This investigation presents a self-contained theory of the phototransistor that is adequate to a state-of-the-art level of the non-photoelectric semiconductor devices theory. A distinguishing feature of the presented theory is the orientation of the investigation of physical process for validation phototransistor properties and data, signal and nose equivalent circuits. The analysis of physical processes and the currents structure is based on a consistent use of minority carriers concentration distributions that specifies behavior currents.
There is a physical and theoretical justification of the amplification mechanism of primary photo and dark currents as a particular case of a more general internal amplification mechanism that is based on the distinction between charge carriers lifetime and transit time.
The primary photo currents concept is experimentally confirmed and also theoretically justified by an analytical development of the dc current equivalent circuit.
The phototransistor response to a sinusoidal modulated optical signal is derived by two ways. One is based on solving the equation of continuity for the variable part of excess minority carriers. The other is based on the proposed presentation of the phototransistor alternative currents by the linear part of the Taylor series near the constant base work point that is exited by a small signal at a current time. The connection between the abstract equations and the physical model is based on taking into account the nature of transistor capacitive currents.
The imaginary part of the variable conduction currents is expressed in terms of the junction diffusion capacitance. The imaginary part of the total currents that takes into account the displacement currents is expressed in terms of the sum of the barrier and diffusion junction capacitance.
The derivation of the small signal equivalent circuit is based on the concept of a generalized photo receiver.
The analysis of the noise characteristics involves the derivation of the signal-to-noise ratio that takes into account the fundamental shot noise photo currents of the signal, the background radiation and the dark current, the thermal noise of the transistor active resistance, the noise of the internal amplification and the following amplifier. The following parameters have been obtained: the noise figure for the process of internal amplification, the quantum limit of the threshold response due to the fluctuations of discrete photon flux of the signal and the noise of internal amplification and also detectivity and NEP.