E2¢¢ E¢¢2 E2¢¢ E¢2 r=d E2¢ E¢¢1 E¢1 E1¢¢¢ E1¢¢ E1¢ Two interacting atom (a) Three interacting atom ‘N’ interacting atom (b) (c) E Empty levels N/2 Filled levels E E Conduction band Eg £ 2 eV Valence band Distance Conduction band empty Eg ≥ 3 eV Valence band filled Distance Fx Ex e- Fext me Vacuum + Fint + + + Crystal + a= Fext Fext a = m* e + x (a) (b) v d E 1 Si Si Si Conduction Band Fifth electron of dopant atom Si P Si Si Si Si Eg Si Ed Ev Valence Band At T = 0 K Si Donor levels 0.01 eV (Ge) 0.05 eV (Si) Ec At T = 0 K Si Si P Si Si Si Si Conduction Band Free electron available for conduction Ec Ed Eg Donor levels Ev Valence Band At T > 0 K At T > 0 K Conduction Band Si Si Ec Si Eg Si Ga Acceptor levels Si Ea Ev Si Si Valence Band Si (a) At T = 0 K (a) At T = 0 K Conduction Band Si Si Si Si Ga Si Si Si Si Ec Eg Acceptor levels Ea Ev (b) At T > 0 K Valence Band (b) At T > 0 K 1 1 e E EF KT E E N/2 EF EF 0 1 f (E) Distance (a) (b) Conduction band in a conductor at 0K (a) Actual distribution of electrons in the band (b) The Fermi-Dirac function. 1 1 1 1 1 e E EF / 0 1 e 1 0 1 1 1 0 1 e 1 e 1 1 E EF / 0 1 1 e0 / 0 Case 2: E E E KT EF KT KT EF EF KT 0 Distance (a) 0.5 f (E) (b) 1 N (E) (c) 1 1 1 0 1 e 1 1 2 Fermi level defined as the energy level at which the probability of electron occupancy Fermi energy, is the average energy possessed by the electrons which participate in conduction process in conductors at temperatures above 0K. E E Conduction Band Empty EC EF Eg EF EV Valence Band Full 0 Distance (a) f (E) 1 (b) 3/ 2 EF EC 2 me* KT KT e 2 h2 2 2 mh* KT h2 3/ 2 e EV EF KT At T = 0K Conduction band • At T > 0K Conduction band Ec Ec at 0K EF • at 0K EF Hole Ev Valence band Valence band -• Ev E Æ Fermi level F -• Ec Æ Bottom of conduction band Ev Æ Top of valence band Fermi level in -type semiconductor (a) at 0°K (b) as function of temperature. Ed EC 2 EF Ea EV EF 2 C.B. Conduction band 0 Eg/2 Ea EF EV EF Acceptor levels Ea EV V.B. Valence Band 0 (a) At 0° K T p-Type (b) Fermi level in -type semiconductor (a) at 0°K (b) as function of temperature. P–type Bar t Bz Ey Jx z E q Ex W F y x I VH + – J x ne Jx BJ x ne n eVH w eVH BJ x w n wBJ x ne wBI neA I A wBI BI net newt VH /w BJ 1 EH x J B JxB Jx B ne x 1 ne 1 Pe B I t Knowing the thickness of the semiconductor () by measuring Hall voltage with voltmeter Concentration of charge carriers 1 BI RH e VH t e 1 BI RH e VH t e Hall angle E H Ex V BJ x H w ne BJ x ne Jx B ne 1 ne 1 BI 1 BI eRH VH t e eRH VH t e VH t ne B I Immobile negative Diffusion of electron Immobile positive acceptor ion donor ion from N to P P Free hole Silicon Silicon N Free electron Immobile negative Immobile positive Depletion layer donor ion acceptor ion P Silicon Silicon N Free hole Free electron p-type E n-type E Conduction Band Conduction Band EFn EFP Valence Band Valence Band (a) Metallurgical junction E Conduction Band EFn Electron current Jm Hole current Jhp EFp Valence Band (b) junction at the instant of formation(a) Energy band diagrams of type and -type semiconductors (b) Energy band diagram at the instant of joining which illustrates the position