Semiconductor Devices - Hour 33
MOS Capacitor,
ms,
band bending, oxide voltage
However, there CAN be a lot of IMMOBILE charge on that bottom plate:
- Charge due to impurities in oxide spacer layer (which is not shown in the sketches above)
Last time we in

Semiconductor Devices - Hour 10
Donor and Acceptor Impurity Atoms
Last time:
In an "intrinsic" (pure) semiconductor, heat promotes electrons from valence band to conduction band
E
k
Bond breaking
picture
Simple band
picture
E vs. k band
picture
Mathematic

Semiconductor Devices - Hour 11
Semiconductors Doped with Donors or Acceptors
Earlier we described "intrinsic semiconductors" where electrons & holes are created only by thermal promotion
Last Time:
Introduced "extrinsic" semiconductors with added mobile

Semicondcutor Devices - Hour 9
Intrinsic (Thermally Generated) Carriers in Semiconductors
For several lectures, have been preparing for today's calculation of how may carriers are in a semiconductor
Pieces that we will use:
1
fF ( E) =
1) Characteristics

Semiconductor Devices - Hour 12
MCD: Thermal Velocity
Carrier Transport: DRIFT of carriers in an Electric Field
Last Time:
Enough of Last Time! We've paid our dues, lets do something interesting with this
doped / undoped / intrinsic / extrinsic / degenera

Semiconductor Devices - Hour 40
Flash Memory to Nano MOSFETS
Bipolar Transistors:
MOSFET transistors:
As indicated by class title, I've limited our discussions to semiconductor devices, not semiconductor circuits
That's a bit strange in that the real powe

Semiconductor Devices - Hour 13
Carrier Transport: Diffusion = Spontaneous Rearrangement
Last Time: Movement of Carriers = "Carrier Transport"
1) "DRIFT" = Movement induced by electric field,
v ( t)
Scattering Limited:
t
"Carrier Mobility" =
Two Scatteri

Semiconductor Devices - Hour 14
Minority Carriers, Generation and Recombination, "Continuity Equations"
Grand recap of recent relevant lectures:
1) DRIFT = Movement of carriers in an electric field,
v ( t)
v ( t)
=>
=>
t
vaverage =
t
=
= "Mobility" = v

Semiconductor Devices - Hour 15
How to simplify and apply the "Minority Carrier Continuity Equations"
Last time: Equations governing population of minority carriers
P-type:
Na > Nd
p > n
p = majority carrier
n = minority carrier
N-type:
Nd > Na
n > p
n =

Semiconductor Devices - Hour 16
Today:
P-N Junctions Part 1: Concepts, Charges and Fields
Apply our bag of tools to the most basic device of microelectronics, the P-N junction
- Basic element of all transistors
-Device onto itself in form of diode / detec

Semiconductor Devices - Hour 5
(MCD: Wave function for 2D QW)
Electron in a Quantum Well => Quantization of Energy
Last Time:
In regions where V is constant, electron wave functions are simple waves:
1 ( x) = A1 e
i k1 x
+ B1 e
i k1 x
k1 =
so long as:
(

Semiconductor Devices - Hour 8
Electrons and Holes
(MCD: Fields when net charge not zero)
Time out for a digression about k's. We have a confusing bunch of them - and are adding another today:
K = "degrees Kelvin" = degrees above absolute zero (e.g. room

Semiconductor Devices - Hour 7
Fermi Statistics
QM to this point:
1) General:
( x , t) = A e
i ( k x t)
+ B e
i ( k x t)
(
)
2 m E V
k=
so long as:
hbar
Also know that for these electron waves:
From form of : k = 2
=
h
p
2
Required by SWE
wherever V = c

Semiconductor Devices - Hour 30
BJT Example: Part II
(MCD: Entire Bipolar Calculation)
Last Time: Started with the physical structure of a bipolar transistor
micron
10
4
Effective thicknesses depend on depletion layers - which depend on voltages applied t

