The findings of a study of impact ionization, avalanche multiplication and excess noise in InAs avalanche photodiodes at 77 K are reported. It is shown that hole impact ionization is negligible in practical devices which continue to operate as electron avalanche photodiodes, as they do at room temperature. A new electron ionization coefficient capable of modeling multiplication at 77 K is presented and it is shown that significant multiplication can be achieved in practical devices without excessive tunneling currents. The characteristic changes observed between room temperature and 77 K are discussed. This paper helps to demonstrate the potential for practical InAs electron avalanche photodiodes, operating cooled.