of Fermi levels on each side and consequent carrier migration across the junction. p-n Junction Conduction Hill (Eg + eVo) Conduction Band eVo 1 Fermi Level EF Eg EF 3 Electron energy decreases Hole energy decreases 2 Hole energy increasses Electron energy increases Depletion region Valence Band Valence Hill 4 p n (a) Forward biasing (b) Symbolic representation of - junction. I R 1 e eV KT (a) Reverse biasing (b) Symbolic representation of - junction. Electron Drifting path of electron I + V - Drift current in a semiconductor. dn dx dn dx dn e dx dn Dn e dx dp Dp e dx D . Dp e dp dx dn dx pe Dn e p E Dp e dp dx ne n E Dn e dn dx hc hc E g 6.62 10 34 8 Eg 12400 A Eg ev p-type n-type Eg hv Ec hv Ev Eg1 > Eg2 > Eg3 Cell 1 (Eg1) Cell 2 (Eg2) Antireflection coating Au grid n-AllnP2 n-GaInP2 Top cell p-GaInP2 p+GaAs Tunnel diode n+GaAs n-AIGaAs n-GaAs Bottom cell p◊GaAs Substrate p+◊GaAs 2 m*e kT h2 3/ 2 2 e 3/ 2 EC EF / kT 2 mh* kT e EF EV / kT 2 h 2 1 ne 1 JBW BI ne net 1 ne 1 eRH BI VH t e 1 eRH BI VH t e VH t BI E Conduction band Ec EF = Ed Nd = 1024 atoms/m3 Ec + Ed 2 Ec Æ Bottom of the conduction band Ev Æ Top of the valence band EF Æ Fermi level Ed Æ Donor energy level Ei Æ Intrinsic Fermi level Ei Nd = 1021 atoms/m3 Ev Valence band O T E Ec Ev EF Ea Ei Æ Æ Æ Æ Æ Bottom of the conduction band Top of the valence band Fermi level Acceptor energy level Intrinsic Fermi level Conduction band Ec Na = 1021 atoms/m3 Ei EF = Na = 1024 atoms/m3 Ea Ec + Ed 2 Ev Valence band O T The discrete energy levels formed by the doped acceptors are called acceptor levels. This acceptor level lies just above the valence band. The discrete energy levels formed by the doped donors are called donor levels. This donor level lies just below the conduction band. In the formation of a -type semiconductor trivalent impurities like Ga or boron is doped to a pure semiconductor like Ge or Si. e e h 4 1.6 10 19 4 2.88 10 0.14 0.04 20 m2 V m2 V e( e 0.47 h) 16 . 1 1 10 e ( 19 e h ) 0.56 i e+ e h 1 e+ e 2 10 4 2 10 4 1 h 1 1.6 10 1 1.6 10 19 19 6 0.2 6.2 1 1.984 10 22 m2 Vs C/m V sec 1 1 2.2 1 2.3 l 10 2 A 10 6 2 m*e k B T 2 h2 3 Eg 2 e 2 k BT 2 3.14 9.11 10 31 1.38 10 2 2 6.625 10 34 3 23 300 3 2 1.1 1.6 10 e 2 1.38 10 23 19 300 16 21.25 2 5.3964 10 2 e l A l A 1 10 2 1 10 3 1 10 2.32 1 10 2 2.32 10 Area = Breadth × Thickness 3 6 1 2 – Eg C e 2k B T – Eg C e 2k B T1 C e 2k B T2 – Eg e Eg 1 1 2 k B T1 T2 1.2 1.6 10 e 2 1.38 10 1.2 1.6 10 e 2 1.38 10 19 23 1.666 10 19 23 3 e 1 1 600 300 3.19872 10 22 2 1.38 10 23 e11.59 V t H IB 37 10 6 1 10 20 10 3 0.5 3 3.7 10 0.01 8 J B W 500 0.6 5 10 3 na e 1020 1.6 10 19 180 ne e 1.772 10 22 1.6 10 19 1 ne i e e h 1 e 1 e h 2 10 4 2 10 4 1 1.6 10 19 1 1.6 10 6 0.2 1 19 6.2 1.984 10 22 1 ne 1 RH e 1 3.66 10 4 1.6 10 19 RH 3.66 10 4 8.93 10 3 e e 3 104 1.6 1019 1300 10 4 3 104 2.08 10 20 2 ni2 ne 1.5 1016 1.4423 10 24 3 e h 9 1.6 3 8 2 ni2 1.5×1016 = nh 3.75×10 24 e 1 e h 1 7.68 10 10 10 h 1 1.6 10 2 19 480 10 4 1350 10 4 22 ni2 nh 2 1.5 1016 1.3 1021 e 1 e e 10 10 e 2 1 1.6 10 19 1 2.16 10 21 1 ne 3.66 8.93 10 10 RH 4 3
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