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We report on the observation of an approximately linear reduction in the maximum operating temperature with an increasing emission frequency for terahertz quantum-cascade lasers between 4.2 and 5.4 THz. These lasers are based on the same design type, but vary in period length and barrier height for the cascade structure. The sample emitting at the highest frequency around 5.4 THz can be operated in pulsed mode up to 56 K. We identify an additional relaxation channel for electrons by longitudinal optical phonon scattering from the upper to the lower laser level and increasing optical losses toward higher frequencies as major processes, leading to the observed temperature behavior

Frequency dependence of the maximum operating temperature for quantum-cascade lasers up to 5.4 THz