1. PHYS208 - spring 2010 - page 1 PHYS208 Lecture Thursday 15 th April 2010 Lecture Wednesday 21 th April 2010 Lecture Thursday 22 th 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

2. PHYS208 - spring 2010 - page 2 For work with P-N junction Exam presentation http://web.ift.uib.no/AMOS/PHYS208/TEXT2010/Exam_2008_LATEX/pn_junction_Ex_2008.pdf thursday's and following week's text (handwritten notes) http://web.ift.uib.no/AMOS/PHYS208/2008/2008_P-N-junction.pdf (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 http://web.ift.uib.no/AMOS/PHYS208/TEXT2008/phys208_Trygve_SLIDES.pdf THE FIRST 18 pages or so – background from previous lectures

3. PHYS208 - spring 2010 - page 3 Electrons and holes When we reverse energy, the holes take the same role as electrons  note the – sign on  2008 SLIDE NOTE

4. PHYS208 - spring 2010 - page 4 Once more about electrons and holes; Ferromagnetic fluid story once more Concept of holes We have discussed one more illustration of holes: BUBBLES

5. PHYS208 - spring 2010 - page 5 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 COPY OF OLDER NOTE

6. PHYS208 - spring 2010 - page 6 Impurity atoms have 3 valence electrons Acceptor P-type (hole, positive charge carriers) Impurity atoms have 5 valence electrons Donor N-type (electron, negative charge carriers) PN COPY OF OLDER NOTE

7. PHYS208 - spring 2010 - page 7 The atom-like states of impurities explained; Bohr-like 'atom' relations More details on the following slide from 2008.... COPY OF OLDER NOTE

8. PHYS208 - spring 2010 - page 8 Impurity States – Donors from 2008 slide

9. PHYS208 - spring 2010 - page 9 Starting P-N junction

10. PHYS208 - spring 2010 - page 10 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

11. PHYS208 - spring 2010 - page 11 Impurity States - Donors

12. PHYS208 - spring 2010 - page 12 Impurity States - Acceptors

13. PHYS208 - spring 2010 - page 13 Impurity States - Acceptors Acceptor Bound State

14. PHYS208 - spring 2010 - page 14 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

15. PHYS208 - spring 2010 - page 15 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

16. PHYS208 - spring 2010 - page 16 'inclined bands' – The forces on electrons

17. PHYS208 - spring 2010 - page 17 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 We have discussed one more illustration of holes: BUBBLES Bubbles travel uppwads Stones are falling downwards

18. PHYS208 - spring 2010 - page 18 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 ?

19. PHYS208 - spring 2010 - page 19 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 (A) (B)

20. PHYS208 - spring 2010 - page 20 Diffusion, Fick's first law of diffusion, conductivity, Ohm's Law, drift velocity, mobility, Equillibrium as cancellation of currents

21. PHYS208 - spring 2010 - page 21 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

22. PHYS208 - spring 2010 - page 22 Einstein – Nernst: Diffusion against force related to Boltzmann Use the same equation as before with different aim: Now the Field is known and constant

23. PHYS208 - spring 2010 - page 23 Einstein – Nernst: gives us the diffusion constant / mobility relation JUST IN THE FORM needed for the potential difference.

24. PHYS208 - spring 2010 - page 24 PHYS208 Lecture Wednesday 21 th April 2010 P-N-Junction Continue – model depletion zone...... pages of new lecture calculations with comments

25. PHYS208 - spring 2010 - page 25 Einstein – Nernst: gives us the diffusion constant / mobility relation - potential difference.

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27. PHYS208 - spring 2010 - page 27 We have shown that The potential difference generated in junction of typical doping degrees can be of the order of Volts

28. PHYS208 - spring 2010 - page 28 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 The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

29. PHYS208 - spring 2010 - page 29 The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

30. PHYS208 - spring 2010 - page 30 The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

31. PHYS208 - spring 2010 - page 31 PHYS208 Lecture Thursday 22 th April 2010 P-N-Junction part 3 Depletion zone and diode characteristic Added scanned handwritten notes from paper-times

32. PHYS208 - spring 2010 - page 32 The potential difference is due to the opposite carrier densities. How are they positioned? MODEL:

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35. PHYS208 - spring 2010 - page 35 Use the n i (pure semiconductor, intrinsic) values see next page

36. PHYS208 - spring 2010 - page 36 We have invented this new representation Use the n i (pure semiconductor, intrinsic) values – DIMENSIONLESS NUMBERS

37. PHYS208 - spring 2010 - page 37 We discussed the fact that this is relevant not only for computers, electronics etc, But also for BASIC SCIENCE Wikipedia links http://en.wikipedia.org/wiki/2DEG Better picture -Wikipedia http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effec t

38. PHYS208 - spring 2010 - page 38 Forward bias Is case A + on p - on n Pulls p down Increases diffusion Reverse Bias Is case B - on p + on n Pushes p up Does not do much

39. PHYS208 - spring 2010 - page 39 Slide 40-58 The scanned handwritten p-n junction files Slide 59-63 SOLAR CELL PRINCIPLE from the web Slide 63-64SOLAR CELL PRINCIPLE with our addition – the cell as seen by electrons – and as seen by holes From wednesday April 23rd, 2008 MODIFIED 2010 P-N-junction workfile

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57. PHYS208 - spring 2010 - page 57 Drift comes from the Drude discussion, may be Diffusion constant – dimension Einstein - Nernst Derivation: Turn arround the Argument

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65. PHYS208 - spring 2010 - page 65 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