ECE 875:Electronic Devices

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

VM Ayres, ECE875, S14

Lecture 31, 28 Mar 14

Chp 04: metal-insulator-semiconductor junction: GATES

Capacitances: Low frequency voltage sweep: 1 Hz to 1KHz High frequency voltage sweep: > 1Mz

- slow ramp: Pr. 4.06- fast ramp

Use Gate voltage:Sweeping Vgate for example ± 4 Volts over and over to turn the channel OFF and ON: binary logic

Low: 1- 1 kHz

Intermediate: 1 kHz - 1 MHz

High: > 1 MHzVgate: Slow rampVgate: Fast ramp

Slow ramp (sweep) Fast ramp (sweep)

C-V curves and Frequencies:

ON/OFF cycles per sec

“counting” charge per sec applied to gate

VM Ayres, ECE875, S14

C /

Ci

C-V curves for n-channel in p-substrate:

ONOFF

Low

High + slow ramp

Intermediate

High + fast ramp

VM Ayres, ECE875, S14

C /

Ci

What looks different in the readout: flat line in Vfor and Cmin shift

ONOFF

Low

High + slow rampCmin

C’min

Vmin

V’min = VT

VM Ayres, ECE875, S14

CDmin = CminCi

Ci + Cmin

Cmin = Ci CDmin

Ci + CDmin

You know the experimental values in the circles.Therefore it’s easy to get a number for Cdmin

Low frequency C-V:

VM Ayres, ECE875, S14

Low: 1- 1 kHz: develop (ON) and later remove (=> OFF) a full inversion layer and a full depletion region

++++++++++

oooooooooo

p-type Si: NA =B

B- B- B- B- B- B- B- B- B- B-

++++++++++

e- e- e- e- e- e- e- e- e- e-

CD Qs region

Ci across insulator region

Low frequency C-V:

VM Ayres, ECE875, S14

> 1 MHz: develop and later remove a full depletion region charge qNAWD. But e-’s don’t have time to form a full inversion layer at the surface

++++++++++

oooooooooop-type Si: NA =B

B- B- B- B- B- B- B- B- B- B-

++++++++++

e- e- e- e- e- e- e- e- e- e-

High frequency + slow ramp:

Fig. 8, (b)

VM Ayres, ECE875, S14

High frequency + slow ramp: simpler:

C’Dmin = s /WDmax

C’min = Ci C’Dmin

Ci + C’Dmin

So total capacitance C’min is:

VM Ayres, ECE875, S14

Qn smaller

WDmax is bigger

Low frequency High frequency,Slow ramp

VM Ayres, ECE875, S14

Have been finding WD = WDm at the start of inversion with s = 2 kT/q ln (NA/ni).

But (Qs, s) can be bigger

High frequency + slow ramp: WDmax

From strong inversion up to thermal energy

VM Ayres, ECE875, S14

High frequency + slow ramp: WDmax:

VM Ayres, ECE875, S14

Assume that Pr. 4.06 the high frequency- slow ramp condition

VM Ayres, ECE875, S14

Qn smaller

WDmax is bigger

Low frequency High frequency,Slow ramp

High frequency,Fast ramp

WDmax is biggest

Qn layer; no time to form at all

Qn biggest

VM Ayres, ECE875, S14

High frequency + fast ramp: during ON:

No Qn and big WDmax: “driven into deep depletion”

VM Ayres, ECE875, S14

s (@x = 0)CD Qs region

VM Ayres, ECE875, S14

Ci across insulator region

VM Ayres, ECE875, S14

s

VGate

Iterate Pr. 3.9 until donor concentration ND-nth – ND-(nth+1) = 0.01 x 1016 cm-3