Microwave Semiconductor Devices || MESFET Devices

Chapter 10

MESFET DEVICES

By 1971, breakthroughs had been made in the development of field-effect transistors. Today, GaA8 metal .remiconductor field-effect transistors (MESFETs) have higher gain, higher power-amplification efficiency, and lower noise figure than bipolar transistors above 4 GHz. More significant is the fact that FETs promise a great deal of potential for further advances. (Quoted from LlECHTI, C.A., "Microwave Field-Effect Transistors -1976," IEEE TI-an.t. Microw. Theory Tech., MTT-24, 279, @1976 IEEE.)

INTRODUCTION

This chapter starts our treatment of three-terminal (as opposed to twoterminal) devices. At the time when this is written, three-terminal devices, especially GaAB MESFETs, have become the dominant solid-state microwave devices. There are several reasons which might be cited to explain this fact:

* Three-terminal devices such as MESFETs are unipolar, i.e. they use only one type of carrier. This makes optimization easier than if two types of carriers have to be considered.

* Most of the materials used in three-terminal devices, such as GaA8, InP, etc. have high mobility compared with silicon.

* A large variety of forms and applications are possible

* Monolithic integration of devices on a semi-insulating substrate is easier to accomplish than for two-terminal devices

* The availability of three terminals means that uni-directional amplification is possible, and circulators are not usually needed

A partial list of the type of applications which have been implemented contains amplifiers (low-noise and power-), limiters, harmonic frequency multipliers, mixers, phase-shifters and oscillators.

The present-day microwave three-terminal devices of course have as their ancestor the bipolar transistor which was invented in the late 1940's. It took a long time before transistors were fast enough to be useful at microwave frequencies, however. Not until 1965 did germanium bipolar transistors start to be employed at L-band (1 - 2 GHz). The idea of a field-effect transistor goes back to Shockley (1952), but took even longer to realize for microwave frequencies. Early field-effect transistors had cut-off frequencies which were inferior to those ofbipolars. For example, the first microwave FET using GaA,

S. Yngvesson, Microwave Semiconductor Devices© Kluwer Academic Publishers 1991

298 Microwave Semiconductor Device&

was reported on in 1968, and had a maximum oscillation frequency (/m .... )*= 3 GHz, but already in 1970, Drangeid et al. (1970) had developed a GaAs FET with 1m .... = 30 GHz, which far surpassed the performance of silicon bipolar devices. Since that time, oscillation has been observed above 100 GHz, and noise figures of GaAs FETs have been shown to be superior at essentially all microwave frequencies. It is now mainly the HFET, a development of the 1980's, which can compete in terms of noise figure. HFETs will be described in the next chapter.

The physical outline and structure of a typical MESFET is shown in Figure 10.1. Note the convention for labeling the gate "length" (the smallest dimension) and the gate "width". A scanning electron microscope picture of a device is displayed in Figure 10.2.

I-V-CHARACTERISTICS OF MESFETs

Long-Channel (Shockley) Models/Constant Mobility

Typical I-V -characteristics for a microwave MESFET are shown in Figure 10.3. Microwave devices are almost universally biased in the "saturation" region. The basic operation of the MESFET is as follows:

At zero applied gate voltage, there is a depletion region next to the gate, due to the built-in (barrier) voltage in the Schottky barrier. The width of the depletion region can be found from the standard semiconductor theory ((1.27) for example, while noting that the "highly-doped" side in this case is the metal, which contributes essentially zero to the width of the depletion layer). The analysis is parallel to that of JFETs, except that the geometry of a MESFET is equivalent to one half of that of a JFET, see Figure 10.4. We use a notation similar to that of Sze (1981). The width of the depletion region is

y(z) = J2f,[V(Z) + VG + fj)l/eND (10.1)

Here, V(z) is the potential at point z in the channel, VG is the applied gate voltage (with respect to the source),t and.p is the barrier potential, while ND is the doping (n- type). The channel potential V(z) varies from zero at the source to the drain voltage at the drain. Consequently, the depletion region widths at the respective ends are:

(10.2)

and (10.3)

* 1m .... is defined later on in this chapter. t VG is negative, but the magnitude of VG is used throughout this section.

Chapter 10 299

a Cross Section

Voo

Semi-insulating GaAs

b TopView

Gate "Width'

Figure 10,1. Typical,tructure of a MESFET. (a) Crou·,ection. (b) Top view.

The pinch-off voltage, Vp , is defined as the total voltage at OIl = Lg for which Y2 = a, i.e. when the depletion region fills the entire channel at the drain end:

(10.4)

We assume a constant mobility, so that the current density at a point OIl

in the channel is given by:

(10.4)

The total current can be expressed as follows:

ID = eNDJ.' (~:) (a - y)Z; (10.5)

300 Microwave Semiconductor Devices

Figure 10.2. A millimeter wave MESFET. (a) Layout. The gate width is 50 pm and the gate length 0.1 pm. (b) Scanning electron microscope picture of the active region. From MIDFORD, T.A. (1990). "FETs: Low-Noise Applications," in Handbook of Microwave and Optical Components, K. Chang, Editor, John Wiley & Sons, New York, Vol. 2, Ch. 11, p. 550.

