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 Diagrams and Doping 3-­‐2 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 Diagrams and Doping 3-­‐3 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 Diagrams and Doping 3-­‐4 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 Diagrams and Doping 3-­‐5 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 Diagrams and Doping 3-­‐6 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 Diagrams and Doping 3-­‐7 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 Diagrams and Doping 3-­‐8 Electron Transitions – Orbital Bonding
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐9 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 Diagrams and Doping 3-­‐10 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
Electric Field
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐11 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
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐12 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 Diagrams and Doping 3-­‐13 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 Diagrams and Doping 3-­‐14 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)
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐15 Donor Ionization - Energy Band Diagram
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐16 Donor Ionization – Orbital Bonding Model
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐17 Donor Doping -Electron and Hole Densities
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐18 Example 3.1: Arsenic Doping
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐19 Example 3.1: Solution
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐20 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)
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐21 Acceptor Ionization - Energy Band Diagram
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐22 Acceptor Ionization – Orbital Bonding Model
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐23 Acceptor Doping - Electron and Hole Densities
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐24 Example 3.2: Gallium Doping
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐25 Example 3.2: Solution
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐26 Compensated Doping
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐27 Example 3.3: Compensated Doping
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐28 Example 3.3: Solution
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐29 Lecture Summary
ELEC 3908, Physical Electronics: Energy Band Diagrams and Doping 3-­‐30