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ELEC 3908, Physical Devices – Lecture 3
Energy Band Diagrams
and Doping
3-­‐2	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Lecture Outline
•  Continue the study of semiconductor devices by looking at
the material used to make most devices
•  The energy band diagram is a representation of carrier
energy in a semiconducting material and will be related to
an orbital bonding representation
•  Devices require materials with tailored characteristics,
obtained through doping, the controlled introduction of
impurities
•  Will discuss electrons and holes, as well as intrinsic, n-type
and p-type materials
•  Later lectures will apply these concepts to diode, bipolar
junction transistor and FET
3-­‐3	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Atomic Electron Energy Levels
•  A free electron can assume any
energy level (continuous)
•  Quantum mechanics predicts a
bound electron can only assume
discrete energy levels
•  This is a result of the interaction
between the electron and the nuclear
proton(s)
3-­‐4	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Crystal Energy Bands
•  Crystal is composed of a large
number of atoms (≈1022 cm-3 for
silicon)
•  Interaction between the electrons of
each atom and the protons of other
atoms
•  Result is a perturbation of each
electron’s discrete energy level to
form continua at the previous energy
levels
3-­‐5	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Covalent Bonding
•  Silicon crystal formed by covalent
bonds
•  Covalent bonds share electrons
between atoms in lattice so each
thinks its orbitals are full
•  Most important bands are therefore
–  band which would be filled at 0 K -
valence band
–  next band above in energy -
conduction band
3-­‐6	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Simplified Energy Band Diagram
•  Movement within a band is not
difficult due to continuum of energy
levels
•  Movement between bands requires
acquisition of difference in energy
between bands (in pure crystal, can’t
exist in between)
•  Main features of interest for first
order device analysis are
–  top of valence band (Ev)
–  bottom of conduction band (Ec)
–  difference in energy between Ec and Ev,
energy gap Eg
3-­‐7	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Orbital Bonding Model
•  Represent valence and conduction bands by separate silicon
lattice structures
•  The two diagrams coexist in space -the same set of silicon
atoms is represented in each diagram
3-­‐8	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Electron Transitions -Energy Band Diagram
•  At room temperature, very
few electrons can gain energy
Eg to move to the conduction
band ( ≈ 1010 cm-3 at 300K =
23°C)
•  In pure silicon at 300K, most
valence band orbitals ( ≈ 1022
cm-3 ) are full, most
conduction band orbitals are
empty
3-­‐9	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Electron Transitions – Orbital Bonding
3-­‐10	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Electrons and Holes
•  Conduction of current occurs through electron movement
•  Two mechanisms of electron movement are possible:
–  movement within the nearly empty conduction band orbital
structure
–  movement within the nearly full valence band orbital structure
•  Conduction in the valence band structure is more conveniently
modeled as the “movement” of an empty orbital
•  Model this empty valence band orbital as a positively charged
pseudo-particle called a hole
•  Density of electrons in conduction band is n (cm-3)
•  Density of holes in valence band is p (cm-3)
3-­‐11	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Electron and Hole Conduction
•  Electron movement in
conduction band can be
modeled directly
•  Movement of electrons in
valence band modeled as
movement (in opposite
direction) of positively
charged hole
Electric Field
3-­‐12	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Intrinsic Material
•  Semiconducting material which has not had any impurities
added is called intrinsic
•  In an intrinsic material, the number of electrons and holes must
be equal because they are generated in pairs
•  Call the density of electrons and holes in intrinsic material the
intrinsic density ni (for Si@300K, ni ≈ 1.45x1010 cm-3)
•  Therefore, for intrinsic material
3-­‐13	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Extrinsic Material
•  Intentional addition of impurities during manufacture or in
specialized fabrication steps is termed doping
•  Doped material is called extrinsic
•  Ability to change the electrical characteristics of the material
through selective introduction of impurities is the basic reason
why semiconductor devices are possible
•  Later lectures will outline the processes used to introduce
impurities in a controlled and repeatable way
3-­‐14	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Mass-Action Law
•  For intrinsic material, n = p = ni, therefore
•  This turns out to be a general relationship called the
mass-action law, which can be used for doped material
in equilibrium
3-­‐15	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Group V Impurity Atom
•  An atom from group V of the periodic table has one more
nuclear proton and valence electron than silicon
•  If the atom replaces a silicon atom in the lattice, the extra
electron can move into the conduction band (ionization)
•  A group V atom is a donor since it donates an electron to the
silicon lattice
•  Density of donor dopant atoms given symbol ND (cm-3)
3-­‐16	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Donor Ionization - Energy Band Diagram
3-­‐17	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Donor Ionization – Orbital Bonding Model
3-­‐18	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Donor Doping -Electron and Hole Densities
3-­‐19	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.1: Arsenic Doping
3-­‐20	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.1: Solution
3-­‐21	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Group III Impurity Atom
•  An atom from group III of the periodic table has one less nuclear
proton and valence electron than silicon
•  If the atom replaces a silicon atom in the lattice, the empty
valence orbital can be filled by an electron (ionization)
•  A group III atom is an acceptor since it accepts an electron from
the silicon lattice
•  Density of acceptor dopant atoms given symbol NA (cm-3)
3-­‐22	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Acceptor Ionization - Energy Band Diagram
3-­‐23	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Acceptor Ionization – Orbital Bonding Model
3-­‐24	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Acceptor Doping - Electron and Hole Densities
3-­‐25	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.2: Gallium Doping
3-­‐26	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.2: Solution
3-­‐27	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Compensated Doping
3-­‐28	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.3: Compensated Doping
3-­‐29	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Example 3.3: Solution
3-­‐30	
  