<[ 80 E

~ 70 VGs.;.°---z ..... '" ..-

'" a: 60 ..-a: .- VGS= -.!lV ::l .-u 50 " '" u a: 4 ::l VGS·-IV 0 en I z

VGS' -1.!lV

" a: 0

.5 1.5 2 2.5 DRAIN - SOURCE VOLTAGE (V)

Figure 10.3. Typical 1- V-characteristics for a microwave MESFET, at low VDS. The solid linea are a beat fit to ezperimental data, uaing an ezpression due to Curtice, later quoted as (10.23). The dotted linea are a fit with the JFET model of the SPICE 11 CAD program. From CURTICE, W. R. (1988). "GaAs MESFET Modeling and Nonlinear CAD," IEEE Trana. Microw. Theory Tech., MTT-36, 220, @1988 IEEE.

Chapter 10

Source

n-Type

Semi-insulating Substrate

x

301

Figure 10.4. Geometry of the MESFET in a per'pective view. Adapted from SZE, S.M. (1985). "Semiconductor Devices: Physic, and Technology," John Wiley & Sons, New York, with permis,ion.

Z is the width of the device, see Fig. lOA.

We can find the differential dV expressed in terms of dy from (10.1):

dV = eND ydy (10.6) E.

This enables us to find an expression for ID in terms of Y1 and Y2, by integrating the left side of (10.5)* from z = 0 to z = L, (note that the total current is continuous), and using (10.6) for the right side, which is then integrated from Y1 to Y2:

1 ill. eND ID = L Zp.eND(a - y)--ydy

II 'Ill €,

= D -(Y~ - yn - -M - tAl Z p.e2 N 2 a3 [3 2 ] 6€.L, a 2 a3

We introduce the following convenient variables and constants

Ip = Zp.e2 Ni>a3 /6€.L, 11. = y/a = [(V(z) + VG + </»/Vpj1/2;

Eq. (10.7) now becomes:

Ul = If; 'U2 = ~;

ID = Ip[3(u~ - un - 2(u~ - u~)l

* Move dz to the left side!

(10.7)

(10.8)

(10.9)


The saturation current, 1D ,al, is obtained when the channel is pinched off, or Y2 = a, i.e. 11,2 = 1:

2 3 VG,+c/J VG +c/J [ ( ) ( )3/2] 1D ,al = 1,(1 - 311,1 + 2ud = 1, 1 - 3 ~ + 2 ~ (10.10)

As the drain voltage is increased beyond that corresponding to pinch-off, the current will still continue to flow, while a section of the channel is pinched off, and we assume that the current from this point on remains at the value right at the pinch-off point. Beyond the pinch-off point, the current flows through a depletion region, and not through a channel full of carriers. This depletion region is of relatively short length compared with the total length of the channel in long-gate FETs, and under these conditions the magnitude of the current is still determined by a channel of about the same length and shape. The development of the pinch-off condition is illustrated in Figure 10.5. The expression in (10.10) now describes the characteristic curves in Figure 10.3. We can also derive the transconductance defined by

aID 2Zp.eND eNDap.Z gm == 8VG == Lg (Y2 - Yd;gma~ == Lg (10.11)

With typical scaling laws for long-gate MESFETs, L/a is kept constant, while ND is increased, as L is made shorter. This results in an increase in gm for shorter gate lengths. For gate lengths of the order of 1 micrometer, gm increases much more slowly with decreasing gate length, as we will discuss below.

In the saturation condition:

gm == gmu(1 - 11,1) == gmae (1 - JVGv.+, c/J) (10.lla)

While useful for long-gate (greater than 1 micrometer) FETs, this expression does not agree well with experimental characteristics for short-channel MESFETs, which to-day may have channels as short as 0.1 - 0.2 micrometers. In such devices, the electric fields reach magnitudes of at least 20 kV /cm, and we know from the study ofGUNN devices (Chapter 2) that a constant mobility is certainly not obtained at such high fields.

I· V· Characteristics /Steady· State Velocity Curve

Next, we will use the steady-state velocity curve for GaAs, replotted in Figure 10.6, in order to discuss conditions in the MESFET channel. Figure 10.7 shows the predicted variation of electric field, drift velocity and electric charge in the channel, versus z. The electric field is highest in the narrowest section of the channel close to the drain (see (10.6)). The velocity will first increase, as z increases, in response to the increasing electric field, but later v will decrease as the critical field is passed. The velocity will then go through

Chapter 10 303

I :~-po

~ O<pietlon r<t,on .~

p"

(a)

(e)

(d)

(e)

I ::--==~lit I L I

(f)

Figure 10.5. Development of the channel in a FET, a8 VDS increa8e8 (8hown for a JFET). (a) VDS = VGS = 0 (b) Small VDS (c) Voltage dutribution in the channel for VDS = 5 V (d) moderate VDS (e) Larger VDS = VDS•at -

pinch-off (f) VDS > VDS•at • Reprintedfrom PIERRET, R. F. (1983). "Field Effect Device8," in Modular Serie8 on Solid State Device8, R.F. Pierret and G. W. Neudeck, Editor8, Volume IV, @1990 b" Addi8on- We8le" Publ. Co.


