1. Lecture 7 OUTLINE Poisson’s equation Work function Metal-Semiconductor Contacts – Equilibrium energy band diagrams – Depletion-layer width Reading: Pierret 5.1.2, 14.1-14.2; Hu 4.16

2. Gauss’ Law:  s : permittivity (F/cm)  : charge density (C/cm 3 ) Poisson’s Equation E(x)E(x) E(x+x)E(x+x) xx area A EE130/230M Spring 2013Lecture 7, Slide 2

3. Charge Density in a Semiconductor Assuming the dopants are completely ionized:  = q (p – n + N D – N A ) EE130/230M Spring 2013Lecture 7, Slide 3

4. Work Function  M : metal work function  S : semiconductor work function  0 : vacuum energy level EE130/230M Spring 2013Lecture 7, Slide 4

5. Metal-Semiconductor Contacts There are 2 kinds of metal-semiconductor contacts: rectifying “Schottky diode” non-rectifying “ohmic contact” EE130/230M Spring 2013Lecture 7, Slide 5

6. Ideal M-S Contact:  M <  S, p-type Band diagram instantly after contact formation: Equilibrium band diagram: Schottky Barrier Height: EE130/230M Spring 2013Lecture 7, Slide 6 qV bi =  Bp – (E F – E v ) FB W p-type semiconductor  Bp

7. EE130/230M Spring 2013Lecture 7, Slide 7 Ideal M-S Contact:  M >  S, p-type p-type semiconductor Equilibrium band diagram: Band diagram instantly after contact formation:

8. Ideal M-S Contact:  M <  S, n-type EE130/230M Spring 2013Lecture 7, Slide 8 Band diagram instantly after contact formation: Equilibrium band diagram:

9. Ideal M-S Contact:  M >  S, n-type Band diagram instantly after contact formation: Equilibrium band diagram: Schottky Barrier Height: EE130/230M Spring 2013Lecture 7, Slide 9 qV bi =  Bn – (E c – E F ) FB W n

10. Effect of Interface States on  Bn Ideal M-S contact:  Bn =  M –  Real M-S contacts: A high density of allowed energy states in the band gap at the M-S interface “pins” E F to be within the range 0.4 eV to 0.9 eV below E c EE130/230M Spring 2013Lecture 7, Slide 10 MM  Bn

11.  Bn tends to increase with increasing metal work function Schottky Barrier Heights: Metal on Si EE130/230M Spring 2013Lecture 7, Slide 11

12. 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. Schottky Barrier Heights: Silicide on Si EE130/230M Spring 2013Lecture 7, Slide 12

13. The Depletion Approximation The semiconductor is depleted of mobile carriers to a depth W  In the depleted region (0  x  W ):  = q (N D – N A ) Beyond the depleted region (x > W ):  = 0 EE130/230M Spring 2013Lecture 7, Slide 13

14. Electrostatics Poisson’s equation: The solution is: EE130/230M Spring 2013Lecture 7, Slide 14

15. Depletion Width, W At x = 0, V = -V bi W decreases with increasing N D EE130/230M Spring 2013Lecture 7, Slide 15

16. Summary: Schottky Diode (n-type Si) EoEo  MM  Si  Bn W qV bi =  Bn – (E c – E FS ) FB n-type Simetal EvEv EFEF EcEc  M >  S Depletion width EE130/230M Spring 2013Lecture 7, Slide 16

17. Summary: Schottky Diode (p-type Si)  MM  Si  Bp W qV bi =  Bp – (E F – E v ) FB p-type Simetal EvEv EFEF EcEc EoEo  M <  S EE130/230M Spring 2013Lecture 7, Slide 17 Depletion width