MSE 410/ECE 340: Electrical Properties of Materials Fall 2016 Micron School of Materials Science and Engineering Boise State University

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1 MSE 410/ECE 340: Electrical Properties of Materials Fall 2016 Micron School of Materials Science and Engineering Boise State University Practice Final Exam 1 Read the questions carefully Label all figures thoroughly Please circle your answers Make sure to include units with your answers Show all steps in your derivations to obtain full credit. Be thorough & neat. Problem Total Points Points Obtained Grand Total: 1

2 Quatum Mechanics and Application to Electronic and Optoelectronic Devices: 1. For the finite barrier problem where E e-<v o, solve for T(E) (or T(k)) using the probability current densities, J's, to show (i.e, fully derive) that T(E) is a ratio of wave function coefficients. (4 points) 2. Write down the equation that describe current density through a barrier (not probability current density) that contains both T(E) and the group velocity (v g). Define all variables. 3. Show how the effective mass is related to both T(E), v g and ultimately the current density through a barrier. Some derivation is required. Assume that all three regions are different materials. 4. Draw a schematic of each of the three quantum mechanical barrier problems we covered and name each one of the quantum barriers. Now name and draw an electronic or optoelectronic device that can be simulated, in a simplified manner, by one of or a combination of these quantum barriers. (4 points) 2

3 Band Structure and Doping: Theory and Applications: (19 pts) 5. Determine whether or not the polymer below is a semiconductor, insulator or metal by plotting the Arrhenius curve and calculating an activation energy /Resistance (1/M ohms) Temperature (K) Courtesy of: Ryan Meyer Dept. Chemistry 3

4 6. Given the plot below and knowing the band gap of GaP is about 2.45 ev answer the following questions: a. What colors would you expect GaP to transmit? Explain your answer. (2 pts) 4.0 Violet Violet Blue Green Orange Yellow Red Deep Red 3.5 Photon Energy (ev) λ Photon (Å) 4

5 b. Draw a p-n junction band structure of GaP where N A=N D. Draw both the shallow dopant energy levels and the Fermi energy. Assume the temperature is nearly 0K. Label all features. (5 pts) c. If a positive bias is applied to the n-type side, will the Fermi level increase or decrease in energy? Explain. (2 pts) d. Write down Poisson's equation and define all variables. (5 pts) 5

6 7. Order the following compound semiconductors from greatest to least bandgap energy: GaN, AlN, InN, BN (2 pts) 8. Draw the band diagram for Cu. Label all features. (3 pts) 9. If you doped GaN with Si, would it be n-type or p-type? Explain your answer. (3 pts) 6

7 Multiple p-n Junctions (bipolar transistors): 10. Draw the equilibrium band structure for a Si p-n-p bipolar transistor. Label all important aspects of the diagram including the emitter, base and collector. (3 pts) 11. Draw the band structure for a Si p-n-p structure in which the first (left side) p-n junction is forward biased and the second (right side) n-p junction is forward biased. Label all important aspects of the diagram including the magnitude of the applied bias. (3 pts) 7

8 12. Draw the band structure for a Si p-n-p bipolar transistor in which the first p-n junction (left side) is forward biased and the second n-p junction (right side) is reversed biased. Label all important aspects of the diagram including the magnitude of the bias. (3 pts) 13. For the structures you drew in the last problem, show the conducting carriers in the collector, base and emitter and use arrows to show the direction of motion. State whether the carriers are majority or minority in the emitter, base and collector. (3 pts) 8

9 Band Theory, Intrinsic and Extrinsic Semiconductors: 14. Draw the dispersion relation for a direct bandgap semiconductor and an indirect bandgap semiconductor. 9

10 15. Draw the dispersion relation of a direct bandgap semiconductor in which the effective mass of a hole is lighter than an electron. 16. What two entities are used to determine the density of electrons in the conduction band. 17. Write down the integral equation used to determine the density of electrons in the conduction band. Ensure that the limits of integration are correct. Define all variables. 18. Write down the integral equation used to determine the density of holes in the valance band. Ensure that the limits of integration are correct. Define all variables. 10

