Abstract
A model allowing theoretical prediction of the maximum possible efficiency for any cathode‐ray or x‐ray phosphor is proposed, based on an earlier statistical analysis of e‐h pair generation by van Roosbroeck. The model is independent of the detailed band structure of a particular solid, and predicts the limiting yield of e‐h pairs, Y, in terms of an energy loss ratio for energetic particles 
. The novelty of the model lies in the emphasis placed on competitive phonon losses during the carrier avalanching process, and it is probably successful because of the dominant role played by carriers with energies a few times greater than threshold where electrons and holes may be expected to behave similarly. A quantitative estimate of the average energy per e‐h pair in a particular phosphor can be made by reference to an index of efficiency
, which is proportional to van Roosbroeck's parameter 
but which is defined in terms of accessible physical constants of the phosphor host lattice: ∈∞, 
,
, and 
. The predicted efficiencies 
are in good agreement with measured values for widely different phosphor types, suggesting that the model is quite generally applicable and may be used in a predictive fashion in the search for new and efficient phosphor systems. Finally, the relationships between the present theory and previous approaches involving plasmon excitation are discussed.