Angular Distribution of Secondary Electrons from (100) Faces of Copper and Nickel

The angular distributions of secondary electrons from (001) faces of copper and nickel single crystals have been measured for secondaries in four energy ranges (0-10 ev, 10-20 ev, 20-40 ev, and 40-90 ev) for primary electron energies of 250, 500, and 800 ev. Fine structure was observed which consisted of weak peaks in the angular distribution superimposed on a background having approximately a cosine distribution. After making corrections for the refraction of secondaries at the surface of the crystal, the internal angular distribution peaks fall along principal low-index directions in the crystal as suggested in the quantum-mechanical collision theories of Wooldridge and of Dekker and van der Ziel. The positions, intensities, and widths of the peaks cannot be accounted for in terms of diffraction of the internal secondaries. The observed peaks are believed to be secondaries produced in the initial collision between the primary electron and a lattice electron of the crystal, enough of these secondaries having escaped the crystal without further collisions to make their observation possible. Details of the angular distribution are in agreement with collision theory based on a screened Coulomb interaction with a velocity-dependent screening length. The velocity dependence of the screening coefficient in the screened Coulomb interaction leads to a sharp drop in the inelastic cross section for energy transfers larger than the plasma excitation energy, and it also leads to increased probability for collisions in which the primary suffers only small deflections. The role of the band structure of the crystal in determining the features of the collision is discussed. In Cu and Ni the vacuum level of potential lies in the second Brillouin zone, so only interzone (umklapp) transitions can lead to secondary electron emission from these metals. Surface refraction is treated in terms of a velocity-dependent refractive index, and the experiment offers a means of determining the velocity dependence of the index. Experimental procedures and precautions required to observe the angular distribution fine structure are discussed.