metallurgical junction

21
President University Erwin Sitompul SDP 7/1 Dr.-Ing. Erwin Sitompul President University Lecture 7 Semiconductor Device Physics http://zitompul.wordpress.com

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Chapter 5. pn Junction Electrostatics. Metallurgical Junction. Doping profile. Step junction idealization. Chapter 5. pn Junction Electrostatics. Poisson’s Equation. Poisson’s equation is a well-known relationship in electricity and magnetism. - PowerPoint PPT Presentation

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Page 1: Metallurgical Junction

President University Erwin Sitompul SDP 7/1

Dr.-Ing. Erwin SitompulPresident University

Lecture 7

Semiconductor Device Physics

http://zitompul.wordpress.com

Page 2: Metallurgical Junction

President University Erwin Sitompul SDP 7/2

Step junctionidealization

Metallurgical JunctionChapter 5 pn Junction Electrostatics

Doping profile

Page 3: Metallurgical Junction

President University Erwin Sitompul SDP 7/3

Poisson’s EquationChapter 5 pn Junction Electrostatics

S 0K

E v DD E

S 0K

S 0K

Ex

Poisson’s equation is a well-known relationship in electricity and magnetism. It is now used because it often containes the starting point in

obtaining quantitative solutions for the electrostatic variables.

In one-dimensional problems, Poisson’s equation simplifies to:

Page 4: Metallurgical Junction

President University Erwin Sitompul SDP 7/4

Equilibrium Energy Band DiagramChapter 5 pn Junction Electrostatics

pn Junction diode

Page 5: Metallurgical Junction

President University Erwin Sitompul SDP 7/5

Band diagram

c ref

1( )V E E

q

Qualitative ElectrostaticsChapter 5 pn Junction Electrostatics

Equilibrium condition

Electrostatic potential

Page 6: Metallurgical Junction

President University Erwin Sitompul SDP 7/6

Electric field

Qualitative ElectrostaticsChapter 5 pn Junction Electrostatics

Equilibrium condition

Charge density

dV

dxE

S 0K

Ex

Page 7: Metallurgical Junction

President University Erwin Sitompul SDP 7/7

Formation of pn Junction and Charge DistributionChapter 5 pn Junction Electrostatics

D A( )q p n N N qNA– qND

+

Page 8: Metallurgical Junction

President University Erwin Sitompul SDP 7/8

Formation of pn Junction and Charge DistributionChapter 5 pn Junction Electrostatics

Page 9: Metallurgical Junction

President University Erwin Sitompul SDP 7/9

DF i n-side

i i

( ) ln lnNn

E E kT kTn n

bi F i n side i F p side( ) ( )qV E E E E

Ai F p-side

i i

( ) ln lnNp

E E kT kTn n

A Dbi 2

i

lnN N

qV kTn

Built-In Potential Vbi

Chapter 5 pn Junction Electrostatics

For non-degenerately doped material,

• Vbi for several materials:Ge

≤ 0.66 VSi

≤ 1.12 VGeAs

≤ 1.42 V

Page 10: Metallurgical Junction

President University Erwin Sitompul SDP 7/10

A1

S

( )qN

x x c

E

A

S

qNd

dx

E

Dn

S

( ) ( )qN

x x x

E

Ap

S

( ) ( )qN

x x x

E

with E(–xp) 0

with E(xn) 0

The Depletion ApproximationChapter 5 pn Junction Electrostatics

On the p-side, ρ = –qNA

On the n-side, ρ = qND

Page 11: Metallurgical Junction

President University Erwin Sitompul SDP 7/11

A p

D n

, 0 , 0 0,

qN x xqN x x otherwise

Ap p

S

Dn n

S

( ), 0

( )( ), 0

qNx x x x

xqN

x x x x

E

2Ap p

S

2Dbi n n

S

( ) , 02

( )( ) , 0

2

qNx x x x

V xqN

V x x x x

Step Junction with VA=0Chapter 5 pn Junction Electrostatics

Solution for ρ

Solution for E

Solution for V

Page 12: Metallurgical Junction

President University Erwin Sitompul SDP 7/12

2 2A Dp bi n

S S

( ) ( )2 2

qN qNx V x

A p D nN x N x

Step Junction with VA=0Chapter 5 pn Junction Electrostatics

At x = 0, expressions for p-side and n-side must be equal:

