Schottky diodes: I-V characteristics

Schottky diodes: I-V characteristics

• The general shape of the I-V curve in the MS (n-type) diode are very similar to that in the p⁺n diode.

• However the dominant current components are decidedly different in the two diodes.

p⁺

n M n

Forward-biased

p

n junction diode v.s. Schottky diode

p⁺

n Forward-biased

• Under small V_A, the dominant current components arise from recombination in the depletion region.

• Under large V_A, the dominant component is the hole injection (minority carrier injection by

diffusion) from p⁺ to n-side.

• Under large V_A, the electron injection from n to p⁺-side is negligible due to the light doping.

p

n junction diode v.s. Schottky diode

M n

• Although the recombination and hole injection currents still exist, because of the relatively low potential barrier seen by electrons in the n-side, the

dominant component is the electron injection from S to M under the

forward bias.

Reverse-biased Forward-based

• Under reverse bias, electron flow from M to S totally

dominates the observed current.

• So, the MS diode is often said to be a “majority carrier device”.

Thermionic emission theory

• The current resulting from majority carrier injection over the potential barrier in an MS diode is referred to as the

thermionic emission current.

• If an electron entering the depletion region from the semiconductor bulk has a velocity v_x directed toward the interface, the kinetic energy in the x- direction is given by

2

*

2 1

x nv

 m KEx

• When KE_x ≥ q(V_bi ─ V_A), the electron can surmount the surface barrier and cross into the metal.

) 2 (

1 _{* 2}

A bi

x

nv q V V

m  

• The velocity required for surmounting the barrier is )

2 (

1 _{* 2}

A bi

x

nv q V V

m  

) 2 (

min * bi A

n

x V V

m v q

v   

• Assuming there are n(v_x) electrons/cm³ in the semiconductor bulk with a velocity, –v_x, which is sufficient to surmount the

barrier.

• The current associated with this set of electrons with –v_x will

be _{( )}

,v x x

M

S qAv n v

I _ x  

• Summing over all electrons with sufficient energies,

x v

x x

M

S qA v n v dv

I   



Thermionic emission theory

• For a non-degenerate semiconductor, n(v_x) is given by

x v

x x

M

S qA v n v dv

I   



2

* /2 ) (

/ ) (

3 2

4 *

)

( _x ⁿ e ^{EF EC kT}e ^{mn kT vx} h

v kTm

n  ^{ }

 



  

• Substituting, integrating, and simplifying the results,

KT qV

KT M

S

A

B

e

e T A

I

 A *

where

Thermionic emission theory

A A 

 



 

0

*

* 0

m

m and ₃ 120 amps/cm² K²

2

4 0

h πqm k A 

• The constant A and A* are called Richardson constant and effective Richardson constant, respectively.

Thermionic emission theory

• Electrons crossing the interface from M to S always see the Schottky barrier height (_B). Consequently,

) 0 (

)

(  _ 



 S A M S A

M V I V

I

• Moreover, under equilibrium, the and currents across the barrier must precisely balance.

S

M  S  M

KT A

M S A

S M

e B

T A

V I

V

I _ (  0)   _ (  0)   A* ^{2  /}

• The total current at an arbitrary V_A is given by ) 0 ( 







 I_SM I_MS I_SM I_MS V_A I

Combining the equations,

KT s

KT qV

s

B A

e T A

I

e I

I

2 / /

*

) 1 (









A

p

n junction diode v.s. Schottky diode

) 1

(



 I

e

I











 



D i p

p A

i n

n

N n L D N

n L qA D I

2 2

0

) 1

(

0



 I e

I

KT s

e

T A

I  A *

V_A > a few kT/q

KT qV

s

e

I

I 

V_A < minus a few kT/q

I

I  

I_s

Deviations from the ideal in Schottky diodes

Forward-biased reverse-biased

series resistance

breakdown

(avalanche) thermal generation??

Schottky barrier lowering

• Differing from the pn junction diode, the non-saturating

reverse current is primarily attributed to a phenomenon known as Schottky barrier lowing.

• Even though it is assumed that _B is bias-independent in the ideal theory, the Schottky barrier is rather lowered under E-field (which is also called image force-induced lowering).

B B0

B

   

 

 

 

where _B0 is the barrier height when E = 0 and

4 _S0 S

B K

q q E





• The electric field at the semiconductor surface (E_S) can be computed from when x = 0. _{W x}

ε K x qN

S

D 





0

) E(

KT s

e

T A

I  A *

) 1

(



 I

e

I

Schottky barrier lowering

4 _S0 S

B K

q qE





• Since I_s exponentially varies with _B, even a small decrease in _B gives rise to a noticeable increase in the reverse-bias current.

Schottky barrier lowering

a.c. response in Schottky diode





a

V V

v  

 variation in the depletion width

 associated change in the depletion capacitance

W K A

C  _S







D

S V V

qN K ε

W  2 ⁰ 

Because ,





D S

S

V qN V

ε K

A C K





0 0

2

 The larger reverse bias, the smaller C.

a.c. response in Schottky diode

Taking the reciprocal and then squared,





D S

S

V qN V

ε K

A C K





0 0

2







S D

V A V

ε K qN

C  ₂ 

0 2

2 1

• The 1/C² plot against V_A gives a straight line.

• The slope of the straight line gives the doping concentration.

• The extrapolated intercept at 1/C² = 0 gives the built-in potential.

a.c. response in Schottky diode





S D

V A V

ε K qN

C  ₂ 

0 2

2





D S

S

V qN V

ε K

A C K





0 0

2



Practical considerations: rectifying contact

• An MS contact is defined to be ideal if the M and S are in intimate contact on an atomic scale, there is no intermixing of components, and there is no adsorbed impurities or surface charges at the MS interface.  practically it’s not the case.

Ex) According to the Schottky-Mott model, But…..

Regardless of the metal employed in a Ge MS diode, nearly all metals form a significant Schottky contact to n-type Ge and an ohmic contact to p-type Ge.

 The E_V of Ge is strongly pinned to the E_FM.











Fermi level pinning due to surface states

Fermi level pinning

E_C

E_V E_i

intrinsic n-type before equil. n-type after equil.

donor-like or accepter-like surface states.

E_F E_C

E_V

E_i E_i = E_F E_C

E_V

ρ

no space charge

ρ

no space charge

ρ

+ -

Practical considerations: ohmic contact

• In ideal cases, for ohmic contact,

_M > _S

_M < _S (n-type) (p-type)

• However, due to the Fermi level pinning, the deposition of any metal on n-type GaAs forms a barrier type contact.

• How are ohmic contacts achieved in practice?

 by heavily doping the surface region

The depletion depth decreases with doping!!

 Tunneling through the narrow W.

Announcements

• Next lecture: p. 563 ~ 575

• Homework: 14.2; 14.3; 14.9