chapter 14 ms contacts and schottky diodes
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Semiconductor Device Physics. Chapter 14 MS Contacts and Schottky Diodes. Chapter 14. Metal-Semiconductor Contacts and Schottky Diodes. pn -junction diode. I. V A. Schottky diode. MS Contact. The metal-semiconductor (MS) contact plays a very important role in solid-state devices. - PowerPoint PPT PresentationTRANSCRIPT
President University Erwin Sitompul SDP 11/1
Lecture 11Semiconductor Device Physics
Dr.-Ing. Erwin SitompulPresident University
http://zitompul.wordpress.com
2 0 1 3
President University Erwin Sitompul SDP 11/2
Chapter 14MS Contacts and Schottky Diodes
Semiconductor Device Physics
President University Erwin Sitompul SDP 11/3
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
President University Erwin Sitompul SDP 11/4
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).
President University Erwin Sitompul SDP 11/5
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
President University Erwin Sitompul SDP 11/6
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
President University Erwin Sitompul SDP 11/7
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
President University Erwin Sitompul SDP 11/8
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.
President University Erwin Sitompul SDP 11/9
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
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Metal-Semiconductor Contacts
EFEc
Ev
EFEc
Ev
EF
Ec
Ev
EF
Ec
Ev
President University Erwin Sitompul SDP 11/11
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 ):
President University Erwin Sitompul SDP 11/12
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
President University Erwin Sitompul SDP 11/13
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
=
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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
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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)
President University Erwin Sitompul SDP 11/16
* 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:
President University Erwin Sitompul SDP 11/17
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
President University Erwin Sitompul SDP 11/18
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
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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
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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
President University Erwin Sitompul SDP 11/21
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.
President University Erwin Sitompul SDP 11/22
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.
President University Erwin Sitompul SDP 11/23
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
President University Erwin Sitompul SDP 11/24
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.