Electron beam lithography (EBL) is a technique for creating extremely fine patterns (sub micron patterns, 0.1m m and below) for integrated circuits. This is possible due to the very small spot size of the electrons whereas the resolution in optical lithography is limited by the wavelength of light used for exposure. The electron beam has wavelength so small that diffraction no longer defines the lithographic resolution.

EBL finds applications in the following areas:

1. E-Beam Lithography Systems:

Figure 1:  Electron Beam Writing Strategies

Direct write EBL systems are the most common EBL systems. Most direct write systems use a small electron beam spot that is moved with respect to the wafer to expose the wafer one pixel at a time. Direct write systems can be classified as raster scan or vector scan, with either fixed or variable beam geometry.

Figure 2:  A comparison of scanning methodolgies; raster scan (left) and vector scan (right)

Figure 3 :  Schematic of an electron-beam exposure system

Several versions of projection and proximity EBL systems have also been developed. The short penetration length of electrons precludes the use of a solid substrate like quartz for the mask, however. A very thin membrane mask can be used, or else a stencil mask with cutouts through which beam can pass is needed. These mask difficulties are sufficient to make projection and proximity e-beam an unattractive technology for IC manufacturing.

As can be seen from the picture above all electron beam exposure systems have four main subsystems: (1) electron source (gun), (2) electron optical column (the beam- forming system), (3) mechanical stage, and (4) the computer used to control the various machine subsystems and transfer pattern information to the beam deflection coils.

2. E-Beam Resists:

Electron beam resists are the recording and transfer media for e-beam lithography. The usual resists are polymers dissolve in a liquid solvent. After baking out the casting solvent, electron exposure modifies the resist. As in optical lithography, there are two types of e-beam resists: positive tone and negative tone, with the usual behavior i.e., positive resists develop away at exposed regions whereas in the case of negative resist the developed region remains behind after development.

Positive e-beam resists undergo main-chain scission when exposed to e-beam as shown below for PMMA.

Figure 4:  Mechanism of radiation-induced chain scission in PMMA

On the other hand negative e-beam resists function on the basis of radiation-initiated cross-linking reactions that result in the formation of interchain linkages, which generate a cross-linked, three-dimensional network, which is insoluble. The cross linking mechanism for COP is shown below.

Figure 5:  COP, Bell Laboratories negative e-beam resist

Some of the positive e-beam resists are:  PMMA (Poly methyl methacrylate), EBR-9 (another acrylate based resist), PBS (Poly butene-1-sulphone), ZEP (a copolymer of a -chloromethacrylate and a -methylstyrene).  

And some of the negative tone e-beam resists are :  COP ( an epoxy copolymer of glycidyl methacrylate and ethyl acrylate) and Shipley SAL (has 3 components, a base polymer, an acid generator, and a crosslinking agent).

Figure 6:

3. Electron Solid interactions:

As the electrons penetrate into the resist material some of them experience small angle forward scattering and many of them experience large angle scattering events leading to backscattering. This causes additional exposure in the resist leading to what is called the electron beam proximity effect.

As the primary electrons slow down, much of their energy is dissipated in the form of secondary electrons with energies from 2 to 50 eV. These are responsible for the bulk of actual resist exposure process. Since their range in resist is only a few nanometers, they contribute little to the proximity effect.

A small fraction of secondary electrons may have significant energies, on the order of 1 keV. These so-called fast electrons can contribute to the proximity effect in the range of few tenths of a micron.

Figure 7:  Electron scattering in electron resist exposure

4. Modeling:

Electron trajectory:

The fundamental parameter necessary to determine developed resist profile is the absorbed energy density and its dependence on spatial position within the resist film.  The Monte Carlo method attempts to simulate the trajectories of the incident electrons within the resist substrate. The procedure involves following an electron through a succession of distinct scattering events during which it undergoes angular deflection and energy loss. The angular distribution of scattered electrons is dependent on the assumed potential V(r). Most calculations employ the Thomas-Fermi potential, which assumes that an incoming electron sees the atomic charge of the nucleus screened by the electron cloud of the atom.

Where a₀ = Bohr radius (0.53 A° ), and Z is the atomic number of the element.

From this atomic potential, the differential scattering cross-section per unit solid angle is given by the Rutherford expression,

Where m is the mass of electron, v its velocity, Z_i the atomic number of the i^th species, a _i is the atomic screening parameter.

Where E is the energy of the incident electron.

Between elastic scattering events the electrons are assumed to travel in straight lines (of length equal to the mean free path) and undergo energy loss. The energy loss is modelled via the CSDA (continuous slowing down approximation) according to the Bethe energy loss formula,

where n_e is the density of atomic electrons, I is the mean excitation energy, a is constant equal to 1.166.

Within the step length the electron is assumed to have a constant energy E_o. The electron energy at point 1 is then calculated by decrementing the energy with respect to its value at point “0” via the Bethe expression for energy loss per unit distance. (The sequence is repeated continuously until the energy has degraded to some arbitrary value close to the mean ionization energy).

By carrying out many such simulations, trajectory patterns can be generated, and an absorbed energy matrix E(r,z) can be calculated.

Figure 8:  Geometry for Monte Carlo in thick targets 

Figure 9: Monte Carlo simulated trajectories of 100 point-source in a target of 1 um thick resist on silicon substrate at 10 (a), 25 (b), and 50 (c) keV incident energy.

5. Development Modeling:

The developed resist profile depends not only on the absorbed energy density, but also on the development process itself. An ability to predict resist profiles as a function of the exposure parameters therefore requires development models integrated with the exposure models. There is usually a change in molecular weight for a given e-beam exposure level given by (for a positive resist),

Where r is the resist density, A₀ is the Avogadro’s number, G(s) is the number of scissions per 100eV of absorbed energy, M_n⁰ is the original number average molecular weight, and M_f is the final number average molecular weight (less than M_n⁰).

Knowing the change in molecular weight for a given exposure level and the dependence of solubility on fragmented molecular weight, the 2-D E(r,z) can be transformed into the solubility rate matrix, and the profile can be determined as a function of development time. For PMMA resists Greeneich has examined these effects using an empirical equation.

where R_{0, b} , and a are empirically determined constants that depend on the developer used.

Figure 10: Actual PMMA Resist Profiles at an incident charge density of 10-4 (a), 8e-5 (b), and 5e-5 (c) C/cm2.

6. References:

1.  Rai-Choudhury, P.  "Handbook of Microlithography, and Microfabrication, " Spie Optical Engineering Press, 1994.

2.  Thompson, Larry; Wilson, Grant; Bowden, Murrae; "Introduction to Microlithography," Second Edition, 1994.

3.  Campbell, Stephen. "The Science and engineering of Microelectronics Fabrication," Oxford University Press, 1996.