Chapter 14 MS Contacts and Schottky Diodes

President University Erwin Sitompul SDP 11/1

Lecture 11Semiconductor Device Physics

Dr.-Ing. Erwin SitompulPresident University

http://zitompul.wordpress.com

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Chapter 14MS Contacts and Schottky Diodes

Semiconductor Device Physics


MS ContactChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

The metal-semiconductor (MS) contact plays a very important role in solid-state devices.When in the form of a rectifying contact, the MS contact is

referred to as the Schottky.When in the from of a non-rectifying or ohmic contact, the

MS contact is the critical link between the semiconductor and the outside.

The reverse-bias saturation current IS of a Schottky diode is 103 to 108 times larger than that of a pn-junction diode, depending on the type of material.Schottky diodes are proffered

rectifiers for low-voltage high-current applications. VA

Ipn-junction diode

Schottky diode


MS ContactChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

A vacuum energy level, E0, is defined as the minimum energy an electron must possess to completely free itself from the material.

The energy difference between E0 and EF is known as the workfunction (Φ).


FM: Metal workfunction FS: Semiconductor workfunction

E0: vacuum energy level

EFM: Fermi level in metal EFS: Fermi level in semiconductorc: electron affinity

cSi = 4.03eV

WorkfunctionChapter 14 Metal-Semiconductor Contacts and Schottky Diodes


B M cF =F

Ideal MS Contact: FM > FS, n-typeChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Surface potential-energy barrier

Band diagram instantly after contact formation

Band diagram under equilibrium condition

E0 is continuous


Ideal MS Contact: FM < FS, n-typeChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Band diagram instantly after contact formation

Band diagram under equilibrium condition

E0 is continuous


Reverse Bias

Forward Bias

Forward bias

Reverse bias

n-type MS ContactChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Current is determined by majority-carrier flow across the MS junction.Under forward bias, majority-

carrier diffusion from the semiconductor into the metal dominates.

Under reverse bias, majority-carrier diffusion from the metal into the semiconductor dominates.


There are 2 kinds of metal-semiconductor (MS) contact:

Rectifying (“Schottky diode”)

Non-rectifying (“Ohmic contact”)

VA

I

Metal-Semiconductor ContactsChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

VA

I


Metal-Semiconductor Contacts

EFEc

Ev

EFEc

Ev

EF

Ec

Ev

EF

Ec

Ev


0 0

0,

== =n n p p

D A( )0, 0q N N

n p = = =

Vbi : “built-in” voltage

bi B c F FB1 ( )V E Eq

= F

The Depletion ApproximationChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

The semiconductor is depleted to a depth W: In the depleted region

(0 x W ):

Beyond the depleted region (x > W ):


E(x) E(x+Dx)

Dx

Area A S ( ) ( )x x x A xA D = DE E

S

( ) ( )x x xx

D =

DE E

S

ddx

=E

2

2S

d Vdx

=

Poisson’s EquationChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

According to Gauss’s Law:

E : electric field intensity (V/m)

S : relative permittivity (F/cm) : charge density (C/cm3)

Or:

S = KS0 0 = 8.854 × 10–14 F/cm For Si, KS = 11.8


D

S

( ) ( )qNx W x

= E

0D

S

W

x x

qNd dx

= E

E

D

S S

qNddx

= E +

–

D

S

( ) ( ) ( )W W

x x

qNV x x dx W x dx

= = E

MS Contact ElectrostaticsChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Poisson’s equation:

The solution is:

Furthermore:

2D

S

( )2qN W x

=


2D

S

( )2qNV x W x

=

S bi

D

2 VWqN

=

Depletion Layer Width WChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

+–

The potential in the semiconductor side is chosen to be the zero reference.

