ECEN 5014, Spring 2016 – Active Microwave Circuits Zoya Popovic, University of Colorado, Boulder

LECTURE 3 –MICROWAVE TRANSISTOR OVERVIEW AND TRANSISTOR EQUIVALENT CIRCUITS

L3.1. MESFETS AND HEMTS The most commonly used active devices at microwave frequencies are the Metal Semiconductor Field Effect Transistor (MESFET), and its variation, the HEMT. The MESFET is a GaAs device with a physical cross section shown in Fig.L3.1(a), and a typical electrode layout is shown in Fig.L3.1(b). The MESFET is a unipolar device, which means that there is only one type of carrier. The MESFET has three terminals: the source, gate and drain. The gate length is the length that the electrons need to travel between the drain and source and is usually a fraction of a micrometer. The gate width is in the direction out of the paper referring to Figure L3.1(b) and can be hundreds of micrometers long. It determines the current that can flow through the device. The three electrodes are deposited on an n-type GaAs epitaxial layer which is grown on a semi-insulating substrate. The epitaxial layer is on the order of 0.1µm thick and the doping is 10 1016 17− cm-3 . The source and drain are ohmic contacts (low resistance, usually made of a gold-germanium alloy), and the gate is a Schottky contact. Associated with the Schottky barrier is a depletion region which affects the thickness of the conducting channel. The gate is biased negatively with respect to the source, and the drain positively. When the voltage is changed on the gate, the thickness of the channel changes, and this controls the current between the drain and the source.

(a) (b) Fig.L3.1. A cross section of a MESFET (a) and photograph and electrode layout (b). When you buy a MESFET, it can come in a package or in chip form. You will also get measured s-parameters at a few different bias points for a certain frequency range. These s-parameters are measured usually with the source terminal grounded and the drain and gate looking into 50Ω, so they are two-port parameters. The s21 parameter corresponds to the gain of the device in

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common-source configuration. The amplitude and the phase of all four parameters are given at many discrete frequencies. Another way to represent the transistor is with an equivalent circuit, like you have probably done in your circuits classes. The idea behind equivalent circuits is to model the device over a range of frequencies with invariant parameters. Let us begin with the simplest linear (small-signal) equivalent circuit, for which it is simpler to use admittance parameters, given by I=YV.

Table L3.1. Conversion formulas between s- and normalized y-parameters. (from “Microwave Engineering” by D. Pozar.)

(a) (b)

Fig.L3.2. (a) Low-frequency MESFET model. (b) High-frequency approximate MESFET equivalent circuit. These circuits are called the intrinsic equivalent circuits because additional parasitics from the package are not included.

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The y-parameters may be converted to s-parameters using the formulas from Table L3.1. At very low frequencies, say below 1GHz, the capacitances and inductances associated with the MESFET are quite small, and we can assume they are negligible. The same is true for the resistive losses. The result is a simple low-frequency model shown in Fig.L3.2(a). This model has an infinite input impedance and cannot be matched at the input. What is the order of magnitude of the elements of this circuit? Let us look at a few examples. The TriQuint TGF2960 device S-parameters at the lowest 100MHz frequency with VDS = 8V, IDS=100mA are: S11= 0.677dB ∠-7.9° ≈ 1∠0 S21= 20dB ∠-175.75°≈ 10∠-180° S12= -41.9dB ∠72.47°≈ 0 S22= -5.06dB ∠-19.43°≈ 0.5∠0 If we wish to find the values of the elements in the equivalent circuit, we would first solve for the S-parameters of the equivalent circuit in terms of the unknown elements, and then set the expressions equal to the known S-parameters, thus getting a system of equations. Finding the expressions for the S-parameters of the equivalent circuit can be quite complicated, and usually the Y-parameters are found and then converted to S-parameters. For the low-frequency model from Fig.L3.2 (with no capacitors), the Y-parameters are

=Υ

dsm gg00

and the S-parameters are obtained as follows:

+−

+−=

ds

ds

ds

m

gg

ggS

11

12

01.

Since you are given the S-parameters, you can find the conductance values; note that they are normalized to 1/50Ω=0.02S. The next example is an Avago MESFET chip with reasonably standard parameters, that at 500MHz with VDS = 3V and IDS = 20mA , has s-parameters as follows:

ssss

11

21

12

22

0 97 20 150 166 50 029 77 0052 11 05

= ∠− °≈= ∠ °≈ −= ∠ °≈= ∠− °≈ −

.