ELEC	
  3908,	
  Physical	
  Electronics:	
  Energy	
  Band	
  
Diagrams	
  and	
  Doping	
  
Lecture Summary

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Elec3908 lect 3

  • 1. ELEC 3908, Physical Devices – Lecture 3 Energy Band Diagrams and Doping
  • 2. 3-­‐2   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Lecture Outline •  Continue the study of semiconductor devices by looking at the material used to make most devices •  The energy band diagram is a representation of carrier energy in a semiconducting material and will be related to an orbital bonding representation •  Devices require materials with tailored characteristics, obtained through doping, the controlled introduction of impurities •  Will discuss electrons and holes, as well as intrinsic, n-type and p-type materials •  Later lectures will apply these concepts to diode, bipolar junction transistor and FET
  • 3. 3-­‐3   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Atomic Electron Energy Levels •  A free electron can assume any energy level (continuous) •  Quantum mechanics predicts a bound electron can only assume discrete energy levels •  This is a result of the interaction between the electron and the nuclear proton(s)
  • 4. 3-­‐4   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Crystal Energy Bands •  Crystal is composed of a large number of atoms (≈1022 cm-3 for silicon) •  Interaction between the electrons of each atom and the protons of other atoms •  Result is a perturbation of each electron’s discrete energy level to form continua at the previous energy levels
  • 5. 3-­‐5   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Covalent Bonding •  Silicon crystal formed by covalent bonds •  Covalent bonds share electrons between atoms in lattice so each thinks its orbitals are full •  Most important bands are therefore –  band which would be filled at 0 K - valence band –  next band above in energy - conduction band
  • 6. 3-­‐6   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Simplified Energy Band Diagram •  Movement within a band is not difficult due to continuum of energy levels •  Movement between bands requires acquisition of difference in energy between bands (in pure crystal, can’t exist in between) •  Main features of interest for first order device analysis are –  top of valence band (Ev) –  bottom of conduction band (Ec) –  difference in energy between Ec and Ev, energy gap Eg
  • 7. 3-­‐7   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Orbital Bonding Model •  Represent valence and conduction bands by separate silicon lattice structures •  The two diagrams coexist in space -the same set of silicon atoms is represented in each diagram
  • 8. 3-­‐8   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Electron Transitions -Energy Band Diagram •  At room temperature, very few electrons can gain energy Eg to move to the conduction band ( ≈ 1010 cm-3 at 300K = 23°C) •  In pure silicon at 300K, most valence band orbitals ( ≈ 1022 cm-3 ) are full, most conduction band orbitals are empty
  • 9. 3-­‐9   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Electron Transitions – Orbital Bonding
  • 10. 3-­‐10   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Electrons and Holes •  Conduction of current occurs through electron movement •  Two mechanisms of electron movement are possible: –  movement within the nearly empty conduction band orbital structure –  movement within the nearly full valence band orbital structure •  Conduction in the valence band structure is more conveniently modeled as the “movement” of an empty orbital •  Model this empty valence band orbital as a positively charged pseudo-particle called a hole •  Density of electrons in conduction band is n (cm-3) •  Density of holes in valence band is p (cm-3)