At x = 0, V = –Vbi

The depletion width is given by

W decreases as ND increases


2D

S

( ) ( )2qNV x W x

=

S bi A

D

2 ( ) V VWqN

=

Depletion Layer Width W for VA 0Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Previously,

At x = 0, now V = – (Vbi – VA)

W decreases as ND increases W increases as –VA increases

+–

– (Vbi – VA)


* 2x n x bi A

1KE ( )2m v q V V=

xS M, x x( )vI qAv n v =

min

S M x x x( )v

I qA v n v dv

=

x min bi A*n

2 ( )qv v V Vm

=

Thermionic Emission CurrentChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Thermionic emission current results from majority carrier injection over the potential barrier.

Electrons can cross the junction into the metal if:

Or:

The current for electrons at a certain velocity is:

The total current over the potential barrier is:


B A* 2S M

kT qV kTI A T e e F = B

* 2F c n x

*2( ) / ( / 2 )n

x 3

4( ) E E kT m kT vkTmn v e eh

=

I –V CharacteristicsChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

22 20

3

4 120 A (cm K )qm kh

= = B

For a non-degenerate semiconductor, it can be shown that:

We can then obtain

Where

And

** n

0

mm

=

B B


I –V Characteristics

M S A S M A( 0) ( 0)I V I V = = =

AS( 1)qV kTI I e=

–IS :reverse bias saturation current

Therefore

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes

In the reverse direction and equilibrium condition, the electrons always see the same barrier FB, so

Finally, combining the total current at an arbitrary VA,

WhereB* 2

S kTI A T e F= B


In an MS contact, charge is stored on either side of the MS junction.The applied bias VA affects this

charge and varies the depletion width.

If an a.c. voltage va is applied in series with the d.c. bias VA, the charge stored in the MS contact will be modulated at the frequency of the a.c. voltage.Displacement current will flow.

advi Cdt

= s C AW

=

Small-Signal CapacitanceChapter 14 Metal-Semiconductor Contacts and Schottky Diodes


bi A2 2D S

1 2 ( )V VC qN A

=

S C AW

=

S bi A

D

2 ( ) V VWqN

=

Small-Signal CapacitanceChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Since in general

ThenS D S

bi ASbi A

D

2( )2 ( )

qNA AV V

V VqN

= =

Or


Practical Ohmic ContactChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

In practice, most MS-contacts are rectifying. In order to achieve a contact that can conduct easily in both

directions, the semiconductor is to be doped very heavily.Depletion width W becomes so narrow that the carriers can

tunnel directly through the barrier.


qVbi

q(Vbi–VA)

q(Vbi–VA)

Voltage Drop Across the MS ContactChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Under equilibrium conditions (VA = 0), the voltage drop across the semiconductor depletion region is the built-in voltage Vbi.

If VA 0, the voltage drop across the semiconductor depletion region is Vbi – VA.


S A bi

A

2 ( ) V VWqN

=

2A

S

( ) ( )2qNV x W x

=

?

?

?

E

V

MS Contact with p-type SemiconductorChapter 14 Metal-Semiconductor Contacts and Schottky Diodes

If p-type semiconductor is used, the depletion layer width W of the MS contact for VA 0 is given by

At x = 0, V = Vbi + VA,

W increases as VA increases W decrease as NA increases


Homework 91.

(Nea.EC.10.27)An MS-junction is formed between a metal with a work function of 4.3 eV and p-type Si with an electron affinity of 4 eV. The doping concentration in semiconductor is 5×1016 cm–3. Assume T = 300 K. (a) Sketch the thermal equilibrium energy band diagram; (b) Determine the height of the Schottky barrier; (c) Sketch the energy band diagram with an applied reverse-bias voltage of

VA = –3V; (d) Sketch the energy band diagram with an applied forward-bias voltage of

VA = 0.25 V.

Chapter 14 Metal-Semiconductor Contacts and Schottky Diodes

Due: 12.12.2013.

Chapter 14 MS Contacts and Schottky Diodes

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Transcript of Chapter 14 MS Contacts and Schottky Diodes