# Parameter Analysis of the MESFET, Channel Width Calculation

Engineering design regularly involves an analysis of the formulae behind the various parameters of a system one is trying to build or improve. Some parameters are static, such a particular qualities of the materials being used. Perhaps there is a constraint made on the system or a goal, such as achieving function at a certain frequency or to reduce the size as much as possible. Today, many programs exist that can perform complicated calculations for the engineer. To construct a problem or calculation that produces the desired result may need more attention.

The MESFET uses a contact between n-doped semiconductor material with highly n-doped semiconductor material to form a junction field effect transistor. The great advantage of not using a p-doped semiconductor material is that the transistor can be built without using hole transfer. Since hole transfer is much slower than electron transfer, the MESFET can function much faster than other types of transistors.

For the MESFET, it may not be possible to examine all parameters. Consider first the following:

Potential variation along the channel (notice the similarity of the following to Ohm’s law, V=IR):

Where the resistance along the channel is:

Depletion Width (also referenced in the above formula) under the gate:

Pinch-off Voltage:

Threshold Voltage:

Built-in Potential:

The above formulas alone would be enough to put to use. While constructing a MESFET, it was found that the doping concentration of donor electrons in the channel played an important role. N_D, the donor doping concentration is found in most of the above formulas. The doping concentration is of particular importance, since it can be directly manipulated. The pinch-off voltage and the donor concentration are directly proportional. By achieving an estimate (or of the values are known) for other parameters, it would be possible to perform a parameter sweep for the MESFET system for doping concentration. This method may become critical for optimizing semiconductor device designs.

# MESFET Design Problem

Let’s say we want to calculate the channel width of an n-channel GaAs MESFET with a gold Schottky barrier contact. The barrier height (φ_bn) is 0.89 V. The temperature is 300 K. The n-channel doping N_d is 2*10^15 cm^(-3). Design the channel thickness such that V_T = +0.25V.

# GaAs MESFET Designs

A GaAs MESFET structure was built using Silvaco TCAD:

• Channel Donor Electrons: 2e17
• Channel thicknes s : 0.1 microns
• Bottom layer: p doped GaAs (5 micron thick, 1e15p doping)
• Gate length: 0.3 micron
• Gate metal work function: 4.77eV
•Separation between the source and drain electrode: 1 micron

The IV curve is as follows. Of primary importance are the two bottom curves, which are for a gate voltage of -0.2V and -0.5V. The top curve is 0V, over which would be undesirable for the MESFET operation.

Now, in terms of designing a MESFET, there is a large amount of theory that one may need to grasp to build one from scratch – you would probably first start by building one similar to a more common iteration. That said, there are a number of parameters that one may wish to tweak and to achieve, to name a few: saturation current, threshold voltage, transit frequency, maximum frequency, pinch-off voltage.

The iteration above does not show a highly doped region under the source and drain contacts. The separation between source and drain may also be increased and the size of the gate decreased.

Channel doping level was found to make a significant difference in overall function. The channel must be doped to a certain level, otherwise the structure may not behave properly as a transistor.

go atlas

Title GaAs MESFET

# Define the mesh

mesh auto
x.m loc = 0 Spac=0.1
x.m loc = 1 Spac=0.05
x.m loc = 3 Spac=0.05
x.m loc = 4 Spac =0.1

# n region

region num=1 bottom thick = 0.1 material = GaAs NY = 10 donor = 2e17

# p region

region num=2 bottom thick = 5 material = GaAs NY = 4 acceptor = 1e15

# Electrode specification
elec num=1 name=source x.min=0.0 x.max=1.0 top
elec num=2 name=gate x.min=1.95 x.max=2.05 top
elec num=3 name=drain x.min=3.0 x.max=4 top

doping uniform conc=5.e18 n.type x.left=0. x.right=1 y.min=0 y.max=0.05
doping uniform conc=5.e18 n.type x.left=3 x.right=4 y.min=0 y.max=0.05

#Gate Metal Work Function
models fldmob srh optr fermidirac conmob print EVSATMOD=1
contact num=2 work=4.77

# specify lifetimes in GaAs and models
material material=GaAS taun0=1.e-8 taup0=1.e-8
method newton

solve vdrain=0.5
LOG outf=proj2mesfet500mVm.log
solve vgate=-2 vstep=0.25 vfinal=0 name=gate
save outf=proj2mesft.str
#Plotting
output band.param photogen opt.intens con.band val.band

tonyplot proj2mesft.str
tonyplot proj2mesfet500mVm.log
quit

# HEMT – High Electron Mobility Transistor

One of the main limitations of the MESFET is that although this device extends well into the mmWave range (30 to 300 GHz or the upper part of the microwave spectrum), it suffers from low field mobility due to the fact that free charge carriers and ionized dopants share the same space.

To demonstrate the need for HEMT transistors, let us first consider the mobility of GaAs compound semiconductor. As shown in the picture, with decreasing temperature, Coloumb scattering becomes prevalent as opposed to phonon lattice vibrations. For an n-channel MESFET, the main electrostatic Coloumb force is between positively ionized donor elements (Phosphorous) and electrons. As shown, the mobility is heavily dependent on doping concentration. Coloumb Scattering effectively limits mobility. In addition, decreasing the length of the gate in a MESFET will increase Coloumb scattering due to the need for a higher doping concentration in the channel. The means that for an effective device, the separation of free and fixed charge is needed.

