6.012 - Microelectronic Devices and Circuits Lecture 9 - MOS Capacitors I - Outline • Announcements Problem set 5 - Posted on Stellar. Due next Wednesday. • Qualitative description - MOS in thermal equilibrium Definition of structure: metal/silicon dioxide/p-type Si (Example: n-MOS) Electrostatic potential of metal relative to silicon: φ m Zero bias condition: Si surface depleted if φ m > φ p-Si (typical situation) Negative bias on metal: depletion to flat-band to accumulation Positive bias on metal: depletion to threshold to inversion • Quantitative modeling - MOS in thermal equilibrium, v BC = 0 Depletion approximation applied to the MOS capacitor: 1. Flat-band voltage, V FB 2. Accumulation layer sheet charge density, q A * 3. Maximum depletion region width, X DT 4. Threshold voltage, V T 5. Inversion layer sheet charge density, q N * • Quantitative modeling -v BC ≠ 0; impact of v BC < 0 Voltage between n+ region and p-substrate: |2φ p-Si | → |2φ p-Si | - v BC Clif Fonstad, 10/8/09 Lecture 9 - Slide 1
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6.012 - Microelectronic Devices and Circuits Lecture 9 - MOS Capacitors I - Outline
• Announcements Problem set 5 - Posted on Stellar. Due next Wednesday.
• Qualitative description - MOS in thermal equilibrium Definition of structure: metal/silicon dioxide/p-type Si (Example: n-MOS) Electrostatic potential of metal relative to silicon: φm Zero bias condition: Si surface depleted if φm > φp-Si (typical situation) Negative bias on metal: depletion to flat-band to accumulation Positive bias on metal: depletion to threshold to inversion
• Quantitative modeling - MOS in thermal equilibrium, vBC = 0 Depletion approximation applied to the MOS capacitor:
• Quantitative modeling - vBC ≠ 0; impact of vBC < 0 Voltage between n+ region and p-substrate: |2φp-Si | → |2φp-Si| - vBC
Clif Fonstad, 10/8/09 Lecture 9 - Slide 1
n-Channel MOSFET: Connecting with the npn MOSFET A very similar behavior, and very similar uses.
MOSET
G
S
D
+
––
+
vGS
vDS
iG
iD
iB
vBE vCE
iC
0.6 V 0.2 V
Forward Active RegionFAR
CutoffCutoff
Saturation
iC ! !F iBvCE > 0.2 V
iB ! IBSe qVBE /kT
Input curve Output family
BJT
B
E
C
+
––
+
vBE
vCE
iB
iC
vDS
iD
Saturation (FAR)
Cutoff
Linear
or
Triode
iD ! K [vGS - VT(vBS)]2/2!
Clif Fonstad, 10/8/09 Lecture 9 - Slide 2
p-Si
B
G+vGS
n+
D
n+
S– vDS
vBS +
iG
iB
iD
MOS structures
An n-channel MOSFET In an n-channel MOSFET, we have two n-regions (the source and
the drain), as in the npn BJT, with a p-region producing a potential barrier for electrons between them. In this device, however, it is the voltage on the gate, vGS, that modulates the potential barrier height.
The heart of this device is the MOS capacitor, which we will study today. To analyze the MOS capacitor we will use the same depletion approximation that we introduced in conjunction with p-n junctions.
Clif Fonstad, 10/8/09 Lecture 9 - Slide 3
The n-MOS capacitor
Right: Basic device with vBC = 0
p-Si
n+
B
SG
SiO2+–
vGS
(= vGB)
C
Below: One-dimensional structure for depletion approximation analysis*
Clif Fonstad, 10/8/09 Lecture 9 - Slide 4
BG
+ –
p-SiSiO 2
x-tox 0
vGB
* Note: We can't forget the n+ region is there; we will need electrons, and they will come from there.
6.012 - Microelectronic Devices and Circuits Lecture 9 - MOS Capacitors I - Summary
• Qualitative description Three surface conditions: accumulated, depleted, inverted Two key voltages: flat-band voltage, VFB; threshold voltage, VT The progression: accumulation through flat-band to depletion,
then depletion through threshold to inversion
• Quantitative modeling Apply depletion approximation to the MOS capacitor, vBC = 0 Definitions: VFB ≡ vGB such that φ(0) = φp-Si