Download MOSFETs: Linear Model

Semiconductor Devices III
Physics 355
Transistors in CPUs
Moore’s Law (1965): the number of components in an integrated
circuit will double every year; and in its present form that time
constant is usually quoted as 18 months although, at least for
Intel's CPUs, the number of transistors in a CPU
doubles roughly every two
years
Field Effect Transistors
• The npn and pnp junction type transistors lead
the way to modern electronic devices, but there
are disadvantages to their use. For example,
the signal is input to the low impedance base
and the base-emitter diode is forward biased.
• Another device achieved transistor action with
the input diode junction reversed biased, and
this device is called a "field effect transistor" or
a "junction field effect transistor", JFET.
• With the reverse biased input junction, it has a
very high input impedance. A high input
impedance minimizes the interference with or
"loading" of the signal source when a
measurement is made.
JFETs: Operation
• JFETs require a drain source
voltage, +VDD and a gate-source
bias voltage, VGS
• The drain supply voltage causes
a current ID (the drain current) to
flow through the n channel.
• The drain current is made up of
the majority carriers, in this case,
electrons.
• The value of the drain current is
dependent on both +VDD and
VGS.
• An input of zero volts, reverse
biases the p-n junction, resulting
in a maximum channel width and
maximum source to drain current.
JFETs
JFETs: Common Source
• Most common configuration
is shown.
• The source is grounded and
common to both the input
and output signals.
+VDD
R3
C3
C1
Output
Source
Input
R1
R2
C2
MOSFETs
• The n-type Metal-OxideSemiconductor Field-EffectTransistor (MOSFET) consists of
a source and a drain, two highly
conducting n-type semiconductor
regions which are isolated from
the p-type substrate by reversedbiased p-n diodes. A metal (or
poly-crystalline) gate covers the
region between source and drain,
but is separated from the
semiconductor by the gate oxide.
• These have very high impedances
- in the range 109 to 1014 ohms.
MOSFETs
MOSFETs: Models
• Linear
The linear model describes the behavior of a MOSFET biased
with a small drain-to-source voltage. As the name suggests, the
MOSFET, acts as a linear device, more specifically a linear
resistor whose resistance can be modulated by changing the
gate-to-source voltage. In this regime the MOSFET can be used
as a switch for analog signals or as an analog multiplier.
• Quadratic
The quadratic model includes the gradual change of the charge in
the inversion layer between the source and the drain due to the fact
that the channel voltage varies from the source voltage to the drain
voltage.
• Variable Depletion Layer
The variable depletion layer model includes, in addition to the
gradual change of the inversion layer charge, the variation of the
charge in the depletion layer between the inversion layer and the
substrate. This model is required to understand the body or
substrate bias effect.
MOSFETs: Linear Model
The general expression for the drain current equals the total charge in the
inversion layer divided by the time the carriers need to flow from the source to
the drain:
where Qinv is the inversion layer charge per unit area, W is the gate
width, L is the gate length and tr is the transit time. If the velocity of the
carriers is constant between source and drain, the transit time equals:
where the velocity equals the product of the mobility and the electric field:
MOSFETs: Linear Model
The constant velocity also implies a constant electric field so that the field equals the
drain-source voltage divided by the gate length. This leads to the following expression
for the drain current:
We now make an assumption about the inversion layer charge density,
namely that it is constant between source and drain and that the charge
density in the inversion layer is given by the product of the capacitance per
unit area and the gate-to-source voltage minus the threshold voltage:
The charge is zero if the gate voltage is lower than the threshold voltage.
Replacing the inversion layer charge density in the expression for the
drain current yields the linear model:
MOSFETs: Linear Model
MOSFETs: Quadratic Model
Considering a small section within the device with width dx and channel
voltage VC + VS one can still use the linear model, yielding:
where the drain-source voltage is replaced by the change in channel voltage
over a distance dx, namely dVC. Both sides of the equation can be
integrated from the source to the drain, so that x varies from 0 to the gate
length, L, and the channel voltage VC varies from 0 to the drain-source
voltage, VDS.
Using the fact that the DC drain current is constant throughout the device
one obtains the following expression:
MOSFETs: Quadratic Model
Drain current saturation therefore
occurs when the drain-to-source voltage
equals the gate-to-source voltage minus
the threshold voltage. The value of the
drain current is then given by the
following equation:
The quadratic model explains the typical current-voltage characteristics
of a MOSFET which are normally plotted for different gate-to-source
voltages. An example is shown in the figure above. The saturation
occurs to the right of the dotted line which is given by ID = m Cox W/L
VDS2. The dotted line separates the quadratic region of operation on the
left from the saturation region on the right.
MOSFETs: Variable Depletion Model
The figure shows a clear difference between the two models: the quadratic model
yields a larger drain current compared to the more accurate variable depletion
layer charge model. However, because of its simplicity, the quadratic model is
widely used. Fitting parameters are often used instead of the actual device
parameters in order to more closely describe the measured characteristics.
Solid State Lasers
Non-Lasers
Lasers
Solid State Lasers
• Ruby
Solid State Lasers: Nd:YAG
Neodymium-Doped : Yttrium Aluminium Garnet
Semiconductor Lasers
Semiconductor Lasers
Semiconductor Lasers
Semiconductor Lasers