The dynamics of external electric field screening in light-emitting p-n heterostructures with InGaN/GaN quantum wells are studied using measurements of transient currents during a forward voltage step and small-signal high-frequency conductance at a direct forward voltage. Experimental results are discussed within the framework of a model that takes into account the increase in tunneling transparency of potential walls of a quantum well by a strong built-in field, which is created by ionized deep centers of defects. At low levels of tunneling injection, the tunneling transparency of the walls increases as the forward bias increases due to an increase in the density of ionized states at the hole tunneling transport level, which leads to an increase in the emission efficiency from the quantum well. The recharging of deep centers and the accumulation of neutral centers is manifested in the capacitive decay of transient current. As the injection level increases, the emission efficiency begins to decrease as a result of an exponential increase in the number of recombination centers and a decrease in the lifetime in the well walls, causing an inductive rise of tunnel-recombination current in the walls and the appearance of negative capacitance. Keywords: gallium nitride, quantum well, tunneling, quantum efficiency, negative capacitance.