Large (0.8 V order) discrepancies of threshold voltage Vth between the predicted Vth values by the Lindhard–Scharff–Schio/tt Gaussian approximate calculation and the Vth of the tungsten nitride (WNx) self-alignment (SA) gate GaAs metal-semiconductor field-effect transistors (MESFETs) were observed. These discrepancies were confirmed by the comparison of the Vth of the WNx-SA-gate MESFETs and the Vth of the (N+: high carrier concentration layers self-aligned of source-drain electrodes)-less conventional MESFETs on 2-in.-diam semi-insulating substrates from liquid-encapsulated-Czochralski-technique-grown 〈100〉 boules. The discrepancy was also analyzed by the capacitance-voltage (C-V) measurement of large-diameter (440 μm) Schottky diodes which were built into the MESFET arrays. It was found that for obtained SA-process carrier depth profiles (Si, 150 keV, 3×1012 cm−2) the carrier concentration at a depth of 0.25 μm decreased from 5.3×1016 to 2.0×1016 cm−3, but, on the other hand, the peak carrier concentration slightly decreased from 12.8×1016 to 12.4×1016 cm−3. By the calculation for Vth on the basis of the actual C-V carrier depth profiles, it was found that the carrier concentration decrease was comparable to the Vth variation (0.8 V). Furthermore, the Vth variation of the shallow channel implantation (50 keV) was comparable to that of the deep channel implantation (150 keV). As a result of the experiment and analysis, it was found that the large Vth variation for the SA N+ process was caused by reoccupation (Ga sites to As sites) of implanted Si atoms in the channel active-layer crystal by tensile stress formed by the thermal-expansion coefficient difference between chemical-vapor deposition (CVD) phosphosilicate glass (or CVD SiO2) film and (100) GaAs substrate crystal. The Si atom reoccupation quantity was, for the first time, explained by the Si atom compensation ratio equation as a function of the bond length (Si-As and Si-Ga) variation, an equation which was again derived based on Otsuki’s work on the Si atom Gibbs free energy in GaAs crystal, using the data of thermal-expansion coefficients for SiO2, GaAs, and WNx in the report of Katz and Dautremont-Smith [J. Appl. Phys. 67, 6237 (1990)] and in the report of Lahav, Grim, and Blech [J. Appl. Phys. 67, 734 (1990)]. Moreover, the analysis suggests that local stress or local distortion, which is introduced by the implanted Si atom itself into the GaAs crystal, performs an important role for the Si atom electrical activation efficiency.
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