1. http://www.eet.bme.hu Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Operation of PN junctions: Electrostatic conditions http://www.eet.bme.hu/~poppe/miel/en/04-diode1.pptx

2. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 2 Diodes: basics ► What are they? Data sheets ► How they are made? ► How do they work?

3. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 3 Diodes: what are they? We learnt: ► …as diodes are presented in vendors' data sheets:

4. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 4 Main features Reverse region I ~ 10 -12 A/mm 2 (Si, T=300 K) Forward region I ~ exp(V/V T ) The characteristic: I = f(V) Rectifies V F  0.7 V

5. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 5 Main features Symbol, reference directions UI A C p n anode cathode U F or V F forward voltage I F forward current

6. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 6 Main features Dynamic properties: capacitance, finite speed of operation Secondary effects such as breakdown

7. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 7 How does it look like? Start from: single crystalline Si wafer Oxidation, window opening, n diffusion, metallization Diecing, die attach soldering, packaging "pn junction" pn junction (metallurgical) die attach solder metal carrier

8. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 8 Diode – doping profile Doping profile: dopant concentration as function of depth metallurgical junction diffusion doping profile base concentration

9. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 9 Our method of study 1. 1D analysis, internal PN-junction only 2. Homogeneous doping “abrupt” profile 3. One side is more heavily doped than the other side (Let it be the n-side) N d >> N a

10. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 10 Two separate pieces of doped Si ► The Fermi-levels shift from the intrinsic level according to the doping: conductnace band valance band

11. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 11 PN junction ► A potential step develops between the p and n sides. This will be so high that the Fermi-levels of both sides will be equal: Due to the large concentration gradient between the two sides majority carriers of both sides will diffuse to the other side until the Fermi-levels get equal. conductnace band valance band

12. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 12 Electrostatic conditions Depleted layers (space charge layers) depleted layers holes electrons

13. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 13 Contact & diffusion potentials According to Kirchoff's voltage law: U fn metal – n-Si contact potential U D diffusion potential between p & n sides U pf p-Si – metal contact potential

14. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 14 n n, p n p p, n p Calculation of the diffusion potential

15. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 15 Calculation of the diffusion potential „built-in” voltage mass effect law

16. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 16 Calculation of the diffusion potential Problem Doping levels of an abrupt Si diode: N d =10 18 /cm 3, N a =10 16 /cm 3. Let us calculate the diffusion potential at room temperature! Obviousely U D < U g,, U D is usually 70-80% of U g

17. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 17 Calculations for the depletion layer The depletion layer is wider on the less doped side. Charges on both sides must be equal

18. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 18 Calculations for the depletion layer parabola sections

19. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 19 Calculations for the depletion layer parabola sections

20. Budapest University of Technology and Economics Department of Electron Devices 24-09-2014 Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 2008-2014 20 Calculations for the depletion layer Problem Doping data of an abrupt Si diode: N d =10 18 /cm 3, N a =10 16 /cm 3. Calculate the widths of the depletion layers! (  r =11.8, U=0V) And if U= -100V ?