Modeling and design of a single photon detector and its various characteristics are presented. It is a type of avalanche photo diode (APD) designed to suit the requirements of a Quantum Key Distribution (QKD) detection system. The device is modeled to operate in a gated mode at liquid nitrogen temperature for minimum noise and maximum gain. Different types of APDs are compared for best performance. The APD is part of an optical communication link, which is a private channel to transmit the key signal. The encrypted message is sent via a public channel. The optical link operates at a wavelength of 1.55?m. The design is based on InGaAs with a quantum efficiency of more than 75% and a multiplication factor of 1000. The calculated dark current is below 10-12A with an overall signal to noise ratio better than 18dB. The device sensitivity is better than -40dBm, which is more than an order of magnitude higher than the dark current, corresponding to a detection sensitivity of two photons in pico-second pulses.