1. Lecture 7 OUTLINE Work Function Metal-Semiconductor Contacts
Energy band diagrams
Depletion-layer width
Small-signal capacitance
Reading: Pierret ; Hu 4.16

2. Metal-Semiconductor Contacts
There are 2 kinds of metal-semiconductor contacts:
rectifying
“Schottky diode”
non-rectifying
“ohmic contact”
EE130/230A Fall 2013
Lecture 7, Slide 2

3. Work Function E0: vacuum energy level FM: metal work function
R.F. Pierret, Semiconductor Fundamentals, Figure 14.1
FM: metal work function
FS: semiconductor work function
EE130/230A Fall 2013
Lecture 7, Slide 3

4. Ideal M-S Contact: FM < FS, n-type
Band diagram instantly
after contact formation:
Equilibrium band diagram:
EE130/230A Fall 2013
Lecture 7, Slide 4
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.2

5. Ideal M-S Contact: FM > FS, n-type
Band diagram instantly
after contact formation:
Equilibrium band diagram:
qVbi = FBn– (Ec – EF)FB
Schottky Barrier Height: n W
EE130/230A Fall 2013
Lecture 7, Slide 5
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.2

6. Effect of Interface States on FBn
Ideal M-S contact:
FBn = FM – c
Real M-S contacts:
A high density of allowed energy states in the band gap at the M-S interface “pins” EF to be within the range 0.4 eV to 0.9 eV below Ec FM
FBn
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-35
EE130/230A Fall 2013
Lecture 7, Slide 6

7. Schottky Barrier Heights: Metal on Si
FBn tends to increase with increasing metal work function
EE130/230A Fall 2013
Lecture 7, Slide 7

8. Schottky Barrier Heights: Silicide on Si
Silicide-Si interfaces are more stable than metal-silicon interfaces and hence are much more prevalent in ICs. After metal is deposited on Si, a thermal annealing step is applied to form a silicide-Si contact. The term metal-silicon contact includes silicide-Si contacts.
EE130/230A Fall 2013
Lecture 7, Slide 8

9. The Depletion Approximation
The semiconductor is depleted of mobile carriers to a depth W
In the depleted region (0  x  W ):
r = q (ND – NA)
Beyond the depleted region (x > W ):
r = 0
EE130/230A Fall 2013
Lecture 7, Slide 9
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4

10. Electrostatics Poisson’s equation: The solution is:
EE130/230A Fall 2013
Lecture 7, Slide 10
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4

11. Depletion Width, W At x = 0, V = -Vbi W decreases with increasing ND
EE130/230A Fall 2013
Lecture 7, Slide 11
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4

12. Voltage Drop across the M-S Contact
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.
EE130/230A Fall 2013
Lecture 7, Slide 12
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.3

13. Depletion Width, W, for VA  0
Last time, we found that
At x = 0, V = - (Vbi - VA)
W increases with increasing –VA
W decreases with increasing ND
EE130/230A Fall 2013
Lecture 7, Slide 13
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4

14. Charge Storage in a Schottky Diode
Charge is “stored” on both sides of the M-S contact.
The applied bias VA modulates this charge.
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
EE130/230A Fall 2013
Lecture 7, Slide 14

15. Small-Signal Capacitance
If an a.c. voltage va is applied in series with the d.c. bias VA, the charge stored in the Schottky contact will be modulated at the frequency of the a.c. voltage
displacement current will flow:
EE130/230A Fall 2013
Lecture 7, Slide 15

16. Using C-V Data to Determine FB
Once Vbi and ND are known, FBn can be determined:
EE130/230A Fall 2013
Lecture 7, Slide 16

17. Ideal M-S Contact: FM > FS, p-type
semiconductor
Band diagram instantly
after contact formation:
Equilibrium band diagram:
EE130/230A Fall 2013
Lecture 7, Slide 17
R.F. Pierret, Semiconductor Fundamentals, p. 482

18. Ideal M-S Contact: FM < FS, p-type
semiconductor
Band diagram instantly
after contact formation:
Equilibrium band diagram:
Schottky Barrier Height:
FBp
qVbi = FBp– (EF – Ev)FB W
EE130/230A Fall 2013
Lecture 7, Slide 18
R.F. Pierret, Semiconductor Fundamentals, p. 482

19. W for p-type Semiconductor
At x = 0, V = Vbi + VA
W increases with increasing VA
W decreases with increasing NA
EE130/230A Fall 2013
Lecture 7, Slide 19

20. Summary For rectifying contacts: small-signal capacitance EF Ec Ev EF
R.F. Pierret, Semiconductor Fundamentals, p. 481
For rectifying contacts:
small-signal capacitance
EE130/230A Fall 2013
Lecture 7, Slide 20

21. Summary: Rectifying Contacts
Schottky barrier height, FB:
Energy barrier that must be surmounted in order for a carrier in the metal to enter the semiconductor
Built-in potential, qVbi:
FBn-(EC-EF)FB for n-type Si, FBp-(EF-Ev)FB for p-type Si
Ideally qVbi is equal to the work function difference between the metal and semiconductor.
In practice, for Si:
FBn  (2/3)EG and FBp  (1/3)EG
EE130/230A Fall 2013
Lecture 7, Slide 21