Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Bipolar transistors 2.

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Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Bipolar transistors 2

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Built-in field, efficiencies ► Calculation of the built-in field ► Injection and transport efficiencies

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of the built-in field The hole concentration in the base has a gradient The holes do not drift There must be an electrical field, which induces a drift current balancing this! n-type diffusion p-type diffusion base concentration emitterbase collector

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of the built-in field

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of the built-in field Problem Let us calculate the built-in potential of the base assuming the following data: N B (0) = /cm 3, N B (w B ) = /cm 3

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Injection and transport efficiency Injection efficiency: Transport efficiency: or emitter efficiency recombination

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of emitter efficiency We assume a transistor with homogeneous base

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of emitter efficiency In case of inhomogeneous doping: Gummel number

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Calculation of transport efficiency We assume a transistor with homogeneous base

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Emitter & transport efficiency Let us calculate the emitter and transport efficiencies of the homogeneous base transistor having the following parameters: N E = /cm 3, w E = 2  m, N B = 4  /cm 3, w B = 1,5  m, D n =0,0026 m 2 /s, D p = 0,0011 m 2 /s,  n = s. Problem

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Operating modes of the transistor, Ebers-Moll model

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET Operating modes of the transistors Normal active Inverse active SaturationClosed EB: open CB: closed EB: closed CB: open EB: open CB: open EB: closed CB: closed

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET The Ebers - Moll model Equivalent circuit in normal active mode:

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET The Ebers - Moll model Equivalent circuit in inverse active mode:

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET The Ebers - Moll model In saturation the two models are superimposed:

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET The Ebers - Moll equations

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET The Ebers - Moll equations