Question

3. Silicon samples with band-gas 1.1 eV at 300 Kelvin, are doped at four different levels and have the properties listed below. Case 1: Case 2: Case 3: Case 4: Ex-Ey = 0.15 eV Ef-Ey=0.88 eV EF-Ey = 0.55 eV Ex-Ey = 1.09 eV The four cases above show the position of the Fermi Level Er relative to the valence band edge Ev.at dilterent doping levels. a) identify each sample as degenerate and nondegenerate. b) which nondegenerate case shows heavy n-type doping c) which case shows nearly intrinsic silicon. (determine the density of electrons and holes) d) for heavy p-type doped sample, what is the approximate value of Ec-Ep. e) which of these elements, Boron (B), Arsenic (As), Germanium Ge, Gallium Ga, will act like an acceptor in samples above. f) use Boltzmann approximation to calculate the density of electrons and holes in cases 4 above. (Ne = 2.82x10 cm, kg=8.62x10 eV/K at 300 K)

Answer 1

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The Pats given inthe 9resitien is as tollouos 8ilicm Sample With Band gap- E Caee-I When Ee-Ev o.15 ev 1lev Semi(onducter We kaea thetthe Fermilere in mtyfe is 3 rmby Ec- EF KrIn ( Where, Ne density of States in Conductim Band ND= Dmer Concen tratien equation Ca be Witen as- E-Ef= Ea-CEF-Ev) En-CEF. Ev)Krn( the Values We get- Ene Eners3p H-Co18)- 0.026 In) KT0.026 at Roan tempaate 0-95 O-026 Nc 36.53 ND NG 232 xid L7D=78 No= 2.32Xlo9 733 x1o5 No= 3.82x(0

we, Knaa that Trtinstc Concentration Fr Sicon mie-a Now Mass actin Lau- Meins npani No PE ni P-2-25xi 3-92X10 P- 5.89x1o1 Fram the above obserehions, itis Ciearthat P Hence Jiven Materia With abore Fermileved is q Semi Condua tor With Hole Concentration ot Ptyfe P E Case-IT When EF-Er=0-33 ev dgin Using equetion En-(EF- Ev)= kth ( 1-1-0.3 =0.026 In 232x19 2.92X19 ND O-22 0.o2 ND= 29.2xld 4.72X103 5.47 xlo/m ND = From the abore obseoretion itis Clear that P hence N is a Semi Cordecter Neyle Nom deg oete SemiGndctor Since Psping Cancentratin is less than lo/cn Ttis a

ase m When EF-Ev 0 35 ev again vaing equtin Ea-CEr-EN)= KTin -1- 0-35- 0-026n 2.82Xld No O55 2.324 o26 (जग) 2.32XL019 (-53 xlo9 Fropm the aboye obsevatens iis Clear thet ND nie 94x1do, Whichis Very Clote to to the Tntrinsic Concen trati on ot ilican Case-T When, E- Ev 1-01ev agán using equetion Wet E4-CEEE)=Kh( 1-CL09) -0026 mfN ND 001m(2.32 ND=2. 8o Xlo9 Since, No2.30 xld Whichis qreater than (d3 Ait the abare obceretin itis Cear that it is Degenrete Seni Conductor th elecrn Concetrstin b2xls Hence

Conclu sion Ce- Nom degemate tyfe SemiCm ducter Case-IT-Nm degemte N-tpe Semi Gnduetor Case- pproxine tely equatto nbingic Concontration Case-TY dgemete N-type Semi Can t ueter- mearly instrinsi c &ilicon be ause ND194x10 Wchis Very Crose to Case - 8hows we obtained Ftinsic Concentration of &liCon a In Case -as We obtained heary hole P Camcentretion ot P 5.39xlo6 Ec-EF E-CEF-E) :EF-EV Ec-EF = 1- 015 Ec-EF 0.95 ev BORDN Trivetent Tinpurity nd acts as ptype Semi Conductor .ARSENICPenta Valent Tmpurity Gnd Qets as SerriCndue tor tyfe Ga acts as Ptye SemiCanduchor Ga, Ge Vget n- 3.92 x1 , P- 539M6 From the Goore Resit Case- 3 6x1 No5.9 x16 Inbinsic hith tbE idfms Case -IT Case- Case- degenateh 2- xla9 03/em2
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