department of physics,john bardeen, william shockley, walter brattain 1948 bell labs. bipolar...

Shingo Katsumoto

Department of Physics,

Institute for Solid State Physics

University of Tokyo

Physics of Semiconductors

8th 2016.6.6

Outline today

Review of pn junction

Estimation of built-in potential

Depletion layer width

Injection of minority carriers

Bipolar junction transistor Base-Collector characteristics

Collector-Emitter characteristics

Depletion layer with reverse bias voltage

Effective capacitance and reverse bias voltage

pn junction FET

Schottky barrier

MES FET

MOS FET

Review of pn junctions

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-

- -

- -

-

- -

-

-

-

-

+

+

+

+ +

+

+ +

+

+ + +

+ + +

+

p n

-

-

- -

- -

-

- -

-

-

-

-

+

+

+

+ +

+

+ +

+

+ + +

+ + +

+

−𝑤𝑝 𝑤𝑛

E x

Balance of diffusion and

drift currents.

Minimize 𝐹 = 𝑈 − 𝑇𝑆

Depletion layer

Space charge

Built-in electric field

Built-in potential 𝑉bi 𝐸F

Estimation of built-in potential concentration

electrons holes

n-layer

p-layer

number of sites: N number of sites: N

particle number: 𝑁1 particle number: 𝑁2

Number of cases:

Estimation of built-in potential (2)

Stirling approximation: ln 𝑁! ≈ 𝑁ln𝑁 − 𝑁

:Mixing entropy

Depletion layer width E x −𝑤𝑝 𝑤𝑛

𝑁A 𝑁D

Current voltage characteristics

External voltage V

Forward bias (against 𝑉𝑏𝑖 ) : lowers barrier for diffusion current 𝑛𝑛

Equilibrium

Electrons

Current balance

Injection of minority carriers

0

0

V

J

minority carrier

current Barrier overflow

Fate of injected minority carriers:

Radiative recombination

Non-radiative recombination

ℎ𝜈 light emitting

diode

phonon

electron Diffusion with lifetime:

Minority carrier

diffusion length

A question for you

0

0

V

J

Consider an ideal light emitting

diode, which has no non-radiative

recombination. Every injected

carrier emits a photon with the

energy 𝐸g. Now apply a voltage

𝑉1 < 𝐸g/𝑒 and a current 𝐽1 flows.

The power of light emission is

𝑃L = 𝐸g𝐽1/𝑒 . 𝐸g

𝑒

𝑉1

𝐽1

On the other hand, the electric power source gives the power

𝑃S = 𝐽1𝑉1, which is smaller than 𝑃𝐿! Does the LED create

energy? Or what is happening inside the LED?

External injection of minority carriers: Solar Cells

V

J

0

0

dark

illuminated

𝑒𝑣𝑛Δ𝑛𝑝

External injection

Two types of transistors

John Bardeen, William Shockley,

Walter Brattain 1948 Bell Labs.

Bipolar junction transistor

n n p

Field effect transistor

p

n

Bipolar transistor structures and symbols

Bipolar transistor structures and symbols

PNP type NPN type

Similar characteristics PNP and NPN: complementary

Base-Collector characteristics

n n p

E B C

−𝐽C

−𝐽 C

𝑉BC

𝐽E

𝑉BC

𝐽E

Base-Collector characteristics

n

p n

𝑉BC

e-

e- e-

e-

e-

e- e+

e+ e+

e+

e+

𝐽𝐸 𝐽𝐶

Collector-Emitter characteristics n n p

E B C 𝐽𝐶

Current amplification : Linearize with quantity selection

𝐽𝐶 = ℎ𝐹𝐸 𝐽𝐵

Emitter-common current gain

Linear approximation of bipolar transistor

⋃ ≖ ∱ ≊ ∲

∡ ∽ ⋃ ≈ ∱ ∱ ≈ ∱ ∲ ≈ ∲ ∱ ≈ ∲ ∲

∡ ⋃ ≊ ∱ ≖ ∲

∡ ∺

𝑗1

𝑉1

𝑉2

⋃ ≶ ∱ ≪ ∲

∡ ∽ ⋃ ≨ ∱ ∱ ≨ ∱ ∲ ≨ ∲ ∱ ≨ ∲ ∲

∡ ⋃ ≪ ∱ ≶ ∲

∡ ∽ ⋃ ≨ ≩ ≨ ≲ ≨ ≦ ≨ ≯

∡ ⋃ ≪ ∱ ≶ ∲

∡

(lower case:

local linear approximation)

Hybrid matrix

h-parameters

𝑗2

Depletion layer width with reverse bias voltage

+ - + +

+

- - -

p n

−𝑤𝑝 𝑤𝑛

𝑉𝑏𝑖 + 𝑉 Poisson equation

Depletion layer width with reverse bias voltage (2)

Charge per unit area:

Effective capacitance and reverse bias voltage

V

−𝑉𝑏𝑖

Doping profiler

Varicap diode

KB505 Frequency modulation

Phase lock loop

pn junction field effect transistor (JFET)

Circuit symbols

D

G

S

D

G

S

n-channel p-channel

pn junction FET

y

L

wd (y)

n

p+

2wt S D

G

p+ G

-NDe

Vg

Vch(y)

pinch off (internal) voltage:

Only valid for wd < wt/2.

conductivity

electric field

channel width

I-V characteristics of JFET

2N5459

From Wikipedia

R(Vg) is non-linear

Schottky barrier

𝐸F

𝑒𝜙𝑀

𝑒𝜙𝑆

𝐸D 𝐸F

𝐸c

𝐸v

𝐸F

𝐸c

𝐸v

𝑤𝑑

metal semiconductor

x 0

- Q

Walter Schottky

1886-1976

Charge balance:

Voltage V --> barrier height e(Vs-V)

MES-FET

MOS-FET

enhancement

depletion

inversion

Simplified

CMOS inverter

circuit

Low leakage

current

Single gate input

both on/off switch

Exercise A

A-1. p-Ge has Seebeck coefficient of 300mV/K and n-type

Bi2Te3 -230mV/K. If one makes a thermocouple from these

two materials, how high is the voltage caused by the

temperature difference of 50K.

A-2. Obtain expressions for electron mobility and for

diffusion constant in terms of the conductivity and the Hall

coefficient.

Submission deadline: 2016.6.20