Electronics B
Joel Voldman
Massachusetts Institute of Technology
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 1
Outline
> Elements of circuit analysis
> Elements of semiconductor physics
• Semiconductor diodes and resistors
• The MOSFET and the MOSFET inverter/amplifier
> Op-amps
TODAY
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 2
Elements of semiconductor physics
> Discrete molecules (e.g., hydrogen
E (eV)
atom) have discrete energy levels that
the electrons can occupy
E (0 eV)
E5 (-0.54 eV)
E4 (-0.85 eV)
E3 (-1.51 eV)
E2 (-3.40 eV)
• Determined via quantum mechanics
Paschen
series
Balmer
series
Hydrogen
> Adding a discrete amount of energy to
the electrons (via light, thermal energy,
etc.) can excite an electron from its
ground state to an excited state
> Different atoms have different number
E1 (-13.6 eV)
Lyman
series
(n = 3, 1 = 1)
p orbital 6
allowed levels
Silicon
(n = 2)
8 electrons
of filled states
• All the action typically happens at the
highest unoccupied state
> Two distinct molecules have identical
and independent energy-level
structures
(n = 1)
2 electrons
(n = 3, 1 = 0)
s orbital 2
allowed levels
Image by MIT OpenCourseWare.
Adapted from Figures 2.1 and 2.6 in Razeghi, M. Fundamentals
of Solid State Engineering. 2nd ed. New York, NY: Springer,
2006, pp. 48 and 59. ISBN: 9780387281520.
Razeghi, Fundamentals of Solid State Engineering
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 3
Elements of semiconductor physics
>
>
>
>
>
Atoms packed into a lattice behave differently than discrete atoms
Their discrete energy levels coalesce into “continuous” energy bands
There may be many energy bands for the molecule
We don’t care about the ones that are filled and inaccessible
We care about the highest one with electrons
6
4
Electron energy
2
0
p
s
4N empty
states
2N+2N
filled states
Isolated
Si atoms
Γ2'
L1
Si
Γ2'
Γ15
Γ15
X4
-4
X1
L1
-8
L2'
Γ1
Γ1
-12
L
Image by MIT OpenCourseWare.
Adapted from Figure 2.5 in: Pierret, Robert F. Semiconductor DeviceFundamentals.
Reading, MA: Addison-Wesley, 1996, p. 28. ISBN: 9780131784598.
Gap
L3,
-6
Si lattice
spacing
Energy
Γ25'
X1
Γ25'
-2
-10
Decreasing
atom spacing
L3
Λ
Γ
∆
X
U,K
Σ
Γ
Wave Vector k
Image by MIT OpenCourseWare.
Figure 1 on p. 559 in: Chelikowsky, J. R., and M. L. Cohen. "Nonlocal
Pseudopotential Calculations for the Electronic Structure of Eleven
Diamond and Zinc-blende Semiconductors." Physical Review B 14, no.
2 (July 1976): 556-582.
Razeghi, Fundamentals of Solid State Engineering
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 4
Elements of semiconductor physics
>
>
>
>
>
The highest normally filled set of electronic states is the valence band
The lowest normally empty set of electronic states is the conduction band
An energy gap separates these states
At T=0 K, all the valence band states are filled
A filled band cannot conduct electricity Î This is an insulator
6
4
2
0
L3
Γ2'
L1
Γ15
Si
Γ2'
Γ15
Energy
Γ25'
X1
Γ25'
-2
conduction
band
Gap
L3,
X4
-4
-6
-10
energy gap
X1
L1
-8
L2'
Γ1
Γ1
-12
L
Λ
Γ
∆
X
U,K
Σ
valence
band
Γ
Wave Vector k
T=0 K
Figure by MIT OpenCourseWare.
Figure 1 on p. 559 in: Chelikowsky, J. R., and M. L. Cohen. "Nonlocal
Pseudopotential Calculations for the Electronic Structure of Eleven
Diamond and Zinc-blende Semiconductors." Physical Review B 14, no.
2 (July 1976): 556-582.
