Use of the concept “area efficiency of emission” in equations describing field emission from large-area electron sources

In the context of electron emission from surfaces, the area efficiency of emission (α) is defined as the ratio of the effective area of high-density emission (called the notional emission area) to the apparent area of an emitting sample as judged by its geometrical size (called the macroscopic area). For practical large-area field emitters, values of α are always very small in comparison with 1, perhaps often less than 10−6. This article argues that to avoid errors of interpretation, it is best to write the equations that describe cold field electron emission from large-area emitters in forms that explicitly include α. Also, definitions of areas and current densities should be stated with care. It is shown that electrostatic arguments can provide a rough upper limit for α, above which the design of an array of identical postlike emitters becomes inefficient. This upper limit (αmax) is of the order of 2/γ2, where γ is the field enhancement factor for one of these emitters when standing isolated. Practical emitters will normally have α⪡αmax. A qualitative relationship between the onset voltage and α is noted.