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 PHYS208 - spring 2010 - page 1

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 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    PHYS208 - spring 2010 - page 3

Electrons and holes When we reverse energy, the holes take the same role as electrons ( note the – sign on m ) 2008 SLIDE NOTE 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 PHYS208 - spring 2010 - page 5

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 PHYS208 - spring 2010 - page 6

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 PHYS208 - spring 2010 - page 7

COPY OF OLDER NOTE The atom-like states of impurities explained; Bohr-like 'atom' relations More details on the following slide from 2008.... COPY OF OLDER NOTE PHYS208 - spring 2010 - page 8

Impurity States – Donors from 2008 slide PHYS208 - spring 2010 - page 9

Starting P-N junction 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 PHYS208 - spring 2010 - page 11

Impurity States - Donors PHYS208 - spring 2010 - page 12

Impurity States - Acceptors PHYS208 - spring 2010 - page 13

Impurity States - Acceptors Acceptor Bound State 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 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 PHYS208 - spring 2010 - page 16

'inclined bands' – The forces on electrons PHYS208 - spring 2010 - page 17

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 PHYS208 - spring 2010 - page 18

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 ? PHYS208 - spring 2010 - page 19

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 PHYS208 - spring 2010 - page 20

Diffusion, Fick's first law of diffusion, conductivity, Ohm's Law, drift velocity, mobility, Equillibrium as cancellation of currents 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 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 PHYS208 - spring 2010 - page 23

Einstein – Nernst: gives us the diffusion constant / mobility relation JUST IN THE FORM needed for the potential difference. PHYS208 - spring 2010 - page 24

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 PHYS208 - spring 2010 - page 25

Einstein – Nernst: gives us the diffusion constant / mobility relation - potential difference. PHYS208 - spring 2010 - page 26

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We have shown that The potential difference generated in junction of typical doping degrees can be of the order of Volts PHYS208 - spring 2010 - page 28

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 PHYS208 - spring 2010 - page 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: PHYS208 - spring 2010 - page 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: PHYS208 - spring 2010 - page 31

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 PHYS208 - spring 2010 - page 32

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: PHYS208 - spring 2010 - page 33

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(pure semiconductor, intrinsic) values see next page Use the ni (pure semiconductor, intrinsic) values see next page PHYS208 - spring 2010 - page 36

We have invented this new representation Use the ni (pure semiconductor, intrinsic) values – DIMENSIONLESS NUMBERS PHYS208 - spring 2010 - page 37

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 http://en.wikipedia.org/wiki/2DEG http://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect Better picture -Wikipedia PHYS208 - spring 2010 - page 38

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 PHYS208 - spring 2010 - page 39

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

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Drift comes from the Drude discussion, may be Diffusion constant – dimension Einstein - Nernst Derivation: Turn arround the Argument PHYS208 - spring 2010 - page 58

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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 PHYS208 - spring 2010 - page 66