PHYS208 - spring page 1 PHYS208 Lecture Thursday 15 th April 2010 Lecture Wednesday 21 th April 2010 P-N-Junction part 1+2 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

PHYS208 - spring page 2 For work with P-N junction Exam presentation thursday's and following week's text (handwritten notes) ( 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

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

PHYS208 - spring 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 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

PHYS208 - spring 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

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

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

PHYS208 - spring page 9 Starting P-N junction

PHYS208 - spring 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 page 11 Impurity States - Donors

PHYS208 - spring page 12 Impurity States - Acceptors

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

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

PHYS208 - spring 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

PHYS208 - spring 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 ?

PHYS208 - spring 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)

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

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

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

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

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

PHYS208 - spring 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:

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

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