Razeghi, Fundamentals of Solid State Engineering
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 5
Elements of semiconductor physics
> T>0 K, electrons have thermal energy (~kT)
> At equilibrium, the only way for an electron to cross the energy barrier
is to be thermally excited
> The number of electrons that can do this is
• increases with thermal energy (and thus T)
• decreases with larger bandgap
> The thermally excited electrons give rise to “electrons”
> The resulting empty states in the valence band give rise to “holes”
• Behave similar to “electrons” but with opposite charge and different mass
“electrons”
“holes”
T=0 K
T=300 K
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 6
Key terminology
> Energy gap EG (1.1 eV in silicon at RT)
> Si atom concentration = 5x1022 /cm3
> The number of carriers in intrinsic Si is
related to
• Probability distribution function of energies
» This obeys Fermi-Dirac statistics
• Allowable states
> ~10-9 (prob of being filled) x ~1019 (density of
states) = ~1010 (carriers)
> ni is the intrinsic carrier concentration
• the equilibrium concentration of holes and
electrons in the absence of dopants
• ~1.5x1010 cm-3 at RT
• This is a material property
> n is the concentration [#/cm3] of electrons
> p is the concentration [#/cm3] of holes
ni ∝ e
−
EG
2 k BT
ni = pi
Every thermally
generated electron
leaves behind a hole
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 7
Key terminology
> Intrinsic carrier concentration of
1014
Si, Ge, and GaAs
1013
Ge
GaAs
Si
Intrinsic carrier concentration (cm-3)
1012
1011
1010
109
108
107
Adapted from Figure 2.20 in: Pierret, Robert F. Semiconductor Device Fundamentals.
Reading, MA: Addison-Wesley, 1996, p. 54. ISBN: 9780131784598.
106
105
200
300
400 500
T (K)
600
700
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Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 8
Doped semiconductors
> Dopants: substitutional impurity
atoms introduced having one
different valence than the
semiconductor
> Acceptor dopant concentrations are
NA
[#/cm3]
Æ p-type material
Si
Si
Si
Si
P
Si
Si
Si
Si
• Boron (3 valence electrons)
> Donor dopant concentrations are ND
[#/cm3] Æ n-type material
• Phosphorous (5 valence electrons)
> These introduce new energy levels
Image by MIT OpenCourseWare.
Adapted from Figure 7.5 in: Razeghi, M. Fundamentals of Solid
State Engineering. 2nd ed. New York, NY: Springer, 2006, p. 238.
ISBN: 9780387281520.
close to valence or conduction
bands (~0.05 eV)
> Dopant concentrations >> ni
T=0 K
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 9
Doped semiconductors
> Energy to ionize << kT (at RT)
> We assume all dopants are ionized at RT
Ec
ED
n-type dopant
Ev
T=0
T>0K
T = 300 K
Ec
p-type dopant
EA
Ev
Image by MIT OpenCourseWare.
Adapted from Figure 2.13 in: Pierret, Robert F. Semiconductor Device Fundamentals. Reading,
MA: Addison-Wesley, 1996, p. 38. ISBN: 9780131784598.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 10
Main results
> Donors or acceptors are fully ionized
> Define n0 and p0 as the electron and hole
N D → N D+ + e −
N A → N A− + h +
concentrations at equilibrium
> n0 and p0 follow a mass-action law
N D ≈ N D+
N A ≈ N A−
n0 p0 = ni2
-
-
+
+
N A− = p N D+ = n
+
n= p
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 11
Main results
> Overall, silicon is neutral
• Can use to determine n0 and p0
> Carrier concentrations typically
vary over many orders of
magnitude
Charge neutrality requires:
N A− + n0 = N D+ + p0
N A + n0 ≈ N D + p0
• Can use this to simplify
> Ex:
• ni ~ 1010 cm-3
• NA, ND ~ 1016-1019 cm-3
> In a given material at equilibrium
• NA > 100ND (p-type)
• ND > 100NA (n-type)
For p-type material:
p0 ≈ N A
ni2 ni2
n0 =
=
p0 N A
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 12
Main results
> Therefore, the equilibrium
majority carrier concentration is
determined by the net doping
and the minority carrier
concentration is determined by
the n0p0 product.
