Examination WS 01/02 Materials and Devices in Electrical Engineering Monday 11 th of March, 9:00 to 11:00, SR 203, International Department building It is allowed to use any kind of media (books, scripts, overheads, notes,...) during the examination. Any type of communication with other people is forbidden. Please write down your name and registration number on every page that contains a part of your results. The examination duration is 2 hours. Information on the exercises The examination consists of two parts: a) multiple choice questions (30*2 = 60) This part contains 30 questions. Notice that for each question, there could be one or more correct answer(s). You have to decide, which one is correct, then cross (X) the corresponding letter. You will get 2 points for each question, only when all the correct answer(s) is/are chosen. The maximum number of points you can achieve is 60. b) calculations (60) The second part contains 4 calculations, each consisting of several tasks a), b), c),... If you are not able to solve one task, go on with the next one using the given value. The problems should be solved on the sheet below the task. If there is not enough space you can ask for additional sheets. Please use an extra sheet for each problem. You can get maximum 60 points for the calculations. The number of points for each task is given in the text. If you solve only a part of a calculation or of a task, or if your results are incorrect, you will get a lower value of points. MC Cal. 1 2 3 4 Σ Result - 1 -
Multiple Choice Questions (30 questions, each 2 points, Σ = 60 points) 1. To compare the atom models in terms of electron distribution, it is true that a) the Bohr atom model assumes electrons to be particles revolving around the nucleus in discrete orbitals. b) in wave-mechanical model we treat electron position as a probability distribution. c) in both atom models the electron is considered to exhibit both wavelike and particlelike characteristics. d) with both atom models, electron position is well defined in terms of its orbital. 2. Among the following statements about quantum numbers, which one is correct? a) Shells are specified by a principle quantum number n, which is related to the position of an electron. b) Quantum numbers determine the number of states within each subshell. For a p subshell, there exist four states. c) The energy of a 4s state is greater than a 3d. d) Valence electrons do not participate in the bonding between atoms. 3. For the elements in the periodic table, a) each horizontal row is called one period, with increasing atomic number from the left to the right. b) Si and P show similar valence electron structures since they both belong to Group VA. c) Electropositive elements are capable of giving up their valence electrons. 4. Once the interatomic separation distance of two isolated atoms reaches equilibrium spacing r 0, then a) the net force between the two atoms F N = F A + F R = 0. b) the net force between the two atoms F N = F A + F R = maximum. c) the net potential energy E N = 0. d) the net potential energy E N = E 0 = minimum. 5. What is correct for atomic bonding in solids? a) The smaller the difference in electronegativity, the smaller the degree of ionicity. b) In covalent bonding, there is a sharing of valence electrons between adjacent atoms, therefore the covelent bonding is nondirectional. c) With metallic bonding, the valence electrons form an electron cloud. d) The chemical bonds in the following materials are: LiF, SiC ionic; H 2 O, Ge covalent; Cu, W metallic. 6. For the FCC crystal structure, a) each corner atom is shared among 4 units cells. b) a total of 8 whole atoms can be assigned to a given unit cell. c) the coordination number and the APF are 12 and 0,74, respectively. 7. When concerning the crystal systems, it is true that a) the three axes (x, y, and z) are mutually perpendicular for 4 crystal systems: cubic, hexagonal, tetragonal and orthorhombic. b) the triclinic system has the least symmetry. c) crystallographic directions are specified by 3 indices as [uvw] in all crystal systems. d) an assumed unit cell, a=b=0,144nm, c=0,154nm; α =β =γ =90, has a tetragonal crystal structure, and the (001), (010) and (001) planes all belong to the {100} family. - 2 -
8. About imperfections in solids, which statement is correct? a) The concentrations of vacancies are significantly lower than that of self-interstitials. b) Dislocations are one-dimensional crystalline defects. For edge dislocations, Burgers vector and dislocation line is perpendicular. c) The number of point defects in crystal lattices increases exponentially with increasing temperature. d) 2-dimensional imperfections include external surface, grain boundaries, twin boundaries, and stacking faults. 9. For steady-state diffusion, which description is correct? dc a) It can be represented as: J = D, in which the diffusion flux (J) is proportional to dx the concentration gradient (dc/dx), and does not change with time. b) The diffusion coefficient D is temperature- and activation energy-dependent. Qd 1 c) There is a relationship of: ln D = ln D0 + ( ). R T d) Two diffusion mechanisms are possible: vacancy and interstitial. 10. Which statement is correct among the following thermal phenomena? a) Thermal expansion is due to the asymmetric nature of the potential energy versus interatomic spacing curve through. b) The larger the interatomic bonding energy, the deeper and more narrow the potential energy trough, as a result, the greater the coefficient of thermal expansion α l. c) Heat is transported in solid materials by free electrons and by vibrational lattice waves (phonons). d) Thermal shock is the fracture of a body resulting from thermal stresses induced by rapid temperature changes. 