1. http://www.eet.bme.hu Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Bipolar transistors 2 http://www.eet.bme.hu/~poppe/miel/en/07-bipolar2.pptx

2. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 2 Built-in field, efficiencies ► Calculation of the built-in field ► Injection and transport efficiencies

3. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 3 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

4. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 4 Calculation of the built-in field

5. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 5 Calculation of the built-in field Problem Let us calculate the built-in potential of the base assuming the following data: N B (0) = 10 17 /cm 3, N B (w B ) = 10 15 /cm 3

6. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 6 Injection and transport efficiency Injection efficiency: Transport efficiency: or emitter efficiency recombination

7. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 7 Calculation of emitter efficiency We assume a transistor with homogeneous base

8. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 8 Calculation of emitter efficiency In case of inhomogeneous doping: Gummel number

9. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 9 Calculation of transport efficiency We assume a transistor with homogeneous base

10. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 10 Emitter & transport efficiency Let us calculate the emitter and transport efficiencies of the homogeneous base transistor having the following parameters: N E = 10 19 /cm 3, w E = 2  m, N B = 4  10 16 /cm 3, w B = 1,5  m, D n =0,0026 m 2 /s, D p = 0,0011 m 2 /s,  n = 10 -6 s. Problem

11. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 11 Operating modes of the transistor, Ebers-Moll model

12. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 12 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

13. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 13 The Ebers - Moll model Equivalent circuit in normal active mode:

14. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 14 The Ebers - Moll model Equivalent circuit in inverse active mode:

15. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 15 The Ebers - Moll model In saturation the two models are superimposed:

16. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 16 The Ebers - Moll equations

17. Budapest University of Technology and Economics Department of Electron Devices 09-10-2014 Microelectronics BSc course, Bipolar transistors 2 © András Poppe & Vladimír Székely, BME-EET 2008-2014 17 The Ebers - Moll equations