13 Electron Beam Lithography – II

Dr. Ajit K. Mahapatro

Learning Objectives

From this module students may get to know about the following

i. Use of Resist in Electron Beam Lithography

ii. Trajectory of Electrons in the Resist Layer

iii. Issues with Electron Beam Lithography

1. Introduction

1.1. Lithography

Lithography provides an advanced tool for designing structures at micro/nano-meter scale by pattering on surface of various materials. It allows the interaction of electromagnetic particles with the organic and inorganic molecules and subsequent chemical dissolving produces features of sizes in the order of the incident wavelengths. Photolithography utilizes photons for patterning at hundreds of nanometers and higher energetic sources of electron beam is utilized for designing structures at tens of nanometer scales. In the electron optics, the refraction index changes continuously and electron interact with each other. Electron lenses are used to converge the electron beam, magnetic lenses are used to twist the beam, and electrostatic optics has larger aberrations than magnetic. Feature sizes at tes of nanometers could be produced using electron beam lithography.

The electron beam lithography is used to create nanoscale patterns by exposing the electron beam of a scanning electron microscope (SEM) to a sensitive chemical termed as e-beam resist. Generally, a SEM system with nano pattern generator system (NPGS) hardware and software could work as e-beam lithography system. Pattern design of the required features to be written on the e-beam resist is programed using a computer aided design (CAD) based NPGS software.

1.2. Specification for E-beam Lithography

The parameters for a specific e-beam lithography system are:

• The pixel exposure time
• The dose for large areas (C/cm2)
• The dose for one pixel
• The pixel area
• The area exposed per second
• The current density in the spot (A/cm2)
• The bandwidth of the deflection and focusing systems as well as resist sensitivity limit the speed of pattern writing.

2. Computer aided desgin (CAD) software programs

Computer aided desgin (CAD) software programs utilizes schematic capture tools or polygon editors for designing and drafting patterns compatible for very-large-scale integration (VLSI) technology. These tools run almost exclusively on UNIX workstations, and generate the standard intermediate graphic database system GDSII format. Software tools in these sets include analog and digital simulators, silicon compilers, schematic capture, wire routers, design-rule checkers for complementary metal–oxide–semiconductor (CMOS) and bipolar technologies. Design Workshop runs under the Macintosh OS, UNIX, and Windows PC compatibles, with output in caltech intermediate form (CIF) or GDSII format, which include tools for rule checkers, routers, simulators, and concentrate on the core graphical editors.

Inexpensive graphical editors include AutoCAD and other general-purpose CAD tools for PC compatibles and the Macintosh. AutoCAD and other similar programs generate Drawing Interchange Format (DXF), which could be easily converted to GDSII with a separate program. AutoCAD has the disadvantage that it was not designed for lithography and can generate patterns for 3D structures that cannot be rendered by e- beam systems. The DXF format does not support datatype tags, which are used to specify individual dose values for geometrical shapes. Datatype tags are important when compensating manually or automatically for the proximity effect.

3. Function of Resists in Electron Beam Lithography

Electron beam lithography follows three important steps (as sketched in Fig. 1) of resist coating using spin coating, e-beam exposure, and developing the resist for patterning features at nanometer scale. This requires a resist that can be chemically changed under exposure to the electron beam. Various resists with different properties exists, which require different chemicals for development and lit-off process. Polymethyl methacrylate (PMMA) is one of standard positive resist with highest resolution for e-beam, and can be purchased in several molecular weight forms (50 – 950 K) that usually dissolve in chlorobenzene. Other organic and inorganic chemicals with positive and negative resists on exposure to electron beam  are tabulated in Tables 1 and 2.

3.1.1. Positive tone resists: They undergo a conversion from low to high solubility upon exposure to electrons. After development, the exposed structure is deeper than the surrounding due to chopping of polymer chains. For example, poly-methyl methacrylate (PMMA), a long chain polymer, broken  into smaller, more soluble fragments by the electron beam. Schematics for this breaking is shown in Fig. 2. Another common positive resist is ZEP 520, which also consists of a long chain polymer.

(c)

Figure 3. (a) Molecular Sketch of the polymer sub unit of poly (methyl methacrylate). (b) Scission of the polymer chain during EBL exposure. (c) Chemical reaction of resist polymer after exposure to e-beam.

3.1.2. Negative tone resists: In a negative tone resist, the electrons convert the material to low solubility upon exposure to beam of electrons. After development, the exposed structure is higher than the surrounding due to crosslinking of polymer chains. For example, hydrogen silsesquioxane (HSQ) undergoes a cross- linking reaction to combine smaller polymers into larger and form less soluble compound.

