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Lecture 15
 

Lecture 15

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Lecture 15 Lecture 15 Presentation Transcript

  • Today’s objectives- Semiconductors and Integrated Circuits
    • Draw band diagrams for metals, insulators, intrinsic semiconductor, and n and p type doped semiconductors, including E c , E f , and E v .
    • How does conductivity change as a function of temperature for metals and intrinsic semiconductors. What about for extrinsic (doped) semiconductors?
    • What are common n and p type dopants?
    • What is the appropriate conductivity equation for intrinsic, n, and p type semiconductors.
    • How does the concentration of free charges change with temperature and doping (for intrinsic and extrinsic semiconductors)?
    • How does mobility change with temperature and doping?
  • Semiconductor Industry in 2003
    • The semiconductor business: $166B.
      • 10 18 transistors produced during the year.
    • US semiconductor industry: $80B.
    • $13B reinvested in research, $10B in equipment. 226 000 jobs in US alone.
    http://www.infras.com/Tutorial/sld001.htm
  • Typical Semiconductors GaAs ZnS (Zinc Blende) Structure 4 Ga atoms at (0,0,0)+ FCC translations 4 As atoms at ( ¼,¼,¼)+FCC translations Bonding: covalent, partially ionic Silicon Diamond Cubic Structure 4 atoms at (0,0,0)+ FCC translations 4 atoms at ( ¼,¼,¼)+FCC translations Bonding: covalent
  • Band structures for semiconductors and insulators
    • Semiconductors and Insulators have totally full valence bands and empty conduction bands with a bandgap between them. E c is at the base of the conduction band, E v is at the top of the valence band, and E f is in the bandgap .
      • The distinction between semiconducting and insulating materials is arbitrarily set to a bandgap of < or > 2 eV, respectively.
    E f , Fermi level Metal (Cu) partially filled 4s (conduction) filled 3p, 2p, 2s, 1p, 1s (valence) Empty 4p (conduction) Band gap Band gap Energy Filled (deep valence) E f Insulator (Al 2 O 3 ) Filled (valence) Empty (conduction) Band gap Band gap Filled (deep valence) E f Semiconductor (Si) Filled (valence) Empty (conduction) Band gap Band gap E c E v
  • Electron Conductivity
    • Metals
      • Dominated by mobility, which decreases with increasing Temperature due to increased probability of scattering.
    • Intrinsic Semiconductors (no dopants)
      • Dominated by number of carriers, which increases exponentially with increasing Temperature due to increased probability of electrons jumping across the band gap.
    n =electrons/m 3 (10 16 for Si) metal
  • Electrical Conduction in Intrinsic SCs Schematic Band Diagram “ Real” Band Diagram (empty at T=OK) (full at T=OK) h + e -
      • # of e - in CB = # of h + in VB
    e - jumping to CB via thermal excitation at T>OK
  • Electron and hole conductivity How can we think of conductivity carried by a hole, something that isn’t there? • Total Electrical Conductivity thus given by: # electrons/m 3 electron mobility # holes/m 3 hole mobility • In a semiconductor, there can be electrons and holes:
  • Intrinsic carriers
    • With intrinsic systems ( only ), for every free electron, there is also a free hole.
    • # electrons = n = # holes = p = n i
    • --true for pure Si, or Ge, etc.
    • Holes don’t move as easily (mobility of holes is always less than for electrons), but still there are so many that they will contribute at least an extra 10-20% to the intrinsic conductivity.
    μ h is ~ 20% of μ e
  • Analogy to metals
    • As a general rule, as temperature increases, scattering also increases. This decreases conductivity drastically for metals.
    • The mobility for an intrinsic semiconductor will also diminish with increasing temperature due to increased scattering.
    • Still, the extra temperature provides lots of extra electrons and holes in the conduction band for intrinsic semiconductors. This causes n to increase exponentially with Temperature.
    • n goes up so fast w/r to mobility that the excess electrons totally wash out the diminishing effect of extra scattering.
      • Thus, conductivity almost always increases with temperature for a semiconductor, the opposite of a metal.
  • Extrinsic SCs P in Si donates an extra electron to the crystal. This electron exists in (or near) the conduction band. The electron thus may be able to carry current in an E field.
  • Typical Donor and Acceptor Dopants for Si
    • For Silicon:
    • Donors (n type):
      • P, As, Sb
    • Acceptors (p type):
      • B, Al, Ga, In
  • Donor electrons
    • For every donor dopant atom (N d ) near the conduction band, there is another free electron (n)
      • NOTE no change in T is needed as for metals.
    • Unlike for intrinsic semiconductors, free electron doesn’t leave a mobile free hole behind. Instead, any holes are trapped in donor state and thus will not contribute substantially to conductivity as for intrinsic semiconductors (thus p ~ 0).
    E f =E donor = E c -0.05eV
  • Extrinsic conductivity—p type
    • We can do the same thing with “acceptor dopants.”
    • Every acceptor generates excess mobile holes (p=N a ).
    • Now holes totally outnumber electrons, so conductivity equation switches to p domination.
  • Acceptor vs. donor doped extrinsic semiconductors E f =E donor = E c -0.05eV E f =E acceptor = E v +0.05eV
    • The electrons that jump into the acceptor states are “trapped” since the states are isolated (analogous to holes at dopant states in a n-doped system).
  • Summary: Intrinsic vs. Extrinsic (n or p) • Intrinsic : # electrons = # holes (n = p) --case for pure Si • Extrinsic : --n ≠ p --occurs when DOPANTS are added with a different # valence electrons than the host (e.g., Si atoms) • N-type Extrinsic: (n >> p) • P-type Extrinsic: (p >> n)
  • Intrinsic vs. Extrinsic— charge concentration vs. Temperature
    • The dopant sites essentially lower the activation energy to generate free electrons at room temperature.
    • Comparison: intrinsic vs extrinsic conduction... For an extrinsic doping level of: 10 21 /m 3 of a n-type donor impurity (such as P). --for T < 100K: &quot; freeze-out” thermal energy only sufficient to excite a very few electrons. --for 150K < T < 450K: &quot;extrinsic&quot; --for T >> 450K: &quot;intrinsic&quot; Adapted from Fig. 18.16, Callister 6e . (Fig. 18.16 from S.M. Sze, Semiconductor Devices, Physics, and Technology , Bell Telephone Laboratories, Inc., 1985.)
  • Actual Conductivity vs. Temperature
    • Conductivity is not as flat as free charge concentration.
    • This is because mobility is always decreasing with increased temperature (more scattering)
    Adapted from Fig. 19.15, Callister 5e . (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75 , p. 865, 1949.) Why the decrease?
  • Carrier mobility vs T
  • Carrier mobility vs. dopant concentration
    • One might worry about whether too many dopants will decrease mobility too (and thus conductivity, the opposite of the reason for putting them there). After all, dopants are defects.
    • This effect is small, roughly an order of magnitude for doping from 10 16 to 10 19 donors (or acceptors) / cm 3 .
  • SUMMARY
    • Draw band diagrams for metals, insulators, intrinsic semiconductor, and n and p type doped semiconductors, including E c , E f , and E v .
    • How does conductivity change as a function of temperature for metals and intrinsic semiconductors. What about for extrinsic (doped) semiconductors?
    • What are common n and p type dopants?
    • What is the appropriate conductivity equation for intrinsic, n, and p type semiconductors.
    • How does the concentration of free charges change with temperature and doping (for intrinsic and extrinsic semiconductors)?
    • How does mobility change with temperature and doping?