for the specific case shown here computationally a spatial overlap between the residence probability 10 of the electrons and the residence probability 11 of the holes of 82 1 arises this constitutes a further improvement with respect to the approaches described previously which has a further positive effect on the laser characteristic data the amplifier region v illustrated has its theoretical emission at 3 3 u03bcm furthermore fig8 illustrates the residence probability 12 for holes in the valence band of the first collector quantum film 4 and the residence probability 13 for holes in the valence band of the second collector quantum film 4 when taking account of a field strength profile as a result of an externally applied voltage of approximately 75 kv cm such as is typically present it becomes clear that resonant tunneling into the valence band of the collector quantum films 4 is possible for electrons that have relaxed into the valence band of the hole quantum film 1 the energy levels are energetically adapted furthermore the depiction shows the residence probability 14 together with the energetic position for electrons in the lowest population state of the conduction band in the injector quantum film 5 in this case the conduction band edge in the injector quantum film 5 is adapted for taking up an electron from the valence band of the collector quantum film 4 consequently electrons from the valence band of the collector quantum films 4 can tunnel into the conduction band of the injector quantum film 5 via.