We have studied tunnelling processes between a multiple quantum dot (M
QD) system and a two-dimensional electron gas (2DEG) system, which are
realized on a GaAs-AlGaAs-GaAs heterostructure. Using a tranfer Hamil
tonian formalism it is shown that the tunnelling probability for trans
itions between a zero-dimensional (0D) and a two-dimensional (2D) stat
e strongly depends on the quantum dot potential profile. In the case o
f a square well potential, only the resonance of the ground state is p
ronounced significantly, whereas for a cosine-shaped quantum dot poten
tial profile a multitude of resonance structures is caused by each 0D
state. From our experimental results we concude that the potential of
the quantum dots is best described by a cosine-shaped profile. In addi
tion, the subband spacings and the extent of the wavefunctions of the
individual subbands are also determined directly.