... .

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For this device, from the measured scattering parameters, the voltage gain is found to be about / 1.2V m dsA g g= = and gm=2.5, gds=3. These conductance values are normalized to 1/50Ω=0.02S.

Finally, consider the Qorvo (RFMD) FPD HEMT device. At 5V and 300mA, the lowest available frequency S-parameter values are at 50MHz: Going through the same approximations as for the FETs above, we get the parameters calculated from the low frequency measured data to be If you look at the measured data at f=600MHz for the same bias point, however, these are the values:

°∠=°∠=°∠=°−∠=

3.1174568.02.38032.05.98587.10

144821.0

11

11

21

11

ssss

Referring back to the discussion about the low-frequency transistor model, you can see that the simple equivalent circuit from before cannot be used. There are capacitances that are already quite pronounced at 600MHz. The reason is that the MESFET device has gain up to much higher frequencies (12GHz) and can give at most a hundred mW of power, while the RFMD HEMT is a 1W device for lower frequency operation. The depletion capacitance of the Schottky barrier gate is represented by gsC and gdC . Usually

gsC is much larger. The reason is that the positive voltage on the drain causes the depletion region on the drain side to be wider than on the source side. Also, the separation between the drain and gate contacts is usually about 1µm larger than that between the source and gate. The capacitance between the source and drain is primarily through the substrate, and is not negligible because of the high dielectric constant of GaAs of 13. The resistance of the gate is significant because the gate contact is long and thin, and a typical value is 10-15Ω. The usual figure of merit for the transistor is the voltage gain /V m dsA g g= . Since both conductances are proportional to the gate width, the voltage gain does not depend on the width. This is important in MMICs, where there is complete control over gate widths, but gate lengths are fixed by the fabrication process. The gate length determines the maximum operating frequency of the device (directly, the RC time constant). An experimentally obtained formula is

175.0145175.0079006.0

3615936124946.0

22

12

21

11

−≈°−∠=≈°∠=−≈°∠=≈°−∠=

ssss

305.28

875.0

===

V

ds

m

AmSGSg

21

3

max33 10 Hzf

L⋅

= ,

where L is the gate length in meters. Several cutoff frequencies are commonly used. Tf is the cutoff frequency when the short-circuited current gain of the device drops to unity. This parameter is often used, but never measured, since a microwave transistor tends to oscillate with a short-circuit load. If the input current for the high-frequency equivalent circuit is inI then we have

gs

mT

gs

mT

in

out

gsmdsout

gsgsin

Cg

f

Cg

II

VgiICjVI

π

ωω

ω

2

1

=

==⇒=

≈≈

⋅≈

The two most important parameters for the high-frequency performance are therefore mg and

gsC - large mg and small gsC result in a high cut-off frequency. A typical procedure used to calculate the cutoff frequency is to derive the short-circuit gain from the measured s-parameters, and extrapolate this curve to the value of the gain equal to 0dB, illustrated in Fig.L3.3. This gives a simplified 6dB/octave response, although the actual one is obviously more complicated (we used only approximate formulas).

Fig.L3.3. Calculating the cutoff unity current gain frequency. This cannot be measured, because the transistor will oscillate when the drain is shorted, due to the feedback capacitance. The maximum frequency of operation is higher than the cutoff frequency, and is defined as a frequency for which a negative resistance (oscillation) can be produced. The two frequencies are related by

max1 22

T

T

ffr f r

=+

,

where

gmVgs

Cgd

Cgs CdsRds

Gate Drain

Source

+

Vgs

-

22

1 2,and 2g S ig gd

ds

R R Rr r R C

Rπ

+ += = ,

and the different resistances are those of the gate and source contacts, the intrinsic resistance between source and gate, and the drain-to-source resistance. The unilateral transistor gain as a function of frequency can be expressed in terms of the cutoff frequency as