Semiconductor Devices - Hour 34
Inversion, Non-Ideal Oxide Charge, Threshold Voltage
And electron energy vs. position:
We are deep in a multi-dimensional calculation where it is very easy to lose track of details and direction
Electron Energy (x)
But elec

Semiconductor Devices - Hour 32
Introduction to MOS Transistors
So through the 1950's, researchers continued to try and find an alternate type of transistor
We've learned about diodes
And there HAD been an even earlier idea - the one we now call a FIELD E

Semiconductor Devices - Hour 35
(MCD: Worked VT example)
2) Build model in head where semiconductor bands start flat:
P-semiconductor at Flat-Band:
Remembering VT and Ion Implantation Threshold Shifting
q Fp
Last Time: Have developed complex equations for

Semiconductor Devices - Hour 37
Important point #2:
MOSFET I versus V
When VG is "above" VT, a surface inversion channel forms
"Enhancement Mode" MOSFETs:
VG > VT for N-channel device (P-substrate)
ENHANCE the source to drain carrier flow by inverting the

Semiconductor Devices - Hour 38
Worked MOSFET Example
MCD: MOSFET
"What we know" part 2)
Some parameters we can choose. Others have to be calculated from other things:
This lecture: Collect what we know of MOSFET's in order to calculate I-V curves:
i) "Ma

Semiconductor Devices - Hour 36
Last Time:
MOS C-V Curves / Basic MOSFET Operation
Comes from definition of capacitance:
d
Heart of the MOSFET is an MOS Capacitor
Q = CDC V
tox
=>
dt
Measurement of AC capacitance can give us ~ ALL
dQ+
ox
d
Q = CAC
d
V
CAC

Semiconductor Devices - Hour 39
This assumes I got the 2nd shadow mask in precisely in the right position with respect to 1st shadow mask
REAL MOSFETs: Processing / "Sub-threshold," "Hot Carrier" & "Short-Channel" Effects
But there is always some error in

Semiconductor Devices - Hour 6
(MCD: Wave Propagation)
Energy Bands / Conductors vs. Insulators
Last time:
2
hbar
Strange equation (due to Schrdinger):
2 m
2
( x , t) + V ( x , t) ( x , t) = i hbar
d
( x , t)
dt
In regions where V is constant, showed

Semiconductor Devices- Hour 17
(MCD: Diode Bands / Capacitance)
P-N Diodes II: Depletion Layers, Applied Voltage
Last Time:
1 Put P and N regions into contact
2) Holes flowed across to N-side, Electrons flowed across to P-side
3) There they recombined wit

MOS Capacitor, ms, band bending, oxide voltage
Semiconductor Devices - Hour 33
Last time we introduced basic principle of field effect transistors (FETs):
Use electric field to PULL carriers INTO place they would not otherwise be ("enhancement")
OR: Use e

Semiconductor Devices - Hour 31
REAL Bipolar Junction Transistors (BJTs)
Up until now, we have considered an idealized bipolar transistor to be ~ always in:
"Forward-active mode"
Implying substantial top-to-bottom (emitter to base) DC bias producing:
Mild

Semiconductor Devices - Hour 34
Inversion, Non-Ideal Oxide Charge, Threshold Voltage
We are deep in a multi-dimensional calculation where it is very easy to lose track of details and direction
So let's back off for a moment and take stock:
We have built a

Semiconductor Devices - Hour 32
Introduction to MOS Transistors
We've learned about diodes
We've learned how back-to-back diodes, if they are close enough, can form bipolar transistors
Bipolar transistors were great amplifiers: Fast, can handle a lot of c

Semiconductor Devices - Hour 35
(MCD: Worked VT example)
Remembering VT and Ion Implantation Threshold Shifting
Last Time: Have developed complex equations for voltage necessary to invert the carriers at surface = V T
This lecture:
- How to remember these

Semiconductor Devices - Hour 37
MOSFET I versus V
"Enhancement Mode" MOSFETs:
ENHANCE the source to drain carrier flow by inverting the surface to form a conducting channel
(-)VG
(+) VG
(+) VD
VS
N
(-) VD
VS
N
P
P
P-substrate
N - substrate
"N-channel enha