Variability is the enemy of semiconductor manufacturing. Structural variations within a chip, between wafers, and across wafers can degrade chip performance, yield, and reliability. Historically, these variabilities were "global," with systematic process errors caused by factors such as wafer flatness or hot plate uniformity occurring on millimeter-scale length scales. Low yield near the wafer edge was one common consequence.

However, as feature sizes of semiconductor devices continue to shrink at the latest nodes, a new type of variability—stochasticity—has emerged and is negatively impacting device yield, reliability, and performance. Stochasticity is the random variation inherent in the patterning process that occurs when dimensions approach the atomic level. Unlike global variability, stochasticity affects the "local" level, where patterned features that are close to each other can differ significantly in size, which can affect yield and cause fluctuations in device performance.

In previous generations of devices, stochastic variability did not significantly impact device yield or performance. But in the latest generation nodes, this local random variation can now account for more than 50% of certain types of manufacturing errors that directly impact the device. Today, uncontrolled random variation can cost manufacturers hundreds of millions of dollars per fab each year in yield losses and production ramp delays. These variations, once negligible, now determine the feasibility of advanced nodes at 2nm and beyond.

Randomness as a percentage of the fab EPE error budget:

Randomness is a growing yield issue that can account for more than 50% of the total pattern error budget in EUV (extreme ultraviolet lithography) technology.

Therefore, it is now critical for device manufacturers to optimize and control randomness, and this requires a different set of tools that focus on the probabilistic nature of randomness.

Types of random effects

In semiconductor manufacturing, there are four types of random effects:

Line edge roughness or line width roughness (LER/LWR): The edges of transistors or other critical features are not smooth. This affects gate leakage current, wire resistance, chip power consumption and reliability.

Figure 1 Line edge roughness causes local critical dimension variation

Local critical dimension uniformity (LCDU): The critical dimensions of adjacent devices are different. This affects yield and chip speed.

Local edge position error (EPE): The edges are randomly positioned, which may cause shorts or opens. This affects yield and reliability.

Figure 2 Edge position error

Random defects: Chip features have wire bridges or breaks, contact holes are missing or merged, etc. These defects affect yield and reliability.

Figure 3 Contact hole missing

Why are random effects becoming increasingly serious?

To explain why randomness is becoming more severe in the latest process nodes, let's take the photolithography process as an example. In semiconductor lithography, scanners use light to expose patterns in photoresist and then etch away unwanted portions to create features of a specific size.

In older generation nodes where device features are relatively large, it can be assumed that all adjacent features are the same size. This is because the random variability (and local variability) of the process is relatively small. For example, the random variability of 100nm feature size is typically only 2% to 3% of the feature size.

For larger feature sizes, this small effect allows device manufacturers to largely ignore random variability in the manufacturing process and still successfully increase their manufacturing capacity to high yields. To achieve this success, device manufacturers have relied on predictive process models, measurement tools that output average measurements, and design rules that treat the lithography, resist, and etch processes as consistent entities. This approach is called deterministic modeling, and the semiconductor industry has successfully used this approach for decades.

However, the industry has now changed.

The situation becomes particularly complicated when line edge roughness (LER) reaches 2nm.

2 Characteristics of nanowire edge roughness

Photon shot noise and the intensification of random effects

Today, many device manufacturers use EUV scanners to create the smallest features in their devices. All else being equal, an EUV scanner exposes the same volume of photoresist with one-fourteenth the number of photons as a 193nm scanner. With EUV processes, two adjacent features may be exposed with significantly different numbers of photons, a phenomenon known as photon shot noise. This results in different sizes of adjacent features, an effect measured by local critical dimension uniformity (LCDU).

To compensate for this effect, we can increase the dose of the EUV tool, which will increase the number of photons per unit area and reduce random variability. But increasing the scanner dose directly reduces the throughput of the EUV scanner, which increases the cost. Therefore, engineers need to weigh the pros and cons and determine the right compromise.

As device feature sizes shrink to the molecular and atomic levels, the relative size of random variability is now 10% or more of the feature size and accounts for more than half of the total variability in the patterning process. And randomness is not just a phenomenon unique to EUV processes - it is also a significant contributor to the total error rate when multiple patterning techniques are deployed using 193nm immersion scanners.

In the latest generation nodes, adjacent printed features can no longer be assumed to be the same size – randomness now needs to be precisely optimized and controlled.

The figure below compares the number of photons absorbed in a given volume for 193nm light (left) and 13.5nm (EUV) light (right) at constant exposure dose and resist absorption coefficient.

Photon shot noise

The need for different measurement and analysis methods

Random variability is now a critical source of error in many manufacturing steps including mask printing, lithography, etching, and deposition. Optimizing and controlling these processes first requires the ability to accurately and precisely measure random effects. After all, what you can't measure you can't control.

Importantly, accurately measuring randomness is extremely difficult because the measurement tool itself (such as a CD-SEM) can introduce measurement errors that are as large as the effect being measured. Therefore, the industry needs specialized measurement and analysis techniques that can remove SEM noise to accurately report random errors. However, traditional measurement methods and tools are less than ideal at measuring and removing this measurement noise.

In addition, to properly analyze randomness, a probabilistic approach must be used, which is very different from the deterministic approach that the industry has historically used. Using just average measurements does not allow for accurate judgments about the impact of randomness.

For example, probabilistic modeling requires accurate error bars to determine the probability of an event occurring. To do this, all randomness measurements need to include accurate error bars that describe the measurement uncertainty. However, determining accurate error bars for randomness requires tools that are different from the statistical tools commonly used in the industry.

When engineers and automated control systems have access to accurate randomness measurement data, they can make informed decisions for each layer during the development phase, reduce variability faster during the ramp phase, and control the process in production. In addition, random errors directly affect the optimization of chip design and the application of OPC (Optical Proximity Correction). Therefore, there is now a need to use randomness-aware OPC modeling in addition to randomness-aware process control.

Traditional analysis tools in the semiconductor industry have been focused on deterministic modeling, but in order to accurately optimize and control randomness, the industry needs a different set of measurement and analysis tools.

Summarize

The latest generation nodes in semiconductor manufacturing have significant random variability, called stochasticity, that needs to be optimized and controlled. This problem becomes more severe with each new generation of technology.

Stochasticity forces fabs to make a trade-off between yield and productivity. For example, by increasing the dose of EUV lithography scanners, fabs can reduce the impact of stochasticity and improve yield. But this comes with a huge cost: a significant reduction in process tool throughput. When fabs accurately control stochasticity, they can simultaneously improve process tool productivity and increase yield.

The first step to controlling stochasticity is to use accurate and precise measurement techniques. You can't control what you can't measure.

Reference link https://www.fractilia.com/intro-to-stochastics

Source: Content from fractilia

View more at EASELINK