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A study of frequency stability and power scaling of single-mode GaSb-based 2.05-μm semiconductor disk laser (SDL) modules is presented. Single-mode emission and wavelength tuning over a range of 120 nm is accomplished by inserting a birefringent filter into the cavity. In order to evaluate the frequency stability, heterodyne beat-note linewidth measurements are performed for different time scales. Furthermore, a deeper insight in relevant noise mechanisms could be obtained by determining the Allan deviation and the frequency noise spectral density. For reducing the frequency noise, side-of-fringe and Pound-Drever-Hall locking are applied with the cavity length, and for the latter locking scheme also the pump diode current, controlled by the active feedback loop. That way, single-mode operation at a few kHz linewidth up to sampling times >;0.1 are achieved. Operating the SDL in a cavity configuration optimized for higher output powers, up to 1-W output power at a 100-μs sampled linewidth of 20 kHz were obtained when using active stabilization.