Question

In electron beam lithography patterns are exposed with electrons. The small wavelength of electrons helps to achieve small feature sizes (in order of nm). Assume an electron gun of energy 100 keV. What is the wavelength of these electrons?
Assume the mass of electron =9.109×10−31 kg and Planck's constant, h=6.626×10−34 J.s. Neglect the relativistic effect.

Answer 1

"Here, the kinetic energy KE for the electrons is 100 keV and mass of electron is 9.109 x10−31 Kg.

Since KE = ½ mv2, the velocity can be calculated from this formula.

For these electrons, v = (2KEm)0.5 = 2 x 100 x 9.109 x10−31 = 18187 ms-1.

As Planck’s constant h is given as 6.626×10−34 Js, the wavelength of electron = h/p, where p is the momentum of the electrons.

Momentum = mv = 9.109 x10−31 Kg x 18187 ms-1.

Hence, wavelength of the electron = 6.626×10−34/ (9.109 x10−31 x 18187)

"