Next generation of extreme-resolution electron beam lithography

Electron beam lithography has been an extremely important patterning tool for microtechnology and nanotechnology research, manufacturing of high performance electronic devices, and photomask production for the semiconductor industry. For decades, there have been steady improvements in resolution, precision, reliability, and throughput in e-beam lithography tools. However, similar to progress in semiconductor manufacturing as embodied in Moore’s Law, both Moore’s Law and improvements in e-beam lithography resolution, precision, and throughput are approaching fundamental limits and are grinding to a halt.

Coincidentally, quantum computing and other nanotechnology applications that take advantage of the emerging properties of materials at the nanoscale are promising to provide us exciting new methods of computing, sensing, and communications. These new developments are challenged by a lack of precision in the highest precision manufacturing tools (e-beam lithography) currently available. Precisely because these new applications depend on the emerging properties of materials at the nanoscale, it is imperative that we improve the manufacturing precision so that there is sufficient control of these emerging properties. If we are to develop quantum computing and other complex and powerful applications, we must develop manufacturing tools that have atomic-scale precision.

While there are several technologies that can potentially be developed into atomically precise manufacturing, we will describe in this paper a significantly different kind of e-beam lithography that has dramatically better resolution and precision and a path to parallelism for increased throughput that avoids the two major pitfalls of conventional electron beam lithography (CEBL).¹ We will review the resolution limits of CEBL and elucidate the reasons for the dramatically higher resolution and precision of hydrogen depassivation lithography (HDL).

The CEBL process uses a finely focused electron beam to expose a thin layer of polymeric resist by making (negative resists) or breaking (positive resists) chemical bonds. For high-resolution patterns, a small electron beam spot size is required. Since the beginning of e-beam lithography, through improved electron sources and optics, there have been significant reductions of the spot size of e-beam lithography systems starting from spot sizes of ∼10 nm in 1981 (Ref. 2) to aberration corrected scanning transmission electron microscopes (STEM) with spot sizes of 0.1 nm.³ However, in present day e-beam lithography, the resolution is limited much more by the point spread function (PSF)⁴ than by the electron beam spot size.

The PSF describes the spatial distribution of energy around an infinitely small spot size electron beam. When the accumulated energy density is above a given threshold, the resist is exposed, i.e., chemical bonds are made or broken. When the accumulated energy density in the resist is below a given threshold, the resist will not develop at an appreciable rate, but the partial exposure is “remembered” and other exposures nearby can add to this partial exposure and potentially accumulate enough exposure dose to cross the threshold and create an unintended exposure region. This is known as the proximity effect that can seriously degrade the precision of CEBL.⁵ 

The PSF results from several other processes that spread the region of resist exposure away from the center of the focused electron beam spot. These effects include

1. forward scattering of the high energy primary electrons incident on the resist;

2. backscattering of the primary electrons after they pass through the resist and are scattered by the substrate and pass through the resist a second time;

3. the low energy (secondary) electrons in the resist that are responsible for exposing the resist by making or breaking chemical bonds receive a small amount of energy through inelastic scattering with the primary and backscattered electrons; they have a range on the order of a few nanometers;

4. Volume plasmons that are charge waves resulting from the primary high energy electrons passing through the resist will travel up to several nanometers and will also alter chemical bonds.⁴ 

These different effects are depicted graphically in Fig. 1.

Berggren⁴ calculated and measured the point spread function using a very fine spot size delivered by a 200 keV aberration corrected STEM. The full width at half maximum electron beam spot size is certainly subnanometer, and because of the point spread function, further reduction in spot size will have a minimal effect on improving achievable resolution. The 200 keV electron beam used in the Berggren reference minimizes forward scattering as does the thin resist [30 nm of hydrogen silsesquioxane (HSQ)]. The backscattered component was minimized (nearly eliminated) by the use of a 10 nm SiN substrate. On the other hand, there is little that can be done about the contributions to the point spread function from the secondary electrons and the volume plasmons.

The following graph uses data from the Berggren paper⁴ and plots the best fit of a point spread function using the conditions described above. The simulations taking the forward scattering, secondary electrons, and volume plasmons were an excellent fit to the experimental data. Contributions due to backscattering were ignored because of the extremely thin substrate.

