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1 1 Name: DEPARTMENT OF PHYSICS AND PHYSICAL OCEANOGRAPHY MEMORIAL UNIVERSITY OF NEWFOUNDLAND Final Exam Physics 3000 December 11, 2012 Fall :00-11:00 INSTRUCTIONS: 1. Answer all seven (7) questions. The marks for each question are indicated. The total number of marks on the paper is 100. Budget time accordingly. 2. Write answers in the spaces provided. If additional space is needed, use the backs of sheets but indicate clearly where your answer is continued. 3. Where appropriate, units must be included for answers to be considered complete. 4. A list of useful formulae, a table of constants, and tables of semiconductor properties are attached at the end of the paper (last three pages). For your convenience, three particularly useful parameters are listed below. Particularly useful parameters: Relative permittivity (dielectric constant) for silicon: Si 11.7 Relative permittivity (dielectric constant) for silicon dioxide: SiO2 3.9 Permittivity of free space: F/cm Intrinsic carrier concentration for silicon at 300 K:, Si cm Thermal voltage at 300 K: 300 K V Electron charge: C Planck s constant: J s ev s cm/s 2 Quadratic equation: roots of ax bx c 0 are x b b 2 4ac 2a Total

2 2 Name: 1. [11 marks] The diagram to the right shows energy bands for a junction between gold and n-type silicon with a region of highly doped silicon at the interface. Assume that the work function for gold is 5.1V and that the electron affinity for Si is m 4.01V. + Au n + n + (a) (4 marks) Calculate the Schottky barrier energy, e B0, at the gold-si interface and clearly indicate the height and location of the Schottky barrier on the diagram. (b) (4 marks) What is the minimum doping concentration required in the n + region in order for the width of the space charge region to be less than 100 Å (i.e cm)? Assume that N is large enough in the n + region that you can assume B0 n where e n Ec EF. d (c) (3 marks) Briefly explain why a junction like this might be useful for making an ohmic contact between a metal contact and a semiconductor.

3 3 Name: 2. [12 marks] (a) (5 marks) The picture to the right shows a pn junction that is to be operated as a light-emitting-diode (LED). Briefly explain the process by which light is generated in the LED. Be sure to indicate which region(s) are involved and to indicate how majority or minority carriers are involved in the process occurring in those region(s). n - + p t (b) The energy-band diagram to the right represents a forward-biased pn junction. (i) (2 marks) Briefly explain what aspect(s) of this diagram show(s) that the p-type and n-type materials in this device are degenerately doped. E Fp E Fn E C E v (ii) (3 marks) Briefly explain why there is a population inversion (i.e. higher concentration of electrons in the conduction band than in the valence band) in the central region of the junction (labeled as thickness t). (iii) (2 marks) What kind of device depends on the presence of a population inversion for its operation?

4 4 Name: 3. [14 marks] (a) Assume that 1.49 ev photons are incident on the surface of a GaAs slab with an intensity 0.09 W/cm. (i) (3 marks) If the absorption coefficient for 1.49 ev photons in GaAs is cm -1, the GaAs surface? what is the photon intensity at a depth of x cm below (ii) (3 marks) What is the electron-hole pair generation rate at that depth? (Hint: be careful with units.) (b) The dots on this diagram represent minority-carrier concentrations at the space charge edges for a forward-biased pn junction. The horizontal dashed lines represent thermal equilibrium minority-carrier concentrations. (i) (2 marks) Attach the labels,,, and to the appropriate features on the diagram. carrier concentratio p n -x p x = x n (ii) (3 marks) Assume that the semiconductor is Si and that the impurity concentrations on the p-type side and n-type side, respectively, are cm and cm. Calculate the thermal equilibrium minority-carrier concentration on the p-type side assuming complete impurity ionization and 300 K. (iii) (3 marks) Calculate the minority-carrier concentration at the space charge edge on the p-type side,, if a forward-bias of 0.6 V is applied to this junction.

5 5 Name: 4. [15 marks] The drawing to the right represents a PIN junction diode operated as a photodiode. (a) (4 marks) Briefly explain why there is an induced electric field in the intrinsic region of this device and indicate the direction of this electric field on the diagram. p + n + i a b c d (b) (4 marks) For this device to operate as a photodiode, should terminal a be biased positive or negative with respect to terminal b? Briefly justify your answer and indicate, on the diagram, the direction of the current that will flow when the device is illuminated. (c) (4 marks) Briefly explain the difference between prompt photocurrent and delayed photocurrent. In which regions of the device are the carriers contributing to the prompt and delayed photocurrent generated? (d) (3 marks) Briefly comment on how the presence of an intrinsic region affects the properties of a PIN photodiode in comparison to those of a pn junction photodiode.

