A new formula for secondary emission yield

Mathematical expressions for the secondary emission yield as a function of impact voltage and direction are required by computer programs for ray tracing, which are also intended to follow secondary trajectories. It is shown that the accuracy requirements are quite severe for lower voltage impacts, up to about three times V_max (where V_max is the voltage at which the normal secondary emission ratio reaches its maximum value, δ_max), but are less stringent above this range. A new formula for the low-voltage region, which agrees with experimental data better than the formula of R.G. Lye and A.J. Dekker (1957), is proposed. For the voltage region above 4 V_max, the Lye and Dekker formula is retained, with a smooth transition centered between 3 and 4 V_max. The directional effect is modeled by adjusting the values of δ_max and V_max before applying either formula, rather than applying either Bruining´s or Muller´s correction factor afterward. This results in an automatic modeling of the known absence of any appreciable directional effect below about half V_max. Some experimental verification of the formula used to modify δ_max is presented