1. PHYS208 – Solid state physics
SPRING 2010
Part 3
Lectures Thursday 15th April 2010
to Thursday 22th April 2010, end of main topics
Semiconductors,
electrons and holes
and P-N-junction
66 pages
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2. P-N-Junction part 1+2+3 PHYS208 Lecture Thursday 15th April 2010
Lecture Wednesday 21th April 2010
Lecture Thursday 22th April 2010
P-N-Junction
part 1+2+3
THE FIRST 18 pages – background from previous lectures
4 pages of new lecture calculations with comments -part 1
Part 2 – applying law of mass action
Part 3 – depletion zone and diode characteristic
Added scanned handwritten notes from paper-times
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3. For work with P-N junction
Exam presentation
thursday's and following week's text (handwritten notes)
(THIS IS INCLUDED HERE)
( to be used together with the above pn_junction_Ex_2008.pdf )
Some of the formalism is nicely discussed also in
THE FIRST 18 pages or so – background from previous lectures   
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4. Electrons and holes When we reverse energy, the holes take the same role as electrons ( note the – sign on m ) SLIDE NOTE
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5. Once more about electrons and holes;
Ferromagnetic fluid story once more
Concept of holes
We have discussed one more illustration of holes: BUBBLES
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6. Starting Impurities OLDER NOTE
COPY OF OLDER NOTE
Starting Impurities OLDER NOTE
Semiconductors might contain various impurities.
However, only the type of impurities discussed below –
DOPING by controlled impurities of one or other type
P or N and the abrupt JUNCTION
( two types of doping in the same crystal structure
with a sharp border )
appears to be useful for devices and instruments
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7. P N COPY OF OLDER NOTE Impurity atoms have 5 valence electrons Donor
N-type
(electron, negative charge carriers)
Impurity atoms have 3 valence electrons
Acceptor
P-type
(hole, positive charge carriers)
COPY OF OLDER NOTE
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8. COPY OF OLDER NOTE The atom-like states of impurities explained;
Bohr-like 'atom' relations
More details on the following slide from
COPY OF OLDER NOTE
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9. Impurity States – Donors from 2008 slide
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10. Starting P-N junction
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11. The following three slides show how the 'acceptor levels'
Can be created ABOVE the valence band edge
We start by showing how the 'donor levels'are created
BELOW the conduction band edge
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12. Impurity States - Donors
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13. Impurity States - Acceptors
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14. Impurity States - Acceptors
Acceptor Bound State
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15. Do these 'inclined bands' Look strange to you?
We have used such picture before!
And with a nice explanation
- see the following 2 slides
Picture from 1954 article on p-n-junction for solar cell
Physical Review
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16. Do the 'inclined bands'of previous slide look strange to you?
We have used such picture before! – The forces on electrons
Copy is here – and a copy of nice explanation on the following slide
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17. 'inclined bands' – The forces on electrons
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18. We have discussed one more illustration of holes: BUBBLES
Bubbles travel uppwads
Stones are falling downwards
We have discussed one more illustration of holes: BUBBLES
And
Helium-filled balloon
And thus the whole story of Archimedes law
and buoyancy – OPPDRIFT (norwegian)
Any floating object displaces its own weight of fluid. – Archimedes of Syracuse
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19. Helium-filled balloon in the same train: How will it place itself ?
Riddle:
Train accellerates. A lamp or rubber ball will hang as shown in the upper picture
Helium-filled balloon in the same train:
How will it place itself ?
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20. how fast did you give the answer:
(B)
A related riddle:
how fast did you give the answer:
A stone is placed on a toy boat. The stone is now moved to the water. What will happen? Result (A) or result (B) ?
Will the level of water in the container rise or sink?
And thus the whole story of Archimedes law
and buoyancy – OPPDRIFT (norwegian)
Any floating object displaces its own weight of fluid. – Archimedes of Syracuse
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21. Diffusion, Fick's first law of diffusion, conductivity, Ohm's Law, drift velocity, mobility, Equillibrium as cancellation of currents
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22. Equillibrium as cancellation of currents; Diffusion caused by gradient of density; what is 'Diffusion constant' D ? ELECTRIC FIELD IS GRADIENT OF ELECTROSTATIC POTENTIAL. Evaluate potential difference
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23. Einstein – Nernst: Diffusion against force related to Boltzmann Use the same equation as before with different aim: Now the Field is known and constant
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24. Einstein – Nernst: gives us the diffusion constant / mobility relation
JUST IN THE FORM needed for the potential difference.
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25. Lecture Wednesday 21th April 2010
PHYS208
Lecture Wednesday 21th April 2010
P-N-Junction
Continue – model depletion zone
pages of new lecture calculations with comments
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26. Einstein – Nernst: gives us the diffusion constant / mobility relation
- potential difference.
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28. We have shown that
The potential difference generated in junction of typical doping degrees can be of the order of Volts
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29. The potential difference is due to the opposite carrier densities
The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:
The drawing to left is showing the whole solution of the model of the charge depletion charge density, electric field and resulting potential difference. This will determine the SIZES OF DEPLETION REGIONS – Right – realistic shapes
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30. The potential difference is due to the opposite carrier densities
The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:
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31. The potential difference is due to the opposite carrier densities
The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:
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32. Lecture Thursday 22th April 2010
PHYS208
Lecture Thursday 22th April 2010
P-N-Junction
part 3
Depletion zone and diode characteristic
Added scanned handwritten notes from paper-times
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33. The potential difference is due to the opposite carrier densities
The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:
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36. (pure semiconductor, intrinsic) values see next page
Use the ni
(pure semiconductor, intrinsic) values see next page
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37. We have invented this new representation
Use the ni (pure semiconductor, intrinsic) values – DIMENSIONLESS NUMBERS
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38. But also for BASIC SCIENCE
We discussed the fact that this is relevant not only for computers, electronics etc,
But also for BASIC SCIENCE
Wikipedia links
Better picture -Wikipedia
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39. Forward bias Is case A + on p - on n Pulls p down Reverse Bias
Increases diffusion
Reverse Bias
Is case B
- on p on n
Pushes p up
Does not do much
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40. P-N-junction workfile
Slide The scanned handwritten p-n junction files
Slide SOLAR CELL PRINCIPLE from the web
Slide SOLAR CELL PRINCIPLE with our addition
– the cell as seen by electrons
– and as seen by holes
From wednesday April 23rd, 2008
MODIFIED 2010
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58. Drift comes from the Drude discussion, may be
Diffusion constant – dimension
Einstein - Nernst Derivation: Turn arround the Argument
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66. The holes run 'uphill' to the right Why ?
The electrons 'can run' to the left, where the conduction edge has lower energy
The holes run 'uphill' to the right
Why ?
The electrons 'see' the bands as shown in the left view
If the holes are to be talked about as 'positive particles', we must change the direction of energy – the right view – flipped up down in energy
Thus also the holes move 'downwards', as they 'see' it
Thus both electrons and holes running 'downwards' result in collection of negative charge in the n-region and positive charge in the p-region
The reason is the p-n junction inner potential step
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