We give a complete condition for any $n$ elements of ${\rm PSL}(2, {\mathbb R})$ to generate a Fuchsian group which is a Schottky group on that set of generators, and apply it to a question of Bowditch on representations of surface groups into ${\rm PSL}(2, {\mathbb R})$.

2000 Mathematical Subject Classification: 20H10, 32G15.

Reactive Ion Etching (RIE) and Photo-Assisted RIE (PA-RIE) induced damage in GaN using simple Schottky structures and a BCl3/Cl2/N2gas mixture have been investigated. Schottky diode I-V characteristics following different RF powers and exposure times show significant changes caused by damage. This damage results in a reduction of the reverse breakdown voltage VB in n-type GaN and an increase in VB for p-type GaN. Our preliminary data on the PA-RIE process points to much reduced damage levels compared to conventional RIE. This result may be due to a change in surface chemistry or to a photo-enhanced diffusion of defects into the GaN layer, leaving a cleaner near-surface region.

Schottky barrier photovoltaic detectors based on Si-doped AlxGa1-xN (0 ≤ × ≤ 0.22) have been fabricated and characterized. Samples were grown on basal plane sapphire by LP-MOVPE. Schottky contacts were made with Au. Responsivities are independent of the diode size and of the incident power in the range measured (10mW/m2 to 2KW/m2). The spectral response shows an abrupt cutoff that shifts linearly to higher energy with increasing Al content. A visible rejection of 3 to 4 orders of magnitude is observed in AlxGa1-xN Schottky photodiodes. Device time response is RC-limited, and a minimum decay time as short as 15ns have been estimated in unbiased Al0.22Ga0.28N diodes. This time response can be further reduced by reverse biasing.