This spatial distribution of energy is responsible for making (for negative resists) or breaking (for positive resist) chemical bonds in a polymeric resist. The density of made or broken chemical bonds follows essentially the same spatial distribution. Negative resists are typically made of small polymer molecules, and positive resists are typically made of large polymer molecules. Electron beam exposure tends to increase the size of small molecules and decrease the size of large molecules. Development of the exposed polymer resists takes advantage of the fact that smaller molecules are significantly more soluble in developers than large molecules. Negative e-beam resists are paired with developers that will dissolve the small molecules in the unexposed regions and not dissolve the larger molecules in the exposed regions. Positive resists, on the other hand, are paired with developers that will not remove the large molecule, unexposed regions and will dissolve the smaller molecule exposed regions. For successful exposure and development of a pattern, a sufficient density of altered chemical bonds must be accumulated in the resist in the desired pattern.

The key item to note in Fig. 2 is that the energy density at a radial distance of 4 nm is still almost 10% of the peak energy density in the center of the beam. This does not imply that features smaller than about 8 nm cannot be written using a beam with such a point spread function. While the exposure process does not have very high contrast at these length scales, high contrast development processes can select a dose threshold for a resist that can produce significantly smaller features. In this same paper, an isolated 5 nm dot was written in HSQ (Ref. 4), and in other works,³ isolated features as small as 1.7 nm were produced in negative tone poly methylmethacrylate with similar methods. However, for many applications, simply having a high resolution is not enough. The precision of the patterning is also important. In particular, in solid-state quantum electronic devices that take advantage of quantum confinement and electron tunneling, the confined energy states depend critically on the size of the confined regions and the tunneling rates vary exponentially with the tunnel barrier width. In Ref. 3, the record resolution reported of 1.7 nm also reported a variation of ±0.5 nm. This is a relative imprecision of ±29%, which is too large for even classical digital electronics, much less quantum devices.

The high contrast development methods applied in Refs. 3 and 4 can select an exposure threshold to divide sharply between developed and undeveloped regions of the resist, allowing for very small patterns to be realized. However, the poor exposure contrast that is inevitably produced by the point spread function in CEBL results in relatively large size variations with minor variations in the exposure level. Given the need to use high energy electron beams to achieve small spot sizes and the physics of electron scattering and energy loss in matter, there appears to be very little that can be done to improve the contrast, and therefore the relative precision, in CEBL exposing polymeric resists.

HDL is a patterning technique developed by Lyding and Avouris⁶ in the mid-1990s using a scanning tunneling microscope (STM) with a specialized control system.⁷ It is e-beam lithography in that it scans a very small spot size electron beam across a substrate and exposes a resist. However, it is significantly different in the methods of producing and scanning this small spot size electron beam. The beam energy is more than 1000× less and the beam current is roughly 100× greater than the CEBL. It also uses a very different resist: a monolayer of H bonded to an Si (100) 2 × 1 reconstructed surface, which self-develops (i.e., desorbs) during exposure by a multielectron process.⁶ HDL also has the significant advantage that the conditions used for STM imaging and for lithography are significantly different, which allows nondestructive imaging of the substrate, before and after exposure, without any H removal. This allows imaging of the surface Si lattice to be used as a global fiducial grid to guide the exposure process. We use two dimers along the dimer rows inherent in the Si (100) 2 × 1 reconstructed surface as a four-atom subnanometer pixel in our exposures,⁸ as shown in Fig. 3. Figure 4 shows the identification of the pixels in an STM image by a Fast Fourier Transform method.

While this technique has been around for more than two decades and some early work was done to understand the lithography mechanism, very little has been done in this century to explain the remarkable resolution and precision of the process. In particular, little is known of the distribution of the tunneling electrons and how that distribution is affected by the current, bias, and tip position above the H-passivated surface. A standard assumption is that since the tunneling current will fall off exponentially with distance from the tip, there will be a very small spot under the tip that will be effective in depassivating the H atoms. We have developed a simple model that demonstrates that there are other important factors.

Figure 5 depicts a model of HDL first described in Ref. 1 and further developed here. The model assumes an infinitely flat conductor as a substrate and a sphere of radius Rt as the apex of an STM tip. The tunneling current from an STM tip can be modeled with a simplified expression⁹ 

where i is the tunneling current, K is a constant, V is the tip to sample bias, Td is the tunnel gap, ɸ is the local barrier height, me is the electron mass, and ħ is Plank’s constant/2π.

Using this equation with V = 4 V (a common HDL bias), ɸ = 4 eV (∼the work function of a tungsten tip), and Td = 1 nm, the constant K can be set to 0.194, which would produce a current of 1 nA which is a typical HDL exposure current. A rough rule of thumb for STM tunneling current as a function of tip height is that changing the tip height by ±0.1 nm will decrease/increase the tunnel current by one order of magnitude. Our model predicts a decrease/increase by a factor of 7.75, lending some credibility to the model.

