Electronics The Thirteenth Lecture eigth week 29/ 6/ 1438 هـ أ / سمر السلمي

Outline for today Chapter 3: Bipolar junction transistor Finding minority carrier distributions & terminal currents in BJT First: the solution of diffusion equation in the base region in BJT Second: Evaluation Values of Terminal Currents in BJT minority carrier distributions for modes of operation for BJT for npn

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Finding minority carrier distributions & terminal currents in BJT we deal with active mode and base common configuration to npn . At the beginning and to make calculation ease, we assume the following : 1- the thickness of base WB is small, therefore, the diffusion here for electronic current from emitter to collector . In addition, we neglects drift current at base. 2- emitter efficiency γ ≈ 1 because emitter current is only electronic current 3- reverse leakage current or reverse saturation current is neglected 4- the action part in base and two junctions have regular section area and electronic current move in one direction or one dimension which is x 5- all currents and voltages are stable A VEB VCB WB xp n p ΔnE ΔnC

First: the solution of diffusion equation in the base region in BJT we deal with active mode and base common configuration to npn . Previously, we study about a excess of minority -carriers of electrons concentration in p-type in base region. Electronic current enter to base from emitter, also come out from base to collector. To calculate excess of electrons to two end-sides of base at two depletion regions from emitter side and collector side to obtain : excess of electrons concentration from end-side depletion regions of emitter end-side depletion regions of collector A VEB VCB WB xp n p ΔnE ΔnC

First: the solution of diffusion equation in the base region in BJT If we assume that emitter & base junction has strong forward bias which means and base & collector junction has strong reverse bias which means , we will obtain We mentioned before of minority carrier diffusion equations which is quadratic equation, hence the solution are Where Ln the diffusion length of minority carrier electron . We must remember that thickness of base is small which means that WB ≤ Ln to move all electronic current from emitter to collector. A VEB VCB WB xp n p ΔnE ΔnC

First: the solution of diffusion equation in the base region in BJT Finding constants C with boundary conditions at the two end-sides of base When multiply the first equation with , we obtain And collected with second equation to obtain C1 by substituting in the first equation to obtain C2

First: the solution of diffusion equation in the base region in BJT by substituting with constants C in we mentioned that high reverse voltage to obtain We can write equation in this from where

First: the solution of diffusion equation in the base region in BJT the figure shows the distribution of minority carriers in the base also in the emitter and collector where δn ΔnE M1ΔnE M2ΔnE

Second: Evaluation Values of Terminal Currents in BJT We will find current by known current density to two end-sides of base At driven excess of electron in base reign in p-type respect of xp This driven at borders of depletion region from emitter Therefore, electronic emitter current by substituting in constants since the So emitter current

Second: Evaluation Values of Terminal Currents in BJT This derivation at the borders of the depletion region from collector side Therefore, collector current is By substituting in constants

Second: Evaluation Values of Terminal Currents in BJT Finally, we can find base current from emitter and collector currents When taking into consideration , we obtain threse approximate value

minority carrier distributions for modes of operation for BJT for npn Active mode: the figure shows the distribution of minority carriers in the base also in the emitter and collector in active mode

minority carrier distributions for modes of operation for BJT for npn Saturation mode: the figure shows the distribution of minority carriers in the base also in the emitter and collector in saturation mode

minority carrier distributions for modes of operation for BJT for npn Cut - off mode the figure shows the distribution of minority carriers in the base also in the emitter and collector in cut off mode

minority carrier distributions for modes of operation for BJT for npn Inverted mode :the figure shows the distribution of minority carriers in the base also in the emitter and collector in inverted mode