Avalanche Breakdown occurs due to avalanche multiplication of charge carriers. The reverse saturation current that crosses collector junction i.e. Ico becomes M*Ico where M is avalanche multiplication factor multiplied due to avalanche effect. If reverse bias voltage is increased much beyond BVcbo then the avalanche multiplication factor becomes infinitely large and hence the current through the transistor rises abruptly. Avalanche multiplication factor is a function of voltage between collector and base and is given by
M= 1 / (1-(Vcb /BVcbo)^n)
where BVcbo is collector to base breakdown voltages with emitter open circuited