11 19. Sketch a plot of the density of states and the Fermi-Dirac distribution function for an intrinsic semiconductor. From that, draw a sketch of the electron and hole density. (hint: see p. 18 of the Modern Theory of Solids notes.) 20. From the plot of the instrinsic carrier concentration vs 1/T, determine the band gap energy of each semiconductor listed. 11

12 21. For an intrinsic semiconductor, why is it that the Fermi energy level is not quite exactly at mid-gap? Explain your answer. 12

13 22. The freeze-out curve for an uncompensated n-type semiconductor is shown at right. Determine E D and N D and E g. On the plot, label all regions that are not named. 13

14 23. The freeze-out curve for compensated doped Ge is shown below. Is the Ge n- or p-type? Determine the dopant energy level (in both the full slope and half slope regions), majority and minority dopant concentrations. Label the plot thoroughly. 14

15 Heterostructure Band Diagrams: (note: for all band diagrams, label your sketches thoroughly to receive full credit) Use the figure above to help you answer most of the questions: 24. How does the band gap change as Al is added to GaAs to form AlGaAs? Explain (3 pts) 25. How would you denote the fractional changes in Al and Ga composition for the chemical formula of AlGaAs? Demonstrate this by including the fractional amounts in AlGaAs for energy band gaps of 1.5 ev and 2eV. (6 pts) 15

16 26. Applying your knowledge of band gap engineering and SP 3 and using the figure above: a. Sketch schematic of the cross section of a light emitting device that emits blue light. Provide the alloy amounts for the cladding layers and active region and state how you obtained the values for these amounts. b. Draw the energy band diagram in flat band condition to support your drawing that includes metal contacts. Draw the energy band gaps to scale and label your figures thoroughly. c. Draw the energy band diagram in equilibrium condition to support your drawing that includes metal contacts. Draw the energy band gaps to scale and label your figures thoroughly. d. Provide a bulleted list of the aspects that demonstrate that your materials systems choices are sound one. 16

17 27. Draw the energy band diagrams at flat band and equilibrium conditions of the following heterojunction or heterostructures: a. p-gan / n-algan b. n-gan / p-algan 17

18 c. For the following structure, draw the energy band diagrams for the following conditions: flat band, equilibrium, and at a bias condition greater than the V turn-on: ohmic contact/n-gan/ i-gasb/ p-gan/ohmic contact. 18

19 28. Using your knowledge of 1) Band Gap Engineering (BGE) and band theory, and (2) quantum mechanics (e.g., tunneling potential barriers and potential wells) (questions on SP 3 will come later), describe how these concepts can be used to design the following (use energy band diagrams to support your arguments they can be in flat band, equilibrium or biased modes): a. A light emitting device that contains a quantum well or several quantum wells (light emitting diode or laser) b. Faster or greater drive current MOS device. Include in your discussion not only on channel current, but also gate leakage current. 19

20 29. Draw and thoroughly label the band diagrams for metal-semiconductor junctions for the following work function cases and state whether they are ohmic or Schottky contacts: a. Φm > Φs/c (p-type S/C) b. Φm < Φs/c (p-type S/C) c. Φm > Φs/c (n-type S/C) d. Φm < Φs/c (n-type S/C) 20

21 MOS Devices and MOS Device Band Diagrams: (note: for all band diagrams, label your sketches thoroughly to receive full credit) 30. Using the figure to the left to aid you, draw the SiO 2/Si interface for the following conditions: a. Depletion E e- or Φ S Oxide S/C?Φ F E c b. Accumulation?Φ F?Φ F 0Φ F E i Φ F E f & E A?Φ F E v c. Onset of inversion d. Threshold of inversion e. Strong inversion 21

22 31. Provide definitions of what separates: a. inversion from depletion b. depletion from accumulation 32. Draw both nmoscap and pmoscap for the following conditions: a. Flat band b. Equilibrium 22