3,-------------------------------------,

~2 <.> ... g >f-g, --1 W >

T=300K

OL---~~--~~--~1~5----~2~O----~2~5~---3~O~--~35

E (kV/cm)

Figure 10.6. Measured velocity-field characteristics for GaAs and InP. Reprinted from SZE, S.M. (1985). "Semiconductor Devices, Physics and Technology," John Wiley £j Sons, New York, with permission.

one more peak, as shown in the figure. As a result, the charge distribution must have an accumulation layer (when the electrons slow down), in order for current continuity to be satisfied, and a corresponding depletion layer, when the electrons again increase their speed. The "dipole" layer thus formed is similar to a high-field domain in a GUNN device, with two differences: (i) the dipole layer is stationary, and (ii) the depletion layer is not completely depleted (a fairly large current flows). Recently, direct evidence was obtained for the existence of this dipole layer and several papers discuss this phenomenon (Engelmann and Liechti, 1977; Shur and Eastman, 1978; Fjeldly, 1986). A common criterion for the creation of a stationary G UNN domain near the anode in GUNN devices was quoted in (2.31). Traveling GUNN domains are formed if ND xL> 1012. The corresponding criterion was derived for the MESFET case by Zhou and Pulfrey (1989). The ND x L product corresponding to the condition (2.31) is equal to 1 x 1012 at a gatelength of about 0.3 micrometers: The critical N D x L product for MESFETs grows rapidly for shorter gates, while decreasing for longer gates, see Figure 10.8. A stationary GUNN domain affects the C-V-characteristic for the drain-to-gate capacitance (Shur, 1987).

The model we now have arrived at is considerably more complicated than the constant-mobility model. Another important feature which is still neglected is that the actual velocity of the electrons under the gate is to some

Chapter 10

a Z , a

Z

5

zo

305

loS/w

(mAI .... l~ 200

. ~ ~."' o 2 •

VDS (Vi

ELECTRIC FIELD

aECTRON DRIFT VELDCtTY

SPACE CHARGE IN CHANNEL

Figure 10.7. Channel croIB-section, di.tribution of electric field, drift velocity, and charge denllity in the channel, for a MESFET in the lIaturated current region. Reprinted from LIECHTI, C.A. (1976). "Microwave FieldEffect 7ran.i.tor. - 1976," IEEE 7ran •. Microw. Theory Tech., MTT-!,4, !79, @1976 IEEE.

extent determined by transient phenomena, i.e. the steady state v IE - curve which we used for GUNN devices is not applicable to short gate MESFETs. No simple model has been developed to take all these phenomena into account, however. Instead, we shall next discuss the two-region model of Statz, Haus and Pucel (Statz et al., 1974; Pucel et al., 1975, 1976).

306

N , E -"

c

~E o

z

Microwave Semiconductor Devices

..

10" '--____ ~,-____ c'::-____ ~_::_----_=':-o 0.5 1.0 1.5 2.0

L if'm)

Figure 10.S. Calculated critical doping denlity-gate length product for Itationary domain formation in a MESFET. Data from devices for which domain formation hal been claimed are shown as lolid symbob (ezperimental) and open symbols (theoretical). Reprinted from ZHOU, H., and PULFREY, D.L. (1989). "A Criterion for Stationary Domain Formation in GaA. MESFETIJ," IEEE Trans. Electron Devices, ED-36, 872, @1989 IEEE.

The Two-Region Model

The MESFET model introduced by Statz, Haus and Pucel (Statz et al., 1974; Pucel et al., 1975, 1976) takes note of the fact that there is both an unsaturated, and a saturated portion of the channel. In what follows, we shall refer to it as the PHS model. In the unsaturated part we can use the previously presented theory with a constant mobility, while the saturated region is treated by assuming a constant velocity. Because of the velocity-saturation, complete pinch-off does not occur. Instead, we assume a constant width of the saturated channel, so that current conservation will be obeyed. The break-point at which velocity saturation occurs is allowed to adjust itself to changing bias conditions by matching the total currents in the two regions. The geometry and velocity versus z are defined in Figure 10.9 A and B.

The current in region I can be found by applying (10.9):

(10.12)

with

Chapter 10

a

S

Substrate y

,....-1---------11 11--------------' vos

b

E~ctric field

307

Figure 10.9. nlu8tration6 related to the PHS model: (a) Geometry of a MESFET (b) Simplified velocity ver8UI electric field relatiomhip (c) Electric field ver6UB z. Adapted /rom STATZ, H., HA US, H.A., and PUCEL, R.A. (1974). "Noile Characteristic8 of Gallium Ar6enide Field-Effect Trami8tor8," IEEE Tram. Electron Device", ED-£l, 549, @1974 IEEE.


(10.13)

In region II, the saturated velocity is Vi = ItE,,,t, and the current is

ID = eNDv,(a - y<)Z = 1,(1-1/.<); (I, == eNDv,aZ) (10.14)

Setting (10.12) equal to (10.14), we find L1 :

L - L (1/.~-1/.n-2/3(1/.~-1/.~) l-Zg 1-1/.. (10.15)

The parameter Z = Vp / E,,,t X L, (note that PHS use e ~). This so-called saturation parameter attains larger values in cases for which the saturation is more important in determining the geometry of the channel. The parameter Z may vary from 2 to several times 10 for microwave MESFETs (short channel length, small a and large ND all increase z).