> For typical numbers, minority
carrier concentration is much
less majority carrier
concentration
p-type
n-type
p0 = N A
n0 = N D
ni2
n0 =
NA
ni2
p0 =
ND
N A ~ 1017 cm −3
p0 = N A = 1017 cm −3
n0 =
2
i
(1010 cm−3 )
2
n
3
−3
10
cm
=
=
NA
1017 cm −3
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 13
Excess carriers
> We can do various things to
create excess carriers
• Shine light
• Apply electric fields
> Excess carriers (n’, p’)
n′ = n − n0
p′ = p − p0
Generally, n′ = p′
represent a departure from
equilibrium
> Excess holes and electrons
are created in pairs
> Excess carriers recombine
Recombination
rate
Electron-hole
pair (EHP)
dn′
n′
∝−
dt
τm
n′(t ) ~ n′(0)e
−
t
τm
exponentially in pairs,
governed by lifetime
• The minority carrier lifetime
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 14
Excess carriers
> GaAs w/ NA=p0=1015 cm-3
> GaAs ni = 106 cm-3
> Create 1014 EHP/cm3 and
calculate carrier
concentrations over time
p
Carrier concentrations (cm-3)
> Therefore, n0= 10-3 cm-3
p(t)
1015
0
1014
n(t)
1013
1012
Adapted from Figure 4.7 in: Streetman, Ben G., and Sanjay Kumar Banerjee.
Solid State Electronic Devices. 6th ed. Upper Saddle River, NJ: Pearson
Prentice Hall, 2006, p. 127. ISBN: 9780131497269.
0
10
20
30
40
50
time (ns)
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Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 15
Drift and diffusion of carriers
> Carriers in semiconductors
obey a drift/diffusion flux
relation
> Drift: carriers move in an
electric field
> Diffusion: carriers move in a
concentration gradient
Electric field [V/cm]
drift
diffusion
J n = qe ( μn nE + Dn∇n )
Diffusivity [cm2/s]
Mobility [cm2/V-s]
Carrier concentration
[cm-3]
> For p-type material
• n is small Î drift current is
•
small
∇n can be big Î diffusion
current dominates
+
+
Drift
Image by MIT OpenCourseWare.
Figure 3.1b) in: Pierret, Robert F.Semiconductor Device Fundamentals.
Reading, MA: Addison-Wesley, 1996, p. 76. ISBN: 9780131784598.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 16
Outline
> Elements of circuit analysis
> Elements of semiconductor physics
> Semiconductor diodes and resistors
> The MOSFET and the MOSFET
inverter/amplifier
> Op-amps
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 17
The semiconductor diode
> A p-n junction has very different
concentrations of carriers in the two
regions, creating a diffusive driving
force
> At equilibrium diffusive driving force =
electric field in the vicinity of the
junction
-
ionized donors and acceptors are
relatively depleted of mobile carriers
near the junction – the space-charge
layer (SCL) or depletion region
-
-
-
-
-
-
+ + + + + +
+ + + + + +
+ + + + + +
- + + + + + +
- + + + + + +
- + + + + + +
E
-
Oxide
n-type substrate
-
> In order to set up this electric field, the
p-type region
n-type
p-type
φ
-
-
-
-
-
-
- + + + + + +
- + + + + + +
- + + + + + +
xp0
xn0
XJ0
Image by MIT OpenCourseWare.
,
Stephen D. Microsystem Design.
Adapted from Figure 14.1 in: Senturia
Boston, MA: Kluwer Academic Publishers, 2001, p. 357. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 18
The exponential diode
> An external voltage modifies the net
potential drop across the space charge
layer
p
Ec
> Forward bias reduces the barrier to
n
diffusion, leading to an increase in
current
Ev
Equilibrium
> Reverse bias increases the barrier, so
only current is due to minority carriers
generated in or near the space-charge
layer
IN
Ec
Oxide
Metal
+
p-type region
n-type substrate
ID
Ev
VD
_
Image by MIT OpenCourseWare.
Adapted from Figure 14.2 in: Senturia, Stephen D. Microsystem Design.
Boston, MA: Kluwer Academic Publishers, 2001, p. 359. ISBN: 9780792372462.
IP
Forward bias
Image by MIT OpenCourseWare.
