Elec3908 lect 3

ELEC 3908, Physical Devices – Lecture 3

Energy Band Diagrams and Doping

3-‐2 ELEC 3908, Physical Electronics: Energy Band

Diagrams and Doping

Lecture Outline

•  Continue the study of semiconductor devices by looking at the material used to make most devices

•  The energy band diagram is a representation of carrier energy in a semiconducting material and will be related to an orbital bonding representation

•  Devices require materials with tailored characteristics, obtained through doping, the controlled introduction of impurities

•  Will discuss electrons and holes, as well as intrinsic, n-type and p-type materials

•  Later lectures will apply these concepts to diode, bipolar junction transistor and FET


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Atomic Electron Energy Levels

•  A free electron can assume any energy level (continuous)

•  Quantum mechanics predicts a bound electron can only assume discrete energy levels

•  This is a result of the interaction between the electron and the nuclear proton(s)


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Crystal Energy Bands

•  Crystal is composed of a large number of atoms (≈1022 cm-3 for silicon)

•  Interaction between the electrons of each atom and the protons of other atoms

•  Result is a perturbation of each electron’s discrete energy level to form continua at the previous energy levels


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Covalent Bonding

•  Silicon crystal formed by covalent bonds

•  Covalent bonds share electrons between atoms in lattice so each thinks its orbitals are full

•  Most important bands are therefore –  band which would be filled at 0 K -

valence band –  next band above in energy -

conduction band


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Simplified Energy Band Diagram

•  Movement within a band is not difficult due to continuum of energy levels

•  Movement between bands requires acquisition of difference in energy between bands (in pure crystal, can’t exist in between)

•  Main features of interest for first order device analysis are –  top of valence band (Ev) –  bottom of conduction band (Ec) –  difference in energy between Ec and Ev,

energy gap Eg


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Orbital Bonding Model

•  Represent valence and conduction bands by separate silicon lattice structures

•  The two diagrams coexist in space -the same set of silicon atoms is represented in each diagram


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Electron Transitions -Energy Band Diagram

•  At room temperature, very few electrons can gain energy Eg to move to the conduction band ( ≈ 1010 cm-3 at 300K = 23°C)

•  In pure silicon at 300K, most valence band orbitals ( ≈ 1022 cm-3 ) are full, most conduction band orbitals are empty


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Electron Transitions – Orbital Bonding


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Electrons and Holes

•  Conduction of current occurs through electron movement •  Two mechanisms of electron movement are possible:

–  movement within the nearly empty conduction band orbital structure

–  movement within the nearly full valence band orbital structure •  Conduction in the valence band structure is more conveniently

modeled as the “movement” of an empty orbital •  Model this empty valence band orbital as a positively charged

pseudo-particle called a hole •  Density of electrons in conduction band is n (cm-3) •  Density of holes in valence band is p (cm-3)


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Electron and Hole Conduction

•  Electron movement in conduction band can be modeled directly

•  Movement of electrons in valence band modeled as movement (in opposite direction) of positively charged hole

smcgarry

Text Box

Electric Field

smcgarry

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Intrinsic Material

•  Semiconducting material which has not had any impurities added is called intrinsic

•  In an intrinsic material, the number of electrons and holes must be equal because they are generated in pairs

•  Call the density of electrons and holes in intrinsic material the intrinsic density ni (for Si@300K, ni ≈ 1.45x1010 cm-3)

•  Therefore, for intrinsic material


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Extrinsic Material

•  Intentional addition of impurities during manufacture or in specialized fabrication steps is termed doping

•  Doped material is called extrinsic •  Ability to change the electrical characteristics of the material

through selective introduction of impurities is the basic reason why semiconductor devices are possible

•  Later lectures will outline the processes used to introduce impurities in a controlled and repeatable way


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Mass-Action Law

•  For intrinsic material, n = p = ni, therefore

•  This turns out to be a general relationship called the mass-action law, which can be used for doped material in equilibrium


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Group V Impurity Atom

•  An atom from group V of the periodic table has one more nuclear proton and valence electron than silicon

•  If the atom replaces a silicon atom in the lattice, the extra electron can move into the conduction band (ionization)

•  A group V atom is a donor since it donates an electron to the silicon lattice

•  Density of donor dopant atoms given symbol ND (cm-3)


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Donor Ionization - Energy Band Diagram


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Donor Ionization – Orbital Bonding Model


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Donor Doping -Electron and Hole Densities


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Example 3.1: Arsenic Doping


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Example 3.1: Solution


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Group III Impurity Atom

•  An atom from group III of the periodic table has one less nuclear proton and valence electron than silicon

•  If the atom replaces a silicon atom in the lattice, the empty valence orbital can be filled by an electron (ionization)

•  A group III atom is an acceptor since it accepts an electron from the silicon lattice

•  Density of acceptor dopant atoms given symbol NA (cm-3)


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Acceptor Ionization - Energy Band Diagram


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Acceptor Ionization – Orbital Bonding Model


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Acceptor Doping - Electron and Hole Densities


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Example 3.2: Gallium Doping


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Compensated Doping


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Example 3.3: Compensated Doping


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Lecture Summary

Devices & Hardware

Elec3908 lect 3