11. About mechanical properties of materials, it is true that a) a material that is stressed first undergoes permanent deformation. b) there are four types of stress-strain tests: tension, compression, torsion, and shear. c) the material that is stressed by tensile load experiences the elastic-plastic deformation transition where yielding occurs. d) tensile strength corresponds to the maximum tensile stress that may be sustained by a specimen. 12. Concerning noncrystalline solids, a) there exist no long range order but only short range order. b) there is a discontinuous decrease in volume with temperature reduction. c) organic molecules that have double and triple covalent bonds are termed unsaturated. d) a glassy material is considered to be supercooled liquids above the glass transition temperature T g. e) semicrystalline polymer consists of crystalline and amorphous regions 13. Metals a) possess resistivity which increases with temperature. b) possess resistivity which can be raised by increasing the concentration of impurities. c) have the electron band structure in which the filled valence band is separated from the empty conduction band by a band gap. d) are extremely good heat conductors because relatively large numbers of free electrons exist that participate in thermal conduction. - 3 -
14. Which description is correct about applications of metals and alloys: a) Thermocouples should have a high Seebeck-coefficient so that the thermoelectric voltage generated by temperature difference can be precisely measured. b) The loop of strain gauge should be arranged for max. length and high accuracy. c) Resistive strain gauges are used as force sensors. d) Precision-resistor should possess low resistivity and very low temperature coefficient. 15. Semiconductors a) are materials with predominantly covalent bonding. b) are electrically insulating at T = 0 K. c) show a relatively narrow band gap E g = E C E V < 0,5 ev. d) possess conductivity which can be raised by increasing the temperature. 16. For insulators, a) the energy corresponding to the highest filled state at 0 K lies near the band gap center. b) at a given temperature, the larger the band gap, the higher the electrical conductivity. c) electrons can be excited into conduction band only when the excitation energy is at lease equal to the band gap. 17. For electrical conduction, which one is true? a) Free electrons participate in the conduction process, while holes do not. b) The electrical conductivity is proportional to both the number of free electrons and the electron mobility. c) The total conductivity of an ionic-bonded material is equal to the sum of both electronic and ionic contributions. d) All polymeric materials are poor electrical conductors. 18. At room temperature, a highly pure silicon crystal a) has a higher electron concentration n than its hole concentration p. b) becomes a p-type semiconductor by doping B atoms. c) becomes a n-type semiconductor by doping B atoms. d) remains an unchanged hole concentration p when it is heavily p-type doped. 19. About semiconductors, which statement is correct? a) Two possible intrinsic compound semiconductors are GaAs and InSb. b) The Hall effect experiment can be conducted for determination of majority charge carrier type, concentration and mobility of a certain material. c) The energy level of a donor state is just below the bottom of the conduction band. d) n = p is still valid for an extrinsic semiconductor. 20. Among semiconductor devices, a) one p-n rectifying junction can be used for amplification of electrical signals. b) transistors are electronic devices that allow the current to flow only in one direction. c) a p-n junction has an extremely small max. current flow for reverse bias voltage I R in comparison to that for forward bias I F. 21. Two parallel plates which were filled with a bulk of dielectric material are connected with constant voltage. Now the material is taken out of the gap. Thus, the capacitance, the electric field and the dielectric displacement of the capacitor: a) all become larger. b) all remain the same. c) all become smaller. d) C, D become smaller, E remains the same e) C, E become larger, D remains the same. - 4 -
22. When electric field present, the polarizability of dielectric materials α Σ can be represented as: a) in Si and C when electric field present: α Σ = α e + α ion. b) in NaCl and H 2 O when electric field present: α Σ = α e + α ion. c) in BaTiO 3 (T > 600 K): α Σ = α e + α ion + α or. d) in BaTiO 3 (T < 300 K): α Σ = α e + α ion + α or. e) in Fe 3+ doped BaTiO 3 barrier layer capacitor: α Σ = α e + α ion + α or + α RL. (*RL: Raumladung space charge) 23. About different types of capacitors, it is true that a) Foil capacitors may have large capacitance due to the very large surface area. b) Electrolyte capacitors possess a high volume capacity, since on the anode there is a very thin anodic oxidation layer which acts as dielectric. c) Electrolyte capacitors possess a high volume capacity, since the electrolyte has a high relative dielectric constant. d) Ceramic barrier layer capacitors with high capacitance can be realized by doped BaTiO 3, which have conductive grains and insulating barrier layers with very high ε r. 24. Pb(Zr,Ti)O 3 a) possesses a minimum coupling coefficient k at the morphotropy phase boundary. b) is a kind of ferroelectric material with spontaneous polarization. c) becomes cubic structure above 500 C, while at room temperature may exhibit different structure concerning its composition. d) is a kind of material from which the mechanical deformation can be excited by the external electric field reversal. 