Adapted from Figu
re 6.1 in: Pierret, Robert F. Semiconductor
Device Fundamentals. Reading, MA: Addison-Wesley, 1996,
p. 236. ISBN: 9780131784598.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 19
Ideal Exponential Diode Analysis
> Linear changes in
voltage lead to
exponential changes in
carrier concentrations
⎛
I D = I0 ⎜ e
⎜
⎝
qeVD
k BT
⎞
− 1⎟
⎟
⎠
Forward bias
0.005
Current (A)
The total current is
0.010
-VB
0.000
Reverse blocking
-0.005
Reverse breakdown
-0.010
-6
-5
-4
-3
-2
-1
0
1
Voltage (V)
Image by MIT OpenCourseWare.
Adapted from Figure 14.3 in: Senturia, Stephen D. Microsystem Design. Boston,
MA: Kluwer Academic Publishers, 2001, p. 360. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 20
The Junction-Isolated Diffused Resistor
> The structure is a diode, but with two
Oxide
Metal
contacts
> The diode action prevents currents
into the substrate provided the diode
is always reverse biased
p-type region
n-type substrate
> The conductivity is controlled by
resistor
doping
> The resistor value is determined by
geometry
desired
v
+
-
undesired
v
+
-
distributed
diode
Image by MIT OpenCourseWare.
Adapted from Figure 14.7 in: Senturia, Stephen D. Microsystem
Design. Boston, MA: Kluwer Academic Publishers, 2001, p.
363. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 21
Outline
> Elements of circuit analysis
> Elements of semiconductor physics
> Semiconductor diodes and resistors
> The MOSFET and the MOSFET
inverter/amplifier
> Op-amps
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 22
MOSFET Structure
> The MOSFET exploits the concept of a field-induced junction
> The electric field between the gate and the channel region of the
substrate can either increase the surface concentration
(accumulation) or deplete the surface and eventually invert the
surface
Source
Gate
Drain
Oxide
D
Channels
p-type substrate
n+ regions
G
B
S
Body
Image by MIT OpenCourseWare.
Adapted from Figure 14.10 in: Senturia, Stephen D. Microsystem Design.
Boston, MA: Kluwer Academic Publishers, 2001, p. 366. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 23
MOSFET qualitative operation
> With D & S grounded,
back-to-back diodes
prevent current flow
between D & S
> To reduce barrier,
apply positive voltage
to G (w.r.t. D & S)
> At some threshold
voltage, this will form
an n-channel inversion
layer that will connect
D&S
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
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JV: 2.372J/6.777J Spring 2007, Lecture 7E - 24
MOSFET Characteristics
1000
> Need VGS>VT for device to turn on
between D & S
> As VDS increases, voltage between
triode
800
ID (µA)
> As VDS increases, current will flow
VGS = 4 V
ID,sat
600
VGS = 3 V
400
G and D decreases
> When VDS gets too big, one side of
saturation
200
channel pinches off, preventing
further increases in current
0
VGS = 2 V
0
1
2
3
4
5
Image by MIT OpenCourseWare.
Adapted from Figure 14.13 in: Senturia, Stephen D. Microsystem Design.
Boston, MA: Kluwer Academic Publishers, 2001, p. 369. ISBN: 9780792372462.
G
D
S
e-
e-
D
G
VDS
S
e-
e-
D
G
S
e-
e-
n-channel
VDS=0
VDS>0
VDS>VGS-VT
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 25
Different kinds of MOSFETs
S
G
S
B
p-channel
G
B
D
D
Enhancement
Depletion
D
D
G
B
S
n-channel
G
B
S
Image by MIT OpenCourseWare.
Adapted from Figure 14.11 in: Senturia, Stephen D. Microsystem Design. Boston,
MA: Kluwer Academic Publishers, 2001, p. 367. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 26
Large-signal and small-signal MOSFET models
D
> Electrical engineers use
circuit models to analyze
circuits involving MOSFETS
2
K/2(VGS-VTn)
G
> Can use either full nonlinear
S
characteristics
Simple large-signal
model, in saturation
> Or linearized small-signal
model
D
• Different models include
different components
G
gm vgs
CGS
r0
+
-
S
Simple small-signal
model, in saturation
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 27
Outline
> Elements of circuit analysis
> Elements of semiconductor physics
• Semiconductor diodes and resistors
• The MOSFET and the MOSFET inverter/amplifier
> Op-amps
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 28
Operational Amplifiers – op-amps
> Let someone else design a high-performance amplifier
> Basic structure and transfer characteristic
v0
Vsat+
Signal path
vv+
_
Slope A0
v0
v+ - v-
+
Differential
amplifier
High-gain
amplifier
Output
amplifier
VsatDIP/SO Package
VS+
v-
_
Output A 1
v0
v+
Inverting input A 2
+
Non-inverting
input A
GND
VS-
3
_A
+ +
B_
4
8
v+
7
Output B
6
Inverting input B
5
Non-inverting
Input B
Top view
Image by MIT OpenCourseWare.
