Study of Metal-Gate Work-Function Variation Using Voronoi Cells: Comparison of Rayleigh and Gamma Distributions

Abstract

We have demonstrated, via validation to experimental data for TiN and Ru, that the grains which appear in the metal gate stacks of nanoscale CMOS devices can be characterized via a two-parameter Gamma distribution (p-values 0.17 and 0.42 for TiN and Ru). Conversely, a previously presented fit which used Rayleigh distribution does not reproduce the experimental data (p-values 3 × 10 −14 and 0.0029 for TiN and Ru). Poisson Voronoi Diagrams (PVDs) are shown as a suitable algorithm to generate grains with Gamma distribution, via fitting of the distribution of 10000 grains. We have also compared the PVD variability against the Rayleigh model. for both TiN and TaN metal gates, and concluded that Rayleigh approach overestimates the device variability (by 11.9% for the TiN and by 7.14% for the TaN).

Internal Photoemission Metrology of Inhomogeneous Interface Barriers

“…One of the hypothesis frequently discussed in the literature relates the EWF lateral variations in polycrystalline electrodes to the WF difference between differently oriented crystallites . In order to evaluate the significance of this crystallographic effect, we compared electron IPE spectra from TiN layers deposited on top of a thermally‐grown SiO 2 film using ionized metal plasma (IMP) or cathodic arc evaporation (ARC) physical vapour deposition (PVD) methods.…”

“…For instance, interaction with hydrogen may cause laterally non‐uniform WF variations as revealed by photoemission microscopy . In this case one has to consider electron transfer between differently oriented crystallites, which gives rise to lateral variations of electrostatic potential along the electrode interface (cf. Figure 18 in Ref.…”

Impact of Cross-Sectional Shape on 10-nm Gate Length InGaAs FinFET Performance and Variability

“…In the study of the MGG, we use Poisson Voronoi Diagrams (PVD) to generate patterns of gate metal grains. This methodology, described in detail in [24], is able to capture the shape of the domains that grow from randomly located nucleation points as seen in real fabrication [25]. The metal used in the gate is TiN with two possible grain orientations having workfunction (WF) values of 4.86 and 4.66 eV and probabilities of occurrence of 60% and 40%, respectively.…”

Characteristic Fluctuations of Dynamic Power Delay Induced by Random Nanosized Titanium Nitride Grains and the Aspect Ratio Effect of Gate-All-Around Nanowire CMOS Devices and Circuits

“…We used TiN, which is a stable compound with a NaCl (sodium chloride) structure as the metal gate. According to the properties of the metal material, TiN has two different orientations: <200> and <111>, with 60% and 40% generated probabilities [19,21,22]. The related work functions (WKs) of the N-/P-type devices are shown in ( b ).…”

“…Hence, we adopt the LWKF method to explore the WKF effect. According to the properties of the metal material, TiN has two different orientations: <200> and <111>, with 60% and 40% generated probabilities [19,21,22]. In addition to WKF, the limitation of process fabrication may lead to geometrical variations in channel cross-sections and affect the operations of devices.…”