Lecture 5 0 Properties of Semiconductors Importance to

Lecture 5. 0 Properties of Semiconductors

Importance to Silicon Chips l Size of devices – Doping thickness/size – Depletion Zone Size – Electron Tunneling dimension l Chip Cooling- Device Density – Heat Capacity – Thermal Conductivity

Band theory of Semiconductors l Forbidden Zone – ENERGY GAP Conduction Band Valence Band

Silicon Band Structure - [Ne]3 s 23 p 2

Fermi-Dirac Probability Distribution for electron energy, E l. Probability, F(E)= (e{[E-Ef]/k. BT}+1)-1 –Ef is the Fermi Energy

Number of Occupied States Density of States Fermi-Dirac T>0

Difference between Semiconductors and Insulators Material Eg(e. V) In. Sb 0. 18 In. As 0. 36 Ge 0. 67 Si 1. 12 Ga. As 1. 43 Si. C 2. 3 Zn. S 3. 6 Ni. O 4. 2 Al 2 O 3 k. BT =0. 0257 e. V at 298˚K 8 Eg>3. 0 e. V transparent

Probability of electrons in Conduction Band Lowest Energy in CB l E-Ef Eg/2 l Probability in CB l F(E)= (exp{[E-Ef]/k. BT} +1)-1 ) l = (exp{Eg/2 k. BT} +1)-1 l exp{-Eg/2 k. BT} for Eg>1 e. V @ 298 K l k. BT =0. 0257 e. V at 298˚K

Variation of Conductivity with T =d /d. T

Intrinsic Conductivity of Semiconductor l Charge Carriers – Electrons – Holes l = n e e e + n h e h l # electrons = # holes – ne e ( e+ h) – ne C exp{-Eg/2 k. BT} ne=2(2 m*e k. BT/h 2)3/2 exp(-Eg /(2 k. BT)) Ef=Eg/2+3/4 k. BT ln(m*h/m*e)

Mobilities

Semiconductor Photoelectric Effect l Light Absorption/Light Emission (photodetector)/(photo diode laser) l Absorption max =hc/Eg

Light Emitting Diode

Photodiode Laser l Color depends on band gap, Eg l =hc/Eg Eg>3. 0 transparent Pb 0. 37 0. 27 0. 33 IR detectors

Diode Laser

Extrinsic Conductivity of Semiconductor l Donor l n-type N=nd+ni Doping Acceptor Doping p-type p= 2(2 m*h k. BT/h 2)3/2 exp(-Ef/k. BT) Law of Mass Action, Nipi=ndpd or =nndn

Extrinsic Conductivity of Semiconductor l Donor Doping Acceptor Doping

Electron Density l Dopant Concentration effects l Electron Density l Electrical Conductivity

Conductivity l Intrinsic Range – Exponential with T l Extrinsic Range – Promoted to CB • – Decreasing , – Joins Intrinsic l Majority/minority Carriers l = ne e e + nh e h

Majority/minority Carriers l Conductivity l = n e e e + n h e h l n-type ne>>nh l Low number of holes due to recombination. l Law of Mass Action – Nipi=ndpd – (For p-type Nipi =nndn )

Extrinsic Conductivity of Semiconductor l Donor Doping l n-type Ed = -m*e e 4/(8 ( o)2 h 2) Ef=Eg-Ed/2 Acceptor Doping p-type Ef=Eg+Ea/2

Effective Mass l Holes l Electrons

Wafer Sales l Following PRIME GRADE Si wafers are all single-side polish $14. 50 each for 25 wafers each $11. 00 for 50 or more (we can double side polish) – – – l 4" P<111> 4" N<100> 4" P<111> 4" P<100> 4" P<111> 3. 0 -6. 6 ohm-cm 4. 0 -6. 0 ohm-cm 7. 0 -21. 6 ohm-cm 12. 0 -16. 0 ohm-cm 3. 0 -5. 0 ohm-cm http: //www. collegewafer. com/

Ga. P Wafer 2" Undoped (100) $180. 00 each 2" S doped (111) $180. 00 each

C&ENews 1/6/03