1. Binary III-V compounds 2 p From which atoms are the 16 binary III-V compounds formed?...column III B, Al, Ga and In...column V N, P, As and Sb...

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1 PROBLEMS part B, Semiconductor Materials Binary III-V compounds 2 p From which atoms are the 16 binary III-V compounds formed?...column III B, Al, Ga and In...column V N, P, As and Sb Semiconductors 1 p Give examples of III-V semiconductors lattice matched to: a) InAs...GaSb... Si...GaP, AlP.... b) InP (a common alloy) In.53 Ga.47 As what is the band gap of this alloy 860meV? E g (In x Ga 1-x As) = x 3. Band gap versus lattice constant 1 p What is the general relation between band gap and lattice constant for (e.g. III-V) semiconductors?...band gap decreases with lattice constant Band gaps of alloys 2 p What are the band gaps of Al x Ga 1-x As for x = 0.4 and x = 0.5? E Γ g(.4) = 1923 mev E X g(.4) = 1973 E L g(.4) = 1965 E Γ g(.5) = 2050 E X g(.5) = 1998 E L g(.5) = Metal/GaAs contact 2 p A metal contact is made to n- doped GaAs, 1x10 16 cm -3, giving V bi = 0.5 V. What is the size of the Schottky barrier? E F = E c kt ln(n c /n) E c E F = kt ln(n c /n) = 25 ln(4x10 17 /1x10 16 ) = 25 x 3.69 = 92 mev Φ SB = = 592 mev 1

2 6. Schottky model 2 p Show the band diagrams (in the Schottky model) for unbiased, forward and reversed biased contacts respectively for a metal with work function, Φ m, in contact with an n-doped semiconductor with the electron affinity, χ < Φ m. 7. Schottky diode 2 p Indicate depletion width, and both Schottky and diffusion (built-in) potentials, in one of the energy band diagrams above and also the circuit (battery + diode symbol) for forward and reverse bias. 8. Band edge offset 1 p Illustrate in a figure the GaAs/InAs and InAs/GaSb band edge offsets. 9. Conduction band offset 2 p a) What is the Al x Ga 1-x As/GaAs/In y Ga 1-y As (bulk/5 nm/bulk) band edge offsets respectively for (x = 0.3 and Qc = 0.65) and (y = 0.15 and Qc = 0.7)? Al x Ga 1-x As/GaAs interface ΔE g (Al x Ga 1-x As, x=0.3/gaas) = 247x0.3 = 374 mev ΔE c = Q c x ΔE g = 0.65 x 374 = 243 mev ΔE v = ΔE g ΔE c = = 131 mev GaAs/ In y Ga 1-y As interface ΔE g = 1064x0.15 = 160 mev ΔE g = 160 mev, ΔE c = Q c x ΔE g = 112 mev and ΔE v = 48 mev b) What is the energy difference when an electron in the conduction band is passing across the GaAs-layer? CB Totally 355 mev 2

3 10. Band edge variation of alloys 3 p Outline the Γ-, X- and L-energy positions in the Al x Ga 1-x As conduction band as a function of x. Assume the position of the valence band maximum is independent of alloy concentration. 11. Semiconductor/semiconductor heterojunction 1 p Describe the typical atomic compositional variation and interface morphology at a single heterojunction Al x Ga 1-x As/GaAs isotype heterojunction 2 p Illustrate the band diagram for this structure when the conduction band interface notch dips below the Fermi level (in the low band gap semiconductor) and electrons are localized to the heterointerface. 13. Alloy band gap 2 p a) Outline the band gap, i.e. the energy positions of the Γ- and the L-points, as a function of x if GaAs is alloyed with Ge to Ge x (GaAs) 1-x. Use the valence band maximum as a reference. 3

4 b)why is Ge x (GaAs) 1-x, rather than Si x (GaAs) 1-x, of more practical interest of the conceptual IV x (GaAs) 1-x semiconductor alloys? 14. Heterostructure band edge variation 4 p The figure shows the conduction band, Γ-edge variation for a GaAs/Al x Ga 1-x As/GaAs heterostructure (20 Å thick and x = 0.3). The value of Qc =.65 and the cross-over point from direct to indirect band gap is at x = a) Show (in the same figure) the variation of the X- and L-points for this heterostructure. b) Make the corresponding figure at the side of the existing one for x = 0.6 and indicate the lowest barrier. 15. Selectively doped 2-DEG structure for HEMT 2 p Describe the heterointerface conduction band variation for a selectively δ-doped, n δ = 2x10 12 cm -2, Al x Ga 1-x As/GaAs structure, with 50 Å thick spacer between doping layer and heterointerface. 4