Page 13: Metallurgical Junction

President University Erwin Sitompul SDP 7/13

Relation between ρ(x), E(x), and V(x)Chapter 5 pn Junction Electrostatics

1.Find the profile of the built-in potential Vbi

2.Use the depletion approximation ρ(x) With depletion-layer widths xp, xn unknown

3.Integrate ρ(x) to find E(x) Boundary conditions E(–xp) 0, E(xn)0

4.Integrate E(x) to obtain V(x) Boundary conditions V(–xp) 0, V(xn) Vbi

5.For E(x) to be continuous at x 0, NAxp NDxn

Solve for xp, xn

Page 14: Metallurgical Junction

President University Erwin Sitompul SDP 7/14

S An bi

D A D

2

( )

Nx V

q N N N

S Dp bi

A A D

2

( )

Nx V

q N N N

n px x W

Dn

A

Nx

N

Depletion Layer WidthChapter 5 pn Junction Electrostatics

Eliminating xp,

Eliminating xn,

Summing Sbi

A D

2 1 1V

q N N

Exact solution, try to derive

Page 15: Metallurgical Junction

President University Erwin Sitompul SDP 7/15

S bi Dn p n

D A

2 , 0

V NW x x x

q N N

S bi2 VW

q N

S bi Ap n p

A D

2 , 0

V NW x x x

q N N

One-Sided JunctionsChapter 5 pn Junction Electrostatics

If NA >> ND as in a p+n junction,

If ND >> NA as in a n+p junction,

Simplifying,

where N denotes the lighter dopant density

Page 16: Metallurgical Junction

President University Erwin Sitompul SDP 7/16

D Abi 2

i

lnN NkT

Vq n

S bi

D

2 VW

qN

n 0.115 mx W

Dp n

A

Nx x

N

Example: Depletion Layer WidthChapter 5 pn Junction Electrostatics

A p+n junction has NA 1020 cm–3 and ND 1017cm–3, at 300 K.

a) What isVbi?

b) What is W?

c) What is xn?

d) What is xp?

17 20

10 2

10 1025.86mV ln 1.012 V

(10 )

1/ 214

19 17

2 11.9 8.854 10 1.0120.115 m

1.602 10 10

30.115 m 10 1.15 Å

Page 17: Metallurgical Junction

President University Erwin Sitompul SDP 7/17

Step Junction with VA 0Chapter 5 pn Junction Electrostatics

• To ensure low-level injection conditions, reasonable current levels must be maintained VA should be small

Page 18: Metallurgical Junction

President University Erwin Sitompul SDP 7/18

A Dbi

i i

ln lnN NkT kT

Vq n q n

Sp n bi A

A D

2 1 1W x x V V

q N N

S Dp bi A

A A D

2,

Nx V V

q N N N

S An bi A

D A D

2 Nx V V

q N N N

Step Junction with VA 0Chapter 5 pn Junction Electrostatics

Built-in potential Vbi (non-degenerate doping):

A D2

i

lnN NkT

q n

Depletion width W :

Page 19: Metallurgical Junction

President University Erwin Sitompul SDP 7/19

Effect of Bias on ElectrostaticsChapter 5 pn Junction Electrostatics

• If voltage drop then depletion width • If voltage drop then depletion width

Page 20: Metallurgical Junction

President University Erwin Sitompul SDP 7/20

Linearly-Graded JunctionChapter 5 pn Junction Electrostatics

S

1dx

E V dx E

Page 21: Metallurgical Junction

President University Erwin Sitompul SDP 7/21

1. (6.4)Consider a silicon pn junction at T = 300 K with a p-side doping concentration of NA 1018 cm–3. Determine the n-side doping concentration such that the maximum electric field is |Emax| 3×105 V/cm at a reverse bias voltage of VR 25 V.

Chapter 5 pn Junction Electrostatics

Homework 5

Deadline: 10 March 2011, at 07:30.

2. (7.6)Problem 5.4Pierret’s “Semiconductor Device Fundamentals”.