VIII.2. A Semiconductor Device Primer

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which, using np= ni 2 , becomes If the acceptor concentration NA >> ND and NA >> ni i.e. the conductivity is dominated by holes. Conversely, if the donor concentration ND >> NA and ND >> ni the conductivity is dominated by electrons. If the conductivity is dominated by only one type of carrier, the Fermi level is easy to determine. If, for example, n >> p can be written yielding p N A N + N D A 2 ni p + N D = + ni ni = p N N c e Ec − E k T B A + 1 D − ( E −E ) / k p T ⇒ If ND >> NA , then Ec-EF must be small, i.e. the Fermi level lies close to the conduction band edge. In reality the impurity levels of common dopants are not close enough to the band edge for the Boltzmann approximation to hold, so the calculation must use the Fermi distribution and solve numerically for EF. Nevertheless, the qualitative conclusions derived here still apply. Introduction to Radiation Detectors and Electronics Copyright © 1998 by Helmuth Spieler VIII.2.a. A Semiconductor Device Primer, Doping and Diodes N p + N = n + N N N n − = F D A A A D p ≈ c F B = N − N ⎛ = log ⎜ ⎝ N D N c − N A N A ⎞ ⎟ ⎠ A , 2 i n n ≈ N A
It is often convenient to refer all of these quantities to the intrinsic level Ei , as it accounts for both Ec and Ev. Then n = p = N N and the Fermi level E F c v e e −( Ec− EF ) / kBT −( EF −Ei ) / k = nie −( EF −Ev ) / kBT −( Ei −E = nie N − E = −k T log i B Variation of Fermi level with doping and temperature, including narrowing of the band gap with temperature: (from Sze) Introduction to Radiation Detectors and Electronics Copyright © 1998 by Helmuth Spieler VIII.2.a. A Semiconductor Device Primer, Doping and Diodes A i F − N n B ) / k D B T T
Page 1 and 2: VIII.2. A Semiconductor Device Prim
Page 3 and 4: The number of occupied electron sta
Page 5 and 6: With these simplifications the numb
Page 7: 2. Carrier Concentrations in Doped
Page 11 and 12: Equilibrium is attained when the tw
Page 13 and 14: As either NA or ND increases relati
Page 15 and 16: 4. The Forward-Biased p-n Junction
Page 17 and 18: This yields the solution n p ( x) =
Page 19 and 20: Since the two electron currents mus
Page 21 and 22: Energy band diagrams showing the in
Page 23 and 24: Since the equilibrium concentration
Page 25 and 26: Note that in the diode equation a)
Page 27 and 28: However, on a logarithmic scale it
Page 29: The discrepancies between the measu

VIII.2. A Semiconductor Device Primer

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