We have developed a time-of-flight (TOF) energy-analyzer for positron-annihilation induced Auger-electron spectroscopy (PAES) at an intense slow positron beamline of the ETL electron linac facility. With the use of a linac-based intense slow positron beam (10(7)-10(8) e(+)/s), the TOF analyzer enables high-speed and high energy-resolution PAES measurements. We have applied the TOF-PAES to the time-resolved analysis of surface chemical reactions and to Auger lineshape analysis which can provide informations on the chemical bonding of the top surface layer. The TOF analyzer can be used also for the energy analysis of re-emitted positrons. We carried out PAES and positron re-emission spectroscopy for 3C-SiC(100) during various surface treatments in ultra high vacuum to investigate the dependence of the positron re-emission on the surface composition.