ECE 875: Electronic Devices Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University

VM Ayres, ECE875, S14 Chp 03: metal-semiconductor junction: INTERCONNECTS Practical detail: Work functions graph Lecture 26, 17 Mar 14 Chp 04: metal-insulator-semiconductor junction: GATES Basics Examples

VM Ayres, ECE875, S14

Chp 03: metal-semiconductor junction: INTERCONNECTS Practical details: Work functions graph Useful experiments Lecture 26, 17 Mar 14 Chp 04: metal-insulator-semiconductor junction: GATES Basics Examples

Chp. 01: Si Chp. 02: pn Chp. 03: Interconnect Chp. 04: MOS: Gate VM Ayres, ECE875, S14

oooooooooo p-type Si + charge on gate: Holes moved out under gate VM Ayres, ECE875, S14

oooooooooo p-type Si: N A =B B- B- B- B- B- + charge on gate Holes moved out under gate B- depletion region left behind VM Ayres, ECE875, S14

oooooooooo p-type Si: N A =B B- B- B- B- B- Increase the + charge on gate Holes moved out under gate B- depletion region left behind Electrons attracted under gate e- e- e- e- e- VM Ayres, ECE875, S14

oooooooooo p-type Si: N A =B B- B- B- B- B- Change: Big - charge on gate Extra holes attracted under gate B- depletion region left behind Super p+ Normal p-type VM Ayres, ECE875, S14

p-type Si VM Ayres, ECE875, S14

p-type “Ideal”: Miraculous choice of metal and semiconductor that achieves flat band: E Fm = E Fs for V= 0 At equilibrium: V = 0 volts, ideal case: VM Ayres, ECE875, S14

p-type - V rev + V rev breaks invariance of E F Brings it down by amount V rev E i – E F greater near surface More holes near surface Accumulation of holes near surface Hole layer near surface Super p+Normal p-type Also have B- layer VM Ayres, ECE875, S14 In V rev : starting from ideal case:

p-type + V for - E i – E F smaller near surface Less holes near surface Can become intrinsic near surface V for breaks invariance of E F Brings it up by amount V for In V for : starting from ideal case: VM Ayres, ECE875, S14

p-type + V for - V for breaks invariance of E F Brings it up by amount V for Now have E F – E i > 0 Electron layer in p-type Si near surface: Inversion Also have B- depletion region near surface In V for : VM Ayres, ECE875, S14

Charge layers near surface: inversion This is similar to Pr Pr turns up in many different circumstances New: ++ charges on gate In V for : VM Ayres, ECE875, S14

New: Battery voltage V is accommodated as drops V i across the insulator and  s = the surface potential (ideal flat band conditions) Charge layers near surface: inversion In V for : starting from ideal case: E –field and potential VM Ayres, ECE875, S14

Metal = battery potential: V p-type Semiconductor potential:  p (x) New: the potential drop across the (ideal) insulator V i Semiconductor surface potential:  s =  p (x=0) Electric field and potentials near surface: in inversion: VM Ayres, ECE875, S14

Grad E ∞ means deep in substrate The total charge density is The Electric field is a function of the charge density. The potential is proportional to the Electric field The surface charge is: In semiconductor: VM Ayres, ECE875, S14

 (x) VM Ayres, ECE875, S14

Chp 03: metal-semiconductor junction: INTERCONNECTS Practical details: Work functions graph Useful experiments Lecture 26, 17 Mar 14 Chp 04: metal-insulator-semiconductor junction: GATES Basics Examples

Example 01 (will be a continuing problem): + VM Ayres, ECE875, S14

Answer: VM Ayres, ECE875, S14

Name these: p p0 = p p (x = ∞) and n p0 = n p (x = ∞) Want: p p (x) and n p (x) as they get near to the junction Can evaluate something related to p p (∞) and n p0 = n p (∞) first VM Ayres, ECE875, S14

Instead of just filling in for N A- and N D+, consider this: VM Ayres, ECE875, S14 Something is: (N D + - N A -): Example 01: You just got numbers for these Next

Instead of just filling in for N A- and N D+, consider this: Use  p set-up as a clue VM Ayres, ECE875, S14 Something is: (N D + - N A -): Example 01: You just got numbers for these

Can find: p p (x) and n p (x) from energy band considerations: VM Ayres, ECE875, S14

Can find: p p (x) and n p (x) from energy band considerations: Note: voltage  p =  p (x) VM Ayres, ECE875, S14

Therefore have: =  p (x) VM Ayres, ECE875, S14

Example: VM Ayres, ECE875, S14

Answer: VM Ayres, ECE875, S14

Also: Can find surface potential  s (x=0) using condition: 2 x  Bp = VM Ayres, ECE875, S14

Example: Evaluate  s in strong inversion condition for example problem 01 with N A = 4 x cm -3 VM Ayres, ECE875, S14

Answer: VM Ayres, ECE875, S14 Note: voltage  s =  p (x = 0)