The development of mode-locked semiconductor disk lasers received striking attention in the last 14 years and there is still a vast potential of such pulsed lasers to be explored and exploited. While for more than one decade pulsed operation was strongly linked to the employment of a saturable absorber, self-mode-locking emerged recently as an effective and novel technique in this field - giving prospect to a reduced complexity and improved cost-efficiency of such lasers. In this work, we highlight recent achievements regarding self-mode-locked semiconductor devices. It is worth to note, that although nonlinear effects in the active medium are expected to give rise to self-mode-locking, this has to be investigated with care in future experiments. However, there is a controversy whether results presented with respect to self-mode-locking truly show mode-locking. Such concerns are addressed in this work and we provide a clear evidence of mode-locking in a saturable-absorber-free device. By using a BBO crystal outside the cavity, green light originating from second-harmonic generation using the out-coupled laser beam is demonstrated. In addition, long-time-span pulse trains as well as radiofrequency-spectra measurements are presented for our sub-ps pulses at 500 MHz repetition rate which indicate the stable pulse operation of our device. Furthermore, a long-time-span autocorrelation trace is introduced which clearly shows absence of a pedestal or double pulses. Eventually, a beam-profile measurement reveals the excellent beam quality of our device with an M-square factor of less than 1.1 for both axes, showing that self-mode-locking can be achieved for the fundamental transverse mode.