  • 11. 3-­‐11   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Electron and Hole Conduction •  Electron movement in conduction band can be modeled directly •  Movement of electrons in valence band modeled as movement (in opposite direction) of positively charged hole Electric Field
  • 12. 3-­‐12   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Intrinsic Material •  Semiconducting material which has not had any impurities added is called intrinsic •  In an intrinsic material, the number of electrons and holes must be equal because they are generated in pairs •  Call the density of electrons and holes in intrinsic material the intrinsic density ni (for Si@300K, ni ≈ 1.45x1010 cm-3) •  Therefore, for intrinsic material
  • 13. 3-­‐13   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Extrinsic Material •  Intentional addition of impurities during manufacture or in specialized fabrication steps is termed doping •  Doped material is called extrinsic •  Ability to change the electrical characteristics of the material through selective introduction of impurities is the basic reason why semiconductor devices are possible •  Later lectures will outline the processes used to introduce impurities in a controlled and repeatable way
  • 14. 3-­‐14   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Mass-Action Law •  For intrinsic material, n = p = ni, therefore •  This turns out to be a general relationship called the mass-action law, which can be used for doped material in equilibrium
  • 15. 3-­‐15   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Group V Impurity Atom •  An atom from group V of the periodic table has one more nuclear proton and valence electron than silicon •  If the atom replaces a silicon atom in the lattice, the extra electron can move into the conduction band (ionization) •  A group V atom is a donor since it donates an electron to the silicon lattice •  Density of donor dopant atoms given symbol ND (cm-3)
  • 16. 3-­‐16   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Donor Ionization - Energy Band Diagram
  • 17. 3-­‐17   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Donor Ionization – Orbital Bonding Model
  • 18. 3-­‐18   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Donor Doping -Electron and Hole Densities
  • 19. 3-­‐19   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.1: Arsenic Doping
  • 20. 3-­‐20   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.1: Solution
  • 21. 3-­‐21   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Group III Impurity Atom •  An atom from group III of the periodic table has one less nuclear proton and valence electron than silicon •  If the atom replaces a silicon atom in the lattice, the empty valence orbital can be filled by an electron (ionization) •  A group III atom is an acceptor since it accepts an electron from the silicon lattice •  Density of acceptor dopant atoms given symbol NA (cm-3)
  • 22. 3-­‐22   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Acceptor Ionization - Energy Band Diagram
  • 23. 3-­‐23   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Acceptor Ionization – Orbital Bonding Model
  • 24. 3-­‐24   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Acceptor Doping - Electron and Hole Densities
  • 25. 3-­‐25   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.2: Gallium Doping
  • 26. 3-­‐26   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.2: Solution
  • 27. 3-­‐27   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Compensated Doping
  • 28. 3-­‐28   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.3: Compensated Doping
  • 29. 3-­‐29   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Example 3.3: Solution
  • 30. 3-­‐30   ELEC  3908,  Physical  Electronics:  Energy  Band   Diagrams  and  Doping   Lecture Summary