Continuous-wave operation of semiconductor terahertz quantum cascade lasers at similar to 3.1 THz based on a bound-to-continuum transition design is described. The material physics and device performance is analyzed in detail. With good injection efficiency in the upper single isolated radiative state and efficient extraction from the lower radiative state, the maximum operating temperature is in excess of 90 K in pulsed and 70 K in continuous-wave mode. The peak power of 112.5 mW was obtained at 10 K in pulsed mode, indicating similar to 36 photons per injected electron for 120 periods of active region. In continuous-wave operation, collected power of 62 mW and 22 photons per electron was also achieved at 10 K. (C) 2013 Elsevier Ltd. All rights reserved.