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Semiconductors

Semiconductors. Filled valence band but small gap (~1 eV) to an empty (at T=0) conduction band look at density of states D and distribution function n Fermi energy on center of gap for undoped. Always where n(E)=0.5 (problem 13-26)

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Semiconductors

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  1. Semiconductors • Filled valence band but small gap (~1 eV) to an empty (at T=0) conduction band • look at density of states D and distribution function n • Fermi energy on center of gap for undoped. Always where n(E)=0.5 (problem 13-26) • D(E) typically goes as sqrt(E) at top of valence band and at bottom of conduction band n D conduction valence EF D*n If T>0 P461 - Semiconductors

  2. Semiconductors II • Distribution function is • so probability factor depends on gap energy • estimate #electrons in conduction band of semiconductor. Integrate over n*D factors at bottom of conduction band P461 - Semiconductors

  3. Number in conduction band using Fermi Gas model = • integrate over the bottom of the conduction band • the number in the valence band is about • the fraction in the conduction band is then P461 - Semiconductors

  4. Conduction in semiconductors • INTRINSIC. Thermally excited electrons move from valence band to conduction band. Grows with T. • “PHOTOELECTRIC”. If photon or charged particle interacts with electrons in valence band. Causes them to acquire energy and move to conduction band. Current proportional to number of interactions (solar cells, digital cameras, particle detection….) • EXTRINSIC. Dope the material replacing some of the basic atoms (Si, Ge) in the lattice with ones of similar size but a different number (+- 1) of valence electrons P461 - Semiconductors

  5. Doped semiconductors • Si(14) 3s23p2 P(15) 3s23p3Al(13) 3s23p1 Si || 4 covalent bonds. Fill all valence Si= Si =Si energy levels (use all electrons) || 1 eV gap Si Si || single electron loosely bound to P Si= P =Si (~looks like Na) || 0.05 eV  conduction band Si Si =Si || || 0.06 eV can break one of the Si=Si Si= Al -Si bonds. That electron  Al. The “hole” || || || moves to the Si atom Si=Si e “hole” P461 - Semiconductors

  6. Doped semiconductors II conduction band .05 eV donor electrons acceptor holes E .06 eV • The Fermi Energy is still where n(EF) = ½.  doping moves EF • Complex compounds shift Fermi Energy and D(E) (AlxOyYz...) valence band P-doped n-type “extra” e .05 eV to move from donor to conduction band Al-doped p-type “missin” e= (hole) .06 eV to move from valence to conduction band P461 - Semiconductors

  7. Doped Semiconductors III • Adding P (n-type). Since only .05 eV gap some electrons will be raised to conduction band  where n(E)= ½ is in donor band • adding Al (p-type). some electrons move from valence to acceptor band. n(E)= ½ now in that band n-type D conduction valence EF D(E) p-type EF P461 - Semiconductors

  8. Doped Semiconductors IV • undoped semicon. have Ncond ~ 10-11Nvalence • doping typically 10-7 increases conductivity • but if raise T then the probability to move from valence band to conduction band increases e-E/kT. Can see this as a change in Fermi Energy with temperature  at some point all the donor electrons are in the conduction band and many valence move to conduction  EF back in middle of gap donor E EF T P461 - Semiconductors

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