Lecture 19: Semiconductor Devices Kittel Ch. 17, p. 503 - 512 + - - PowerPoint PPT Presentation

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Lecture 19: Semiconductor Devices Kittel Ch. 17, p. 503 - 512 + - - PowerPoint PPT Presentation

Nov 08, 2022 186 likes •574 views

Lecture 19: Semiconductor Devices Kittel Ch. 17, p. 503 - 512 + extra material in lecture notes - - + - + + - - - - + + - + - + + + - - - + - - + + - - + - + - + - + - Depletion p-type n-type region

slide-1
SLIDE 1

Physics 460 F 2006 Lect 19 1

Lecture 19: Semiconductor Devices Kittel Ch. 17, p. 503 - 512 + extra material in lecture notes

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Depletion region conduction band minimum

µ

valence band maximum

slide-2
SLIDE 2

Physics 460 F 2006 Lect 19 2

Comment

  • If the universe were a homgeneous crystal, it

would be a very dull place

  • It is the inhomogeneities that create our

interesting world

  • Sun - earth - …
  • Metals - insulators together to make useful circuits
  • The power of semiconductors is the ability to

control their electrical (and optical) properties to make devices

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SLIDE 3

Physics 460 F 2006 Lect 19 3

Outline

  • What is a semiconductor device?
  • Key point 1 - Bands and Fermi energy

Bands Relative to Fermi energy

  • Key point 2 - inhomogeneous material or doping

Variation in concentrations of electrons and holes by controlled doping profiles

  • p-n junctions - rectification- forward - reverse bias
  • Metal-semiconductor junctions

Schottky barriers - rectification

  • Solar Cells
  • Light emitting diodes
  • Bipolar transistor n-p-n p- n-p
  • Kittel Ch. 17, p. 503 - 512 + added materials in the

lecture notes

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SLIDE 4

Physics 460 F 2006 Lect 19 4

What determines the Band Energies and the Fermi Energy?

  • Recall that the product

n p = 4 (kB T/ 2 π2) 3 (mc mv) 3/2 exp( -(Ec - Ev)/kB T) is independent of the Fermi energy

  • BUT the concentrations n and p vary depending on

the Fermi energy relative to the band energies

  • n = 2(mc kB T/ 2 π2) 3/2 exp( -(Ec - µ)/kB T)

= N0 exp( - (Ec - µ )/kB T)

  • p = 2(mv kB T/ 2 π2) 3/2 exp( -(µ - Ev)/kB T)

= P0 exp( -(µ - Ev)/kB T)

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SLIDE 5

Physics 460 F 2006 Lect 19 5

Band Energies and the Fermi Energy

  • Key Points:
  • 1A: Band energy differences, e.g., Egap = Ec - Ev are

intrinsic properties of a material

  • 1B: The absolute energy of the bands is NOT an

intrinsic property. The electron band energies all shift by -eV( r) due to an electrostatic potential V( r).

Egap Egap Battery

  • eV

µe

Electrochemical potential Same material

  • +
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SLIDE 6

Physics 460 F 2006 Lect 19 6

Band Energies and the Fermi Energy

  • Key Points:
  • 1C: The Fermi energy µ is the energy to add or

remove an electron, which is everywhere the same if the system is in equilibrium. One can either work with µ or with the “electrochemical potential” µe = µ +eV(r) due to an electrostatic potential V(r).

Egap Egap Battery Same material or Different materials Electrochemical potential µe

  • eV
  • +
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SLIDE 7

Physics 460 F 2006 Lect 19 7

What determines the Band Energies and the Fermi Energy?

  • If there are inhomogeneous variations in the

concentrations n and p as a function of position, the relations can be written

  • n = N0 exp( - (Ec - eV(r) - µ)/kB T) = N0 exp( - (Ec - µe )/kB T)
  • p = P0 exp( -(µ - Ev + eV(r) )/kB T) = P0 exp( -(µe - Ev)/kB T)
  • Either form is correct and the relations obey the law of

mass action:

n p = N0 P0 exp( - (Ec - Ev )/kB T) = N0 P0 exp( - Egap/kB T)

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SLIDE 8

Physics 460 F 2006 Lect 19 8

Band Energies and the Fermi Energy

  • Examples
  • Line up of Fermi energy
  • f two metals in contact
  • Two semiconductors in

contact

  • Band are shifted by
  • eV(r) so that is the same.