5 16. Subbands in a 2-DEG potential 3 p Describe the sub-band structure at an Al x Ga 1-x As/GaAs heterointerface if the 2-DEG density is 1x10 12 cm -2. Assume the GaAs CB-potential variation is constant (varying 3 mev over 30 Å) at the interface. Use the infinite, unsymmetric, triangular potential well approximation to calculate the subband levels DEG mobility 1 p Which are the most important electron scattering mechanisms for 2-DEG conduction in the structure above and outline the 2-DEG mobility as a function of temperature. 18. Bulk GaAs growth 2 p a) The growth of bulk single crystals of GaAs are divided into two main groups: pulling and non-pulling. Name one important method in each group pulling non-pulling b) What is the difference in conductivity in LEC-grown GaAs when the As atomic fraction in the melt is varied ±2 % around the "critical As composition"?... c) What is the reason? Evaporation temperature 1 p a) How is the atomic or molecular flux of a material related to its temperature? b) What is the theoretical upper limit in growth rate? 5

6 c) What is the expression for flux from an evaporation source? 20. MBE growth 1 p How is the arrival flux in the molecular beam related to the growth rate on GaAs(001) (formula, units and numbers)? 21. Growth parameters 1 p The following settings for MBE growth was used to grow GaAs: T Ga = 920 C, T As = 300 C, T Si = 970 C, T substrate = 580 C and p background = 3x10-7 torr. Which parameters are important (and which are not) for the GaAs growth rate? 22. Growth rate calibration 2 p A growth rate mesurement gave R 870 = 0.85 µm/h for T Ga = 870 C. A second measurement was made with parameters given in the compendium "Semiconductor heterostructures": "A typical set of parameters for evaporating Ga, T Ga = 970 C, p Ga (1243 K) = 2.2x10-3 torr, M Ga = 70, A = 2 cm 2 and l = 15 cm, gives J Ga = 7.5x10 14 cm -2 s -1. This is somewhat more than one monolayer (ml) per sec. for GaAs growth in the (001) direction. One ml is atoms/cm 2." What is the expected GaAs growth rate, R, for the settings in Problem 21? 23. Alloy concentration from fluxes 1 p How is x in Al x Ga 1-x As realted to the Ga- and Al-fluxes? 24. Growth of an Al x Ga 1-x As alloy 2 p Which Ga-furnace temperature is needed (for the same experimental conditions as above) to grow an Al 0.3 Ga 0.7 As-alloy if the AlAs growth rate has been calibrated to 0.1 ml/sec? 6

7 25. RHEED oscillations and ML-growth by MBE 1 p Why is the RHEED-intensity oscillating when a GaAs-layer is grown by MBE? 26. Thickness calibrations by RHEED 1 p What is the thickness of a GaAs layer, embedded in Al.6 Ga.3 As, after 5 periods in a RHEEDoscillation measurement recorded during the GaAs growth? 27. Use of RHEED oscillations 2 p a) How long time is needed to grow a 100 Å thick GaAs layer on GaAs (001) if the RHEEDoscillation period in b) is 1.2 sec.? b) Calculate the arrival flux rate in a) for arsenic and gallium. 28. Potential variations in a superlattice 3 p a) A GaAs/Al x Ga 1-x As superlattice was grown by MBE. RHEED gave 30 periods during the Al x Ga 1-x As (x = 0.3) growth and 20 periods during the GaAs growth. Outline the periodic variation including thicknesses, the valence band edge and the Γ- and X-conduction band edges. The conduction band offset is 65 %. 29. Particle-in-box used for Al x Ga 1-x As/GaAs SQW 2 p Calculate the confined electron energy states (using the infinite barrier height, particle-in-box model) for a 56 ml thick GaAs SQW. How many states are confined for x = 0.3 (according to the infinite barrier model)? 7

8 b) Indicate the CB-subbands in the figure above. 30. Quantum state energy depends on layer parameters 2 p a) Consider a single QW grown with the same parameters as above. Describe the qualitative change of the confined state energies (electrons and holes) with reference to this QW if: - x is decreased - the QW layer thickness is decreased 31. Single QW 2 p What is the relation between energy and QW width, for the ground and first excited states, in a SQW with potential depth, V 0, and width L? 8

9 32. Electron concentration in a HEMT structure 2 p What is the electron concentration at the interface of an Al x Ga 1-x As/GaAs heterostructure when the first subband (i=1) is filled and the next is half filled (assume x=0.3 and E i = E i!1 + "E c /i 2 ) 33. Molecular layer 2 p a) What is the LUMO-HOMO energy difference if the molecules emitt blue light (λ = 420 nm)? E = 1241/420 = 2.95 ev b) what is a typical size of such a molecule? Assume atoms are separated 2 Å.!E = (N + 1)!2 " 2 2m 0 1 (Nd) 2 = (N+1)x37.3/(N2) 2 4x2.95/37.3 = 0.32 = (N+1)/N 2 N (N+1)/N

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