L 27 Solid State Physics 2 Lecture Outline

L 27. Solid State Physics 2 Lecture Outline 1. Structure of Semiconductors 2. Electrical Conduction in Semiconductors 3. Doped Semiconductors 4. The p-n Junction Diode 1

1. Structure of Semiconductors § Semiconductors are covalently bonded; Energy gap Eg ~ 1 e. V § Example: silicon, Si (Z = 14) 10 core electrons (tightly bound) 4 valence electrons (loosely bound) § 1 atom ↔ 4 covalent bonds 2

Structure of a semiconductor 3

2. Electrical Conduction in Semiconductors § Increasing temperature increases probability of breaking bond and freeing electron § Electrons ‘promoted’ to conduction band § For Si at T = 300 K, free electron concentration ~ 1010 cm-3 4

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 5 negative, positive, or both

Charge carriers – electron/hole pairs § Applying an electric field creates a current due to the movement of electrons and holes in opposite directions 6

Effect of temperature (breaking bond) 7

Effect of electric field (movement of charge) 8

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) 9

Example 1: An LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy gap is 1. 9 e. V. What is the wavelength of the emitted light? 10

3. 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) 11

3. Doped Semiconductors Ctd § 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 12

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) 13

n-type semiconductor (energy view) § Donor electron’s potential energy is just below the bottom of conduction band (by ~ 0. 01 e. V) § 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 14 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 15

p-type semiconductor (energy view) § Electrons forming covalent bonds (valence band) can easily transfer to acceptor level (~ 0. 01 e. V 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 16

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 17

4. 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 18

The p-n Junction Diode Ctd § Electrons from the n-type flow towards the ptype § 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 19 carriers can carry electricity

The p-n junction diode Depletion layer 20

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) 21

Biasing a p-n junction diode Ctd § 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 22

When a p-n junction is connected to an external circuit (see below) and the potential difference (Vp – Vn = V) across the junction is varied, the current ( I ) also varies. 23

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 I 0: 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) 24

Reading: Fundamentals of Physics – Halliday pg 1150 – 1155 Videos http: //www. youtube. com/watch? v=Dgm 1 Jz. NMXOk Answers: 650 nm to 2 sig. figs. likely red 25