ELEC 3908, Physical Devices – Lecture 3

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

ELEC 3908, Physical Electronics: Energy Band 3-2 Diagrams and Doping 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)

ELEC 3908, Physical Electronics: Energy Band 3-3 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-4 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-5 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-6 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-7 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-8 Diagrams and Doping Electron Transitions – Orbital Bonding

ELEC 3908, Physical Electronics: Energy Band 3-9 Diagrams and Doping 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)

ELEC 3908, Physical Electronics: Energy Band 3-10 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-11 Diagrams and Doping 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 10 -3 intrinsic density ni (for Si@300K, ni ≈ 1.45x10 cm ) • Therefore, for intrinsic material

ELEC 3908, Physical Electronics: Energy Band 3-12 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-13 Diagrams and Doping 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

ELEC 3908, Physical Electronics: Energy Band 3-14 Diagrams and Doping 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 -3 • Density of donor dopant atoms given symbol ND (cm )

ELEC 3908, Physical Electronics: Energy Band 3-15 Diagrams and Doping Donor Ionization - Energy Band Diagram

ELEC 3908, Physical Electronics: Energy Band 3-16 Diagrams and Doping Donor Ionization – Orbital Bonding Model

ELEC 3908, Physical Electronics: Energy Band 3-17 Diagrams and Doping Donor Doping -Electron and Hole Densities

ELEC 3908, Physical Electronics: Energy Band 3-18 Diagrams and Doping Example 3.1: Arsenic Doping

ELEC 3908, Physical Electronics: Energy Band 3-19 Diagrams and Doping Example 3.1: Solution

ELEC 3908, Physical Electronics: Energy Band 3-20 Diagrams and Doping 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 -3 • Density of acceptor dopant atoms given symbol NA (cm )

ELEC 3908, Physical Electronics: Energy Band 3-21 Diagrams and Doping Acceptor Ionization - Energy Band Diagram

ELEC 3908, Physical Electronics: Energy Band 3-22 Diagrams and Doping Acceptor Ionization – Orbital Bonding Model

ELEC 3908, Physical Electronics: Energy Band 3-23 Diagrams and Doping Acceptor Doping - Electron and Hole Densities

ELEC 3908, Physical Electronics: Energy Band 3-24 Diagrams and Doping Example 3.2: Gallium Doping

ELEC 3908, Physical Electronics: Energy Band 3-25 Diagrams and Doping Example 3.2: Solution

ELEC 3908, Physical Electronics: Energy Band 3-26 Diagrams and Doping Compensated Doping

ELEC 3908, Physical Electronics: Energy Band 3-27 Diagrams and Doping Example 3.3: Compensated Doping

ELEC 3908, Physical Electronics: Energy Band 3-28 Diagrams and Doping Example 3.3: Solution

ELEC 3908, Physical Electronics: Energy Band 3-29 Diagrams and Doping Lecture Summary

ELEC 3908, Physical Electronics: Energy Band 3-30 Diagrams and Doping