3.2. Characteristic features of resist films

i) Resolution: It defines smallest feature size that could be generated.

ii) Sensitivity: It defines the minimum electron dose required for chemical modification for the whole layer thickness (termed as clearing dose). It is dependent on the accelerating voltage and developer, and independent of resist thickness.

iii) Few examples of organic and inorganic e-beam resists are tabulated in the Tables – 1 and 2.

Table 1. Organic e-beam resists

Table 2. Inorganic e-beam resists

3.3. Resist Development

After exposure, the resist is immersed in a liquid developer to dissolve the fragments of positive tone and non-cross-linked molecules of negative tone resists. Temperature and duration are crucial parameters for resist development. The hotter and longer the development is, farther along the continuum of solubility the dissolution extends. During development, the solvent enters into the polymer matrix and starts dissolving the surrounded fragments. Gel formation takes place as the molecules starts interacting and is sketched in Fig. 4.

Figure 4. Positive resist during development. Polymer-solvent interactions can result in gel formation and swelling

The thickness of the gel layer depends on the amount of fragmentation and strength of the solvent used. Swelling of the polymer can also occur. Once completely surrounded by solvent, the fragments detach from the matrix and diffuse into the solvent. Longer fragments are less mobile and more strongly bound to the matrix, thus takes a longer time to dissolve. Exposure and development are interrelated, as short exposure with long or aggressive development can be equivalent to heavier exposure with short development.

4. Trajectories of Electrons in the Resist Layers

A good quality electron beam is categorized by a stable and high brightness electron source used to achieve high positional accuracy with limited astigmatism and small spot size. The quality of the spot is determined by the electron optics and degree of focus. The electron column under vacuum reduces gas scattering of the beam. At higher currents and lower energies, mutual electrostatic repulsion by the electrons leads to divergence of the beam. As the electrons enter the resist, they begin a series of low energy elastic collisions (Fig. 5), deflecting the electrons slightly. This forward scattering broadens the beam by an amount that increases with thickness, and this effect is more pronounced at low incident energies scattering usually limits the final resist pattern to a larger size.

Most of the electrons pass entirely through the resist and enters deeply into the substrate. Exposure produces both the forward scattering and backscattering, as shown in Fig. 5. Fraction of those electrons eventually undergoes large angle collisions to re-emerge into the resist at some distance from the point at which they left it. These backscattered electrons may cause exposure microns away at higher energies from where the beam entered. This leads to the proximity effect where electrons writing a feature at one location increase the exposure at a nearby feature, causing pattern distortion and overexposure. The density of features becomes an important factor in determining necessary exposure levels. Backscattering can be minimized by exposing on a thin membrane substrate.

Another electron trajectory consideration can be described by secondary electrons. These are low energy (upto few tens of eV) electrons produced through ionization resulting from inelastic collisions by the primary incident electrons. Secondary electrons have short range (several nanometers) due to their low energy but may ultimately limit the resolution possible with EBL. These secondary electrons are capable of breaking bonds at distances away from the original collision. They can also generate additional, lower energy electrons, resulting in an electron cascade. Hence, it is important to recognize the significant contribution of secondary electrons to the spread of the energy deposition.

Another issue is electrostatic charging, if writing onto an insulating substrate. If there exists no pathway for the absorbed electrons to dissipate, charge build up occurs and defocus the electron beam. In such cases, a thin metal or conductive polymer layer is required above or below the resist.

In general, for a molecule AB

e− + AB → AB− → A + B−

This reaction is known as electron attachment or dissociative electron attachment, and is most likely to occur after the electron has essentially slowed to a halt, as it is easier to capture at that point. At higher energies, the cross-section for electron attachment is inversely proportional to electron energy, and approaches a maximum limiting value at zero energy.

5. Proximity Effect and Resolution Limit

The proximity effect is predominantly a result of back-scattered electrons with high kinetic energy, reflected from the substrate and entered again into the resist layer, causing exposure of the resist away from the region of incident beam, as shown in Fig. 6. The backscattered electrons originated from collision with atoms in the substrate and travel in the resist at wide angles compared to electrons in the primary beam. The amount of backscattered electrons, and thus the amount of the proximity effect depends strongly on the accelerating voltage and the substrate composition. The smallest features produced by electron-beam lithography have generally been isolated features, and the electrons from exposure of an adjacent region spill over into the exposure of the defined feature and effectively enlarge its image. Hence, the desired feature resolution is harder to control. For most resists, it is difficult to go below 25 nm lines and spaces. The proximity effect manifests secondary electrons leaving from the top surface of the resist and then returning at tens of nanometers distance away.

Figure 6. Resolution limit for an electron beam line, showing the proximity effect.