This means that there must be electrostatic potentials V(r) to make this happen µ

Egap Egap

µ

p-type n-type

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SLIDE 9

Physics 460 F 2006 Lect 19 9

Inhomogeneous Semiconductors

  • First Example: one material doped differently in

different regions

  • How can this happen?
  • Key assumption:

variations are slow on the atomic scale

  • can treat as smoothly varying

Egap

µ

p-type n-type Egap

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SLIDE 10

Physics 460 F 2006 Lect 19 10

Inhomogeneous Semiconductors

  • First Example: one material doped differently in

different regions

  • Looking more closely at the doping near the boundary:

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Fixed acceptor sites holes Fixed donor sites electrons Depletion region

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SLIDE 11

Physics 460 F 2006 Lect 19 11

p-n junction

Depletion region p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

conduction band minimum

µ

valence band maximum

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SLIDE 12

Physics 460 F 2006 Lect 19 12

What causes bands to shift?

  • Electric fields - just like a capacitor

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Depletion region neutral neutral Electric field

  • µ

+

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SLIDE 13

Physics 460 F 2006 Lect 19 13

What causes bands to shift?

  • Electric fields - just like a capacitor

p-type n-type + + + +

  • +

Depletion region neutral overall neutral neutral Electric field E + + Lp Ln Density p < n implies Lp > Ln

  • e V(x)
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SLIDE 14

Physics 460 F 2006 Lect 19 14

Equilibrium

  • In equilibrium with no applied voltage there is no net

current, but there is always a generation and absorption

  • f holes and electrons across the interface.
  • Electrons on p side (np) easily go to n side at rate Anp
  • Electrons on n side go to p side at rate C exp(-∆E/kBT)

Egap

µ

p-type Egap ∆E Thermal distribution

  • f carriers

n-type

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SLIDE 15

Physics 460 F 2006 Lect 19 15

Equilibrium

  • In equilibrium the current density of electrons is given

by the difference of terms for left fl right and right fl left j = Cexp(- ∆E /kBT) - Anp = 0

  • Similarly for holes

Egap Egap ∆E = EL - ER

µ

p-type n-type

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SLIDE 16

Physics 460 F 2006 Lect 19 16

How can a pn junction be used to make a diode?

  • A device that passes current easily in one

direction

  • Low resistance for voltage applied in one direction

(the forward direction)

  • High resistance for voltage applied in the other

direction (the reverse direction)

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SLIDE 17

Physics 460 F 2006 Lect 19 17

Forward bias

  • Apply a voltage V to reduce the difference between the

two sides to ∆E - e∆V (∆V > 0) (∆E = EL

0 - ER 0 )

Depletion region p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

neutral neutral “Built in” Electric field Battery +

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SLIDE 18

Physics 460 F 2006 Lect 19 18

Forward bias

  • Reduce the difference between the two sides to

∆E = EL

0 - ER 0 - e(VL - VR) = ∆E0 - e∆V (with ∆V > 0)

  • The net electron current is

j = Cexp(- (∆E - e∆V)/kBT) - Anp = Anp [ exp( + e|∆V | /kBT) - 1]

  • Similarly for holes
  • Current increases exponentially!

Egap Egap ∆E0 - e∆V

  • e∆V

p-type n-type

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SLIDE 19

Physics 460 F 2006 Lect 19 19

Forward bias

  • The difference between bands on the left and right

increases

  • Below is figure of band energies near the “flat band”

condition

  • Current flows easily

µ

valence band maximum conduction band minimum e∆V +

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SLIDE 20

Physics 460 F 2006 Lect 19 20

Reverse bias

  • Apply a voltage V to increase the difference between the

two sides to ∆E + eV (V > 0)

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Width of Depletion region increases! neutral neutral Battery (reversed) +

  • “Built in”

Electric field

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SLIDE 21

Physics 460 F 2006 Lect 19 21

Reverse bias

  • Current obeys same formula but with with ∆V < 0
  • Now the net electron current is (Similarly for holes )

J = Anp [ exp( - e|∆V| /kBT) - 1]

  • Current saturates at small value!
  • Acts like capacitor with increased depletion width

Egap Egap

  • e∆V

∆E0 - e∆V p-type Few carriers can get

  • ver the barrier

n-type

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SLIDE 22

Physics 460 F 2006 Lect 19 22

Reverse bias

  • The difference between bands on the left and right

increases

  • Current saturates at small value!
  • Acts like capacitor with increased depletion width

p-type n-type Few carriers can get

  • ver the barrier

µ

valence band maximum conduction band minimum e∆V +

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SLIDE 23

Physics 460 F 2006 Lect 19 23

Rectification

  • I - V characteristic

Breakdown Reverse Forward exponential increase V I Leakage current eV = energy gap

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SLIDE 24

Physics 460 F 2006 Lect 19 24

Forward bias (again)

  • How does the current actually flow?
  • Electrons flow from right, holes from left - combine near

the depletion region

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Depletion region neutral neutral Electric field Battery +

  • J
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SLIDE 25

Physics 460 F 2006 Lect 19 25

How can a pn junction be used to convert electric current into light?

