Transcript Lecture 7
Lecture 7 OUTLINE • Work Function • Metal-Semiconductor Contacts – Energy band diagrams – Depletion-layer width – Small-signal capacitance Reading: Pierret 14.1-14.2; Hu 4.16 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 Work Function E0: vacuum energy level R.F. Pierret, Semiconductor Fundamentals, Figure 14.1 FM: metal work function EE130/230A Fall 2013 FS: semiconductor work function Lecture 7, Slide 3 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 Ideal M-S Contact: FM > FS, n-type Band diagram instantly after contact formation: Equilibrium band diagram: Schottky Barrier Height: qVbi = FBn– (Ec – EF)FB n FBn FM W EE130/230A Fall 2013 Lecture 7, Slide 5 R.F. Pierret, Semiconductor Fundamentals, Fig. 14.2 Effect of Interface States on FBn • Ideal M-S contact: FBn = FM – • 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 Schottky Barrier Heights: Metal on Si • Metal FM (eV) Er 3.12 Ti 4.3 Ni 4.7 W 4.6 Mo 4.6 Pt 5.6 FBn (eV) 0.44 0.5 0.61 0.67 0.68 0.73 FBp (eV) 0.68 0.61 0.51 0.45 0.42 0.39 FBn tends to increase with increasing metal work function EE130/230A Fall 2013 Lecture 7, Slide 7 Schottky Barrier Heights: Silicide on Si Silicide ErSi1.7 TiSi2 CoSi2 NiSi WSi2 PtSi FM (eV) 3.78 4.18 FBn (eV) 0.3 FBp (eV) 0.8 4.6 4.65 4.7 5 0.6 0.64 0.65 0.65 0.84 0.52 0.48 0.47 0.47 0.28 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 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 Electrostatics • Poisson’s equation: • The solution is: r qN D x s s x qN D s W x V x ( x)dx EE130/230A Fall 2013 Lecture 7, Slide 10 R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4 Depletion Width, W qN D W x 2 V x 2K S 0 At x = 0, V = -Vbi 2 sVbi W qN D • W decreases with increasing ND EE130/230A Fall 2013 Lecture 7, Slide 11 R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4 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 Depletion Width, W, for VA 0 Last time, we found that V x qN D W x 2 2K S 0 At x = 0, V = - (Vbi - VA) 2 s (Vbi VA ) W qN D • 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 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 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: CA EE130/230A Fall 2013 s W Lecture 7, Slide 15 dva iC dt Using C-V Data to Determine FB CA s W A s 2 s Vbi VA qN D qN D s A 2Vbi VA 1 2(Vbi VA ) 2 C qN D s A2 Once Vbi and ND are known, FBn can be determined: qVbi F Bn ( Ec EF ) FB F Bn EE130/230A Fall 2013 Lecture 7, Slide 16 Nc kT ln ND Ideal M-S Contact: FM > FS, p-type 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 Ideal M-S Contact: FM < FS, p-type p-type semiconductor Band diagram instantly after contact formation: Equilibrium band diagram: Schottky Barrier Height: F Bp EG F M FBp qVbi = FBp– (EF – Ev)FB W EE130/230A Fall 2013 Lecture 7, Slide 18 R.F. Pierret, Semiconductor Fundamentals, p. 482 W for p-type Semiconductor V x qN A W x 2 2 K S 0 p-type semiconductor At x = 0, V = Vbi + VA 2 s (VA Vbi ) W qN A • W increases with increasing VA • W decreases with increasing NA EE130/230A Fall 2013 Lecture 7, Slide 19 Summary EF Ec Ec EF Ev Ev Ec EF EF Ev Ev R.F. Pierret, Semiconductor Fundamentals, p. 481 2 s (Vbi VA ) For rectifying contacts: W qN D W 2 s (VA Vbi ) qN A small-signal capacitance C A s / W EE130/230A Fall 2013 Lecture 7, Slide 20 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