Theoretical approach of the photofield emission of a degenerated semiconductor. Case of tipped, weakly P-doped, silicon photocathodes

We study theoretically the field and photofield emission in a degenerated semiconductor: a tipped silicon is weakly doped with boron (ϱ = 3000 Ω cm) and the field near the tip is greater than 1 GV/m. Due to this important field, the conduction band bends down to the Fermi level near the surface. The degenerated electrons are confined in a well near the surface barrier. We develop a new theoretical approach using few discrete energy levels in the well. We calculate field emission current and compare with experimental results. The photoelectric transition probability is calculated for different values of the wavelength of the incident laser. A growth of the photofield current with the increase of the wavelength is shown theoretically, taking into account the optical properties of the semiconductor. Experimentally, we observe such a behaviour with continuous lasers [1–3]. With a pulsed picosecond laser (35 ps from a Nd-Yag) we observed with harmonic 4 (4.68 eV) a pure photoemission charge of 70 pC and a photofield charge with harmonic 2(2.34 eV) as high as 700 pC [4]. We hope to obtain more charges with harmonic 1 (1.17 eV). This original development should enable us to predict the behaviour of our tipped photocathodes in actual photoinjectors. An experiment with CANDELA is in progress.