Introduction : Three-terminal devices are
far more useful than two-terminal ones because they can be used in a various applications,
ranging from signal amplification to digital logic and memory.
Three terminal devices make use of voltage between two terminals to control the current flowing in the third
terminal. It can be used as a controlled source, which is the basis for amplifier design. Also, It can be used to cause the current in the third terminal to change from zero to
a maximum value, thus allowing the device to act as a switch.
There are two major types of three-terminal semiconductor devices: the metal-oxide semiconductor field-effect transistor (MOSFET) and the
bipolar junction transistor (BJT). Compared to BJTs, MOSFETs can be made quite small that is it requires a small area on
the silicon IC chip. Therefore MOSFET is most widely used electronic device in the design of integrated circuits
(ICs), which are entire circuits fabricated on a single silicon chip.
Device structure : The enhancement-type MOSFET is the most widely used field-effect transistor. Here we will study n-channel enhancement-type MOSFET.
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| Fig 1. |
Fig 1 shows the physical structure of the n-channel enhancement-type MOSFET. The
transistor is fabricated on a p-type substrate, which is a single-crystal silicon wafer that
provides physical support for the device (and for the entire circuit in the case of an integrated
circuit). Two heavily doped n-type regions, indicated in the figure as the n+ source and
the n+ drain regions, are created in the substrate.
a heavily-doped (conductive) piece of polysilicon (simply called “poly”) operating as the gate. A thin layer of silicon dioxide (SiO2) of
thickness tox , which is an excellent electrical insulator, is grown on
the surface of the substrate, covering the area between the source and drain regions. Metal is
deposited on top of the oxide layer to form the gate electrode of the device. Metal contacts are also made to the source region, the drain region, and the substrate, also known as the body.
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Thus four terminals are brought out: the gate terminal (G), the source terminal (S), the drain
terminal (D), and the substrate or body terminal (B).
Structure is symmetric with respect to S and D. In reality, the substrate
potential greatly influences the device characteristics. Since in typical MOS operation, the S/D junction diodes must be reverse-biased, we assume that the substrate of NMOS transistors is connected to the most negative supply in the system.
MOSFET is also known as IGFET as the gate terminal is electrically insulated from the device body by the oxide layer. It is this insulation that
causes the current in the gate terminal to be extremely small.
MOSFET is treated as a three-terminal device, with the terminals being the gate (G), the source (S), and
the drain (D). A voltage applied to the gate controls current flow between
source and drain. This current will flow in the longitudinal direction from drain to source in
the region labeled “channel region.”
I/V Characteristics :
Here we analyze the generation and transport of charge in MOSFETs as a function of the
terminal voltages.
1 ) Threshold Voltage
Consider an NFET connected to external voltages as shown in below figure.
What happens as the gate voltage, VG, increases from zero? Since the gate, the dielectric, and the substrate form a capacitor, as VG becomes more positive, the holes in the p-substrate are repelled from the gate area, leaving negative ions behind so as to mirror the charge on the gate. In other words, a depletion region is created, refer below figure
Under this condition, no current flows because no charge carriers are available. As VG increases, so do the width of the depletion region and the potential at the oxide-silicon interface. In a sense, the structure resembles a voltage divider consisting of two capacitors in series: the gateoxide capacitor and the depletion-region capacitor as shown below,
When the interface potential reaches a sufficiently positive value, electrons flow from the source to the interface and eventually to the drain. A“channel” of charge carriers is formed under the gate oxide between S and D, and the transistor is “turned on.”
The value of Vg for which this occurs is called the “threshold voltage,” Vth. If Vg rises further,
the charge in the depletion region remains relatively constant while the channel charge density continues to increase, providing a greater current from S to D .
Formula Derivation :
To obtain the relationship between the drain current of a MOSFET and its terminal voltages
First, consider a semiconductor bar carrying a current I. If the mobile charge density
along the direction of current is Qd coulombs per meter and the velocity of the charge is v meters per
second, then
I = Qd · v ----- ( 1 )
Consider below figure to understand the significant of above formula which is helpful to analyze the semiconductor devices.
Snapshot of the carriers one second apart
Now by referring above figure, all the charges are enclosed in v meters of bar which is carrying current I. Charges must be passed through the cross section in one second. The charge density is Qd, then the total charge in v meters equals Qd.v
Now to use above formula, we have to determine the mobile charge density in MOSFET. Now consider the mosfet whose drain and source terminals are connected to ground. Then what is the charge density in the channel formed ? We know that channel gets formed at Vgs = Vth. The charge density in the channel formed i.e. charge per unit length along the source-drain path is ;
Qd = WCox (Vgs − Vth)
where Cox is multiplied by W to represent the total capacitance per unit length.
Let the voltage at drain is changed from zero to some value greater than zero. Now lets talk about the potential at channel. It varies from zero at source and Vd at drain. therefore the voltage difference between the gate and the channel varies from Vgs - 0 ( near the source ) to Vgs - Vd ( near the drain )
Let the V(x) be the channel potential at x point on channel.
Thus the potential difference between the gate and the channel at point x can be given as Vg - V(x)
Therefore we get the charge density at a point x along the channel can be written as
Qd (x) = WCox [Vgs − V(x) − Vth] ----- ( 2 )
and the current is given by from eq (1) and (2)
Id = −WCox [Vgs − V(x) − Vth]v
The negative sign indicated the charge carriers are negative. v is the velocity of the electrons in the channel. For semiconductors, v =μE, where μ is the mobility of charge carriers and E is the electric field. Noting that E(x)=−dV/dx and representing the mobility of electrons
by μn, we have
Id = WCox [Vgs − V(x) − Vth]μn . dV(x) / dx
To find Id , multiple both sides by dx and perform integration with respective derivative terms at both sides. we get,
since Id is constant along the channel,
------- ( 3 )
above figures the indicated the parabola formed by the above equation but here we will consider only the triode region , if we calculate ∂ ID/∂VDS, we get the peak of each parabola occurs at
Vds = Vgs − Vth and the peak current is
Here, Vds = Vgs − Vth is the overdrive voltage and W/L the “aspect ratio.” If Vds ≤ Vgs − Vth, we say the device operates in the triode region.
If in Eq. (3) VDS << 2(VGS - VTH ), we get the drain current is a linear function of VDS.
The linear relationship implies that the path from the source to the drain can be represented by a linear
resistor equal to ,
VDS << 2(VGS - VTH )
the dotted encircled region indicates the linear region in triode region when MOSFETs can be used as resistor whose value is controlled by the overdrive voltage as long as VDS << 2(VGS - VTH )
Application :
1. MOSFETs operating as controllable resistors play a crucial role in many analog circuits. For example, a voltage-controlled resistor can be used to adjust the frequency of the clock generator in a laptop computer if the system must go into a power saving mode.
2. MOSFETs also serve as switches.