Adapted from Figures 14.23 and 14.24 in Senturia, Stephen D. Microsystem Design. Boston, MA: Kluwer Academic Publishers,
2001, p. 382. ISBN: 9780792372462.
LM158
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
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JV: 2.372J/6.777J Spring 2007, Lecture 7E - 29
Ideal and non-ideal behavior
> We do first analysis using ideal
linear model
> Op-amp data sheets have pages
and pages of limitations
> A sampling
• Input offset voltage voff: zero
v0 ( s ) = A( s ) ( v+ ( s ) − v− ( s ) )
where
A( s ) =
A0 s0
s + s0
volts at input gives non-zero
output
• Frequency limitations: op-amps
can only amplify up to a
maximum frequency
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 30
The Inverting Amplifier
Assume op-amp draws no
current
R2
R1
Vs
v-
+
-
Use Nodal analysis:
-
Vo
v+
+
⇓
R1
+
-
vv+
+
-
Vs − v− v− − V0
=
R1
R2
⇓ V0 = A(0 − v− )
R2
Vs
KCL:
Vo
A(v+-v-)
⎡
⎤
⎢
⎥
Vo
R2 ⎢
1
⎥
=−
Vs
R1 ⎢ 1 ⎛ R2 ⎞ ⎥
⎢1 + ⎜ 1 + ⎟ ⎥
R1 ⎠ ⎥⎦
⎢⎣ A ⎝
⇓ A→∞
Vo
R
=− 2
Vs
R1
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 31
Short method for analyzing op-amps
> Assume linear region operation
• This implies that the two inputs are essentially at the same
voltage (but never exactly equal)
> Assume zero currents at both inputs
> Analyze the external circuit with these constraints
> Check to verify that the output is not at either
saturation limit (±VS)
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 32
More op-amp configurations
Vs
v− = v+ = VS
+
V0
_
R1
R2
Vs = V0
R2 + R1
V0
R1
= 1+
VS
R2
R2
Non-inverting
Image by MIT OpenCourseWare.
Adapted from Figure 14.28 in Senturia, Stephen D. Microsystem Design.
Boston, MA: Kluwer Academic Publishers, 2001, p. 388. ISBN: 9780792372462.
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
JV: 2.372J/6.777J Spring 2007, Lecture 7E - 33
More op-amp configurations
R1
Is
_
V0
+
Image by MIT OpenCourseWare.
Adapted from Figure 14.29 in Senturia, Stephen D. Microsystem Design.
Boston, MA: Kluwer Academic Publishers, 2001, p. 389. ISBN: 9780792372462.
Transimpedance amplifier
V0 = − R1 I S
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
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JV: 2.372J/6.777J Spring 2007, Lecture 7E - 34
Integrator
C
R1
Vs
+
vC _
_
+
_
V0
+
Image by MIT OpenCourseWare.
Adapted from Figure 14.30 in Senturia, Stephen D. Microsystem Design. Boston,
MA: Kluwer Academic Publishers, 2001, p. 389. ISBN: 9780792372462.
1
V0 = −
Vs (t )dt
∫
R1C
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
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JV: 2.372J/6.777J Spring 2007, Lecture 7E - 35
Differentiator
R1
C
Vs
_
+
_
V0
+
Image by MIT OpenCourseWare.
Adapted from Figure 14.31 in Senturia, Stephen D. Microsystem Design. Boston,
MA: Kluwer Academic Publishers, 2001, p. 390. ISBN: 9780792372462.
The differentiator is less "ideal"
Vs
0 − V0
=
1
R1
sC
V0
= − sR1C
Vs
Cite as: Joel Voldman, course materials for 6.777J / 2.372J Design and Fabrication of Microelectromechanical Devices, Spring 2007. MIT
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JV: 2.372J/6.777J Spring 2007, Lecture 7E - 36