Beyond the saturation point, the electric field continues to rise (see Fig. 10.9.C) and integrates to the correct drain voltage. Since the field increases, the velocity will stay saturated. The potential V(I) at z = Ll can be obtained by integrating (10.6). In region II, the potential will be V(I) plus a contribution, V(II), due to the free charges on the drain electrode, which we assume is located at the drain end of the channel, and at y = a (note that the saturated channel is very thin, and can be assumed to be at y = a). A series-expansion of this potential was first suggested by Shockley (1952). It was used by Grebene and Ghandhi (1969), and adopted by PHS. This expansion is given by*:

V(z, y) = ~ An sin [(2n + 1) ;:] sinh [(2n + 1) lr(z ~ Ll)] (10.16)

The above solution vanishes at the boundary plane, z = L 1 , as well as on the gate electrode (y = 0). Following the earlier references, PHS found it sufficient to use the first term in this expansion (higher order exponentials in the z-direction obviously vary much too fast). A solution which makes the longitudinal electric field at z = Ll equal to the saturation field, E,a!, is the following:

( ) 2aE . lry • h lrZ V Z, Y = - - ,at sm - SIn -2

11' 2a a (10.17)

To the above potential, we must add the z-independent potential produced by the ionized impurities in the depletion region, which can be obtained from Poisson's equation. A satisfactory solution is the constant potential V(I) = Vp (1/.~ - un inside the saturated channel, with a parabolic variation in the depletion region. We only require the potential for y = a, actually, as remarked

* As mentioned earlier, PHS assume a symmetric FET (like a JFET), with y = 0 in the center. We have changed the definition of y = 0 to be at the gate electrode, and also assume an asymmetric, MESFET-like, structure.

Chapter 10 309

earlier, and then find the potential at the drain, i.e. the drain-to-source voltage, as follows:

VDS = V(I) + VeIl) = Vp { (u,~ - u'n + ~ z~ sim. [1I'(L'2: L1)]} (10.18)

Curves of(I-u,1) and (1-u,c) for typical devices are shown in Figure 10.10. (The parameters for the PHS l~m device are L,/a = 2.86 and z = 19.57, see Problem 1.) These curves show that the channel opening at the source and at the drain are quite similar. Figure 10.11 shows the fraction of the channel length represented by Region I (Ll! Lg ). Problem 1 explores these calculations further.

The drain current calculated by PHS for a 1.0 micron gate length device is shown in Figure 10.12. Other parameters used were ~ = 4,500cm2 /Vsec and E.at = 2.9kV /cm, resulting in v. = ~E.at = 1.3 x 107cm/sec. The agreement with experimental data is remarkably good, considering the fact that phenomena such as the dipole layer and over-shoot velocities have been neglected completely. Figure 10.13 also shows the calculated transconductance and source-to-gate capacitance for the same device. The expression for the transconductance is quite complicated:t (see Goronkin et al., 1985)

I. (1 - u,t) cosh ( "(L~~Ll») - (1 - u,c) 9= = -- x .[-------------,~~----~~~~-----------

Vp 2u,c(1 - 'Uc) + ~ (p.-)] cosh .. (L~~L,) - 2u,c(1 - 'Uc) (10.19)

Further calculations of 9= for 1 micron gate devices are quoted from Goronkin et al. (1985), in Figure 10.14, together with measured data for a number of devices. The highest 9= is obtained for the largest values of the doping channel depth product (ND X a). The measured data show the right general trend.

In concluding this section, we may note that agreement between measured and calculated I-V-characteristics is reasonably easy to obtain, in the sense that it is unnecessary to model completely the physics of the device. Apparently the crucial factor to include is the saturation of the drift velocity in most of the channel. It is also easy to find simple analytical expressions for the I-V-curves, which can be utilized in CAD programs. One such expression is discussed by Shur (1987). From (10.14), we can derive the following expression by normalizing the saturation current with respect to 9max x Vp, and assuming that the entire channel is saturated (so that u'c = U,1):

1 1 1 [ J~+VG] Is = -[1- U,1] ~ - 1- --z z Vp

(10.20)

t Note that the variables 8, p and d used by PHS are related to the ones

[ ]1/2

used here as: U,1 == 8; 'Uc == p; d == vo+t;-Vps ;

310 Microwave Semiconductor Devices 100 -~-I--'----'-----'--'--'· iii

.. z

8 !!; J

~ Z ~ 10-1 :< u

~ ... :I ~ z

10·' 10'

/jOHMALlZfO CUllHENT. 10/1.

Figure 10.10. The dependence of the normalized channel opening at the ,ource (1 - 1£1), and at the boundary between Regions I and II (1 - 1£.), as a function of normalized drain current. Curve (1) is 1 - 1£.; Curves (2)-(.1) are 1-1£1; (2) z = 19.57, Lg/a = 2.86, (3)z = 19.57, Lg/a = 10, (4) z = 10, Lg/a = 10. For all curves Vp = 5.65 and VDD = 4 V, with parameters given in the table for Problem 1. A typical device has ID/Is = 0.5 or less.

<II ..J .... ... ..J

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0 0.2 0.-4 0.6

VOO/VP 0.8

Figure 10.11. Normalized length of region I (LdLg), as a function of VDD /Vp . The parameter value. are the ,ame a. in the table in Problem 1. (1) ID = 74 rnA; (2) ID = 10 rnA.

Chapter 10 311

110

Unit 70632H I L,~O V\lQ=OV

100 L::: l~m

;:; Nd =6.5XlQ16 cm

~ 8 -IV

.:: c ~ -2V 0 u

c -3V '0 0

-4V

4 Drain vOltage VOd(volts)

Figure 10.12. Compari60n between the theoretical and measured drain current voltage characteristic for an X-band MESFET. Reproduced from PUCEL, R.A., MASSE', D.J., and KRUMM, C.F. (1976). "Noise Performance of Gallium Arsenide Field-Effect Transistors, II IEEE J. Solid-State Circuits, SC-11, £43, @1976 IEEE.

32

UNIT 706~2-H

28

2 E "-~ 2_ 0.

., j ~

g 20

°1 51

i 16

~ ~ 0._ ~

~ . /c .. - ~ E 0.3 ..

