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

Lecture 27, 19 Mar 14 Chp 04: metal-insulator-semiconductor junction: GATES Examples VM Ayres, ECE875, S14

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

Use energy band diagram to find: p-type Si Use energy band diagram to find: VM Ayres, ECE875, S14

Use energy band diagram to find: Electron concentration in channel p-type Si Use energy band diagram to find: Electron concentration in channel V requirements: battery = $ E –field/Vi across the insulator: breakdown not good VM Ayres, ECE875, S14

Usual approach: Q(x) E (x) V  y(x) Everything else VM Ayres, ECE875, S14

Usual approach: = d E dx 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: = d E dx ∞ means deep in substrate VM Ayres, ECE875, S14

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

Answer: = 2.32 x 104 cm-3 In forward bias: b = 38.6 V-1 @ r.t. VM Ayres, ECE875, S14

Example: what is the electron concentration at x = 0? = 2.32 x 104 cm-3 In forward bias: b = 38.6 V-1 @ r.t. VM Ayres, ECE875, S14

Answer: need yp = yp(x) = 2.32 x 104 cm-3 In forward bias: b = 38.6 V-1 @ r.t. VM Ayres, ECE875, S14

Can find potential yp(at x=0) using strong inversion condition: 2 x yBp = VM Ayres, ECE875, S14 ys = yp(x=0)

Example: Evaluate ys in strong inversion condition for example problem 01 with NA = 4 x 1015 cm-3 VM Ayres, ECE875, S14

Answer: yp(x = 0) = VM Ayres, ECE875, S14

To find yp(x) (and therefore concentration) must use this approach: Q(x) E (x) V  y(x) Everything else Will get E -field first and also wanted to know that VM Ayres, ECE875, S14

Electric field and potentials: in inversion: Breakdown info here concentration info here New: the potential drop across the (ideal) insulator Vi Metal = battery potential: V p-type Semiconductor potential: yp(x) Semiconductor surface potential: ys = yp(x=0) VM Ayres, ECE875, S14

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LD : the Debye length VM Ayres, ECE875, S14

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Can easily find E (x=0) = E s: Take the square root of E 2 in eq’n 10 and use yp(x=0) = ys to evaluate: VM Ayres, ECE875, S14

Can easily find Q(x=0) = Qs: VM Ayres, ECE875, S14

Example: Evaluate Qs for ys = 0.67 V VM Ayres, ECE875, S14

Answer: VM Ayres, ECE875, S14

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s VM Ayres, ECE875, S14

Note that an important part of the concentration we’d like to know could be defined as charge/area under the Gate (different than usual units) VM Ayres, ECE875, S14

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Answer: VM Ayres, ECE875, S14

VM Ayres, ECE875, S14