618 326

1. 618 326 Physics of electronic materials and devices I Lecture 13: Final review

2. Ex: Donors & Acceptors A Si sample is doped with 1017 As atoms/cm3. • (a) What is the equilibrium hole concentration p at 300K. • (b) Fill out the energy levels of A, B, and C in the figure below

3. Ex: Donors & Acceptors • Soln

4. Ex: Donors & Acceptors • Si is doped with In at room temperature but not all acceptor atoms are ionized so that EA = EF. If effective hole mass of In is = 0.39m0, Find • (a) The doping concentration NA for which EA = EF at room temperature • (b) Free majority and minority carrier density

5. Ex: Donors & Acceptors • Soln (a)

6. Ex: Donors & Acceptors • At room temperature (300 K) a piece of silicon sample, called “sample A”, is doped with 1015 Arsenic atoms/cm3. • a) What is the minority carrier? • b) What is the intrinsic carrier density (ni)? • c) What is the donor level energy (ED)? • d) What is the minority carrier concentration? (Assume a complete ionization of the impurity dopants) • e) What is the Fermi level measured from the bottom of the conduction band?

7. Ex: Donors & Acceptors • Soln

8. Ex: p-n junction A Si p-n diode is shown in the figure. Calculate xn, xp, W, -Em, andVbi.

9. Ex: p-n junction • Soln

10. Ex: p-n junction • Determine the n-type doping concentration to meet the following specifications for a Si p-n junction: NA = 1018 cm-3, |Emax| = 4 x 105 V/cm atVR= 30 V, T = 300 K

11. Ex: p-n junction • Soln

12. Ex: p-n junction • An abrupt Si p-n junction has NA = 1018 cm-3 and ND = 5x1015 cm-3. • a) Calculate the Fermi level positions in the p- and n-regions. • b) Draw an equilibrium band diagram and find the built-in potential from this diagram. • c) Compare the result with built-in potential from the Eq.(4) lecture 8.

13. Ex: p-n junction • Soln

14. Ex: p-n junction • An abrupt Si p-n junction with A = 10-4 cm2 has the following properties at 300 K: • What is the forward current if V = 0.5 V? • What is the current at V = -0.5 V?

15. Ex: p-n junction

16. Ex: Depletion capacitance • From the previous exercise, what is the depletion capacitance at -4V?

17. Ex: p-n junction • Another piece of silicon sample, called “sample B” is doped with 1018 Boron atoms/cm3. A sample ‘A’ from problem 2 is brought into contact with sample ‘B’ as shown: • a) Sketch the space charge distribution using the rectangular approximation. Indicate the exact interceptions on both axes. Also, calculate the width of depletion region. • b) Calculate Em and find the expression of E(x) and then sketch the profile of the electric field E(x). • c) Calculate n, p, and Vbi and sketch the profile of (x). • d) Find a junction capacitance Cj with a reverse bias of 10 V.

18. Ex: p-n junction

19. Ex: p-n junction

20. Ex: p-n junction breakdown • For a GaAsp+n one-sided abrupt junction with ND = 8 x 1014 cm-3 andNA = 1018cm-3 • (a) Calculate the depletion width at breakdown • (b) If the n-type region of this diode is reduced to 20 micron, calculate the breakdown voltage.

21. Ex: p-n junction breakdown • Soln

22. Ex: Excess carriers • Assume that 1013 EHP/cm3 are created optically every microsecond in a Si sample with n0 = 1014 cm-3 and n = p = 2s. Find the majority and minority carrier concentration in equilibrium and steady state.

23. Ex: Excess carriers

24. Ex: Excess carriers • From previous example, find the electron fermiEfn-Ei and hole fermi level Ei-Efp.

25. Ex: Heterojunction • How to draw a band diagram of heterojunction.

26. Ex: Haynes-Shockley experiment • From example 3 of lecture 7, find the diffusion coefficient D. • Soln

27. Ex: Schottky diode • Explain the meaning of “hot carriers”and why is aSchottky-diode sometimes called “hot-carrier diode”?

28. Ex: Types of contacts • What is the difference between ‘Ohmic contact’ and ‘Rectifying contact’? Tell the processes that make the current flow when ohmic contact is reverse-biased.

29. Ex: Transistor • A Si p-n-p transistor has impurity concentrations of 5x1018, 2x1017, and1016 cm-3 in the emitter, base, and collector, respectively. The base width is 1.0 μm, and the device cross-sectional area is 0.2 mm2. When the emitter-base junction is forward biased to 0.5 V and the base-collector junction is reverse biased to 5 V, calculate • (a) the neutral base width • (b) the minority carrier concentration at the emitter-base junction

30. Ex: Transistor • Soln (a) The emitter-base junction is forward biased. The depletion-layer width in the base is

31. Ex: Transistor Soln(Cont’d) Similarly, we obtain for the base-collector function

32. Ex: Transistor Soln(Cont’d) Therefore the neutral base width is (b)

33. Ex: Transistor • A Si p-n-p transistor has impurity concentrations of 5x1018, 2x1017,and1016 cm-3 in the emitter, base, and collector, respectively. The base width is 1.0 μm and the device cross-sectional area is 0.2 mm2. The emitter-base junction is forward biased to 0.5 V and the base-collector junction is reverse biased to 5 V. The diffusion constants of minority carriers in the emitter, base, and collector are 52, 40, and 115 cm2/s, respectively; and the corresponding lifetimes are 10-8, 10-7, and10-6 s. Find the current components IEp, ICp, IEn, ICn, andIB as shown in the figure.

34. Ex: Transistor • Soln

35. Ex: Transistor • Soln

36. Ex: Transistor • Soln

37. Ex: Transistor • Sketch the similar figures but for n+-p-n transistor working in the active(normal) mode.

38. Ex: Transistor • Explain the difference between ‘Bipolar junction transistor’ and ‘Unipolar transistor’

39. Ex: Frequency response • Sketch a frequency response of a transistor.

40. Ex: Light sources • Sketch P-I characteristics(Light output power vs. current) of an LED and a LASER. Explain briefly how they can emit the light.

41. Ex: Laser • What is “population inversion”?