0.2

0 -1 -2 -3 -4

Gale - source bios volfaoe V,II (V)

Figure 10.13. Comparison between the theoretical and measured values of the gate-source capacitance C,g, and terminal transconductance g ... ,., for an X-band MESFET device. Reprinted from PUCEL, R.A., MASSE', D.J., and KRUMM, C.F. (1976). "Noise Performance of Gallium Arsenide FieldEflect Transistors, II IEEE J. Solid-State Circuit., SC-11, £.3, @1976 IEEE.


200

+

2.0

100 + + -++.

+

w -.

Figure 10.14. Curves of constant N D X a overlaid on measured data of grn for 1 I'm MESFETs. Reprinted from GORONKIN H., GRONDIN, R.O., and FERRY, D.K. (1985). "Low-Noise GaAs Microwave MESFETs,!! in Gallium Arsenide Technology (David K. Ferry, Editor), Sama: A Division of Macmillan Camp. Publ., Vol. I, Ch. 5, p. 155, with permission.

Shur (1987) uses a = l/z, and shows that (10.20) can be interpolated with a simple formula:

11 = _a_ (1 _ ¢ + VG) 2

5 1 + 3a Vp (10.21)

This formula is structurally identical to one used for JFETs in the CAD program SPICE (with VT == Vp - ¢):

Is = ,8(VG - VT)2 (10.22)

MESFETs with low pinch-off voltages « 2 volts) have been successfully modeled using this expression. For devices with larger Vp , Statz (1987) has proposed the following alternative expression:

Is = ,8(VG - VT )2 1 + b(VG - VT )

(10.22a)

In order to model the I-V-curves outside the saturation region, one may use an expression due to Curtice (1981):

IDS = Is x (1 + ,\ VDS) tanh(a VDS) (10.23)

A critical comparison of MESFET CAD models is given by Hu et al. (1990).

Chapter 10 313

@ r------------------, t INTRINSIC MODEL : I I

Gal< RQ: CdQ :

~ i Rd Drain

: R~: : Rj :

I I I

Source ids" Ym Vc Source

Ym= 9me- 11OI 1'o

Figure 10.15. (a) The equivalent circuit 0/ a MESFET (b) Ph1l.icallocation o/the element. in (a). Reprinted from LIECHTI, C.A. (1976). "Microwave Field-Effect Tran.i.torll - 1976," IEEE Trans. Microw. Theory Tech., MTT-1.4, 179, @1976 IEEE.

SMALL-SIGNAL EQUIVALENT CIRCUIT MODEL

The small-signal equivalent circuit of a MESFET is shown in Figure 10.15 (Liechti, 1976). This model is quite similar to other well-known models of FETs. Measured values for the elements in a circuit model must be obtained by first measuring the small-signal S-parameters ofthe device, and then fitting these to agree with the equivalent circuit model. It is beyond the scope of this book to describe this procedure in detail, and we refer to for example (Gonzales, 1984; Fu et al., 1990) instead. Commercial microwave CAD packages usually include options for this procedure. If the device is placed in a micros trip fixture one must calculate the intrinsic FET parameters by a deembedding technique,

314 Microwave Semiconductor Device6

and considerable errors may result. Recently introduced microprobes contact the device directly on its "chip" and allow determination of the equivalent circuit parameters with greater accuracy (Fu et al., 1990).

It is important to note that DC-measurements of especially Rd., but also 9m, often give results which are very noticeably different from measurements at microwave frequencies. Frequency-dispersion of these parameters is observed in the frequency-range of Hz-kHz, and has been correlated with traps, either at the surface, or at the buffer-layer/active layer interface (Golio et al., 1990; also see references given in this paper). One thus must be quite careful in using DC data, instead of S-parameter data, for some of the parameters. We comment below on some of the elements:

* 9m - Note the frequency dispersion of 9m discussed in the previous paragraph. Since the drain current is delayed by a time = the transit-time, with respect to the gate voltage, we must also use a phase-factor, exp( -jW7lJ), to take this into account (not included in the PHS model).

We also must distinguish the external 9m •• (measured from the terminals) from the intrinsic value, 9m.o. These are related as follows:

(10.24)

* Cdg and C g, are capacitances from the gate to the channel (source end and drain end, respectively). We of course can not exactly pin-point the channel location of the lower capacitance electrode, but the success of the equivalent circuit model depends on the extent to which measured Sparameter data can be fitted to the predictions based on the model. Cdc also ends at the source end of the channel. The electric field lines in Cd, are primarily routed through the semi-insulating substrate.

* Other series resistances Rs, Rd connect the "actual channel" with the source and drain contacts,respectively. Also, the gate fingers have a resistance, Rg •

* Rd, is the actual channel resistance

* We often need to take into account lead inductance6 for all three terminals

Some typical values for MESFETs with different gate lengths are given in Table 10.1. Two HFETs have been included for comparison (HFETs will be described in Chapter 11).

Cut-Off Frequencies

Several different cut-off frequencies can be defined on the basis of the equivalent circuit model.

