TUTORIAL 1 EMT 471/3 – SEMICONDUCTOR PHYSICS 1. Based on the portion of the periodic table which relates to semiconductors, name TWO (2) elements from: i) Group III ii) Group IV iii) Group V 2. Give the definition of intrinsic semiconductor. 3. State TWO (2) MOST important mechanisms in electron mobility 4. Sketch Miller indices of <100> and <111> cubic crystals. 5. Sketch FOUR (4) diagrams which include the schematic energy band diagram, density of state, Fermi level distribution function and carrier concentration for (i) p-type semiconductor (ii) n-type semiconductor, respectively. 6. Using the physics principle of energy conservation and considering the number of electron-hole pairs 1 – 1’, 2 – 2’, 3 – 3’ during the avalanche process, show that the required kinetic energy for ionization E0 must be larger than band energy gap Eg, where E0 1 2 m1v s 1.5E g 2 7. An n-type Si sample has 3 x 1017 arsenic atom/cm3, 1015 bulk recombination centers/cm3 Nt, and 1010 surface recombination centers/cm2 Nsts. Given, Vth for Si is 107cm/s, p for Si is 505 cm2/V-s, the values of p and s are 5 x 10-15cm2 and 2 x 10-16cm2 respectively. Under low injection of carrier, find a. the bulk minority carrier lifetime p b. diffusion length Lp c. the surface recombination velocity Slr 8. Calculate the built-in potential for a silicon p-n junction with NA=2x1018cm-3 and ND=5x1015cm-3 at 300K [ni=9.65x109 cm-3]. 1 Solution: 1. Group III: Boron/Aluminum/Galium/Indium Group IV: Carbon/Silicon/Germanium Group V: Nitrogen/Phosphorus/Arsenic/Antimony 2. An intrinsic semiconductor is one that contains relatively small amounts of impurities compared with thermally generated electrons and holes 3. Lattice scattering & mobility scattering 4. Miller indices of <100>: Miller indices of <111>: 5. n and p-type semiconductor n-type p-type EA Schematic band diagram NA density of states Fermi distribution function 2 Carrier concentration 6. Before collision: Fast moving electron 1, K .Ebc 1 m1v s2 2 (1) pbc m1v s And momentum, (2) (b.c: before collision, vs – saturation velocity) After collision, assumed that the three carriers have same effective mass, same K.E and same momentum, p, thus total K.E and p are 1 ac And 3 K .E 2 (m m m )v 2 m v p (m m m )v 3m v ac 1 1 1 1 1 1 2 f f 1 1 2 f f (3) (4) (where m1 = m2 =m3, and ac: after collision, vf – velocity after collision) Using physics principle of conventional energy, K.Ebc = K.Eac, and pbf = pac, thus 1 3 m1v s2 E g m1v 2f 2 2 (5) And m1vs 3m1v f (6) Where Eg – energy band gap (minimum energy required to generate electron-hole pair after the collision). Substitute (6) to (5), yields 1 1 m1v s2 E g m1v s2 2 6 1 m1v s2 E g 3 m1v s2 3E g E0 1 m1v s2 1.5E g 2 Thus, K.E for ionization process E0 > Eg 3 7. (i) Bulk minority carrier lifetime p 1 p th N t Dp 5 10 15 1 2 10 8 s , [Vth (Si) = 107cm/s] 10 7 1015 kT p = 0.0259 (505) = 13cm2/s q ( p for Si = 505 cm2/V-s) [Sze, pg 538, Appendix G] Diffusion length, L p D p p 13 10 8 3.6 10 4 cm Surface recombination velocity S lr th s N sts 10 7 2 10 16 1010 20 cm/s 8. Vbi n p kT N A N D ln 2 q ni (1.38 10 23 )(300 ) 2 1018 5 1015 ln 9 2 1.6 10 19 (9.65 10 ) 0.0259 ln 1.074 1014 0.837V 4