23 c. Accumulation. State whether or not the carriers are majority or minority. d. Onset of inversion. State whether or not the carriers are majority or minority. 23

24 e. Threshold weak inversion. State whether or not the carriers are majority or minority. 24

25 33. Thoroughly draw and label axes and all regions in the following plots: a. Charge versus semiconductor surface potential, φ s b. Total capacitance versus gate voltage, V g. Also include the Cox (or C insulator) and C Si on the plot. 25

26 34. Answer all the following questions relative the MOSFET pictured below: a. What type of MOSFET is in the figure?(2 pts) V G V S Metal gate Electrode Gate oxide V D b. Draw the flat band & equilibrium band diagrams for the two regions which are encircled. Source (n+) p-type Si Drain (n+) V sub 26

27 c. Consider that the MOSFET is biased into inversion: i. What polarity is the gate voltage (V G)? ii. What type carriers are attracted to the Si/SiO 2 interface (channel region) and are they minority or majority carriers? iii. Assuming that both the source voltage (V S) and the substrate voltage (V SUB) are grounded, what polarity would the drain voltage (V D) need to be to turn on the device? iv. Draw the band diagrams for the condition in iii for the two regions which are encircled. 27

28 d. Consider that the MOSFET is biased into accumulation: i. What polarity is the gate voltage (V G)? ii. What type carriers are attracted to the Si/SiO 2 interface (channel region) and are they minority or majority carriers? iii. Assuming that both the source voltage (V S) and the substrate voltage (V SUB) are grounded, what polarity would the drain voltage (V D) need to be to turn on the device? 28

29 iv. Draw the band diagrams for the condition in iii for the two regions which are encircled. 29

30 35. Answer the following questions relative the MOSFET below: a. Consider that the work function of the metal is less than the work function of the p-type Si. Draw the band diagrams for the following: V G i. Flat band Metal gate V ii. Equilibrium S Electrode Gate oxide iii. Inversion Source (n+) p-type Si Drain (n+) V D V sub 30

31 b. Consider that the work function of the metal is greater than the work function of the p-type Si. Draw the band diagrams for the following: i. Flat band ii. iii. Equilibrium Inversion 31

32 36. Answer the following questions relative the MOSFET pictured below: a. What type of MOSFET is in the figure?(2 pts) V G V S Metal gate Electrode Gate oxide V D b. Draw the flat band & equilibrium band diagrams for the two regions which are encircled. Source (p+) n-type Si Drain (p+) V sub 32

33 c. Consider that the MOSFET is biased into inversion: i. What polarity is the gate voltage (V G)? ii. What type carriers are attracted to the Si/SiO 2 interface (channel region) and are they minority or majority carriers? iii. Assuming that both the source voltage (V S) and the substrate voltage (V SUB) are grounded, what polarity would the drain voltage (V D) need to be to turn on the device? iv. Draw the band diagrams for the condition in iii for the two regions which are encircled. 33

34 d. Consider that the MOSFET is biased into accumulation: i. What polarity is the gate voltage (V G)? ii. What type carriers are attracted to the Si/SiO 2 interface (channel region) and are they minority or majority carriers? iii. Assuming that both the source voltage (V S) and the substrate voltage (V SUB) are grounded, what polarity would the drain voltage (V D) need to be to turn on the device? 34

35 iv. Draw the band diagrams for the condition in iii for the two regions which are encircled. 35

36 37. Use energy band diagrams to show why MOSFETs operate in inversion as a minority carrier device rather than in accumulation as a majority carrier device. Assume that the source and drain are doped n+-type for both the minority carrier MOSFET and the majority carrier MOSFET. 36