Interaction of electrons with the resist leads to beam spreading through elastic and inelastic scattering in the resist, back scattering from the substrate and generation of secondary electrons. This result higher line width for very low spot sizes too. For example, 10 nm beam line could produce patterns at 100 nm precision. In practice, although, the range of secondary electron scattering is quite far, sometimes exceed 100 nm, but becoming very significant below 30 nm.

The electrons enters the resist and few of them experience small angle scattering events (forward scattering), which tend to broaden the initial beam diameter while some experience large angle scattering events (backscattering). The backscattered electrons cause the proximity effect, where the dose that a pattern feature receives is affected by electrons scattering from other features present nearby. During this process the electrons are continuously slowing down, producing a cascade of low energy electrons called secondary electrons with energies from 2 to 50 eV. They are responsible for the bulk of the actual resist exposure process. The range of secondary electrons in resist is only a few nanometers and contributes little to the proximity effect. The net result could be an effective widening of the beam diameter by roughly 10 nm. This largely accounts for the minimum practical resolution of 20 nm observed in the highest resolution electron beam systems. In basic SEM conversion systems the proximity effect caused by the backscattered electrons limits the resolution to 100 nm. This resolution level can be increased using dose correction method. The consequence of proximity effect is that small features are exposed less than the larger features, and causes significant distortion in very small features.

The simplest dose correction method uses double layer e-resist and only works for quite large features (~1µ). The other dose correction methods usually consist of calculating the cumulative exposition rate that a feature receives directly from the beam and also from other features, and then compensating for the excess dose by adapting the beam current (from feature to feature), the speed with which the beam scans over the sample, or the shape of the drawn features.

EBL is developed using scanning electron microscopes to which a pattern generator and beam blanker is added to control areas of the viewing field to be exposed. Modern EBL tools are fully dedicated patterning systems that employ high brightness electron sources for faster throughput and high resolution mechanical stages to be able to expose step-by-step large substrates under the relatively narrow field of focus of the electron beam. These direct writing systems have the advantage of extremely high resolution and the ability to create arbitrary patterns without a mask. Their disadvantage is the long times taken to write large, complex patterns. Efforts to overcome this challenge include projection EBL and the use of parallel beams.

6. Issues with E-beam Lithography

(i) Uneven distribution of resist on the substrate: This changes the working distance along the substrate and few areas are better focused than others.

(ii) Improper or insufficient focusing: The pattern may be under-dosed and may not allow features as desired.

(iii) Astimagtism: Lack of uniformity in the desired pattern(iv) Under/over-exposing the resist: Each substrate requires different dosage and different sized patterns have variations in optimal dosage.

(v) Proximity effect: Generally, the features need less dosage due to spreading of secondary electrons.

(vi) Physical defects are more varied, and can include sample charging (either negative or positive), backscattering calculation errors, dose errors, fogging (long-range reflection of backscattered electrons), outgassing, contamination, beam drift and particles.

7. Defects in Electron-Beam Lithography

(i) Shaping error: This occurs in variable-shaped beam systems when the wrong shape is projected onto the sample. These errors can originate either from the electron optical control hardware or the input data that was taped out. As might be expected, larger data files are more susceptible to data-related defects.

(ii) Physical defects are more varied, and can include sample charging (either negative or positive), backscattering calculation errors, dose errors, fogging (long-range reflection of backscattered electrons), outgassing, contamination, beam drift and particles. Since the write time for electron beam lithography can easily exceed a day, “randomly occurring” defects are more likely to occur. Here again, larger data files can present more opportunities for defects.

Summary

i) The electron beam lithography used for writing arbitrary patterns on the resist with high resolution, high density, high sensitivity and high reliability. These characteristics are interrelated to fabricate complex device structures at molecular level precision.

ii) Factors that complicate these objectives are delocalization of electrons due to forward and backscattering (proximity effects), collapse of the pattern due to swelling and capillarity forces, and fluctuations in the sizes of features (line edge roughness).

iii) Interaction of electrons with the resist leads to beam spreading through elastic and inelastic scattering in the resist, back scattering from the substrate and generation of secondary electrons. This result higher line width for very low spot sizes too. For example, 10 nm beam line could produce patterns at 100 nm precision. In practice, although, the range of secondary electron scattering is quite far, sometimes exceeding 100 nm, but becoming very significant below 30 nm.

iv) The procedure followed during e-beam lithography includes pattern designing using CAD software and then written on the e-beam resist by electron beam exposure followed by developing the exposed wafer to take off the resist from the unwanted region for the mask.

v) The resolution depends on a number of factors including resist thickness, density, writing speed, and beam current.