2max

≈

ff

Gu

In this approximation, the gain is 1 when maxf f= . The maximum frequency is usually two to three times higher than the cutoff frequency. In order to obtain a high maxf , the cutoff frequency needs to be maximized, as well as the ratio of channel resistance to ( )g S iR R R+ + , and gdC needs to be minimized. The transit time is decreased by decreasing the gate length L, but this also results in a decrease in channel depth in order to maintain a geometry that gives a high mg . In turn, this means that the doping in the channel must increase, to maintain a low channel resistance. The limit on the doping is set by the avalanche breakdown in the gate-drain region which has the highest fields, and it is about 17 -35 10 cm⋅ . Now it is maybe clear why it is difficult to make high-frequency power devices. A method for reducing the series resistance in the source is to recess the gate, by making a mushroom type structure for the gate metallization, by self-alignment. The cutoff frequency can be directly related to the transit time of electrons under the gate by the following approximate argument. Assume a small positive change in the gate voltage gv∆ . This results in: (1) the gate charges up by gs gq C v∆ = ∆ since it is one of the capacitor electrodes; (2) the other electrode of the capacitor is the channel, so the same amount of negative charge must be drawn into the channel. Negative charge in the channel means an increase in carrier (electron) density, so (3) the current through the channel ( dsi ) increases. The time that the electrons take to transit the gate region is found from

dsT

qiτ∆

∆ =

The current can also be expressed in terms of the gate voltage as g

ds gsT

vi C

τ∆

∆ = ⋅

and from the definition of transconductance, the following can be written 1m

gs T

gC τ

= ,

where the left-hand side is the significant ratio for the cutoff frequency that we derived earlier. We can therefore express the cutoff frequency in terms of the transit time as follows:

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Lv

Cg

f sat

Tgs

mT ππτπ 22

12

≈== ,

where satv is the carrier saturation velocity. So, this gives a very simple rule: if you wish to make a device with a high cutoff frequency, you need to increase the saturation velocity and decrease the gate length. The saturation velocity in bulk GaAs is limited to about 710 cm/s , and to overcome that the semiconductor material under the gate must be modified. This is done is High Electron Mobility Transistors (HEMTs). If you wish to make a device with a high cutoff frequency, you need to:

- increase the saturation velocity of electrons in the channel and - decrease the gate length of the device.

It is somewhat obvious what issues need to be solved in decreasing the gate length and that they are purely technological, i.e. require better photolithography. To increase the saturation carrier velocity, however, requires a new device design. What is the limit in saturation velocity in a GaAs MESFET? If no collisions occur, electrons in GaAs are accelerated by the electric field and follow Newton’s second law, with the mass replaced by the effective mass m*:

d*d

*

vF m a m eEt

eEv tm

= ⋅ = =

= ⋅ ,

where e is the electron charge. At room temperature, the mean free path for the electrons can be estimated from the measured mobility, and the value of about 0.1µm is reasonable. If the electron starts at x=0, then at time τ it has traversed the entire gate length L,a nd the following can be written:

2

0

d2 *eEL v tm

τ

τ= ⋅ =∫ .

If an average electron with a mean free path before the first collision of 0.1µm is chosen, the value for τ is found to be

1.0107.8*2 14 ≈⋅≈= − seE

Lmτ ps,

for a value of 410E = V/cm. Therefore, the maximum velocity that the electron can acquire is given by

7max

2 7.3 10 cm/s*

eELv am

τ= ⋅ = = ⋅ .

Since the peak steady-state velocity of electrons in GaAs is in the range of 7 71.5 10 cm/s - 2 10 cm/s⋅ ⋅ , the maximum velocity derived above is an “overshoot” velocity that

an electron acquires when in a very short gate region with a large electric field.

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Keeping in mind the cross-section of a MESFET, consider a device that has a cross-section as in Fig.L3.3. In this High Electron Mobility Transistor (HEMT), GaAs is not the only material that is used. There are a number of so-called hetero-junctions, i.e. semiconductor junctions between different materials. The most important one in terms of device operation is that between the silicon-doped AlGaAs and the undoped GaAs. Due to the higher band-gap of AlGaAs compared to GaAs, free electrons diffuse from the AlGaAs into the GaAs forming a two-dimensional electron gas at the interface. These electrons are confined to a very thin sheet because of the built-in potential barrier. It is easy to understand qualitatively why the transport properties of electrons in this region are superior to those in the channel of a MESFET: the MESFET channel must be doped to have current, and the electrons scatter off the dopant ions. In the thin layer of electons in the a HEMT, there are no ions to scatter off, so the electrons can gain very high velocities , i.e. their mobility is very high. This is somewhat of a subtle point: initially it was thought that the excellent properties of HEMTs are due to the high mobility of electrons (thus the initial name), but later it became clear that it is in fact the average high electron velocity that enables high frequency operation with superior noise figure.

