$ to 0, 0.2, 0.4, 0.6, 0.8, and 1 for the JL and IM DMG GAA NWFETs. All the simulations are carried out using a dedicated randomization algorithm provided in Sentaurus. In the simulation, the models selected or activated include the drift-diffusion model in combination with the density gradient for quantum corrections; the mobility model that incorporates the high-field saturation, doping dependence, and field perpendicular to the semiconductor–insulator interface; the Shockley Read Hall (SRH) model for recombination generation; and the evaluation of the SRH lifetimes according to the Scharfetter model. To observe the effects of WFV, 200 samples are randomly generated for each of the above-mentioned cases, and the average metal grain size is set to 5 nm ⁽²¹⁾.

III. RESULTS AND DISCUSSION

In Fig. 2, it can be seen that WFV causes dispersion of the drain current as the gate-source voltage ($V_{GS}$) is swept from 0 to 1 V at a drain voltage ($V_{DS}$) of 1 V. As shown by the dispersion of the transfer curve for the simulated devices with $L_{1}$/$L$ varying from 0 to 1 in steps of 0.2 in these figures, WFV can cause electrostatic integrity variability in both IM and JL DMG GAA NWFETs. As the $L_{1}$/$L$ decreases, the area occupied by the discrete curve is found to increase gradually, which implies that the WFV-induced performance variability in both IM and JL DMG GAA NWFETs becomes more severe. In particular, when $L_{1}$/$L$ is less than 0.4, the dispersion of the drain current increases sharply. Moreover, it can be seen that as $L_{1}$/$L$ decreases, the current in the “off” state increases significantly. This increase occurs because the threshold voltage ($V_{TH}$) decreases with $L_{1}$/$L$ ^(8,22).

To better analyze the experimental results, the WFV-induced variation of $V_{TH}$, transconductance ($g_{m}$), saturation current ($I_{sat}$), and subthreshold slope (SS) are determined for each case in terms of their average and standard deviation, and these parameters are plotted in Fig. 3-6. Note that $V_{TH}$ is extracted using the constant-current method, where the fixed current is set to 0.1 μA/μm. $I_{sat}$ is based on the maximum current value in the $I_{d}$-$V_{g}$ curve. $g_{m}$ is the maximum transconductance of the given $I_{d}$-$V_{g}$ curve. In addition, SS is extracted by SS = d $V_{gs}$/d(log₁₀$I_{d}$). Because TaN alone is not suitable as a metal gate, SS and $V_{TH}$ for the devices are absent when $L_{1}$/$L$ = 0. As shown in Fig. 3, the average $V_{TH}$ decreases with $L_{1}$/$L$, especially when $L_{1}$/$L$ is less than 0.4. Further, when $L_{1}$/$L$ lies between 0.6 and 1, the relative deviations of $V_{TH}$ for both JL and IM GAA NWFETs do not change significantly.

Fig. 3. Average and relative deviation of $V_{TH}$ variations caused by WFV at different values of $L_{1}$/$L$.

However, the fluctuation in the WFV-induced $V_{TH}$ increases sharply when $L_{1}$/$L$ is less than 0.4. Moreover, it can be seen from Fig. 3 that the relative deviations of $V_{TH}$ for the IM device are smaller than those for the JL device. In other words, the IM DMG GAA NWFET has stronger immunity to the $V_{TH}$ variation caused by WFV compared to its JL counterpart of the same size at different $L_{1}$/$L$. This difference in immunity can be attributed to the larger effective gate area of the IM device ⁽¹⁹⁾. In addition, it can be observed that the average $V_{TH}$ of the JL GAA NWFET is lower than that of the IM GAA NWFET. Thus, it can be concluded that the JL GAA NWFET and the IM GAA NWFET have different conduction mechanisms: an inversion layer is formed when the IM GAA NWFET is turned on ⁽²³⁾. Meanwhile, when $L_{1}$/$L$ is decreased from 1 to 0.6, the variability of $V_{TH}$ is small, but the average $V_{TH}$ of the JL and IM DMG GAA NWFETs decreases by approximately 0.15 V. Thus, it is verified that the DMG can be used to adjust $V_{TH}$.

Fig. 4. Average and relative deviation of $I_{sat}$ variations caused by WFV at different values of $L_{1}$/$L$.

Fig. 5. Average and relative deviation of SS variations caused by WFV at different values of $L_{1}$/$L$.

