16 PN Junctions - nanohub.org

Lundstrom ECE 305 S16

ECE-305: Spring 2016

Intgroduction to

PN Junctions I:

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA [email protected]

2/16/16

Pierret, Semiconductor Device Fundamentals (SDF) pp. 195-209

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2 Lundstrom ECE 305 S16

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ECE 305: Spring 2016: Exam 2

Out of 75 points:

Lundstrom ECE-305 S15 3

N: 22 Mean: 74.8% (56.1/75) SD: 17.5% Min: 26.7% Max: 96% Median: 80.7% (60.5/75)

20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

9

10

Count

E X AM 2 P erc ent %

How to succeed in ECE 305

Lundstrom ECE-305 S15 4

1)  Do the assigned reading before class.

2)  Listen to lecture, ask questions.

3)  Review the lecture notes and reading afterwards.

4)  Work the HW problems, then look at solutions.

5)  Ask questions.

https://www.edx.org

NP junction (equilibrium)

5

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0


“the semiconductor equations”

6

∂ p∂t

= −∇i

!Jpq

⎛

⎝⎜⎞

⎠⎟+Gp − Rp

∂n∂t

= −∇i!Jn−q

⎛⎝⎜

⎞⎠⎟+Gn − Rn

0 = −∇i ε

!E( ) + ρ

Three equations in three unknowns:

p!r( ), n !r( ), V !r( )

ρ = q p − n + N D

+ − N A−( )

!

E !r( ) = ∇V !r( )Lundstrom ECE 305 S16

equilibrium

NP junction

7

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0

transition region

Find: electric field, electrostatic potential, n(x), p(x), rho(x)

xp−xn 0

+

-

EVL > VR

ρ < 0NA

−

ρ > 0ND

+


energy band approach

8

EC

EVEF

Ei V = 0

EC

EV

Ei

1) Fermi-level must be constant in equilibrium. 2) Positive electrostatic potentials lower the electron energy 3)  Left side must develop a positive potential, Vbi.

EF

qVbiV = Vbi


eq. energy band diagram

9

EFEF

1) Begin with EF 2) Draw the E-bands where you know the carrier density 3) Electrostatic potential by flipping E-band upside down. 4) E-field from slope 5) n(x), p(x) from the E-band diagram 6) rho(x) from n(x) and p(x) 7) diffusion current from (5) or from (6)

EC x( ) = EC− ref − qV x( )

E x( ) = 1

qdEC x( ) dx


energy band diagram

10

EF

EC

EV

x

E

Ei

x = xpx = 0x = −xnLundstrom ECE 305 S16

“read” the e-band diagram

11

1)  Electrostatic potential vs. position

2)  Electric field vs. position

3)  Electron and hole densities vs. position

4)  Space-charge density vs. position


electrostatics: V(x)

12

V

x

N P

xp−xn

Vbi


NP junction

13

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0

transition region


xp−xn 0

+

-

EVL > VR

ρ < 0NA

−

ρ > 0ND

+


electrostatics: E (x)

14

E

xN P xp−xn


NP junction

15

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0

transition region


xp−xn 0

+

-

EVL > VR

ρ < 0NA

−

ρ > 0ND

+


carrier densities vs. x

16

log10 n x( ), log10 p x( )

xN P xp−xn

p0P = NA

p0N = ni2 ND

n0N = ND

n0 p = ni2 NA

n0N << ND p0P << NA


NP junction

17

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0

transition region


xp−xn 0

+

-

EVL > VR

ρ < 0NA

−

ρ > 0ND

+


electrostatics: rho(x)

18

ρ

x

N P

xp−xn

qND

−qNA


NP junction

19

N P

p0 ! NA

ρ ! 0 n0 ! ND

ρ ! 0

transition region


xp−xn 0

+

-

EVL > VR

ρ < 0NA

−

ρ > 0ND

+


the built-in potential

20

EC

EVEFP

Ei V = 0

EC

EV

Ei

EFN

qVbiV = Vbi

n0 = nieEFN −Ei( ) kBT p0 = nie

Ei−EFP( ) kBT

n0p0 = NDNA = ni2e EFN −EFP( ) kBT = eqVbi kBT

Vbi =kBTqln NDNA

ni2

⎛⎝⎜

⎞⎠⎟

NP junction electrostatics

21

How do we calculate rho(x), E(x), and V(x)?


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