Fig.L3.4. Sketch of the cross-section of a HEMT device, with approximate dimensions of the different layers grown by MBE. From Fig.L3.4 one can see that the layers of different semiconductors are extremely thin. Technology was not mature enough to enable such material structures until Molecular Beam Epitaxy (MBE) was invented in Bell Labs in the 1970’s. The problems in growing such structures are associated with lattice mismatches between different semiconductor crystals. The first heterostructures were grown to investigate optical spectroscopy by a physicist from Bell Labs, R. Dingle. He wrote: “...since multiple layers could be readily grown, we simply grew a multilayer AlGaAs/GaAs structure containing 10 or 20 layers interleaved with AlGaAs support layers. The growth technique was described as “semi-automatic” and consisted of watching the second had of a darkroom timer and manually rotating a shutter on the aliminum effusion oven of the MBE system it initiate and terminate AlGaAs layer growth. In early 1974 a multilayer structure with 200 A- thick GaAs layers and thicker AlGaAs support layers was gown. With the help of Len Kopf, we measured the absorption spectrum at 2K and observed the first direct evidence for size quantization of electron motion in GaAs. There was great jubilation in my lab – we even danced a bit, as I recall! I began to believe in quantum mechanics!” What was in effect observed was electron motion in the 2-D electron gas. A mobility of 10,000-20,000cm2/Vs was first measured at low temperatures, while the common bulk GaAs mobility was 6,000cm2/Vs. Eventually, as high as 2,000,000 was obtained at low temperature and 8,500-9,000cm2/Vs at room temperature.

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When one looks through FET device specifications, one often runs into the acronym PHEMT. The “P” stands for “pseudomorfic” and what it means is that, in order to improve the performance of a HEMT, the two-dimensional electron gas is confined to a thin layer of InGaAs instead of GaAs. This allows for even higher sheet charge density of the 2-D electron gas, and therefore higher transconductance. The cross-section of a typical PHEMT, along with a SEM photo of the 0.15µm T-gate structure is given in Fig.L3.5.

(a) (b) Fig.L3.5. (a) Cross-section of a typical PHEMT, and (b) SEM photo of the 0.15µm T-gate metal on top of a HEMT channel.

L3.2. HETEROJUNCTION BIPOLAR TRANSISTORS (HBTS) The high-frequency equivalent circuit is the same for a MESFET and HEMT, and from the circuit designer’s point of view, the two devices differ only in maximum attainable gain, frequency and the lower noise figure (we will discuss noise later). A very different device, based also on hetero-structure growth, is the Hetero-junction Bipolar Transistor (HBT), which is gaining increase use at microwave frequencies for both analog and digital applications. A cross-section of a HBT is shown in Fig.L3.6, along with an approximate high-frequency circuit model usually extracted from measured s-parameters.

(a) (b)

Fig.L3.6. (a) Cross-section of a typical HBT device, and (b) approximate high-frequency equivalent circuit.

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The HBT was first proposed by Herb Kreomer (who was a professor in our department at CU-Boulder and later won the Nobel Prize) in 1957. He realized the following fact about bipolar devices. If a high-bandgap emitter and low-bandgap base materials are used for an npn device, injection of electrons into the base is favored, while reducing hole injection into the emitter. This advantage can be maintained even when the base is heavily doped (for low base resistance) and the emitter lightly doped (low capacitance). In a HBT, the n-type emitter is formed in the wide band-gap AlGaAs while the p-type base is formed in the lower band-gap GaAs. A SEM photo of a HBT is shown in Fig.L3.7, as well as a photo of a small HBT MMIC circuit.

(a) (b)

Fig.L3.7. (a) SEM photo of a HBT device and (b) a HBT MMIC. Recently, there have been huge advances in silicon bipolar devices, bringing their operating frequencies well into the GHz range. However, some advantages of HBTs over silicon bipolar devices remain:

- due to the wide-band-gap emitter, much higher doping in the base can be used, resulting in low base resistance (lower R in the RC time constant, higher powers possible);

- emitter doping can be lowered, reducing base-emitter capacitance (lower C in the RC time constant);

- high electron mobility, built-in drift fields, and velocity overshoot combine to reduce electron transit time;

- semi-insulating substrate reduces pad parasitics and allows easy integration. Advantages of HBTs over FETs can be summarized as follows:

- the HBT is a vertical device, so the electron transit time is governed by epitaxial growth, not by lithography. This allows high Tf with modest processing requirements;

- the entire emitter area conducts current, leading to high current handling capabilities and increased mg ;

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- the control region of the device (which is the base-emitter junction) is well shielded from the output voltage, leading to low output conductance (high output resistance). Since the voltage gain is given by /V m outA g g= , very large values of gain can be obtained;

- the breakdown voltage is directly controllable by the epitaxial growth; - the threshold voltage for output current flow is determined by the built-in potential of the

base-emitter junction. This leads to highly uniform (well-matched) characteristics for devices on a single wafer;

- the device is shielded from traps (imperfections) in the bulk and surface regions, which contributes to low 1/ f noise, good for oscillator applications.

Finally, a useful summary of the small-signal figures of merit for microwave transistors in terms of MESFET, HEMT and HBT relative characteristics is given below:

- the cutoff frequency Tf is lowest for MESFETs and highest for HBTs – HBTs have highest speed (useful for digital applications);

- the maximum frequency of operation maxf is highest for a HEMT, and lowest for a HBT. HEMTs are most useful for high-frequency operation;

- the gain-bandwidth product is high for HEMTs and HBTs. The HEMT is used for wideband applications at high frequencies;

- the noise figure NF is lowest for HEMTs, and highest for HBTs. HEMTs are used in all transistor low-noise amplifiers (LNAs) today;

- the phase noise is lowest for HBTs, and highest for HEMTs. HBTs should be used for low-noise and voltage controlled oscillators VCOs;

- the voltage gain /V m outA g g= is highest for HBTs and lowest for MESFETs. HBTs are best for highly linear amplifiers;

- the linearity for (nonlinear) power amplifiers measured by the third order intercept IP3 is best for a HBT at low frequencies and for a MESFET at high frequencies;

- the best uniformity of devices is for HBTs, so they are best for LSI; - the large signal efficiency (drain or collector) is best for HBTs, but is also good for

HEMTs. It is not still clear what device is the best; - the power density is best for HBTs and MESFETs. HBTs could potentially be the best

power devices, but it is still not clear. New III-V material devices, such as GaN and SiC are now increasingly used for high-power and high-temperature applications. The GaN devices have been shown to work into the millimeter-wave range, with impressive power levels in the lower microwave range (currently 120W from one device around 2GHz is commercially available). They can be grown on Si as well as SiC substrates, the former being inexpensive, while the advantages of the latter is excellent thermal conductivity and handling. Major advantages of these devices are high breakdown voltage, translating into high available power levels, and relatively high input and output impedances, which in turn means higher gain and broader bandwidth. In fact, you will use a Qorvo (TriQuint) GaN device for several of your projects.

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Other current device technologies:

• A variety of MOSFET devices in Si are used in many applications, ranging from greater than 200W output power 2-GHz LDMOS devices in cellular base-stations, to complementary CMOS in RFICs. The latter are becoming a very large part of the industry due to the low cost of Si as a substrate, and well-established Si technology. The table below shows an overview of CMOS technology scaling for operation at microwave frequencies. Roughly, a new technology “node” (related gate size) was introduced every 2 years: the device area was halved in every new node technology, i.e. a reduction of 0.7x in both gate length and width. Note that the physical gate size is much smaller than the lithography node. Also, there has been a significant increase in Ion with the introduction of strained silicon and a thin epitaxial layer of SiGe increases electron/hole mobility. A big reduction of equivalent oxide thickness was a result of new high-permittivity and glass dielectrics.

• Bipolar devices (BJTs) are also used in RFICs in both Si and SiGe. An important advantage of these devices is very low 1/f noise, making them the best candidate for low phase noise (clean) oscillators.

Other things we talked about in class: The carrier mobility is a different way of looking at an I-V curve. I is the integral through a surface of the current density vector J, and J=Nev. The voltage is the integral of the electric field over some distance (e.g gate length), so plotting I vs. V is really the same qualitatively as plotting the carrier velocity vs. the electric field:

|||| Ev

VGI µ=

⋅=

where µ is the mobility with a unit of m2/Vs, usually quoted in cm2/Vs. From the above, you can find mobility or doping (charge concentration) if you measure conductivity. This in turn can be done with a 4-point probe with fine tips. The tips need to be fine in order to break the reverse Schottky diode.

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