Since the early 1970’s it has been recognized that by accelerating a focused beam of electrons at the surface of a resist, a very high resolution pattern can be produced, where the wavelength of electrons are smaller than the photons of ultra violet radiation by more than three orders of magnitude. Electrons are scanned across a resist surface. To write a pattern into the resist directly, a computer generated pattern file controls the electron beam by deflecting and turning the beam off and on according to the pixilated patterns and this directs the focused electron beam to exposure locations on the resist.
For electron beam lithography (EBL), it is most important to determine the clearing dose of the resist material. This is defined by the exposure parameters that allows the electron to penetrate the resist to achieve excellent pattern definition and this is governed by the area dose and is given by
Where I is the current of the incident beam, t is the dwell time, which is the time taken for the electrons to penetrate the resist and S is the step size. This is the parameter that governs the position that the beam moves from one position to its next position. The schematic below shows a Monte Carlo simulation representing the step size parameter to demonstrate its impact to the proximity effect. As the electron beam is rastered over the surface of the resist to position A, the electrons penetrate the resist and it can be seen that the foot print is larger at the bottom of the resist than at the top, therefore, if the electron beam is placed too close to the previous position (as indicated by position b) that was already exposed, then the new exposure will intersect (illustrated by the red line) with the last exposure and this contributes to the proximity effect. Thus has been over exposed. This will have direct effect on the definition of the pattern. However, if the electron beam is placed too far away from the previous exposure as shown by position d and e, the result of the pattern will become under exposed. Therefore, the step size must be balanced as seen by c and d. here both exposures are placed by enough distance part from each other, so that they intersect at the bottom of the resist and this is illustrated by the red line.
Over exposure may also result if the current I is too large as more Secondary Electrons (SE) can be generated as they scatter from the atoms at an angle of 80. The SEM image shows an example of resist that has been over exposed. As the resist profile has an under cut. If the current density is reduced then this may result in under exposure, where the electrons have not completely penetrated through the resist.
Of course, in reality this is dependent upon thickness. The current and step size can be reduced, if the thickness was decreased then the scattering events inside the resist would also be decreased. This reduces the proximity effect because the number of electrons (current density) must be enough to overcome the stopping power of the atoms in the resist.
These parameters values will change depending on the incident energy associated to the electrons. This is due to as an electron collides with the atoms in the resist molecule, they will scatter in arbitrary directions. As this occurs, a fraction of this energy associated to that electron will be lost. This process will be repeated more frequently from this point onward until all its energy has been lost. If the resist thickness is large and associated energy is small (e.g. 10KeV) the then more collisions will happen and the electrons will scatter in directions and generate SE which will damage the resist in a lateral direction as well as a vertical direction, thus, contributing to the proximity effect.