Insulators - Energy Bands

• Insulators: Fermi level is between two energy bands;

• Large energy gap: E_g ~ 5 eV

• Filled valence band;

• Empty conduction band.

Semiconductors - Energy Bands

• Semiconductors: Fermi level is between two energy bands;

• Small energy gap: E_g ~ 1 eV

• Filled valence band;

• Empty conduction band, but thermal excitation increases the probability of electrons ‘jumping’ into the conduction band.

Semiconductors

Structure of Semiconductors

• Semiconductors are covalently bonded; Energy gap E_g ~ 1 eV

Electrical Conduction in Semiconductors

• Increasing temperature increases probability of breaking bond and freeing electron

• Electrons ‘promoted’ to conduction band

• For Si at T = 300K, free electron concentration ~ 10¹⁰cm^-3

Movement of charges

• When an electron is thermally excited into the conduction band, it leaves a vacancy (or ‘hole’) in the valence band

• An electron from the valence band can fill the hole, leaving another hole behind

• The net effect can be viewed as a migration of the hole in the opposite direction to that of the electrons

• The hole behaves as a positive charge carrier in the valence band

• Charge carriers in semiconductors can be negative, positive, or both

C harge carriers – electron/hole pairs

• Applying an electric field creates a current due to the movement of electrons and holes in opposite directions

Photo-excitation (photocell)

• Photons can provide the energy required for an electron to move from the valence band to the conduction band

• Photocells use light to increase the electrical conductivity of semiconductor materials

• Photocell conductivity increases with temperature and light intensity (if f >Eg / h)

Doped Semiconductors

• Conduction properties of semiconductors can be modified by adding impurities in a semiconductor crystal

• Adding such atoms is a process called doping

• An intrinsic semiconductor (no impurities) then becomes an extrinsic semiconductor (containing impurities)

The doping process:

• modifies the energy structure of a semiconductor

• modifies a semiconductor’s electrical conductivity

2 types of doping depending on the electronic structure of atom used as impurity: n-type / p-type doping

n -type semiconductor (lattice view)

• Contains donor impurities (5 outer electrons)

• Donor atom integrates to lattice by forming 4 covalent bonds → brings an extra electron to the semiconductor

• Germanium (Ge) semiconductor with Arsenic (As) impurities

• Donor electron almost free (has high potential energy level)

n-type semiconductor (energy view)

• D onor electron’s potential energy is just below the bottom of conduction band (by ~ 0.01 eV)

• Thermal excitation can easily promote a donor’s electron into the conduction band

• The majority of conducting electrons come from donor atom

• Charge carrier density is defined by the density of impurity

p-type semiconductor (lattice view)

• Contains acceptor impurities (with 3 outer electrons)

• Acceptor atom only forms 3 covalent bonds → can borrow an electron from neighboring atom

• Germanium (Ge) semiconductor with Gallium (Ga) impurities

• Electrons from neighboring atoms can easily transfer into acceptor hole

p-type semiconductor (energy view)

• Electrons forming covalent bonds (valence band) can easily transfer to acceptor level (~ 0.01 eV above valence band)

• Thermal excitation can easily promote an electron from the valence band to the acceptor level, creating a hole in the valence band

• The majority of charge carriers is made of holes provided by acceptor atom

Semiconductor Doping (summary)

• Intrinsic (non-doped) semiconductors:

- only have thermally created electron/hole pairs

• Extrinsic (doped) semiconductors:

- still have thermally created electron/hole pairs

- but majority of charge carriers are brought by impurities

n-type:

- majority charge carriers: electrons

- minority charge carriers: holes

p-type:

- majority charge carriers: holes

- minority charge carriers: electrons

The p-n Junction Diode

• A p-n junction diode is a widely used semiconductor device

• In an electrical circuit, a diode passes current in only one direction (not the other)

• A p-n junction diode is simply created by physically joining an n-type and a p-type semiconductor together

• Electrons from the n-type flow towards the p-type

• Holes from the p-type flow towards the n-type

→ electrons and holes recombine at the junction

• → Positive ions on the n-side / negative ions on the p-side

→ Electric field created and directed towards p-side, slowing the electron/hole diffusion process

• A depletion layer is formed where no charge carriers can carry electricity

Biasing a p-n junction diode

• Depletion layer prevents the diode from conducting current

• Applying an external voltage can either:

- increase size of the depletion layer (decrease conductivity)

- decrease size of the depletion layer (increase conductivity)

• A diode is forward biased when the positive terminal of the battery is connected to the p-side of the junction. The depletion layer becomes smaller and current can flow

• A diode is reverse biased when the positive terminal of the battery is connected to the n-side of the junction. The depletion layer becomes larger and current cannot flow

Diode current-voltage characteristic

• In striking contrast to the symmetric behavior of resistors that obey Ohm’s law and give a straight line on an I–V graph, a p-n junction conducts much more readily in the direction from p to n than the reverse.

• The current I flowing through a diode can be expressed as:

where

I₀: Saturation current (small)

V: Voltage across diode

e: Electron charge

T: Temperature (in K)

k: Boltzmann constant (k = 1.38×10⁻²³ J K^-1)