1. P461 - Semiconductors1 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 EFEF D valence conduction n D*n If T>0

2. P461 - Semiconductors2 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

3. P461 - Semiconductors3 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

4. P461 - Semiconductors4 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

5. P461 - Semiconductors5 Doped semiconductors Si(14) 3s 2 3p 2 P(15) 3s 2 3p 3 Al(13) 3s 2 3p 1 Si || 4 covalent bonds. Fill all valence Si= Si =Si energy levels (use all electrons) || 1 eV gap 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”

6. P461 - Semiconductors6 Doped semiconductors II The Fermi Energy is still where n(E F ) = ½.  doping moves E F Complex compounds shift Fermi Energy and D(E) (Al x O y Y z...) conduction band valence band.05 eV.06 eV donor electrons acceptor holes 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 E

7. P461 - Semiconductors7 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 EFEF D valence conduction D(E) EFEF n-type p-type

8. P461 - Semiconductors8 Doped Semiconductors IV undoped semicon. have N cond ~ 10 -11 N valence 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  E F back in middle of gap E T donor EFEF