ECE606: Solid State Devices Lecture 26: Schottky Diode (II)

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ECE606: Solid State DevicesECE606: Solid State DevicesLecture 26: Schottky Diode (II)

Muhammad Ashraful [email protected]

Alam ECE‐606 S09 1

OutlineOutline

1) DC Thermionic current (detailed derivation)

2) AC small signal and large‐signal response

3) Additional information

4) Conclusions

Ref. SDF, Chapter 14

Alam ECE‐606 S09 2Alam ECE‐606 S092

Energy Resolved Thermionic Flux occupation

( )min

E Eυ

β∞ ∞ − Ω∫ ∫ ∫

~ DOS

( )34

Fs x xm

E Ey zJ q dk edk dk β υ

π− −

→−∞ −∞−∞

Ω= − ∫ ∫ ∫

minυ

V

q(Vbi‐VA)VA

EC‐EF


x

Thermionic Flux from Semi to Metal .. E

( )min

34F

s m x y z xE EJ q dk dk edk β

υ

υπ

−∞ ∞

→−

∞ −∞ −∞

−

−

Ω= − ∫ ∫ ∫

ECEF

∞ −∞ −∞−

( ) * 2 * 2 * 21 1 12 2

( ) ( )2C x y zC F C FF E E E EE E m m mE E υ υ υ− + ++− =− −= +

( ) ( ) ( ) ( ) ( )min2 2 2* *

2

* x y

c F

zx y z

m m mE E d m d m d m υυ υ

ββυυ υ υ−∞ ∞

−−+

−+

Ω∫ ∫ ∫

( )2 2 2y

( ) ( ) ( ) ( )2

34c F y

xE Eqe eβ υ

π−∞ −∞ −∞

= ∫ ∫ ∫

( ) ( )

2 22min

3 * ***2 22

3 34

y xz

c F

m mmE E

s m y z x x

q mJ e e d e d d e

υ υυβ βυββ υ υ υ υ

π

⎛ ⎞ ⎛ ⎞⎛ −⎞⎜ ⎟∞ ∞− −− ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟− − ⎝ ⎠ ⎝ ⎠ ⎝ ⎠→

−∞ −∞ −∞

⎡ ⎤ ⎡ ⎤⎡ ⎤Ω ⎢ ⎥ ⎢ ⎥⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦

∫ ∫ ∫


∞ ∞ ∞⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦

Thermionic Current … ( )min *

2bi A

q V Vm

= −υ

( ) ( )

2 22min

3 * ***2 22

y xz

c F

m mmE Eq m

J e e d e d d eυ υυ υβ ββ

β υ υ υ υ

⎛ ⎞ ⎛ ⎞⎛ ⎞ −⎜ ⎟∞ ∞− −− ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟− ⎝ ⎠ ⎝ ⎠ ⎝ ⎠−⎡ ⎤ ⎡ ⎤⎡ ⎤Ω ⎢ ⎥ ⎢ ⎥⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎢ ⎥∫ ∫ ∫

m

3 34s m y z x xJ e e d e d d eυ υ υ υπ→

−∞ ∞ −∞−⎢ ⎥ ⎢ ⎥⎢ ⎥

⎣ ⎦ ⎣ ⎦⎢ ⎥⎣ ⎦∫ ∫ ∫

( )1bi AV Vqe β−−

* 24 k

π π 2bi Ae

( )2

203

4 bF C i A AE E qV qV Vqs m

qm kJ T e e A eh

β β βπ→

− −= =

( )0 1AqT s m m s

VJ J J A e β→ →= − = −

5

Compare with p‐n junction … where is the bandgap, doping?

Recombination/Generation/Impact‐ionization

EFMEc

EFEFSEFM

EV

6SAME technique as in p‐n junction except integrate to xp only

Outline




4) Conclusions


Topic Map

Equilibrium DC Small Large CircuitsEquilibrium DC Small signal

Large Signal

Circuits

Diode

Schottky

BJT/HBT

MOS


AC response

ConductanceJunction Capacitance

Series

Capacitance

ResistanceDiffusion Capacitance


Forward Bias Conductance

gFB( )( )/ 1A Sq V R I m

oI I e −= −β

ln ( ) /oA S

I I q V R I mI+

= − β

1 m

0I

Am dV

0

1( )S

FB

mRg q I I

= ++β( )

AS

o

m dV Rq I I dI

= −+β


Junction Capacitance (Majority Carriers)

Junction Capacitance

0s AC κ ε=JC

W=

Aκ ε 0

02 ( )

sJ

sbi A

ACV V

qN

κ εκ ε

=−


DqN

No Diffusion Capacitance in Schottky Diode

p‐n Diode Schottky diode

n

x

VA

No minority carrier transport and


No minority carrier transport and therefore no diffusion capacitance ..

Reducing diffusion capacitance in p‐n diode

p‐n Diode Schottky dioden

x

VA

13

Short minority carrier lifetime in p-n junction diode equivalent to rapid energy relaxation in SB diode.

Outline




4) Conclusions


Ohmic Contact vs. Schottky contacts ..

OxideMetal

n+

n‐Si

Low Doping Moderate Doping High Doping


Lowering of Schottky Barrier

E

qφ1qφB qφ1qφB

SemiMetal

‐I

Metal Semi

‐‐

‐‐‐

‐

‐Surface Charge

ElectronImage Charge

Alam ECE‐606 S09 16Ref. Sze/Ng., p. 143x

Chargex

Fermi‐level PinningDensity of States

Ec

Regardless the workfunction, no modulation in potential. (e g Modern high-k dielectrics)

Full

Full

EcEf

Ev

(e.g. Modern high k dielectrics)

Metal MetalSemiconductor

EcE

Shift in the Band edge

Full

Metal

Full

Metal

Ef

Ev


A BMetalMetal

Conclusion

1) Schottky diodes have wide range of applications in

practical devices.

2) The key distinguishing feature of Schottky diode is that

it is a majority carrier device.it is a majority carrier device.

3) We use a different technique to calculate the current in

a majority carrier device It is called thermionica majority carrier device. It is called thermionic

emission.


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ECE606: Solid State Devices Lecture 26: Schottky Diode (II)