ENZ-theory in the semiconductor industry

We see three application areas for the ENZ-theory in the semiconductor industry:

1. Optical lithography and EUV-lithography
2. Aerial image calculations and photo resist modelling
3. Optical inspection microscopes

In all three areas high-quality optical systems are being used that can be described accurately by the ENZ-theory.

Optical lithography

The first application area of the Extended Nijboer-Zernike (ENZ) theory is optical lithography. Here advanced optical projection printers with high quality lenses are used in the manufacturing process of chips. The ENZ-theory provides a method to quantify certain parameters of the optical tools such as the lens aberrations and transmission errors. In addition, parameters related to the photosensitive layer can be quantified and accounted for.

Optical lithography is about chip making. Chips are electronic components used in many consumer products, such as computers, TV’s, flash memories, reading screens, mobile phones and mobile computing applications. Figure 1 shows examples of mobile phones of the present generation with internet access. The interior of such a modern phone contains various powerful chips. We mention the high-frequency antenna signal amplifier, video and sound processors and the random-access memory with, at this moment, a size of 16 or even 32 GBytes.

Figure 1. Examples of state-of-the-art mobile phones. Impressive amounts of on-board processing power and memory storage are available.

Optical lithography is a photographic process where the circuit patterns of the chip are printed on a silicon wafer. The dimensions of the circuit features are very small; usually well below 1 micron, i.e. much smaller than 0.001 millimeter.

New products have more functionality, are smaller, have more memory or have a faster microprocessor. Optical lithography is seen as a critical step in the manufacturing process. The most advanced chips also have the smallest details and the largest number of transistors. And this number is growing. The trend in figure 2 shows the evolution of the number of transistors per chip in time.

Figure 2. Increasing number of transistors over time

Chips on a silicon wafer
Figure 3 shows an example of a silicon wafer (left) with an array of many chips. The wafer has a diameter of typically 8 inch or 150 millimeter. A chip has a size of typically 20 mm square. The smallest details within an advanced chip are of the order of 50 nanometer.

Figure 3. The left picture shows a silicon wafer with an array of dies. The enlargement in the mid picture shows a single chip. The right picture shows the smallest features, with a lateral size of about 50 nanometer

Wafer steppers and scanners
The technique of optical lithography uses so-called wafer steppers. These machines image repeatedly or “step” a certain pattern onto a photosensitive layer on a silicon wafer. After development of the photosensitive layer a pattern is formed that determines the functionality of the chip. The original pattern is on a mask and forms a “blue print” of the chip.


Figure 4. A schematic picture of a waver

Figure 4 shows a schematic view of a wafer stepper. A light source illuminates a mask which is imaged by the projection lens onto a wafer.

The light source is usually a deep-ultra violet (DUV) laser with a very short wavelength of λ=248 nanometer. Advanced steppers also use a source with an even shorter wavelength of 193 or 157 nanometer. Extreme Ultra Violet (EUV), or soft X-ray, systems use a wavelength of 13 nanometer. These systems use mirrors instead of lenses.

A key parameter of an optical system is the resolution and is related to the wavelength and numerical aperture as follows:

Resolution = k1 λ/NA,

with kl a process constant of about ½. The resolution of the projection lens needs to accommodate the smallest dimensions of the chip. In recent years, the resolution of the projection lens has been dramatically decreased by a continuous reduction of the wavelength λ and increase of the numerical aperture NA. Figure 5 shows a modern wafer scanner and a projection lens. These impressive machines have a typical weight of about 18000 kg, and have dimensions of about 2x3x5 meter. The projection lens weights about 1000 kg, and has a length of approximately 1 meter. The imaging quality of these very expensive and complicated projection lenses is very critical to allow the lowest possible k1-factor . They are measured using optical interferometry in the fabrication stage. Other measurement methods are welcome to complement the interferometric technique at the fabrication stage; the ENZ-method using through-focus intensity measurements is a good candidate (see the description of aberration retrieval using the ENZ-method). During operation of the wafer stepper in the factory environment, interferometry is a rather awkward technique. At this stage, during the full life-time of the projection lens, the ENZ-method for aberration retrieval is a very practical and accurate measurement tool for these high-quality projection lenses.

Figure 5. The left picture shows an advanced wafer scanner for chip production. The bright cylinder represents the optical projection lens. The right figure shows a detailed picture of the projection lens


Figure 6. Example of a prototype EUV optical mirror


Aerial image calculation (extended objects)

Figure 7. A partial chip circuit and its aerial image calculated using the ENZ-theory
Figure 7 shows an example of a part of a chip circuit (black lines) and an aerial image calculation using the ENZ-theory. The chip circuit or mask is a black-and-white pattern or a so-called binary mask. Inside the black lines the mask is non-transparent and blocks the light. Outside the black lines the mask is transparent. The projection lens of the stepper images this pattern and the aerial image is formed on the wafer.

For this example, the resolution of the projection lens is marginal. As a result not all features are well resolved and could cause failures to the chip. The solution would be to use a more advanced stepper with a higher numerical aperture or a shorter wavelength (the expensive solution) or to adapt the features on the mask so that the contrast in the final resist image is improved. Various methods have been proposed for resist image enhancement, among others adding small phase and absorptive structures along the main features on the mask. To evaluate the effect of these extra mask structures, an accurate and fast algorithm is needed that takes care of the image formation process of the projection lens. It is in this field that the ENZ-theory could also contribute.

Photo resist modelling

Photo resist, or simply resist, is a thin layer spun onto a wafer. After exposure with light by the stepper, a pattern is formed that is used in subsequent processing. The process is somewhat similar to taking an ordinary photograph. In the ideal case, the resist pattern would be identical to the optical image projected by the stepper. Unfortunately, this is not the case. Resist processing causes blur of the image. The physical cause is a diffusion process that takes place during the development phase of the resist. The ENZ-theory is fully capable to describe the effect of the diffusion process. The ENZ-theory can therefore be used as a simulator to predict the printability of a microcircuit (click here for an example).

Mask inspection tools

Figure 8. An example of a mask inspection tool

Also mask inspection tools use high quality objective lenses. The goal is to evaluate the quality of the mask and locate defects. Not all defects are equally important; certain defects may be so small that they will not affect the optical image. Only defects that print in the photo resist are relevant. For this reason, the mask inspection tool mimics the stepper exposure conditions and operates at the same wavelength and numerical aperture. Also, for mask inspection tools, the optical aberrations are important. Large aberrations could cause a false detection of defects. The assessment of the imaging quality of the inspection tool is crucial and the ENZ-method is a good alternative for more elaborate interferometric methods regarding quality monitoring of these objective lenses.


A wealth of information and pictures can be found on the Internet. In this page we especially used the following sites:

Figure 9. Inside the clean room, the people wear special clean room suits for dust prevention

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