Referring to Fig. 5, we can predict the distribution of the current on the substrate as a function of radial distance on the surface away from the point directly under the apex of the tip by the formula

where Td is the tunneling distance from the tip to sample, d is the distance from the tip apex to the sample, Rt is the radius of the tip apex, and Lr is the radial distance on the substrate away from the point directly under the apex of the tip.

Using formula (2) to calculate Td as a function of d, Rt, and Lr allows us to calculate a normalized distribution of the current with d = 1 nm, Rt = 0.162 nm (covalent radius of a tungsten atom¹⁰), and the previous values listed for Eq. (1). Figure 6 shows a graph of the calculated tunnel current as a function of Lr.

Realizing that we rarely know the exact details of the apex of an STM tip, we checked the sensitivity of this calculation to Rt varying it from 0.162 to 0.324 nm and found that the normalized current at Lr = 0.51 nm was only increased by 28% at the 0.324 nm radius. Seeing the relatively minor variation, we chose to do all subsequent calculations with Rt = 0.162 nm.

Interpolating the data in Fig. 6 to find the full width at half maximum of the spot size yields a spot size of 0.6 nm. While the tails of the HDL spot are much shorter because they drop off exponentially as opposed to the long tails of a gaussian beam, this is a significantly larger spot size than the spot size in CEBL of 0.1 nm reported in Ref. 3. However, subnanometer features¹¹ and even single H atom removal¹² is reported and routinely achieved with HDL. One could argue for no effective point spread function due to the very low energy (∼4 eV) of the exposing electrons, but that still would not explain a resolution smaller than the full width at half maximum of the exposing beam. However, the reason for this dramatic difference compared to CEBL can, in fact, be understood by considering the self-development process.

Lyding and Avouris⁶ demonstrated that the self-development process is a multielectron process with a very strong current dependence. The theory that they suggested to account for this is a vibrational heating model where any single electron with energy less than ∼7 eV imparting energy to the Si–H bond cannot break the Si–H bond but can add vibrational energy and create a “hot” ground state. It takes multiple electron hits to move up the vibrational ladder of states in order to break the bond and have the H atom desorb (depassivate) from the surface. However, there are phonon-mediated processes that reduce the vibrational energy competing with the electron hits that raise the vibrational energy. Therefore, the depassivation efficiency depends more on the dose rate than on an accumulated dose.

Figures 7 and 8 plot the theory predicted and experimental data points from Ref. 6 and power law trend lines. The higher depassivation efficiency (H/e) with lower temperatures and higher biases support the vibrational heating theory. At lower temperatures, there is less phonon-mediated reduction of vibrational energy, allowing lower currents to win the race to depassivation. Higher biases also require a fewer number of electrons in a given time to raise the vibrational energy to achieve depassivation. If we average the power of these eight power law fits, we see a depassivation efficiency that goes with the 8.11 power of the current. When we apply this power law current dependence to the spatial distribution of the tunneling current from the STM tip, we can see the effective H depassivation spatial dependence under the tip as shown in Fig. 9.

It is instructive to compare this effective spatial exposure zone to experimental data. For a given bias, current, and tip speed (or dose which determines the tip speed), there is an effective exposure zone that will deliver the required minimum current for the minimum amount of time to depassivate H atoms. Figure 10 shows the spatial relation of an STM tip to the Si (100) 2 × 1 hydrogen passivated surface that is useful for understanding the following discussion. A routinely achievable pattern is a single dimer row, which is 0.768 nm wide¹¹ and has a large tolerance in terms of current and dose. The tip is scanned along the dimer row near the center of the dimer row and both atoms are desorbed. A typical lithography setting is 4 V bias, 1 nA current setpoint, and a tip speed of 20 nm per second. While the pitch of the dimer rows is 0.768 nm, the Si atoms are approximately 0.3 nm apart. This means that the minimum exposure zone radius is at least 0.15 nm. We also know that there is on the order of ±0.13 nm tolerance in the tip position away from the center of the dimer row, suggesting that an upper bound of the radius of that exposure zone is approximately 0.28 nm. An exposure zone of radius 0.28 nm would also explain why there is a large tolerance in being able to reliably expose a single dimer row without exposing H atoms on adjacent dimer rows. The silicon atom spacing from one dimer row to the adjacent one is approximately 0.47 nm. This means that at even the limit of tip tolerance away from the center of a dimer row, there is 0.49 nm lateral spacing to the closest H atom on the adjacent dimer row. According to our model, the depassivation efficiency at a lateral distance of 0.49 nm is reduced by more than seven orders of magnitude.

We should be clear that this simple model does not take into account the atomic-scale corrugations of the Si (100) 2 × 1 surface, the electronic states of this surface, or the change of electronic states when H atoms are depassivated. Nevertheless, it does fit reasonably well with the well-established HDL experimental data.