From Fig. 4, it can be seen that the relative deviation of $I_{sat}$ of the IM device is larger than that of the JL device. This is because, in the “on” state, the conducting current is concentrated at the channel center (called the body current effect) for a JL device and on the channel surface for an IM device. Thus, the interface scattering effects of the JL are smaller than those of the IM device ^(3,8,19). Therefore, the variability of $I_{sat}$ is more severe in the IM device.The SS characteristics of the IM and JL DMG GAA NWFETs as $L_{1}$/$L$ is varied from 0 to 1 in steps of 0.2 are shown in Fig. 5. Compared with the corresponding SMG GAA NWFET that employs TiN, the DMG GAA NWFET has a larger SS.This is mainly because SS is inversely proportional to the effective length ^(11,24), and the effective length of the IM and JL DMG GAA NWFETs is only slightly greater than $L_{1}$ in the subthreshold region ⁽¹¹⁾. By contrast, the effective length of the SMG GAA NWFET is slightly greater than $L$. As $L_{1}$ or $L_{1}$/$L$ decreases, the effective length decreases; therefore, the SS of the DMG GAA NWFET increases gradually ^(11,22). The average and relative deviation of SS are both not large when $L_{1}$/$L$ lies between 0.4 and 1; however, when $L_{1}$/$L$ is less than 0.4, both increase sharply for the IM and JL DMG GAA NWFETs.

Fig. 6. Average and relative deviation of $g_{m}$ variations caused z.

Fig. 6 shows the characteristics of $g_{m}$ for the JL and IM DMG GAA NWFETs with different $L_{1}$/$L$. Note that $g_{m}$ remains basically unchanged when $L_{1}$/$L$ is varied from 0.6 to 1. By contrast, the relative deviation of $g_{m}$ decreases when $L_{1}$/$L$ is varied 1 to 0.6 in steps of 0.2. However, the fluctuation of $g_{m}$ increases sharply as $L_{1}$/$L$ decreases below 0.4.

Fig. 7(a)-(e), shows the scatter plots of SS and $V_{TH}$, which indicate good agreement between the JL and IM DMG GAA NWFETs at different $L_{1}$/$L$. In addition, the scatter plots of $g_{m}$ and $I_{sat}$ are shown in Fig. 7(f)-(j). The correlation coefficients (ρ) of the JL and IM GAA NWFETs are calculated according to Eq. (1). When $L_{1}$/$L$ is greater than 0.2, the correlation coefficient between SS and $V_{TH}$ is small; by contrast, when $L_{1}$/$L$ is reduced to 0.2, it increases. This occurs because the effective length of the IM and JL DMG GAA NWFETs is only slightly greater than $L_{1}$ in the subthreshold region ⁽¹¹⁾. Moreover, the changes in the correlation between SS and $V_{TH}$ of the JL and IM DMG GAA NWFETs are similar to the changing trend of $L_{1}$/$L$. However, it is interesting that we found from Fig. 7(f)-(j) that the correlation between $g_{m}$ and $I_{sat}$ is not obvious with the changing trend of $L_{1}$/$L$ compared with that of SS and $V_{TH}$.

Fig. 8. Electric field (MV*cm$^{-1}$) in DMG IM and JL GAA NWFETs at $L_{1}$/$L$ = 0.6 near the source (a, c) and drain (b, d).

Fig. 8 shows the electric field distribution of the DMG IM and JL GAA NWFETs at $L_{1}$/$L$ = 0.6 near the source and drain. It can be observed that the strength of the electric field in the channel near the drain is relatively high. Thus, the electric field distribution in the channel near the drain is not uniform. Therefore, the region near the drain is expected to experience more severe fluctuation in the electrostatic potential compared to the region near the source ⁽²⁵⁾.

For $g_{m}$, $V_{TH}$, and SS, when $L_{1}$/$L$ is less than 0.4, their relative deviations increase sharply. Moreover, changes in $L_{1}$/$L$ do not have a significant effect on the $I_{sat}$ of the device. Thus, it is necessary to weight the value of $L_{1}$/$L$ for a DMG device. Some studies have considered it suitable to set $L_{1}$/$L$ = 0.5 when the effect of WFV is ignored ⁽¹¹⁾. However, we find that $L_{1}$/$L$ should be slightly greater than 0.5 when the effect of WFV is considered.

IV. CONCLUSIONS