Chapter 10 315

Table 10.1

Data for some representative MESFETs and HFETs (@IEEE)

1JLm 0.25JLm 0.25J,tm 0.25J,tm MESFET MESFET CONV.HFET InP-Based HFET (Liechti, (Heinrich, (Fu et aI., (Fu et aI.,

1976) 1989) 1990) 1990)

L, 1J,tm 0.25JLm 0.25J,tm 0.25J,tm Z 500JLm 300J,tm 150J,tm 50J,tm

Intrinsic Elements

To 5.0 psec 1.9 psec 1.7 psec -C" 0.62 pF 0.22 pF 0.171 pF 0.055 pF Cd, 0.014 pF 0.016 pF 0.036 pF 0.013 pF Cdc 0.02 pF 0.04 pF ~ 2.60 10 Rd, 4000 150 0 grn 53 mmho 63 mmho 99.8 mmho 49.9 mmho

Extrinsic Elements

Cd, 0.12 pF Rg 2.90 2.90/35JLm 0.90 1.20 Rd 30 3.6 0 7.00 R, 2.0 0 3.70 6.4 0 L 0.06 nH 0.3-0.4 nH ~0.3 nH

C" ... 1 0.Q16 pF DC Bias

VDS 6V 2.0 V 1.0 V VGS OV -0.3 V -0.2V IDS 70mA 25 mA 6.1 rnA

IT is the frequency for which the 6hort-circuit current gain of the MESFET is down to one. This parameter is often used, although microwave transistors are almost never measured with a short-circuited load (they may often oscillate under such conditions). We can derive a simple relationship for IT by assuming a simplified equivalent circuit, which includes only C" and gm, as shown in Figure 10.16.

The input current for this circuit is

IrN ~ V" X jwC" (10.25)

The magnitude of the output current is

IIoul1 ~ iDS ~ gm Vg, (10.26)


: ~g, 1 T

Figure 10.16. Simplified equivalent circuit 01 a MESFET.

If the ratio of the output and the input currents is set to 1.0, we obtain:

\ lout \ 9m lin = 1 => W == WT = C,. (10.27)

or

(10.28)

The two most important parameters for the high-frequency performance therefore are expected to be 9m and Cg.i large 9m and small C g• result in a high cut-off-frequency. A typical procedure used to find IT is to derive the short-circuit gain (h21) from the measured S-parameters, and extrapolate this curve to h21 = 0 dB. The actual frequency-dependence of the current gain may often be more complicated than that indicated by the simplified model used above, which results in a "canonical" 6 dB per octave (one-pole) response.

A somewhat more realistic parameter is the "maximum frequency of oscillation", lu or Im"~. It is the maximum frequency for which a negative resistance can be produced by the device and is given by (Liechti, 1976):

(10.29)

where

(10.29a)

The unilateral gain of a MESFET versus frequency can be approximately expressed as (Mason, 1954):

(10.30)

In this approximation, Gu = 1 at I = Im"~'

Chapter 10 317

Another useful quantity is the maximum available gain (MAG), which is found from the equivalent circuit (Figure 10.15) (e.g. DiLorenzo and Wisseman, 1979):

1 x .--.~-----------------------------------------------

(R~.) (Rg + ~ + Rs + 7rITLs) + 47rITCdg(2Rg + ~ + Rs + 27rITLs) (10.31)

MAG becomes 1 at I ~ Ima2' The MAG can be realized provided that the device is stable at the operating point in question, which is not always the case. Standard S-parameter criteria can be used to test the stability (Gonzales, 1984). Equation (10.31) also shows the importance of a high value for Rd. -the inverse of the slope of the IDs/VDs characteristic curves. Some devices have lower values of Rd. due to various leakage phenomena, which results in a VDs-dependence of the saturated current. It is important to try to eliminate these effects, since a smaller Rd. lowers MAG.

For the parameter values given in the first column of Table 10.1 we calculate that IT = 14 GHz, and Ima2 = 46 GHz. Data of the measured gain for a recent GE 0.25 micrometer MESFET are given in Figure 10.17. They are extrapolated to Imu = 160 GHz.

In order to obtain a high Ima2' we must maximize IT as well as the ratio of channel resistance to (R, + ~ + Rs ), and minimize Cd,. We will discuss the effect of decreasing gate-length below in connection with the transit time of the device. We should note that in decreasing L" we need to also decrease 'a', the channel depth, in order to maintain the geometry which yields high grn' In decreasing 'a', we also must increase the doping in the channel, since otherwise the channel resistance becomes too high. The limit to how much the doping can be increased is set to about 5 x 1017 cm- 3 by avalanche break-down in the drain-gate region, which has the highest fields.

A method for reducing the series resistance in the source connection, Rs, which is often used, is to "recess" the gate, as shown in Figure 10.18. A normal (non-recessed) structure is shown in A of that figure. Note that the depletion region stretches all the way to the source, along the surface, which results in diminished channel height in this region, and thus higher Rs. In B, the gate region has been etched, and also a highly doped epitaxial layer has been added under the source and drain contacts. The advantage with the recessed structure is that the portion of the channel between the source and the left edge of the gate now has a much greater depth, and consequently has a smaller resistance. Figure 10.19 (Goronkin et al., 1985) shows the calculated reduction of Rs as a function of the gate recess depth.

The structure in Figure 10.18 C has been made with a "self-aligned" technique, which involves using a refractory metal gate. This gate material allows


"r-----------------------.

"

klB/OCTAVE

·~5~~"--~'.L-~,.~ •• ~.~.~.~.~1~ •• -,~5.~'.' FREQUENCY (CHI)

Figure 10.17. Measured gain versus frequency for MESFETs with 0.f5 I'm gatelength. Reproduced from SMITH, P.M., CHAO, P.C., MISHRA, U.K., PALMATEER, S.C., DUH, K.H.G., and HWANG, J.C.M. (1985). "Millimeter Wave Power Performance of 0.f5 I'm HEMTs and GaAs FETs," Proc. IEEE/Cornell Con/. on Adv. Concepts in High Speed Semiconductor Device, and Circuits, IEEE, Pi,cataway, N.J., p. 189, @1985 IEEE.

