FinFET structure design and variability analysis enabled by TCAD

FinFET variability
FinFET variability
As feature sizes get smaller, as FinFET aim to do, random variations of device properties become increasingly important.  It is generally recognized that the most important source of variability is due to random doping fluctuations (RDF). RDF is a result of the statistical nature of the position and the discreteness of charge of the dopant atoms. Whereas in past technologies the effect of the dopant atoms could be treated as a continuum of charge, FinFETs are so small that the charge distribution of the dopant atoms becomes ‘lumpy’ and variable from one transistor to the next, hence the name RDF.

With the introduction of metal gates in advanced CMOS processes, a second highly important source of variability has emerged arising from the formation of the finite-sized metal grains with different lattice orientations: random workfunction fluctuations (RWF). In this effect, each metal grain in the gate, whose crystalline orientation is random, interacts with the underlying gate dielectric and silicon in a different way, with the consequence that the channel electrons no longer see a uniform gate potential.

RDF and RWF manifest themselves as variation in the output characteristics of FinFETs and circuits, and the systematic analysis of these effects has become a priority for technology development and IP design teams alike.

One of the key challenges in simulating device variability is in describing and solving the variability in a computationally efficient way. A brute force approach, whereby each device sample is explicitly defined and its performance characteristic computed leads to heavy computational burden as hundreds of device samples must be simulated to actually sample the statistical distribution. This brute force method, also known as atomistic, has been highlighted in the academic literature as a vehicle to estimate the variability effects – however, its computational burden is impractical for industrial use.

Fortunately, a new method known as the impedance field method (IFM) reduces dramatically the simulation time without sacrificing the accuracy of the statistical variation output that device and design engineers are interested in. The key concept in IFM is to treat the randomness of the doping, metal grains and other sources as perturbations of a reference device.

To illustrate the IFM, we present its application to the static random access memory (SRAM) cell, a component so ubiquitous and critical to the operation of most integrated circuits that it warrants special consideration. The reduction of SRAM cell size is constrained by, among other factors, its electrical variability. Moreover, the transistors comprising the SRAM cell are typically packed so closely together that they influence each other’s performance – these are called proximity effects.

Owing to the importance of capturing the proximity effects, recent progress in 3-D TCAD simulation now enables the simulation of the variability of the static noise margin (SNM) of an entire SRAM cell [1]. In this approach, the 3-D TCAD representation of the SRAM cell includes the details of the process so as to capture the proximity effects among the transistors (see figure 6).

 
The initial step in the IFM method is the computation of the full 3-D TCAD solution for the nominal case representing the average of the statistical distribution. Then, the perturbations describing all important variation sources are applied and the linear response is computed. The mathematics involved in this step is based on a so-called impedance field, from which the name for the method is derived. One key advantage of the impedance field approach is that it relies on the well-established and calibrated TCAD transport models and their calibrated parameters.  Figure 7 shows the voltage transfer characteristics (VTCs) of SRAM cell inverter. From these curves the static noise margin for the cell can be extracted.


Whereas in the aforementioned atomistic method the total simulation time is proportional to the number of device samples, in IFM the only computational effort is taken up by the single 3-D TCAD solution of the reference device and the computation of the impedance fields. The additional computation effort of the random variation sources is negligible. This makes IFM a practical method for variability analysis in the industry.

References
 [1] Karim El Sayed et al, “Investigation of the Statistical Variability of Static Noize Margins of SRAM Cells Using the Statistical Impedance Field Method, IEEE Trans. Electron Devices, Vol. 59, No. 6, June 2012, pp. 1738-1744.

About the author
Victor Moroz is a Synopsys Scientist, engaged in a variety of projects on modeling 3D ICs, transistor scaling, FinFETs, stress engineering, defect engineering, solar cell design, innovative patterning, random and systematic variability, junction leakage, non-Si transistors, and atomistic effects in layer growth and doping.  Several facets of this activity are reflected in three book chapters and over 100 technical papers, invited presentations, and patents.  Has been involved in technical committees at ITRS, IEDM, DFM&Y, ECS, IRPS, and ESSDERC.

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