ece 875: electronic devices

ECE 875:Electronic Devices

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

VM Ayres, ECE875, S14

Lecture 27, 19 Mar 14

Chp 04: metal-insulator-semiconductor junction: GATES

Examples

VM Ayres, ECE875, S14

Chp. 01: Si

Chp. 02: pn

Chp. 03: Interconnect

Chp. 04: MOS: Gate

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p-type Si

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Use energy band diagram to find:

p-type Si

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Use energy band diagram to find:

Electron concentration in channel

V requirements: battery = $

E –field/Vi across the insulator: breakdown not good

Q(x)

E (x)

V (x)

Everything else

Usual approach:

VM Ayres, ECE875, S14

= d E dx

∞ 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:

Usual approach:

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Example 01 (will be a continuing problem):

+

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Answer:

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= 2.32 x 104 cm-3

In forward bias:

= 38.6 V-1 @ r.t.

Example: what is the electron concentration at x = 0?

VM Ayres, ECE875, S14

= 2.32 x 104 cm-3

In forward bias:

= 38.6 V-1 @ r.t.

Answer: need p = p(x)

VM Ayres, ECE875, S14

= 2.32 x 104 cm-3

In forward bias:

= 38.6 V-1 @ r.t.

Can find potential p(at x=0) using strong inversion condition:

2 x Bp =

VM Ayres, ECE875, S14s = p(x=0)

Example:

Evaluate s in strong inversion condition for example problem 01 with NA = 4 x 1015 cm-3

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Answer:

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p(x = 0) =

Q(x)

E (x)

V (x)

Everything else

To find p(x) (and therefore concentration) must use this approach:

VM Ayres, ECE875, S14

Will get E -field first and also wanted to know that

Metal = battery potential: V

p-type Semiconductor potential: p(x)

New: the potential drop across the (ideal) insulator Vi

Semiconductor surface potential:s = p(x=0)

Electric field and potentials: in inversion:

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Breakdown info here concentration info here

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LD : the Debye length

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Example:

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Answer:

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Take the square root of E 2 in eq’n 10 and use p(x=0) = s to evaluate:

VM Ayres, ECE875, S14

Can easily find E (x=0) = E s:

VM Ayres, ECE875, S14

Can easily find Q(x=0) = Qs:

Example:

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Evaluate Qs for s = 0.67 V

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Answer:

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VM Ayres, ECE875, S14

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s

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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)

Example:

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Answer:

VM Ayres, ECE875, S14

VM Ayres, ECE875, S14