  A matrix Berry phase can be generated and detected by {\it all electric
means} in II-VI or III-V n-type semiconductor quantum dots by changing the
shape of the confinement potential. This follows from general symmetry
considerations in the presence of spin-orbit coupling terms. The resulting 2 x
2 matrix Berry phase can be characterized by two numbers of geometric origin.
We investigate how these parameters depend on the shape and area of closed
adiabatic paths. We suggest how the matrix Berry phase may be detected in
transport measurements.
