1. EEE 3394 Electronic Materials Chris Ferekides Fall 2014 Week 8

2. What happens when we bring two metals together ?? F ( M o ) = 4. 2 0 e V Electrons Vacuum Fermi level PtMo Vacuum Fermi level Electrons F ( P t ) = 5. 3 6 e V Fermi level F (Pt) ­ F (Mo) = 1.16 eV = e D V Vacuum Vacuum 5. 3 6 e V 4. 2 0 e V -e transfer due to difference in energy -net e-transfer leaves behind a positive charge, while making the other metal more negative -the result is charge separation … E- field and V! known as the Contact Potential Metal to Metal Contacts

3. Net diffusion of electrons from the “hot” to the “cold” region of a metal … -Fermi function at a higher T “spreads” more toward higher energies -High energy e’s move to fill in lower energy states... -This process leaves behind a net positive charge … therefore E-field … Voltage! -The Seebeck Coefficient or Thermoelectric Power is: Seebeck Effect

4. The electron movement is NOT always from Hot to Cold because the diffusion process depends on several parameters including the mean free path … which also depends on T! The Seebeck coefficient can be –ve or +ve depending on which mechanism dominates … Seebeck Effect

5. 100 °C 0 °C Cold Hot  V Metal type B Metal type B Metal type A Metal 100 °C Cold Hot  V Metal Metal 0 °C What is a thermocouple ?? Can we measure the voltage generated by the temperature difference ?? 0 So how can we utilize the Thermoelectric Power ?? 0 Thermocouple

6. The difference in Seebeck coefficients will result in a net Voltage across the two wires … 100 °C 0 °C Cold Hot  V Metal type B Metal type B Metal type A 0 Thermocouple

7. Thermionic Emission Heated filament in a vacuum will emit electrons !

8. Thermionic Emission - Rectifier Why does the current saturate ? What happens when the voltage is reversed ?

9. Thermionic Emission Equation Where B o is a constant called the Richardson- Dushman constant

10. Bonding Model: - Rem: four nearest neighbors; - covalent bonding - sharing of electrons between neighboring atoms; - each atom contributes four “shared” electrons; - each atom accepts four shared electrons from its neighbors; Note: at room temperature some bonds are “broken” i.e. free electrons. Silicon: - 14 electrons; - 10 are tightly bound to nucleus; (core electrons); - 4 weakly bound; valence electrons - participate in chemical reactions. (Ge similar to Si with 28 core electrons) Silicon (Si) Bonding Model

11. CHARGE CARRIERS:  In conductors:electrons  In semiconductors?:  At 0ºK no broken bonds i.e. no free electrons.  At 0ºK no electrons in conduction band, valence band completely filled- energy band model  electrons in valence band can still move but net momentum (quantized) is zero; therefore no NET current flow.  At room temperature “some” bonds are broken and there exist electrons in the conduction band: conduction electrons.  Breaking of a bond also creates a “void”; vacancy in the valence band: a HOLE is also a charge carrier. (see figs)  TERMINOLOGY:  Dopants: certain impurity atoms added to semiconductors in order to control the number of holes/electrons.  Intrinsic semiconductor: pure (undoped) semiconductor.  Extrinsic semiconductor: doped semiconductor; properties determined by added impurities. Semiconductor Terminology

12. What Happens @ 0 K ?

13. - Intrinsic means … n=p

14. From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

15. REM – We are considering Si for most examples  a donor atom has 5 valence electrons;  when a donor atom replaces a Si atom 4 of its 5 valence electrons will participate in the formation of the four covalent bonds;  the 5th electron is weakly bound to the donor atom;  what does weakly bound means?  It takes about 1 eV to break a Si-Si bond (i.e. to free an electron in pure Si.)  it takes about 0.1 eV or less to remove the extra electron from the donor atom.  Most donor and acceptor binding energies are about 1/20 Eg (Si).  (Same can be described for an acceptor atom with one less electron!). Note:  when a donor atom gives up its extra electron the net charge of the donor is +1. This charged donor is FIXED. Bonding Model

16. n-type Doping From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

17. p-type Doping From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

18. Light Effects From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) (a) A photon with an energy greater than Eg can excite an electron from the VB to the CB. (b) When a photon breaks a Si-Si bond, a free electron and a hole in the Si-Si bond is created.

19. Semiconductors – Bonding/Energy Band Model Donor Acceptor  the binding energy for a donor electron is about 1/20 Eg.  if energy equal to binding energy is supplied to the crystal the extra electron will leave the donor and end up in the conduction band. Note:  at OºK no thermal energy therefore no donor electrons can be excited to the conduction band.  The creation of a free electron from a donor atom does not result in the creation of a hole (rem. Intrinsic semiconductor).

20. Semiconductors n & p

21. EQUILIBRIUM CARRIER CONCETRATIONS REM:  g C (E)d(E)represents the number of available states (cm -3 ) in the energy interval E+dE.  f(E)is the probability a state is occupied by an electron; (1-f(E) holes);  g C (E)f(E)d(E)gives the number of electrons (cm -3 ) in the interval E+dE; Therefore the TOTAL number of electrons n (and holes p) in the conduction band (and in the valence band) can be obtained by integrating the relationships: