# Some Issues from Advanced Lithography

General

| A somewhat better equation than the one in the backbone for the resolution limit or minimal feature size dmin of an optical system is
dmin | » | k · l NA
--- | --- | ---
|  | l is the wave length. The parameter k lumps together the effects of, e.g., photoresist response, or reticle properties.
|  | The numerical aperture NA can be defined as NA = n · sinF with n = refractive index of the medium above the photo resist, and F = largest angle of converging rays hitting the resist at a "point".
| If we want the ultimate in resolution, we have to work at all three parameters

Wavelength

| The visible range of wavelengths extends from about 780 nm (red) to 380 nm (violet). Obviously we need to go to even smaller wavelengths in the ultraviolet part of the spectrum if we want to make structures in the 100 nm region. Obvious, so where is the problem? Well, there are two major problems with this approach.
| First, we need a powerful and fairly monochromatic illumination source, and second we need materials to make an extremely good lens from.
| Let's look at the illumination source issue first:
|  | A powerful light source we need because we cannot afford to wait forever before an exposure is finished. The maximum exposure time should be below a second or so, and you simply need intense light for that.
|  | Monochromatic light we need, because we cannot possible built a supreme lens for many wavelengths (there are things like chromatic aberration and so on). Taking a small part of the spectrum out of some blackbody radiation (the spectrum emitted by something hot like a light bulb), however, leaves very little intensity.
| The solution lies in going for an intense line in the emission spectrum of some element - mercury (Hg) in this case.
|  | In the 80ties, the so-called G-line at 436 nm was used (coming from a high-pressure Hg discharge lamp). Next came the I-line at 365 nm, and then a 250 nm line.
|  | But that was already pushing the Hg lamp to its limits, and it was soon replaced by so-called DUV (for deep ultraviolet) excimer lasers.
|  | Excimer lasers are based on rather strange materials: Compounds of noble gases like KrF, or ArF. Rather unstable stuff, but emitting at 248 nm (KrF) or 193 nm (ArF). With the KrF system, dimensions down to 130 nm have been realized, but this is already pushing it quite a bit.
|  | The ArF excimer laser has been used from about 2003, so it is still in its infancy. It is expected to cover the "65 nm node", and possibly also the 45 nm node.
|  | That will be the end. After that, the age of "EUV" (extreme ultraviolet) might start, at a wavelength around 12 nm (its really rather soft X-rays). There is no way of having a lens anymore, "optical processing" must then be done with mirrors.
| If we now look at the lens issue, we first should realize that high-aperture lenses are generally difficult to make. But the overwhelming issue is to find suitable materials that have a sufficiently large index of refraction at the wavelength considered.
|  | We already looked at this issue, e.g. in the context of the frequency dependence of the dielectric constant, so we need not repeat the problems encountered here. Check the following links: General remarks to the frequency dependence of e and n Dielectrics and optics The CaF2 lens
| Illumination source and lens materials are not the only problems encountered by switching to a smaller wavelength. Of course, there are many others, too.
|  | To mention just one: The "pellicles", the thin foils protecting the mask, will turn dark in intense UV illumination. Not good, so let's take a better material. Easy fix, but do you know a better material? No? Too bad - since nobody else does either, you missed your change of getting rich quickly.

Numerical Aperture

| In air, NA obviously than has a maximum value of 1. The best lenses built so far have a NA of about 0.8; but 0.9 is already aimed for
|  | Keep in mind that what you gain in resolution by increasing NA, you loose in the depth of focus. Large NA lenses thus only make sense in the context of rather perfect planarization.
| Nevertheless, increasing NA even more helps, and there is - in principle - a simple way of doing it: Replace the air between your lens and the wafer with something that has an appreciable index of refraction, e.g. oil.
|  | "Oil immersion objective lenses" have been used for about a century in conventional optical microscopes; in this way the numerical aperture and thus resolution can be increased in a rather simple way by up to 40%.
|  | But this is far easier said than done. Just consider that the name "stepper" comes from the fact, that you step the wafer (rather rapidly) below the lens. How do you keep you oil in place? And how will the wafer respond to be covered with oil?
|  | Well, let's not use oil, let's use high-purity water (n = 1.437 at 193 nm), but that only solves some of many problems and creates some new one (your CaF2 lens, for example, will dissolve in water).
|  | Nevertheless, "liquid immersion lithography" will most likely be the next big fashion in lithography, with the potential to keep microelectronics alive well into the next decade (i.e. after 2010).

Recticles and Resists

| What is left is to make the parameter k as small as possible, i.e. to pay some attention to reticles and resist, or, more general, to resolution enhancing techniques.
|  | There is quite a potential here, "historically" parameter k has decreased steadily form about 0.8 in the 1980s to 0.4 today.
|  | While optimizing the resist is critical, it does not introduce new principles, and we will not cover it here.
|  | That leaves the reticle and the way it is illuminated. There is quite a bit that can be done, but you must pay the prize of sharp increases in complexity.
|  | The proper catchwords giving some idea to what is meant are: Off-axis illumination Optical proximity correction (OPC) Phase shift masks (PSM)
|  |  | For the latter two cases the general idea is to have a structure on the reticle that is different from what you want to have projected into the resist on the wafer. If, for example, a sharp corner is "smeared out" to a roundish image, than make the corner look different. The figure gives a rough idea what that means
|  |  | In phase shift masks you add structures that do not only manipulate the amplitude of the light transmitted through the mask, but also the phase.
|  |  | In this way you can produce constructive or destructive interference in the image plane in places where that is helpful to sharpen the image.
| Of course, all these additional features on the mask must first be computed (not easy), than made (very difficult), and finally tested (exceedingly difficult).
|  | Testing your mask is essential, that any mistake in the mask will automatically be transferred to the chip and, remember Murphy's law, more likely than not kill the chip.
| In the grand total a set of masks will quickly cost you up to 2.000.000 €. You must a sell a hell of a lot of chips (at a profit) just to recover that cost
|  | For customized chips, that are not made by the untold millions, its simply not possible to pay that prize.
|  | This drives a large-scale effort to find some better solutions. For mor details (and for the source of some of the data here), refer to "Materials today" from Feb. 2005.

With frame

6.6.2 Resist and Steppers

CaF2 Lenses

© H. Föll (Electronic Materials - Script)