37 MOS SP 3 : Using your knowledge of (1) Quantum mechanics (e.g., tunneling potential barriers and potential wells) (2) Band Gap Engineering (BGE) and band theory, and (3) SP 3 to aid you in answering the following questions. 38. Write down the equations for I D,lin and I D,sat. When a MOSFET is in the On-state, do you want I D large or small? When a MOSFET is in the Off-state, do you want I D large or small? 39. Proportionally, how do the following MOSFET parameters relate to the drive current (drain current, I D)? Please also write down the mathematical proportionalities. Considering the On-state of a MOSFET, state whether or not you would increase or decrease the parameter and explain using one sentence. a. Width, W. b. Length, L. c. Oxide capacitance, C ox. d. Oxide thickness, t ox. e. Oxide relative dielectric constant, k f. Mobility, µ g. Effective mass, m eff h. Threshold Voltage, V t 37

38 40. Proportionally, how do the following MOSFET parameters relate to the capacitance (C ox)? Please also write down the mathematical proportionalities. a. Dielectric constant, κ. b. Width, W: c. Length, L: d. Oxide thickness, t ox: 41. Explain using band gap engineering and SP 3 what approaches can be used to change the value of the parameter to improve MOSFET performance. e. Dielectric constant, κ. f. Effective mass, m eff: 38

39 DIBL and GIDL: 42. We described DIBL and GIDL in the course. Using energy band diagrams and sketches of an n-mosfet in cross section, describe both mechanisms. Provide potential solutions that would minimize DIBL and GIDL. 39

40 Advanced MOSFETs: 43. An advanced MOSFET device structure is shown below in which Si is alloyed with Ge to form SiGe and placed in the channel region. By doing so, the drive current, or drain current (I D), is increased. Do the following to help you determine why growing a SiGe alloy in the channel would increase the drive current. a. Draw the flat band & equilibrium band diagrams in the encircled regions. V G V S Source (n+) Metal gate Electrode Gate oxide p-type SiGe Drain (n+) V D p-type Si V sub 40

41 b. Draw the band diagrams in the encircled regions when the device is biased in inversion and the device is on (i.e., V D = V DD). c. Using your answers in part a and b and your knowledge of SP 3, Band gap engineering and quantum effects in MOS devices, describe the following: i. Advantages of this device. Substantiate your answer. ii. Disadvantages of this device. Substantiate your answer. 41

42 44. An advanced MOSFET device structure is shown below in which HfO 2 is grown on Si forming a HfO 2/SiO 2 gate oxide. If the effective oxide thickness (EOT) of the HfO 2/SiO 2 gate stack is the same as the physical thickness of a MOSFET with SiO 2, is the leakage current through the HfO 2/SiO 2 gate oxide stack more or less than the MOSFET with SiO 2 only? Do the following to help you answer the question. a. Draw the flat band & equilibrium band diagram of the encircled region of the advanced MOSFET. b. Draw the flat band & equilibrium band diagram of the same region, but of a MOSFET with SiO 2 without HfO2 with the same physical thickness as the EOT of the advanced MOSFET. Use the diagrams to answer the question. V G Metal gate Electrode V S Source (n + -Si) HfO 2 Gate oxide SiO 2 Gate oxide p-type Si Drain (n + -Si) V D p-type Si V sub 42

43 MULTI-DIELECTRIC DEVICES: Device 1: 10V applied Device 2: 10V applied 45. Note the band diagrams for device 1 and 2. Each device has a physical thickness of 6nm, 4nm and 2nm (left to right), respectively, for each dielectric layer (12 nm total). a. Rank the electric field through each dielectric layer in terms of highest electric field (1) to lowest electric field (3) for device 1 and 2. b. Rank each dielectric layer in terms of highest dielectric constant (k) (1) to lowest dielectric constant (k) (3) for device 1 and 2. c. Which device has the lowest effective oxide thickness (EOT), device 1 or device 2? d. Each device has one or more layers of SiO 2 one or more layers of high K dielectric material. For the two devices, label the dielectric layers on each of the devices as either: i. SiO 2 or ii. High k e. Which device would make the better memory device? Explain using a bulleted list. 43

44 f. Write down the equation that describes the tunneling current through the tunnel layer or oxide. g. Write down the equation that describes the tunneling current through the tunnel layer or oxide. Explain using band gap engineering and SP 3 what approaches can be used to change the value of the tunnel current to improve the improvement of the memory device. 44