Oh, sorry. That is what you mean.
Well, one can use valence band to create a QCL. This basically means you switch to hole injection instead of electron injection. QCLs based on valence band transitions are used, e.g. in Si/SiGe. Here the valence band offsets are larger than the conduction band offsets and also the effective mass of the electron along the tunneling direction is quite large. Accordingly one would need really thin tunnel barriers to get the tunneling process to work. The effective hole mass is lower, so in this material system hole sublevels will be used.
However, in most materials the effective mass of the electron is smaller than that of the hole, so it is more "natural" to design a QCL based on transitions of the electron.