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non_equil_old - EE151 Class Notes: Equilibrium PN Junctions...

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EE151 Class Notes: Equilibrium PN Junctions S.K. Tewksbury Sept. 22, 1997 Contents 1 Introduction 1 1.1 Charges Impacting Operation of the Diode ............................ 2 1.2 General Development of Depletion Region ............................. 2 1.3 Energy-Band Diagram for Diode .................................. 5 2 Built-In Voltage 6 3 Electric Field Across the Depletion Region 8 3.1 Electric Field in the Depletion Region on the P-Type Side .................... 8 3.2 Electric Field in the Depletion Region on theN-Type Side 8 3.3 Total Charge Balance ........................................ 9 4 Voltage Across Depletion Region 9 4.1 Voltage in the Depletion Region on the P-Type Side ....................... 10 4.2 Voltage in the Depletion Region on the N-Type Side 10 4.3 Voltage Equality at Junction and Depletion Layer Widths 11 4.4 Using Right Equations for Calculations of Depletion Layer Widths ............... 12 1 Introduction This handout provides a summary of the physics and equations related to silicon diodes. Such diodes are formed when a P-Type region of silicon is adjacent to an N-Type region of silicon. The primary principles behind the analysis in the following sections are contained in the various equations given in the first handout combined with the condition that under equilibrium the Fermi energy level E f is constant through the material (even if passing from an N-Type to a P-Type region of the semiconductor). First, some questions appearing in class regarding ion charge and mobile carrier charge are addressed next. 1
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Table 1: Standard donor and acceptor atoms used for silicon. N- or P-Type Atom Chemical Name Dopant Energy Level N-Type Phosphorus P E c - E donor =0 . 045 eV N-Type Arsenic As E c - E donor . 054 eV P-Type Boron B E acceptor - E v . 045 eV P-Type Aluminum Al E acceptor - E v . 067 eV 1.1 Charges Impacting Operation of the Diode A semiconductor with no impurities (dopants) is intrinsic and has a low carrier density given by the intrinsic carrier density n i . When a standard dopant is added, either holes or electrons are generated, in each case far in excess of n i and dominating the electrical behavior of the semiconductor. Standard dopants 1 for N-Type and P-Type, along with their energy position in the silicon band gap, are given in Table 1. The rules for calculating charge in a region are as follows (Figure 1 illustrates the conditions). Charge in N-Type Silicon: In N-Type silicon, the dopant is a doN or atom, which, starting in the neutral charge state donates one of its electrons to the conduction band (providing a free electron) and leaving the donor atom in the positive ion state. In particular, the neutral donor atom D becomes D D + and e - . Taking all donors as ionized, N + d n . Charge in P-Type Silicon: In P-Type silicon, the dopant is an acceP tor atom, which, starting in the neutral charge state accepts (or “steals”) an electron bound to a neighboring silicon atom, generating a free hole and leaving the acceptor atom in the negative ion state. In particular, the neutral acceptor atom A becomes A A - and h + . Taking all acceptors as ionized, N - a p .
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non_equil_old - EE151 Class Notes: Equilibrium PN Junctions...

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