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
3-‐3 ELEC 3908, Physical Electronics: Energy Band
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)
3-‐4 ELEC 3908, Physical Electronics: Energy Band
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
3-‐5 ELEC 3908, Physical Electronics: Energy Band
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
3-‐6 ELEC 3908, Physical Electronics: Energy Band
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
3-‐7 ELEC 3908, Physical Electronics: Energy Band
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
3-‐8 ELEC 3908, Physical Electronics: Energy Band
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
3-‐9 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Electron Transitions – Orbital Bonding
3-‐10 ELEC 3908, Physical Electronics: Energy Band
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)
3-‐11 ELEC 3908, Physical Electronics: Energy Band
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
3-‐12 ELEC 3908, Physical Electronics: Energy Band
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 intrinsic density ni (for Si@300K, ni ≈ 1.45x1010 cm-3)
• Therefore, for intrinsic material
3-‐13 ELEC 3908, Physical Electronics: Energy Band
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
3-‐14 ELEC 3908, Physical Electronics: Energy Band
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
3-‐15 ELEC 3908, Physical Electronics: Energy Band
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
• Density of donor dopant atoms given symbol ND (cm-3)
3-‐16 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Donor Ionization - Energy Band Diagram
3-‐17 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Donor Ionization – Orbital Bonding Model
3-‐18 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Donor Doping -Electron and Hole Densities
3-‐19 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.1: Arsenic Doping
3-‐20 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.1: Solution
3-‐21 ELEC 3908, Physical Electronics: Energy Band
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
• Density of acceptor dopant atoms given symbol NA (cm-3)
3-‐22 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Acceptor Ionization - Energy Band Diagram
3-‐23 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Acceptor Ionization – Orbital Bonding Model
3-‐24 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Acceptor Doping - Electron and Hole Densities
3-‐25 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.2: Gallium Doping
3-‐26 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.2: Solution
3-‐27 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Compensated Doping
3-‐28 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.3: Compensated Doping
3-‐29 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Example 3.3: Solution
3-‐30 ELEC 3908, Physical Electronics: Energy Band
Diagrams and Doping
Lecture Summary