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 throughout the sample and n(x = O) = 1016 cm-3. The hole and electron diffusion coefficients are Dp = 40 cm2/s and Dn = 110 cm2/s, respectively . ..,~ \olb tl1i.¾'\.-1:l) 1. (a) Determine the electron concentration, n(x), in the sample. [6] ........__,_;_ (b) Sketch the electron concentration profile of the semiconductor. Indicate, in the same diagram;the drrechons ... of the electron flux and the corresponding current arising from the non-uniform electron concentration. -3 - I ll.-tt"" [4] -

Section B (50 marks) Answer ALL questions in this section. All questions carry equal marks •. . 1 ·n this sectron. You should spend about 1 hour and 15 minutes on the quest ons 1 I ---'-l '=v)-= "l,\'l,X\n-~ . '=' Th 1iiiWobability of 6. A urufonnly doped semiconductor has a bandgap of 2.07 eV. e 11!!:!=-:_5 Add'f 1 finding @t the valence band edge of the semiconductor is 9 .12x 10 • ; 1~n~ donor impurity atoms of Nd cm-3 are added to the semiconductor to achieve the esi~e doping level and the resulting probability of finding a hole at the valence band e ge decreases to l.85x 1 o-7. Assume n, = 400 cm-3 and T = 300 K. \ __ _£ { c v) : r, ts k \f,>' 1 (a) Find the value of Nd. (b) The additionally doped semiconductor is illuminated uniformly with a / suitable wavelength light to produce a steady state"'excess carrier Her concentration of An0. Ther~after the light is turned off at time' t = 0. Determine the excess minority carrier concentration as a function of time f-J ()1 iJ after the light is turned off, assuming that it is a high-level injection 4 condition, i.e. An0 > > Po . The rate of change of the minority carrier ""() concentration with respect to time t is given by 2:.,1) ? l)j 11., dn -{. -=GL+G -R 4 dt In L '11) -t-Ltor~ ( c) Identify and describe the dominant scattering mechanism in the additionally .doped semiconductor. How WI e c er mo ility change when the temperature of the semiconducto decreases. r;;;J The additionally doped semiconductor is subsequently converted to a p + semiconductor through further doping. A metal-insulator layer is then deposited onto the p + semiconductor to form a metal-oxide-semiconductor (MOS) device. A voltage is applied across the MOS device and the resulting band diagram is illustrated in Figure 2 ommeiit the polarity of the voltage that is applie~ to the MOS device and the pe of carrier that can be found in region Rx ·(Discuss how the carrier con~gio~ Rx compares with those m the bulk of the semiconductor, i.e. towards the right side of region Rx. vw, i-e 7 f p+ Semiconductor j 0~ \,\Af'£., Metal Ee E -~ FM ••••••• ( ·- ••••••••••••••• EFS Ev region Rx Figure 2 -4- [8] [7] [5] [5]

diode at st d -amer I ibutton plot of ~~ilicon abrupt p-n junction ea y state Symbols h th • -conce tr . • ave e1r usual meanings. The intrinsic carrier n atton at 300 K is 1 5 1010 -3 h · · · · · e i,,.X cm , t e relative perm1tt1v1ty 1s li.7, the lifetimes of xcess electrons and hole b th O r 1300 2 8 are O .1 µs, and the electron ole mobilities are cm /V-s and 400 cm2N-s, respectively. /4 ,v '0!J carrier cone. l~on 7.2x1015 cm-3 .8x1013 cm-3 I '-"f "'?t =f\it?o I I I I I L.________________ . 3.4x103 cm-3 ---------L----L..l._ ______ ~x l-ipo Xn O Xp Figure 3 <( Is the diode under ~or reverse bias? Explain your answer. fo"etermine the b~ voltage applied. Is the low-level injection assumption valid? Justify your answer. ( c) Reproduce the ffia~ on your answer book and complete it to reasonable accuracy, indicating the missing carrier concentration values and the values 1 • S k \ () ..,~ l G) Y '7 > 0 . 7 \ J v .. ( d) Determine t e steady state diode current density. Hence, estimate the electric field deep in the quasi-neutral N region, i.e., at x -co. ( e) Derive an expression for the excess hole charge density stored in the quasi- re • . Hence, calculate the • sion ca acit e densi aue to s holes stored. What impact tloes the diffusion cap c1tance has on the diode operation? END OF PAPER -5 - [2] [6] [5] [6] [6]