\~~ "~l--r . ~ _, .... ,t

IAI Ie)

1·1

Figure 10.18. Crol6-,ection of three MESFET ,tructures. Reprinted from GORONKIN, H., GRONDIN, R.O., and FERRY, D.K. (1985). "Low-Noise GaA, Microwave MESFETs," in Gallium Arsenide Technology (David K. Ferry, Editor), Sams: A Division of Macmillan Camp. Publ., Vol. I, Ch. 5, p. 155, with permission.

Chapter 10 319 1O~--------------------------------------,

6 v, - 15V

o Vp ~ 2.0V

o v, ~ 25V

RECESS DEPTH (IJm)

Figure 10.19. Dependence of the parasitic source resistance on gate receu depth. Reprinted from GORONKIN, H., GRONDIN, R.O., and FERRY, D.K. (1985). "Low-Noise GaAs Microwave MESFETs," in GalliUln Arsenide Technology (David K. Ferry, Editor), Sams: A Division of Macmillan Compo Publ., Vol. I, Ch. 5, p. 155, with permission.

I=========~- GaAs BUFFER S.I. SUBSTRATE

FET

Figure 10.20. Gate structure with small Rg ("mushroom gate"). Reprinted from SMITH, P.M., CHAO, P.C., MISHRA, U.K., PALMATEER, S.C., DUH, K.H.G., and HWANG, J.C,M. (1985). "Millimeter Wave Power Performance of 0.£5 p.m HEMTs and GaAs FETs," Proc. IEEE/Cornell Conf. on Adv. Concepts in High Speed Semiconductor Devices and Circuits, IEEE, Piscataway, N.J., p. 189, @1985 IEEE.


selective doping by ion implantation in the regions which give rise to the parasitic source resistance. Unfortunately, this method also leads to larger gate resistance, Rg • For very small gatelength it is instead common to build up the gate as shown in Figure 10.20, so that the gate resistance (Rg) is decreased.

Relation Between iT and the Transit Time, Te

The cut-off frequency IT can be directly related to the transit time of electrons under the gate by the following approximate argument. We use the structure of a MESFET shown in Figure 10.15 and the following definitions.

(10.32)

We assume a small positive change in gate voltage, aVG. This gives rise to the following changes:

1) The gate charges up by an amount aqG = e g• x aVG, since it is one "plate" of a capacitor

2) The other "plate" of the capacitor is the channel, so an amount of charge = -aqG must be "drawn into" the channel due to the charging of the gate. A charge of -aqG means a positive increase of the electron density in the channel, and therefore .....

3) We get an increase in the current through the channel, aiDS. Also,

aiDS = [increase in charge] I [time it takes for -aqG to travel the distance = Lg]

The time in this expression is the transit time for the electron to go a distance = the gate length (Lg), thus

and, if we use the second definition in (10.32),

0\' e aVG J.>'DS = g. X -

Te

(10.33)

(10.34)

Further, from the definition of transconductance (10.26), we find that

Um eg•

1 (10.35)

The ratio in (10.35) is just exactly the significant quantity which we arrived at in the expression for iT, (10.2B). We can therefore express IT in

Chapter 10 321

terms ofthe transit time (or L,/v" if the carriers are assumed to move at the saturated velocity):

IT - grn _ 1 ~ v, - 21rC" - 21rTt - 21rL,

(10.36)

Equation (10.36) gives us a very simple way of judging the high-frequency properties of different field-effect transistors by calculating the transit time for the electrons under the gate. For example, if we increase the width of the gate fingers without changing their length, then Tt is unchanged, and the cutoff-frequency should also remain the same. Looked at in another way, in this case, both Gg , and grn are proportional to the width, and their ratio should therefore be independent of the width of the gate. The derivation also makes it clear that it is the length of the actual gate region which is important, not the entire distance from the source to the drain, which may be many tenths of micrometers greater.

Equation (10.36) is extremely useful since it gives us a very simple criterion on the high-frequency performance, which side-steps working out the details of the effects of the various elements in the equivalent circuit, or in the physical operation of the MESFET. This is especially true for modern MESFETs with very short gates. The general conclusions from this equation are that for improved high-frequency performance, we should:

1) increase the effective saturation velocity - this will be discussed shortly

or

2) decrease the gate length, Lg

If we make a rough estimate of T for a MESFET with a 1 micrometer long gate, we find (assuming a saturation velocity of 1 x 107 cm/sec):

L 1O-4cm 1 Tt ~ - = 7 / = 10- lsec(10 psec)

v, 10 cm sec (10.37)

The corresponding Ix is 1/21rTt = 16 GHz, which agrees with the value of 14 GHz derived earlier from measured values of gm. and Gg , for a 1 micrometer MESFET. We will return to an estimate of IT for shorter gate transistors in the next section. We can also find an estimate for the expected size of grn by calculating Gg" assuming a model of a parallel plate capacitor with plate spacing hg, and neglecting the fringing field at the edges:

Then,

LgZ Gg , = €'h

9

Zv, grn = f'h

g

(10.38)

(10.39)


I GoA. Epi

:l-m~uu_ .. a I I

a x

Figure 10.21. Simplified illustration of the occurrence of velocity over-shoot in a MESFET. The mazimum drift velocity under equilibrium conditions is vI" for an electric field, Ep. The highest field in the device is greater than Ep. A s the electrons enter the high-field region, their velocity initially ezceeds vI" and then approaches the equilibrium value. Reproduced from LIEGHTI, G.A. {1976}. "Microwave Field-Effect Transistors - 1976," IEEE Trans. Microw. Theory Tech., MTT-24 , 279, @1976 IEEE.

