Practicable Method for Estimating Thermal Depths from Phonon-Broadened Photoexcitation Cross-Section Bands. III. Generalization for Charged Centres

The zero‐phonon threshold behaviour of thermally broadened absorption cross‐sections σ(hv, T) is examined for deep traps retaining a non‐zero net charge after the carrier excitation processes in consideration. The influence of a corresponding attractive or repulsive Coulomb potential on threshold properties of these absorption cross‐sections is described within the framework of conventional Sommerfeld factors. Concerning the characteristic vertex positions of transformed excitation curves ϱ(hν, T) ≡ exp (‐ hν/2kT) σ(hν, T), we attain in simple ways to analytical expressions for upper and lower bounds representing the limiting regimes of extremely strong and vanishing electron‐phonon coupling. Specializations for alternative charge‐state regimes give average vertex‐position versus thermal‐depth shifts of (½ + f) 2kT for attraction and \documentclass{article}\pagestyle{empty}\begin{document}$\(\sqrt[3]{{\pi ^2 R/2kT}} + \frac{5}{{12}} + \frac{2}{3}f) $\end{document} 2kT for repulsion (where f = 0 or 1 in cases of allowed or forbidden transition and R is the relevant Coulomb‐barrier Rydberg energy). The absorption threshold behaviours of hole excitation curves due to a series of second donor levels in silicon can be well understood under the assumption of allowed transitions affected by a repulsiue barrier whose actual strength is determined just by the light hole band (R → 15 meV). From experimental σp(hν, T) curves given by Grimmeiss and Skarstam we detect hole ionization energies Jp(T → 0) of about 553 meV for Si : S and 572 meV for Si : Se. Assessing the experimental σp(hν, 77 K) curves given by Tilly et al. we come to hole ionization energies Jp (77 K) of about 251 meV in case of Si: Ti and 356 meV in case of Si: V. All these semiempirical Jp values are found to be in reasonable agreement with other available data. Das Nullphononen‐Schwellverhalten von thermisch verbreiterten Absorptionsquerschnitten σ(hν, T) wird untersucht für tiefe Störstellen, an denen eine nichtverschwindende Störstellenladung nach dem bctrachteten Photoanregungsprozeß verbleibt. Der Einfluß eines entsprechend anziehenden oder abstoßenden Coulomb‐Potentials auf das Schwellverhalten der zugehörigen Absorptionsquerschnitte wird im Rahmen konventioneller Sommerfeld‐Faktoren beschrieben. Bezüglich der charakteristischen Vcrtexpositionen der transformierten Anregungskurven ϱ(hν, T) ≡ exp (− hν/2kT) σ(hν, T) kommen wir auf einfache Weise zu analytischen Ausdrücken für obere und untere Gre