UMD ENEE 313 - Examples on Doping and Fermi Levels (5 pages)

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Examples on Doping and Fermi Levels



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Examples on Doping and Fermi Levels

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Pages:
5
School:
University of Maryland, College Park
Course:
Enee 313 - Introduction to Device Physics
Introduction to Device Physics Documents

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ENEE 313 Spr 09 Supplement II Examples on Doping and Fermi Levels Zeynep Dilli Oct 2008 rev Mar 2009 This is a supplement presenting examples on the relationship between doping carrier concentrations and the Fermi level at equilibrium Required Constants For silicon at T 300 K ni 1 45 1010 1 cm3 The Boltzmann constant kB k 8 61 10 5 eV K Silicon bandgap energy Eg 1 12 eV 1 Consider a silicon crystal at room temperature 300 K doped with arsenic atoms so that ND 6 1016 1 cm3 Find the equilibrium electron concentration n0 hole concentration p0 and Fermi level EF with respect to the intrinsic Fermi level Ei and conduction band edge EC This is an n type material as it is doped with donor atoms Therefore n0 ND 6 1016 1 cm3 1 Then we can use the Law of Mass Action to find the hole concentration p0 2 1 1020 n2i 3 5 103 1 cm3 n0 6 1016 2 To find the Fermi level with respect to the intrinsic Fermi level we use the expression that links electron concentration to Ei and ni n0 ni exp n0 EF Ei EF Ei kT ln kT ni 3 At room temperature kT 8 61 10 5 300 0 026 eV 4 We will be using this quantity often Then the separation of the Fermi level and intrinsic Fermi level is from Eqn 3 6 1016 0 026 15 24 0 396 eV 1 45 1010 Ei 0 396 eV EF Ei 0 026 ln EF 5 Drawing the band energy diagram we can then place the Fermi level in the correct place with respect to the intrinsic Fermi level middle of bandgap and also find its separation from the conduction band edge EC See Figure 1 1 Figure 1 Solution to Problem 1 This is an n type material doped at 6 1016 1 cm3 2 2 Consider a silicon crystal at 300 K with the Fermi level 0 18 eV above the valence band What type is the material What are the electron and hole concentrations We start with drawing the band energy diagram for the crystal as in Figure 2 Figure 2 The energy band diagram for the crystal presented in Problem 2 The separation between EF and EV is given Then as can be seen from the figure we can calculate the separation between Ei and EF Ei EV



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