2024 NTU H3 Finals

Section A (50 marks} Answer ALL questions in this section. All questions carry equal marks. You should spend about J hour 15 minutes on the questions in this section. r I I lj,A .,,1 p \\--t )'? l, '('... . 1. A Schottky co~act is to be made on an n-type semiconductor. The ~ork functton of the metal used is 4.5 eY. The semiconductor has an electron affiruty of 3.5 eV, L.v\.~ XI bandgap energy of 1 tV, a critical electric field of 2. 7x 10~5 V /cm, a relative pennittivity of 12.5 and an intrin ic carrier concentration o~ -3 £300K) < f,,.. 12 ~.· Jc-:~ (a) What should th/doping concentration of the semicobductor be if the desired built-in voltage is 0.75 V? vb . 1, \1¥io' I [3] (b) Calculate the bias ~6ltage that will give a maximum electric field equal to the critical fiely 1c , [3] ,{c)IBriefly describe what will happen to the ~ct when the conditio~ C~'j in part (b) is met. [4] R.11-1OJ-t I, J_ 2. A light emitting diode has~rward biased current of 10.3 mA. The radiative recombination efficiency is 0.95. ifhe bandgap energy and refractive index of the semiconductor are 1.42 eV an 3.3, respectively. n f 7Svi"" ( a) Estimate the wavelength of the light emitted. Which part of the electromagnetic spectrum does the wavelength belong to? [2] I"' t<~ i-c,J . 0. () "~"" (b) Determine the optical power generated in the semiconductor. Only a small fraction of the emitted photon flux becomes useful light output. Why? [ 6] (c) Assuming a~emiconductor surface, estimate the fraction of emitted photon flux that would become useful light output. --[2] (,f~ % 3. (a) Figure 1 Figure 1 shows the position of atoms on a hexagonal plane (which is made up of six equilateral triangles) of a semiconductor. Determine the surface density of atoms on the plane. (.'i,1.-{\l)IS [6] 8Explain what is meant by the effective mass of a carrier in a semiconductor. (4] -2 - -

- ----~ \~L ... ----"4 I fr:1i- ...... 'L "• hC: v ~}v r L: J (;f:. -l~v -:. ().).. o, v' 4• Ap-type semiconductor sample has a bandgap energy of 3.2 eV and its Fermi level is 0.2 eV above the valence band edge. The effective density of states in the conduction ,u.m...\4l-l~'P--b-.... ~"~rl__, are 2.23xl018 cm-3 and 4.62xl019 cm-3, respectively. Assume that t../( 2 n = 11 cm Is and rn = 0.1 µs. b. l b x \ o • 1 r n '· 1ne the value of (nj) and hence calculate the majority carrier concentration in this semiconductor sample. 7 ), \ x.,1\~ [5] - i' I)':. • (b) Excess ro.mori~ carriers are injected continuously at one end of the sample such that the excess carrier concentration at x = 0 is 3Jx1014 cm-3 under steady state condition. Determine the position in the sample where the minority carrier diffusion current density is 225 mA/cm2. _,_ c:),Ql,11., [5] 5. The electric field in an n-type semiconductor samfle §Ps k8T 106x t\CltJ { = ( q) 106xz + 1 V /cm f(1,i i,,~~J•"'l The distance xis in unils of cm and is valid for.O :5 x :5 22 µm. The torai};lectron current density is zero throug