Budapest University of Technology and Economics Department of Electron Devices Microelectronics, BSc course Operation of PN junctions: Electrostatic conditions

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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET Main features Reverse region I ~ 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

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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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

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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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

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

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

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

Budapest University of Technology and Economics Department of Electron Devices Microelectronics BSc, Operation of PN junctions: Electrostatic conditions © A. Poppe & V. Székely, BME-EET 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 ?