1. Department of EECS University of California, Berkeley EECS 105 Fall 2003, Lecture 6 Lecture 6: Integrated Circuit Resistors Prof. Niknejad

2. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Lecture Outline Semiconductors Si Diamond Structure Bond Model Intrinsic Carrier Concentration Doping by Ion Implantation Drift Velocity Saturation IC Process Flow Resistor Layout Diffusion

3. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Resistivity for a Few Materials Pure copper, 273K1.56×10 -6 ohm-cm Pure copper, 373 K2.24×10 -6 ohm-cm Pure germanium, 273 K200 ohm-cm Pure germanium, 500 K.12 ohm-cm Pure water, 291 K2.5×10 7 ohm-cm Seawater25 ohm-cm What gives rise to this enormous range? Why are some materials semi-conductive? Why the strong temp dependence?

4. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Electronic Properties of Silicon Silicon is in Group IV – Atom electronic structure: 1s 2 2s 2 2p 6 3s 2 3p 2 – Crystal electronic structure: 1s 2 2s 2 2p 6 3(sp) 4 – Diamond lattice, with 0.235 nm bond length Very poor conductor at room temperature: why? (1s) 2 (2s) 2 (2p) 6 (3sp) 4 Hybridized State

5. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Periodic Table of Elements

6. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley The Diamond Structure 3sp tetrahedral bond

7. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley States of an Atom Quantum Mechanics: The allowed energy levels for an atom are discrete (2 electrons can occupy a state since with opposite spin) When atoms are brought into close contact, these energy levels split If there are a large number of atoms, the discrete energy levels form a “continuous” band Energy E1E1 E2E2...E3...E3 Forbidden Band Gap Allowed Energy Levels Lattice Constant Atomic Spacing

8. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Energy Band Diagram The gap between the conduction and valence band determines the conductive properties of the material Metal – negligible band gap or overlap Insulator – large band gap, ~ 8 eV Semiconductor – medium sized gap, ~ 1 eV Valence Band Conduction Band Valence Band Conduction Band e-e- Electrons can gain energy from lattice (phonon) or photon to become “free” band gap e-e-

9. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Model for Good Conductor The atoms are all ionized and a “sea” of electrons can wander about crystal: The electrons are the “glue” that holds the solid together Since they are “free”, they respond to applied fields and give rise to conductions ++++++ ++ ++++++ ++ ++++++ ++ On time scale of electrons, lattice looks stationary…

10. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Bond Model for Silicon (T=0K) Silicon Ion (+4 q) Four Valence Electrons Contributed by each ion (-4 q) 2 electrons in each bond

11. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Bond Model for Silicon (T>0K) Some bond are broken: free electron Leave behind a positive ion or trap (a hole) + -

12. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Holes? Notice that the vacancy (hole) left behind can be filled by a neighboring electron It looks like there is a positive charge traveling around! Treat holes as legitimate particles. + -

13. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Yes, Holes! The hole represents the void after a bond is broken Since it is energetically favorable for nearby electrons to fill this void, the hole is quickly filled But this leaves a new void since it is more likely that a valence band electron fills the void (much larger density that conduction band electrons) The net motion of many electrons in the valence band can be equivalently represented as the motion of a hole

14. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley More About Holes When a conduction band electron encounters a hole, the process is called recombination The electron and hole annihilate one another thus depleting the supply of carriers In thermal equilibrium, a generation process counterbalances to produce a steady stream of carriers

15. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Thermal Equilibrium (Pure Si) Balance between generation and recombination determines n o = p o Strong function of temperature: T = 300 o K

16. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Doping with Group V Elements P, As (group 5): extra bonding electron … lost to crystal at room temperature + Immobile Charge Left Behind

17. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Donor Accounting Each ionized donor will contribute an extra “free” electron The material is charge neutral, so the total charge concentration must sum to zero: By Mass-Action Law: Free Electrons Free Holes Ions (Immobile)

18. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Donor Accounting (cont) Solve quadratic: Only positive root is physically valid: For most practical situations:

19. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Doping with Group III Elements Boron: 3 bonding electrons  one bond is unsaturated Only free hole … negative ion is immobile! -

20. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Mass Action Law Balance between generation and recombination: N-type case: P-type case:

21. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Compensation Dope with both donors and acceptors: – Create free electron and hole! + - - +

22. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Compensation (cont.) More donors than acceptors: N d > N a More acceptors than donors: N a > N d

23. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Thermal Equilibrium Rapid, random motion of holes and electrons at “thermal velocity” v th = 10 7 cm/s with collisions every  c = 10 -13 s. Apply an electric field E and charge carriers accelerate … for  c seconds (hole case) x

24. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley Drift Velocity and Mobility For electrons: For holes:

25. EECS 105 Fall 2003, Lecture 6Prof. A. Niknejad Department of EECS University of California, Berkeley “default” values: Mobility vs. Doping in Silicon at 300 o K