25. Above Curie temperature, a P(E) diagram of the ferroelectric material shows: a) the linear correlation of P ~ E. b) a distinct hysteresis. c) the correlation of P ~ E². 26. Nonlinear resistors: a) PTC resistors consist of semiconducting, polycrystalline ferroelectrics which indicate temperature-dependent potential barrier at grain boundaries. b) The materials for varistors can be n-doped ZnO or BaTiO 3. c) The physical effect of NTC is the hopping-conduction or valence exchange of the cations in transition metallic oxide such as NiMn 2 O 4. d) PTC resistors are suitable for self-regulating heating components, since above the reference temperature the resistance rises strongly. 27. Which statement is correct for magnetic properties? a) MnO is a kind of antiferromagnetic material which possesses no net magnetic moment as a whole. b) In paramagnetic materials H << M is valid. c) The B-versus-H behavior for a ferrimagnetic material is linear. d) There are two different sources of magnetic moments for electrons. 28. The susceptibility of diamagnetic materials a) is negative. b) is positive but < 1. c) is temperature independent. d) rises with temperature. - 5 -
29. For ferromagnetic materials, a) the atomic dipoles are induced and aligned opposite to the external magnetic field. b) the saturation magnetization is reached when all the magnetic dipoles are aligned. c) there is no spontaneous alignment of permanent magnetic dipoles when H = 0 at T < T C. d) Hard magnetic materials show a higher coercive force H C than soft ones. 30. Superconductivity a) exists in all metals and metallic oxides when T < T C. b) is temperature independent. c) is caused by the existence of Cooper-pair. d) does not exhibit when T > T C or magnetic filed strength is higher than critical value. e) can be shown by YBa 2 Cu 3 O 7 and Tl 2 Ca 2 Ba 2 Cu 3 O 10. Calculations (Σ = 60 points) 1. A copper wire of 50 m long must experience a voltage drop of less than 1,0 V when a current of 2,5 A passes through it. (Σ = 12 points) a) Using the data in Table 19.1, computer the minimum diameter of the wire. (3 points) b) Compute the electric field strength and the current density across the two ends of the wire, respectively. (4 points) - 6 -
c) At room temperature the number of free electrons per cubic meter for copper is 1,25 10 29 m -3. Now calculate the electron drift velocity v d for Cu when the magnitude of the electric field is 1000 V/m. ( e = 1,6 10-19 C) (5 points) 2. (Σ = 8 points) As shown in Fig. 1, a plate of iron is exposed to a carbon-rich atmosphere on one side and a carbon-deficient atmosphere on the other side at 700 C. Assume a condition of steady state is achieved, and the concentrations of carbon at positions of 10 mm and 15 mm beneath the surface of the plate are 0,8 and 0,4 kg/m 3, respectively. Suppose a diffusion coefficient of 3 10-11 m 2 /s at this temperature. Fig. 1 carbon-rich atmosphere iron plate carbon-deficient atmosphere direction of diffusion of carbon a) calculate the diffusion flux of carbon through the plate. (4 points) b) calculate the atomic packing factor (APF) and determine the coordination number for the crystal structure of α-iron. (Table 3.1 is available.) (4 points) - 7 -
3. The single crystal represented in Fig.2 consists of high-purity silicon. At the both left and right surfaces electrodes are attached for electric contacting. (Σ = 17 points) Fig. 2 Si-single crystal Aluminium-film electrode Table 1 Characteristics of intrinsic silicon at 300 K Semiconductor Si Band gap E g (ev) Dielectric constant ε r Electron mobility µ e (m²/vs) Hole mobility µ h (m²/vs) Electrical conductivity σ i (Ωm) -1 1,11 11,9 0,14 0,048 4 10-4 e = 1,6 10-19 C a) Using the associated data given in Table 1, computer the electron and hole concentrations of Si single crystal at room temperature. (3 points) Now the silicon block is covered by an aluminium film, and the whole arrangement is stored in a diffusion oven at a high temperature for a long time. Assuming that the aluminium atoms diffuse homogeneously into the silicon block to give a concentration of 1,5 10 19 m -3 of charge carriers at room temperature. b) Is this material n-type or p-type? Give a short explanation. Which kind of other elements can be used instead of Al? (6 points) c) How to call the energy level introduced by this type of impurity? Where is it located in the energy band? (4 points) - 8 -
d) Calculate the conductivity of this doped silicon at room temperature, assuming that charge carrier mobility is the same as for the intrinsic material. (4 points) 4. A charge of 5,5 10-11 C is to be stored on each plate of a parallel-plate capacitor having an area of 100 mm 2 and a plate separation of 1 mm. (Σ = 23 points) a) If a material A having a dielectric constant of ε r, A = 4,8 is positioned within the plates, what voltage is required? (4 points) (If you have not solve this task, go on using V = 10 V.) b) Computer the dielectric displacement and the polarization of part a). (6 points) - 9 -
c) If another dielectric material B is now used to substitute for material A, and an external electric field is applied to remain the charge on each plate unchanged. If the polarization of B is measured to be P = 5,0 10-7 C/m 2, what is the dielectric constant of material B? (6 points) d) Material C is a ferroelectric material which exhibits the following characteristics at room temperature (300 K): Remanent polarization: 0,30 C/m 2 Saturation polarization: 0,38 C/m 2 at 2000 kv/m Coercive field: 1000 kv/m Assuming that the material was initially unpolarized, sketch the entire ferroelectric hysteresis curve in the given range, scale and label both coordinate axes, denote all the characteristic points in the curve. (7 points) 0-10 -