ENGR-1600 Materials Science for Engineers Lecture 25: Semiconductors 1.

ENGR-1600Materials Science for Engineers

Lecture 25: Semiconductors

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Electron Energy Band Structures• Pauli Exclusion Principle:

no two e- in an interacting system can have exactly same energy

• When N atoms are far apart, they do not interact, so electrons in a given shell in different atoms have same energy

• As atoms come closer together, they do interact, perturbing electron energy levels

• Electrons from each atom then have slightly different energies, producing a “band” of allowed energies

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Band Theory for Metals and Semiconductors

Metals:

Semiconductors:

@ 0 K @ room temp

very large n

modest n

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vd = eE = n e e

Microscopic Electric Conductivity

• When an electric field E is applied, e- experience a force. Hence, they accelerate.

• This force is counteracted by scattering events (analogy to friction).

• When the forces balance out, there is a constant mean value of e- velocity vd.

vd drift velocity [m/s] μ e- mobility [m2/Vs] n # of free electrons|e| charge of an e- [C]

• The vd is proportional to E by the factor μ, the “electron mobility”

each line between scatter events is

very slightly curved under bias

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metal >> semi

Conductivity of Metals and Semiconductors

The Silicon Age

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image from Wikipedia

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Two types of electronic charge carriers:

negative charge in conduction band

positive charge of a vacant electron state in the valence band

Move at different speeds - drift velocities

Charge Carriers in Semiconductors

1. Free Electron:

2. Hole:

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Intrinsic Semiconductors (for pure substances only)

Si Si Si Si

Si Si Si Si

Si Si Si Si

E field

n = # of free electrons e-

p = # of holes h+ left behind

At a given temperature, intrinsic semiconductors have some electrons with enough energy to excite through the bandgap. What they leave behind is a “hole”

Both e- and h+ are charge carriers, they move in opposite directions.

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Intrinsic Semiconductors: Conductivity vs T• Pure Silicon: - σ increases with T - opposite to metals

material Si Ge GaP CdS GaAs SiC

band gap Egap (eV) 1.11 0.67 2.25 2.40 1.43 2.86

/2

0egapE kT

in n

Larger electronegativity difference larger bandgap.

n = p

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Team Problem

Team Problem

1. Which of ZnSe and CdTe will have the larger band gap energy Eg ?

2. Which of ZnSe and CdTe will have the higher intrinsic carrier concentration at room temperature?

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Extrinsic Semiconductors: the role of impurity

These elements have one less valence e-

relative to Si

When present as impurities, they will create lots of extra

holes

called “p-type”

These elements have one more valence e-

relative to Si

When present as impurities, they will create lots of extra

mobile e-

called “n-type”

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• Extrinsic: -- electrical behavior is determined by impurities that introduce excess electrons or holes -- n ≠ p

Extrinsic Semiconductors: n-type

• n-type Extrinsic: (n >> p)een

Extrinsic Semiconductors: n-type

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Extrinsic Semiconductors: p-type

• p-type Extrinsic: (p >> n) hep

Extrinsic Semiconductors: p-type

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Intrinsic vs. Extrinsic Semiconductors

Extrinsic n-typeIntrinsic Extrinsic p-type

een hep

n for “negative” p for “positive”

Team Problem

What’s the difference between intrinsic and extrinsic semiconductors?

Which do you think would be more useful in modern technology?

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Extrinsic Semiconductors: Conductivity vs. Temperature

T1 T2

1) T<T1: Freeze-out region, thermal energy is not high enough to excite electron from donor state to CB

2) T1<T<T2: Extrinsic region, thermal energy is high enough to excite electron from donor state to CB

3) T>T2: Intrinsic region, thermal energy is high enough to excite electron from VB to CB

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Mobility vs. Impurity concentration

@ room temp

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Mobility vs. Temperature

een hep

Team Problem• Si is doped with As at a concentration of 1022 As atoms 1/m3. • Is this a lot or a little bit of doping?

MW [g/mol]

ρ [g/cm3]

So, the As is present at about 0.001 atomic %. That’s a tiny bit

• Allows flow of electrons in one direction only (e.g., AC/DC).

-- No applied potential: no net current flow.

-- Forward bias: carriers flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows.

-- Reverse bias: carriers flow away from p-n junction; junction region depleted of carriers; little current flow.

p-n Rectifying Junction

+ -

+-

Properties of Rectifying Junction

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p-n-p junction Voltage amplifier

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M.O.S.F.E.T. device

• Positive electric field at the gate: drives holes out of the p-type channel• This reduces conductivity to the drain (ON/OFF, a binary communication device)• Tiny change in gate voltage = big change in conductivity across the channel