Tunnel diodes constitute an essential part of multi-junction concentrator photovoltaics. These tunnel junctions exhibit a transition from low-resistance tunneling to high-resistance thermal diffusion, commonly at current densities of the order of 102-103 mA/mm2. Experimental evidence of a fundamentally new effect is reported and confirmed in distinct cell architectures: the dependence of the threshold current density on the extent of localized irradiation. It is also shown that photovoltaic cells with a non-uniform metal grid can possess an additional spatial dependence to the threshold current density. These new phenomena should be observable in all solar cell tunnel diodes subjected to inhomogeneous illumination, and are posited to stem from the lateral spreading of excess majority carriers (similar to current spreading in LEDs). The implications for concentrator solar cells are also addressed.