MOSFETs: Types and Structure

MOSFET

• MOSFETs are the dominant transistor in microelectronics
• They were conceived in the 1930s but first realized in the 1960s.
• Unique properties have revolutionized the semiconductor industry enabling modern microprocessors, memories, and communication circuits

Types of MOSFETs

• Depletion and Enhancement MOSFETs are the two types
• Further divided into n-channel and p-channel enhancement MOSFETs
• MOSFETs can be used to construct amplifiers, logic gates, and memory devices

Structure of MOSFET

• An n-channel enhancement MOSFET is also called NMOS.

• The substrate is a p-type semiconductor

• Source and drain terminals connect to n-type regions via metallic contacts

• There is no channel between the n-doped regions without operation

• During operation a channel is formed or induced

• A silicon dioxide (SiO2) layer isolates the gate metal terminal from the channel region between the drain and source

• A Substrate or body terminal may be available as a fourth terminal

• The substrate is internally connected to the source terminal if there is no fourth terminal

Basic Operation

• A voltage VGS is applied between the gate and source terminals

• A voltage VDS is applied between the drain and source terminals

• If VGS = 0V, no current flows between the drain and source terminals due to the absence of a conducting channel

• With no conducting channel it is in an OFF state

• If VGS is set to a positive voltage, holes in the substrate are repelled from the gate

• This attracts free electrons (minority charge carriers) towards the gate.

• The SiO2 layer prevents electrons from being absorbed into the gate terminal

• Electrons accumulate near the gate, between the source and drain n-doped regions

• As VGS increases, the concentration of free electrons near the gate increases

• This induces a channel of electrons between the source and drain

• With a conducting channel it is in an ON state

• The threshold voltage VTh is the value of VGS required to form a channel

• Once the channel is formed, charge carriers flow freely from source to drain, resulting in drain current

• As VGS increases above VTh, the number of free electrons in the induced channel is increased

• This results in increased drain current.

• The drain current is proportional to voltage VDS for small VDS values

• If VGS is constant and VDS increases, the gate-to-drain voltage reduces, reducing the attraction of free electrons near the drain

• The channel thickness near the drain becomes less than near the source.

• If VDS is further increased, then the channel is reduced to the point of pinch-off - establishing saturation condition

• This occurs when VDS is high enough that VGS – VDS becomes less than VTh

V-I Characteristics

• V-I (current versus voltage) characteristics include drain characteristics (ID vs. VDS) and transfer characteristics (ID vs. VGS)

• Drain characteristics are plotted by holding VGS constant, varying VDS, and noting variations in the drain current ID

• For VGS < VTh, the drain current is zero due to the absence of a channel

• At VGS = VTh, a thin channel forms - a small drain current flows, this is known as the cut-off region

• For VGS > VTh, the channel is fully formed and a substantial drain current flows

• Keeping VGS constant, as VDS is increased in small amounts, the current ID increases linearly with VDS - triode or linear region

• If VDS is further increased, the drain current eventually reaches a saturation level

• Any further increase in VDS has no effect on the drain current, which remains constant at the saturation level - saturation region

• The device acts like a voltage-controlled current source

• The value of VDS at which the drain current saturates is denoted by VDS Sat and it is equal to VGS – VTh

• For higher VGS values, VDS Sat is higher, depicted by the locus in the characteristics

• Also, as VGS increases, the spacing between the maximum levels of drain current also increases

• The expression for drain current in the saturation region: 𝐼𝐷 = 𝑘(𝑉𝐺𝑆 − 𝑉𝑇ℎ )2

• Where k is a constant with the unit A/V2

• 𝑘= 𝜇𝑛 𝐶𝑜𝑥 (𝑊/2𝐿)

• µn is the mobility of free electrons

• Cox is oxide capacitance per unit area

• W is the width of the channel

• L is the length of the channel

• Overdrive voltage VOV is the quantity VGS – VTh.

• Drain current is proportional to the W/L ratio

• An increase of W, while keeping L constant, increases the drain current, and vice versa

• An increase of L, while keeping W constant, decreases the drain current, and vice versa

• Circuit designers adjust the W/L ratio to achieve the required drain current

• Drain current is proportional to Cox (oxide capacitance per unit area), which is inversely proportional to the oxide thickness

• Current is inversely proportional to the oxide thickness.

• If the oxide thickness is reduced, then the drain current will be more, and vice versa

• Transfer characteristics is the graph of saturated drain current versus VGS

• Obtained from the drain characteristics

• Drain current is zero for VGS ≤ VTh

• As VGS increases beyond VTh, the saturation level of drain current increases

PMOS

• A p-channel enhancement MOSFET (PMOS) structure is the reverse of an n-channel MOSFET

• It uses an n-type substrate with p-type doped regions for the drain and source

• Terminals are identical, but voltage polarities and current directions are reversed

• induced holes between the doped regions of source and drain form the channel

• Drain characteristics will show increasingly negative VGS values resulting in increased drain currents

• Transfer characteristics are a mirror image of the n-channel MOSFET, and threshold voltage VTh is negative

Symbols

• Dashed lines between drain and source reflect that there is initially no channel in the circuit symbols of n-channel and p-channel enhancement MOSFETs
• The channel is induced by applying gate-to-source voltage
• Arrows point from p-type to n-type:
  • In n-channel MOSFET, the arrow points from the p-type substrate to the n-type channel -In p-channel MOSFET, the arrow is from the p-type channel to the n-type substrate

Channel Length Modulation

• Keeping VGS constant, the drain current will eventually reach a saturation level if VDS is increased