Because of the very different exposure and development processes, and in spite of the fact that the full width at half maximum of the electron beam spot size of HDL is on the order of six times larger than the finest focused electron beams of CEBL, HDL has a significantly better resolution and far superior precision. This is best illustrated in Fig. 10 that compares the spatial distribution of deposited energy density from the state-of-the-art CEBL with the spatial distribution of depassivation efficiency of HDL.

It is readily apparent from Fig. 11 that HDL is a much higher contrast patterning method than CEBL and will produce finer resolution patterns. However, because of the very different energy deposition and resist removal processes, this comparison is not direct. The HDL data inherently take into account the development process that is the removal of the unwanted resist, whereas the CEBL process does not. Furthermore, in CEBL, the modification of chemical bonds in the resist must exceed a density threshold of the modified chemical bonds for the developer to produce the desired pattern. Areas of the resist that have modified chemical bonds below this threshold have a partial exposure that the resist “remembers” and that contributes to the e-beam proximity effect, which impairs both resolution and precision.⁵ On the other hand, with HDL, any broken Si–H bond results in removing the resist, and any unbroken Si–H bond quickly returns to its ground state, as the vibrational excitation dissipates, i.e., the resist “forgets” and there is no partial exposure, making this a very digital process.⁸ In both HDL and CEBL, there are some electron interactions with the resist that fail to modify chemical bonds, which reduces the exposure efficiency. This is particularly pronounced in HDL where the cross section for transferring energy from the tunneling electrons to the Si–H bond is very small, contributing to the extremely low sensitivity of the H resist. Even when energy is transferred to the Si–H bond, this does not ensure that the bond will break, only that its vibrational energy will be increased, as the self-development process is a multielectron process. Only if the current is high enough, that is, if the electron interactions occur frequently enough to overcome the rate of phonon interactions that reduce the vibrational energy, will the bond break. If the current is too low, or not applied for a long enough time, then the vibrational energy will be lost by phonon processes in a very short period of time. Therefore, HDL effectively has no proximity effect in that there is no partial exposure of the resist.¹³ 

Unlike CEBL, HDL is able to image the sample and the exposed areas without any latent exposure taking place. The typical STM imaging modes operate at biases and currents, ∼2 V and 100 pA or below, that do not provide enough vibrational heating to depassivate H atoms. This allows HDL to use the Si lattice as a global fiducial grid to provide a digital address grid for guiding the tip for lithography. The depassivated patterns created by HDL provide excellent imaging contrast so that alignment marks may be written and referred to for accurate pattern placement. Any previously exposed patterns may also be imaged and used effectively as alignment marks.

CEBL typically uses alignment marks on the sample or, in the case of mask writing, on the stage, but everywhere the electron beam impinges on the sample there is at the very least a partial exposure of the resist. Also, exposed areas provide little if any exposure contrast. Even if they did provide some imaging contrast, there would be no way to examine them without changing the patterns.

The ability of HDL to image the substrate and previously written features also provides a capability that does not exist with CEBL, the ability to inspect exposed and self-developed patterns, and do some error detection and correction.⁸ It is straightforward to correct opaque defects (H atoms that were intended to be removed but were not) by simply doing more lithography. Recently, one method has been demonstrated that can correct for clear defects, which is to replace H atoms that were mistakenly removed.¹⁴ While not fully implemented at this point in time, there is the distinct possibility of essentially perfect lithography.^15–17 

The continued progress on improving resolution in conventional e-beam lithography is currently running into its fundamental limits in resolution and precision just at a time when quantum solid-state devices require significantly better resolution and precision than appears to be available from conventional electron beam lithography. Hydrogen depassivation lithography has already demonstrated far superior resolution and precision than is possible with CEBL. This paper presents a simple model that helps explain why such high resolution and precision are possible and points out some of the fundamental advantages of HDL over CEBL. On the other hand, the basic apparatus carrying out HDL, the scanning tunneling microscope, while capable of enabling valuable atomic resolution patterning for research, must be significantly improved if it is to become a reliable manufacturing tool for solid-state quantum devices.¹⁸ While there is little (essentially no) hope of HDL being used for consumer electronics, there are clear engineering paths to the reliability and throughput, through massive parallelism, to becoming an important manufacturing tool for integrated solid-state quantum electronic devices including quantum computers.

This work has been supported by research contracts from the Defense Advanced Research Projects Agency (DARPA) through the Air Force Research Laboratory (Contract No. FA8650-15-C-7542) and the Army Research Office (Contract No. W911NF-13-1-0470). This material is based on the work supported by the U.S. Department of Energy’s (DOE) Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office Award No. DE-EE0008322.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.