The tunnel junction structure comprises a p-type tunnel junction layer of a first semiconductor material, an n-type tunnel junction layer of a second semiconductor material and a tunnel junction between the tunnel junction layers. At least one of the semiconductor materials includes gallium (Ga), arsenic (As) and either nitrogen (N) or antimony (Sb). The probability of tunneling is significantly increased, and the voltage drop across the tunnel junction is consequently decreased, by forming the tunnel junction structure of materials having a reduced difference between the valence band energy of the material of the p-type tunnel junction layer and the conduction band energy of the n-type tunnel junction layer.