• This is caused by pinch-off at the drain-end of the channel

• Any further increase in VDS has no effect on the drain current, which remains constant at the saturation level

• The drain current increases slightly if VDS is increased beyond the point of pinch-off - channel-length modulation

• The effective length of the channel reduces from L to L1, after pinch-off with further increasing of VDS

• Since drain current is inversely proportional to channel length, drain current increases due to shortening of the channel

• To account for the channel-length modulation, the current equation is multiplied by the addition of corrective term: -𝐼𝐷 = 𝑘(𝑉𝐺𝑆 − 𝑉𝑇ℎ )2 (1 + 𝜆𝑉𝐷𝑆 ) -λ (lambda) is the channel-length modulation coefficient

Transconductance

• MOSFET is characterized by its transconductance

• 𝑔𝑚 = 𝜕𝐼𝐷/𝜕𝑉𝐺𝑆

• gm indicates the device's ability to amplify signals

• Higher gm values means greater change in drain current for a given change in gate-to-source voltage

• 𝐼𝐷 = 𝜇𝑛 𝐶𝑜𝑥 (𝑉𝐺𝑆 − 𝑉𝑇ℎ )2(𝑊/2𝐿)

• Differentiating w.r.t. VGS -𝑔𝑚 = 𝜇𝑛 𝐶𝑜𝑥 (𝑉𝐺𝑆 − 𝑉𝑇ℎ )(𝑊/𝐿)

• gm is directly proportional to W/L ratio and overdrive voltage VGS – VTh

• Alternate expressions for gm:

• 𝑔𝑚 = √(2𝜇𝑛 𝐶𝑜𝑥 𝐼𝐷 (𝑊/𝐿))

• 𝑔𝑚 = 2𝐼𝐷/(𝑉𝐺𝑆 − 𝑉𝑇ℎ )

Large and small signal models

• MOSFETs can be replaced by they're equivalent models to analyze and design circuits
• These models allow quick/intuitive understanding of complex circuits

large signal model

• Large-signal models are used when the magnitude of the applied signal is comparable with the supply voltage, in the design of circuits
• Non-linear effects of the transistor are considered in the model
• With VGS > VTh and VDS > (VGS – VTh), the MOSFET operates in the saturation region and acts like a voltage-controlled current source
• The current changes slightly with VDS.
• With VGS > VTh and VDS < (VGS – VTh) the MOSFET operates in the triode region, and its current varies almost linearly with VDS
• The gate remains an open circuit, with zero gate current

small signal model

• Small-signal models are sued when magnitude of the signal applied to the device is much smaller when compared to the supply voltage
• The bias voltage of MOSFET is slightly disturbed during the signal
• The non-linear large-signal model can be reduced to a linear small-signal model
• The basic small-signal model consists of a voltage-controlled current source iD = gmvGS.
• Lowercase letters represent small signals
• This gate terminal is open, like in the large-signal model
• To represent channel length modulation, a parallel resister is included in the current source - R0

MOSFET Biasing

• The MOSFET must operate in the saturation region to be used as an amplifier

• This assures that VGS > VTh and VDS > (VGS – VTh)

• Amplification properties depend on gm and ro values

• Proper VGS, VDS, and ID values are known as biasing circuit

• Voltage-divider circuits can be used to bias the MOSFET -The voltage at the gate terminal is: 𝑉𝐺 = (𝑉𝐷𝐷 𝑅2) / (𝑅1 + 𝑅2) -The gate-to-source voltage is: 𝑉𝐺𝑆 = 𝑉𝐺 − 𝐼𝐷 𝑅𝑆 -The drain current is: 𝐼𝐷 = 𝜇𝑛 𝐶𝑜𝑥 (𝑉𝐺𝑆 − 𝑉𝑇ℎ )2(𝑊/2𝐿)

• Self-bias circuits or drain-to-gate feedback bias circuits can also be used for MOSFETs

• The voltage drop across RG is zero, and VGS = VDS

• MOSFET will always be biased in the saturation region

• The equations governing the circuit are: 𝐼𝐷 𝑅𝐷 + 𝑉𝐺𝑆 + 𝐼𝐷 𝑅𝑆 = 𝑉𝐷𝐷

• 𝐼𝐷 = 𝜇𝑛 𝐶𝑜𝑥 (𝑉𝐺𝑆 − 𝑉𝑇ℎ )2(𝑊/2𝐿)

MOSFET Amplifiers

• Three amplifier configurations are possible in MOSFET:
  • Common-source (CS). -Common-gate (CG) -Common-drain (CD) amplifiers
• CS amplifier input signals are applied to the gate terminal and output signal at drain terminal
• MOSFET converts small variations in the input signal into proportional changes in the drain current
• Equations: -𝐴𝑉 = 𝑣𝑜𝑢𝑡/𝑣𝑖𝑛 = −𝑔𝑚 𝑅𝐷 -With channel-length modulation: 𝐴𝑉 = 𝑣𝑜𝑢𝑡/𝑣𝑖𝑛 = −𝑔𝑚 (𝑟𝑜 ||𝑅𝐷 )
• A negative sign indicates a 180° phase-shift
• Voltage gain depends on gm and RD values
• Transconductance gm is proportional to drain current ID
• With increases of RD or ID, the voltage drop across RD increases
• The MOSFET should remain in the saturation region: -𝑉𝐷𝐷 − 𝐼𝐷 𝑅𝐷 > 𝑉𝐺𝑆 − 𝑉𝑇ℎ -𝐼𝐷 𝑅𝐷 < 𝑉𝐷𝐷 − 𝑉𝐺𝑆 + 𝑉𝑇ℎ