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This is what book that I studied from says:
Since moving charges trough valent zones is harder than moving of free electrons, holes mobility is lower...
This is my translation from my language, so sory if you dont understand it...
I think this, and much more can be found here:
Milman J., Gabriel A.: Microelectronic, McGraw Hill, New Yourk, 1987, chapter 1.3
the answer to this question is not that simple. Mobility of an electron or hole depends on what is known as the conductivity effective mass ,of the electron or hole. The effective mass is actually a tensor(meaning unlike vector, it has many directions or components). It is given indetails in good text books of quantum mechanics/solid state devices... this is one good link i could find : https://ece.colorado.edu/~bart/book/book/chapter2/ch2_3.htm