6 5. [15 marks] M O S 6 Name: M O S E c 0 E Fs E Fi a b Diagram (a) above shows the energy band diagram on the semiconductor side of a metal-oxidesemiconductor (MOS) capacitor at threshold bias. (a) (2 marks) Is the semiconductor p-type or n-type? Briefly justify your answer. E v (b) (2 marks) Is the voltage applied to the metal gate positive or negative? Briefly justify your answer and indicate the Fermi level of the metal gate on diagram (a). (c) (3 marks) On diagram (b), carefully draw the charge distributions on the metal gate and in the semiconductor in this bias state. You should show the charge density on the metal, Q, the space charge density in the semiconductor, and any charge density induced in the semiconductor. m (d) The diagram to the right shows an IV curve, corresponding to I D(sat) 0.4 ma and V DS (sat) 4.35 V, for a n-channel MOSFET with a threshold voltage of 0.65 V. I D 0.4 ma V DS (sat) (i) (2 marks) What is the gate voltage corresponding to this curve? 4.35 V V DS (ii) (3 marks) What is the conduction parameter, K n, for this device? (iii) (3 marks) What is the current I if D V 4.0 V and V 3.0 V? G DS

7 7 Name: 6. [16 marks] An enhancement mode, n-channel MOS transistor is fabricated on a p-type silicon substrate with 10 cm. The gate material is n + polycrystalline silicon. The threshold voltage is V T 1.2 V. Relative permittivities are given on the front page of the exam. Assume 300K. (a) (2 marks) Using the graph to the right, estimate the metalsemiconductor work function potential difference, ms, for this device. (b) (3 marks) What is the potential difference E E Fp 1 F Fi e between the Fermi energy and the intrinsic Fermi level in the substrate? Assume complete ionization? (c) (3 marks) What is the maximum space charge width,, in the semiconductor? (d) (2 marks) What is the magnitude of the maximum space charge density per unit area, max, in the depletion region of the semiconductor? (e) (3 marks) If the equivalent fixed oxide charge is 810 C/cm, what is the oxide capacitance per unit area? (f) (3 marks) What is the oxide thickness?

8 8 Name: 7. [17 marks] The diagram shows a pn junction solar cell connected to a resistive load. When illuminated, the net current in this device is I I L I F where I L is the photocurrent and I F is the forward bias current. p n (a) (3 marks) On the diagram, indicate the directions of I, I L, I F. (b) (3 marks) Briefly explain how the photocurrent is generated and why it flows in the direction you have indicated. R (c) (3 marks) Briefly explain what causes the forward-bias current and why it flows in the direction you have shown. (d) (4 marks) A silicon pn junction solar cell is illuminated such that the photocurrent is I L 0.42 A at T 300 K. Its open circuit voltage is found to be 0.6 V under these conditions. What is its reverse saturation current. (Hint: recall that for a forward-biased pn junction, the current is exp 1.) (e) (4 marks) The bandgap in silicon is 1.12 ev. Would you expect this solar cell to work better when illuminated by electromagnetic radiation with wavelength 0. 8 μm or when illuminated by electromagnetic radiation radiation with wavelength 1. 4 μm? Justify your answer. (Hint: you may find it useful to calculate the wavelength of a 1.12 ev photon.)

9 9 Name: Potentially useful formulae Photons: photon ; / ; ; Bohr Atom: ; Drift curr. density: ; Eff. mass: ext ; Free particle: Densities of states: / ; / F-D prob. function: ; M-B approx.: exp exp Carrier distributions: ; 1 Effective densities of states: 2 / ; 2 / Therm. equil. carrier concentrations.: exp ; exp Intrins. carr. concentration & Fermi level: exp ; midgap ln Extrinsic semiconductor relationships: exp ; exp Fundamental semiconductor equation: Donor electron relationships: Acceptor hole relationships: Compensated semiconductors, complete ionization: ; exp exp ; exp exp Fermi energy level relationships: ln ; ln ; ln ln Conduct. & resist.: Drift curr. dens.: Total current density: Mobility: ; Diffusion curr. dens.: Einstein relation: Graded impurity distribution: Equil. generation & recombination rates: ; ; Excess carrier recombination (p-type): 0 / ; ; Excess carrier recombination (n-type): 0 / ; ; Hall effect: ; ; ; ; Built in potential barrier (pn junction): ln

10 Poisson s equation: 10 Name: Potentially useful formulae (continued) Sp. charge width: / ; ; / Electric field: max Schottky barrier: Junction Capacitance: / pn diode: exp 1 Schottky barrier diode: exp exp 1 exp 1 MOS depletion width (p-type): / ; ln MOS depletion width (n-type): / ; ln Metal-semiconductor work function difference (p-type): Metal-semiconductor work function difference (n-type): Flat-band voltage: ox Maximum space charge density: max Threshold voltage: max ox 2 ox MOSFET (general): 2 ; ox ; ox ox ox MOSFET (saturation): sat ; sat Electron inversion charge density: exp Channel length mod.: sat Δ sat; Mobility variation: eff max ; eff eff / Forward-biased pn junction.: minority carrier conc. at space charge edge: exp ; exp reverse saturation current density: common-base current gain: photon flux intensity: common-emitter current gain: electron-hole pair generation rate: pn junct. solar cell: exp 1; oc ln 1 ; 1 exp 1 photoconductor: pn photodiode prompt photocurrent: photoconductor gain: Γ ph PIN photodiode prompt photocurrent: Φ 1

11 11 Name: Constants and Conversions J/K ev/k C kg F/cm J-s = ev-s cm/s 1 ev= J Silicon, gallium arsenide, and germanium properties at T = 300 K Property Si GaAs Ge Atoms/cm Atomic weight Crystal structure Diamond Zincblende Diamond Density (g/cm 3 ) Lattice constant Melting point ( o C) Dielectric constant Bandgap energy (ev) Electron affinity, (V) Effective density of states in conduction band, cm Effective density of states in valence band, cm Intrinsic carrier concentration cm Electron mobility, (cm 2 /V-s) Hole mobility, (cm 2 /V-s) Electron effective mass (DoS) Hole effective mass (DoS)

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