Inverse photoemission

• P. D. Johnson
Part of the Condensed Matter book series (volume 45B)

Abstract

In this chapter the theory behind the inverse photoemission process is discussed in detail.

Inverse photoemission is a related technique that developed to allow studies of the unoccupied states in a system. It is usually considered as the time reversal of the photoemission process. Thus rather than an incident photon exciting an electron from a bound state, an incident electron is “captured” by a bound state resulting in the emission of a photon. Johnson and Davenport considered the differential cross section / for such an event. The density of final states for the emitted photons results in a differential cross section given by [85J1]
$$\frac{d\sigma}{d\Omega}=\frac{\alpha }{2\pi}\frac{\omega }{mc^2}\frac{1}{k}{\left|\left\langle b\left|A.p\right|k\right\rangle \right|}^2$$
(91.1)
where the incident electron has momentum ħk and the outgoing photon energy ħω. Within the same framework with consideration of the density of final states for the outgoing electrons, Eq. 91.3 describing the photoemission process would be given by
$$\frac{d\sigma}{d\Omega}=\frac{\alpha }{2\pi}\frac{k}{m}\frac{1}{\omega }{\left|\left\langle k\left|A.p\right|b\right\rangle \right|}^2$$
(91.2)
Thus for the same time-reversed transition, the ratio of the two cross sections will be given by
$$R=\frac{{\left| d\sigma /d\Omega \right|}_{inv}}{{\left| d\sigma /d\Omega \right|}_{pes}}=\frac{\omega^2}{c^2{k}^2}=\frac{q^2}{k^2}={\left|\frac{\lambda_{elec}}{\lambda_{phot}}\right|}^2$$
(91.3)

with q the wave vector of the photon. Thus in the UV range, with R proportional to the square of the wavelength of the incident “particle,” the cross section for inverse photoemission is lower than that of photoemission by a factor of approximately 105. This fact makes the experiment considerably more difficult, and as yet the ultrahigh resolutions available in photoemission have not been achieved in inverse photoemission.

References

1. [85J1]
Johnson, P.D., Davenport, J.W.: Phys. Rev. B. 31, 7521 (1985)