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Probability of Level Occupation in a Silicon Device

Calculate the probability of occupation of a level 0.05 eV above the conduction band edge in a Silicon device with given parameters. Understand the carrier densities in extrinsic semiconductors based on doping. Explore band structures of n-type and p-type semiconductors. Discover the atomic structure of p-type and n-type semiconductors. Analyze the temperature dependence of an extrinsic semiconductor. Learn about carrier densities in p-n diodes and their applications.

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Probability of Level Occupation in a Silicon Device

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  1. Semiconductor Devices 22 Atsufumi Hirohata Department of Electronics 11:00 Monday, 24/November/2014 (P/L 005)

  2. Exercise 1 Find the probability of occupation of a level of 0.05 eV above the conduction band edge of a Silicon device if the Fermi level is 0.7 eV above the valence band edge. Assume the bandgap (Eg) of Silicon is 1.1 eV and the effective mass of electron in Silicon is 0.40  (0.91  10-30 kg). The Boltzmann constant (kB) is 1.4  10-23 J/K, the Planck constant is 6.6  10-34 Js and the temperature is 300K. Use the conversion ratio: 1 eV = 1.6  10-19 J.

  3. Answer to Exercise 1 Carrier density can be defined by Here, the effective density of states at the conduction band is defined as where me is the effective mass of electron.

  4. 22 Extrinsic Semiconductor • Doping • Donor / acceptor • Carrier density

  5. Extrinsic Semiconductors n-type band structures : p-type band structures : Donor level Acceptor level Group IV semiconductors: Si and Ge Acceptors: B and Al Group III-V semiconductors: GaAs and GaN Acceptors: Be, Zn, Cd and Ge Group IV semiconductors: Si and Ge Donors: P and As Group III-V semiconductors: GaAs and GaN Donors: Se, Te, Si and Ge * http://www.wikipedia.org/

  6. Atomic Structure of p-Type Semiconductors p-type semiconductor structures : Group IV semiconductors: Group III-V semiconductors: Si and GeGaAs and GaN Acceptors: B and Al Acceptors: Be, Zn, Cd and Ge * http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_04.html

  7. p-Type Acceptors Energy potential created by an acceptor ion : Conduction band Energy bandgap Acceptor ion Acceptor Acceptor level (EA) Hole Valence band * http://www.phys.chuo-u.ac.jp/labs/wakabaya/lecture/applphys/2C_$4.3.pdf

  8. Atomic Structure of p-Type Semiconductors p-type band structures : * http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_04.html

  9. Carrier Number Density n EC (Eg) EF nA EA EV (0) p valence band Numbers of holes in the valence band EV should equal to the sum of those of electrons in the conduction band EC and in the acceptor level EA : Similar to the intrinsic case, Assuming numbers of neutral acceptors are NA, For EA - EF > kBT,

  10. Carrier Number Density (Cont'd) n EC (Eg) EA nA EF EV (0) p valence band At low temperature, one can assume p >> n, As nA is very small, EA > EF By substituting For T ~ 0, At high temperature, one can assume n >> nA, Similar to the intrinsic case, for me* = mp*,

  11. Typical Band Structures Acceptor level near the valence bands : * http://www.phys.chuo-u.ac.jp/labs/wakabaya/lecture/applphys/2C_$4.3.pdf

  12. Atomic Structure of n-Type Semiconductors n-type semiconductor structures : Group IV semiconductors: Group III-V semiconductors: Si and GeGaAs and GaN Donors: P and As Donors: Se, Te, Si and Ge * http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_04.html

  13. n-Type Donors Energy potential created by a donor ion : Donor ion Conduction band Conduction electron Donor level (ED) Energy bandgap Valence band * http://www.phys.chuo-u.ac.jp/labs/wakabaya/lecture/applphys/2C_$4.3.pdf

  14. Atomic Structure of n-Type Semiconductors n-type band structures : * http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_04.html

  15. Temperature Dependence of an Extrinsic Semiconductor Thermal excitation * H. Ibach and H. Lüth, Solid-State Physics (Springer, Berlin, 2003); ** http://akita-nct.jp/tanaka/kougi/2007nen/3e/3-4hujunbutu.pdf

  16. Carrier Densities of Extrinsic Semiconductors n-type band structure : p-type band structure : * http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C02/co/Contenu_04.html

  17. p-n Diode A junction made by attaching p- and n-doped semiconductors : Widely used to insulate transistors. Common circuit to convert ac to dc in a battery charger. * http://www.wikipedia.org/

  18. Exercise 2 For the Silicon material with doping, estimate the dopant concentration (ND) needed to manufacture a 1 MW resister measuring 100 mm in length and 5 mm2 in cross section. Assume that the transport of current will be carried out by majority carriers and that for Silicon, intrinsic carrier density: ni = 1016 m-3, mobility of electrons: me = 0.135 m2/Vs and mobility of holes: mh = 0.05 m2/Vs. 5 mm2 100 mm

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