  • A device in which a current leads to emission of

light

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SLIDE 26

Physics 460 F 2006 Lect 19 26

Light Emitting Diode

  • Forward biased junction in a system where the

combination of the electrons and holes creates light

  • Example GaAs or GaN

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Depletion region neutral neutral Electric field Battery +

  • J

Light

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SLIDE 27

Physics 460 F 2006 Lect 19 27

Forward bias (again)

  • Forward biased junction in a system where the

combination of the electrons and holes creates light

  • Example GaAs or GaN

Light

µ

valence band maximum conduction band minimum e∆V +

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SLIDE 28

Physics 460 F 2006 Lect 19 28

How can a pn junction be used to convert light into electric current?

  • A device in which absorption current leads of

electric current

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SLIDE 29

Physics 460 F 2006 Lect 19 29

Solar Cell

  • Light absorbed in depletion region creates electron-

hole pairs

  • Made of Si, ...

p-type n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

Depletion region neutral neutral Electric field J Light Meter

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SLIDE 30

Physics 460 F 2006 Lect 19 30

Solar Cell

  • Light absorbed in depletion region creates electron-

hole pairs

neutral neutral

  • +

Light Generated Current Electric field

  • +

µ

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SLIDE 31

Physics 460 F 2006 Lect 19 31

Shottky Barrier

Depletion region metal n-type +

  • +
  • +

+ + + +

  • +

+ + + + + + +

  • +

valence band maximum conduction band minimum Fixed by details

  • f interface

µ

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SLIDE 32

Physics 460 F 2006 Lect 19 32

Rectification in Shottky Barrier

  • Similar to p-n junction
  • Current increases exponentially (until it saturates) for

forward bias that tends to make the semiconductor bands bend less (in the case of n-type semiconductor the potential is negative on semiconductor)

  • Reverse bias acts like capacitor with increased depletion

width

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SLIDE 33

Physics 460 F 2006 Lect 19 33

Transistor

  • Invented in 1947 - Bardeen, Brattain, Schockley
  • Equilibrium

p-type p-type n-type

µ

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SLIDE 34

Physics 460 F 2006 Lect 19 34

Transistor

  • Applying voltages - one junction forward and the other

reverse - (remember holes like to go uphill)

+ p-type n-type p-type Battery +

  • +
  • Battery

forward reverse + LARGE Collector Current Small Base Current Base Collector Emitter

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SLIDE 35

Physics 460 F 2006 Lect 19 35

Transistor

  • Amplifier - Small current controls LARGE current

+ p-type n-type p-type Battery +

  • +
  • Battery

forward reverse + LARGE Collector Current Small Base Current Base Collector Emitter

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SLIDE 36

Physics 460 F 2006 Lect 19 36

Summary

  • Semiconductor device – inhomogeneous doping

to create a structure with electron and hole conduction that can be controlled Main points

  • Key general points:
  • Band gaps are fixed by the material Si, GaAs, …
  • Bands Relative to Fermi energy determined by doping
  • In equilibrium (no current)

the Fermi energy µ is the same everywhere

  • Fermi energy and bands

shift due to applied voltages

µ

valence band maximum conduction band minimum

µ

valence band maximum conduction band minimum

e∆V +

slide-37
SLIDE 37

Physics 460 F 2006 Lect 19 37

Summary continued

  • Main points - continued
  • p-n junctions - rectification- forward - reverse bias
  • Light emitting diode: electron, hole fi photon
  • Solar Cell: photon fi separated electron and hole

Other points (important but you are not responsible for these) Metal-semiconductor junctions Schottky barriers - rectification

  • Bipolar transistor n-p-n p- n-p
  • Kittel Ch. 17, p. 503 - 512 + added materials in the

lecture notes

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SLIDE 38

Physics 460 F 2006 Lect 19 38

Next time

  • Semiconductor structures

Confinement of carriers by voltages and materials

  • MOSFET Transistor
  • Quantum Wells, Wires, Dots
  • Carriers in Quantum Wells in a magnetic field

Quantized Hall effect

  • Covered briefly in Kittel Ch 17, p 494-503, 507- 511
  • added material in the lecture notes