A heterojunction consisting of n+ AlGaAs and p- GaAs material is used to combat this effect. A spacer layer of undoped AlGaAs is placed in between the materials. In a heterojunction, materials with different bandgaps are placed together (as opposed to a homojunction where they are the same).

This formation leads to the confinement of electrons from the n- layer in quantum wells which reduces Coloumb scattering. An important distinction between the HEMT and the MESFET is that the MESFET (like all FETs) modulates the channel thickness whereas with an HEMT, the density of charge carriers in the channel is changed but not the thickness. So in other words, applying a voltage to the gate of an HEMT will change the density of free electrons will increase (positive voltage) or decrease (negative voltage). The channel is composed of a 2D electron gas (2DEG). The electrons in the gas move freely without any obsctruction, leading to high electron mobility.

HEMTs are generally packed into MMIC chips and can be used for RADAR applications, amplifiers (small signal and PAs), oscillators and mixers. They offer low noise performance for high frequency applications.

The pHEMT (pseudomorphic) is an enhancement to the HEMT which feature structures with different lattice constants (HEMTs feature roughly the same lattice constant for both materials). This leads to materials with wider bandgap differences and generally better performance.

# Transistor IV curves and Modes of Operation/Biasing

In the field of electronics, the most important active device is without a doubt the transistor. A transistor acts as a ON/OFF switch or as an amplifier. It is important to understand the modes of operation for these devices, both voltage controlled (FET) and current controlled (BJT).

For the MOSFET, the cutoff region is where no current flows through the inversion channel and functions as an open switch. The “Ohmic” or linear region, the drain-source current increases linearly with the drain-source voltage. In this region, the FET is acting as a closed switch or “ON” state. The “Saturation” region is where the drain-source current stays roughly constant despite the drain source voltage increasing. This region has the FET functioning as an amplifier.

The image above illustrates that for an enhancement mode FET, the gate-source voltage must be higher than a certain threshold voltage for the device to conduct. Before that happens, there is no channel for charge to flow. From there, the device enters the linear region until the drain-source voltage is high enough to be in saturation.

DC biasing is an extremely important topic in electronics. For example, if a designer wishes for the transistor to operate as an amplifier, the FET must stay within the saturation region. To achieve this, a biasing circuit is implemented. Another condition which effects the operating point of the transistor is temperature, but this can be mitigated with a DC bias circuit as well (this is known as stabilization). “Stability factor” is a measure of how well the biasing circuit achieves this effect. Biasing a MOSFET changes its DC operating point or Q point and is usually implemented with a simple voltage divider circuit. This can be done with a single DC voltage supply.  The following voltage transfer curve shows that the MOSFET amplifies best in the saturation region with less distortion than the triode/ohmic region.

# The Bipolar Transistor, Modes of Operation

The transistor is a multifunction semiconductor device that, when used with other circuit elements has the ability to produce a current gain, voltage gain and signal-power gain. The transistor is referred to as a passive device, while the diode is passive. The three basic types of transistor technologies are the bipolar transistor, the metal-oxide-semiconductor field effect transistor (MOSFET) and the junction field effect transistor (JFET). The bipolar transistor most often functions as a voltage-controlled current source.

The Bipolar Junction Transistor

The BJT has three separately doped regions and two pn-junctions, which are close enough to interact between each other. The BJT can either be constructed as an NPN or PNP transistor, which stands for the arrangement of positive and negatively doped regions.

The main connections of a BJT transistor are referred to as the collector, base and emitter. Generally, the emitter side is doped to a higher level than the collector. The result of this is that when a supplied a voltage, the electrons will flow in the direction from the emitter to the collector. The direction of current then will be from the collector to the emitter.

BJT Modes of Operation

There exist three modes of operation for the BJT transistor. In reference to the diagram below, when the Base-Emitter voltage is zero or reverse biased, the majority of carrier electrons from the emitter will not be injected into the base. This mode where all currents in the transistor are zero is referred to as cut-off. When the Base Emitter voltage is positive (forward biasing), an emitter current is generated. As the Base Emitter voltage increases, the collector current will continue to increase until a certain point at which both the Base Emitter and Base Collector junctions become forward biased. This mode is called saturation.

# BJT vs. FET

Transistors are important components that are used in a variety of applications. Some types can be used for switching, some for amplification or both. Other transistors perform exclusive tasks, such as the phototransistor, which responds to light by producing a current.

The main premise of a transistor is that by feeding a transistor a source voltage or current (depending on the type), the transistor allows for the passage of electrons. This process is accomplished through pnp or npn semiconductor structures. The following diagrams provide a general example of the function of a transistor:

Bipolar Junction Transistors (BJT) are controlled using a biasing current at the base pin. This means that they will also consume more current than other transistors such as the FET. One advantage of BJT transistors is that they offer greater output gain than an FET. However, BJT can be much larger in size than FET and for this reason, they are less popular, despite being easier to manufacture.

Field Effect Transistors (FET) are voltage-controlled. For this reason they essentially draw no current and therefore do not pose a substantial load to a circuit. FETs are not as useful for gain as BJT, however if the intent is not for amplification then this is not a problem. FETs can be manufactured very small and this is important in manufacturing integrated circuits that use many transistors. FETs and especially the MOSFET subtype are more expensive to manufacture, but remain more popular than the BJT.

Some FET transistor types are even constructed on the nano-scale. The FinFET for example is about 10 nm, currently used by Intel, Samsung and others.