This expression does not contain L, explicitly; however, the effective height of the depletion region (hg) is usually scaled as Lg is made shorter. For a 1 micrometer gate length device, with L/a = L/hg = 3, and v, = 1 X 107

cm/sec, we find a typical gm of 34 mS/mm gate width. Much larger values can be obtained by decreasing hg, and because the effective value of v, increases as the gate length is shortened.

One word of caution is in order regarding the accuracy ofthe approximate derivation in this section. We have assumed that there is only one significant time-constant - that required for charging ego. Other time-constants may become important for very short gate devices. Research in this direction has given an increased understanding of these phenomena recently. Since the application has been mainly to HFETs, we defer the discussion of other time-constants to the next chapter.

Chapter 10 323

ULTRA-FAST ELECTRONS, OR HOW BALLISTIC CAN AN ELECTRON BE

The estimation ofthe transit time of electrons in modern short-gate MESFETs is interesting enough that it requires its own section. A large amount of effort has gone into making the gatelength in MESFETs shorter, and this process has been very successfull in pushing the cut-off frequency a little higher every year. Parallel to the fabrication effort, one has attempted to calculate the transit time for sub-micrometer devices and predict how future devices might be made which would be even faster. The concept ofa "ballistic" transistor has been mentioned often, and we need to explore this topic. The general problem is stated in Figure 10.21. In a short gate transistor, the electron encounters a fairly high electric field over a region with quite small length. The fast acceleration which occurs makes it impossible to assume that the electron velocity will follow the variation of the field, which is specified by the steady-state curve (which we used to explain, for example, GUNN-devices). Instead, we may expect a peak velocity which is higher than even the peak on that curve -this is termed an "over-shoot" velocity. The average velocity of the electron in its transit under the gate may also be considerably higher than the normally quoted saturation velocity, and a shorter transit time will result. The higher velocity is due to the fact that it takes a finite time for collisions to bring the velocity of the electron down to the steady state curve. The most extreme case we may assume is that there are no collisions at all, i.e. the electron moves under the laws of ballistics.

Purely ballistic electrons

If no collisions occur, the electrons in GaAB, for example, accelerated by a constant electric field (to take a simple case for the purposes of illustration) are moving up the energy band curve of t: versus wave-vector, k, see Figure 10.22. If the effective mass is constant (this is not strictly true for energies of a few times 0.1 eV, but again we simplify) = mO = 0.067 mo, then Newton's law for acceleration due to a constant force applies, i.e.:

F = mO x a (10.40)

where, F = -e x E, and a = dv/dt for the electron. Ignoring the minus-sign, we have

dv eE eE = mO - => v = - x t

dt mO (10.41)

At room temperature we can estimate the mean free path (m.f.p.) for the electrons from the measured mobility (see (1.20)), and we find a value of about


u 0.32eV

Acceleration k

Figure 10.22. Acceleration of an electron in GaA6 from the lower to the upper valley.

0.1 micrometers, or 10- 5 cm.* If the electron starts at z = 0, then at time T

it has arrived at z = L, given by

L = vdt = _e_r 2 ; i T E o 2m·

(10.42)

We choose an "average" electron for which L = m.f.p. = O.lp.m = 10- 5

cm before its first collision. Therefore (10.42) applies up to this time, and

r = J2m. L (10.43) eE

If E = 104 V /cm, we find that T = 8.7 X 10-14 sec, or roughly 0.1 psec. The maximum velocity attained by the average electron is found from

eE J2m.L 11m ... = a x T = ;;;:; X ~

C~~) x L = 7.3 X 107 cm/sec.

(10.44)

The actual velocity at a given electron energy is determined by the shape of the energy band (assuming no interband transfer). This curve is given

* The m.f.p. will be a function of the electron energy, but this value is of the right order of magnitude.

Chapter 10

~

~ w > 1.10·emfs

~ a? <!)

z o a: f-

hl GJ

o o

o

325

GoAs (100) DIRECTION

ELECTRON TRANSFERS

, [III) [100)

.2 3 A .5 .6

ELECTRON ENERGY (eV)

Figure 10.23. Electron group velocity a6 a function of electron energy, for electron .. traveling in the [100J direction in GaA... Reprinted from EASTMAN, L.F. (1985). "The Physical Electronic .. of High Speed Transistors," Proc. IEEE/Cornell Conf. on Adv. Concept, in High Speed Semiconductor Device .. and Circuits, IEEE, Pi6cataway, N.J., p. 1, @1985 IEEE.

in Figure 10.23, and could be used to make a small correction to our result in (10.42). We may remind ourselves that the peak steady-state velocity for electrons in GaAs is in the range 1.5 to 2 x 10Tcm/sec (see Chapter 2).

In a more realistic calculation, we should assume a random distribution of the collision times, and find the average velocity. However, the above very simple calculation gives an indication that it is reasonable to expect overshoot velocities for electrons in GaA8 in very short devices. Since no devices exist which have gate-lengths much shorter than 0.1 micrometers, it is also clear that the case of pure ballistic transport does not occur in any practical devices. The much discussed term of ballistic electron .. therefore is mis-leading. For example, groups at Bell Labs and IBM have been competing in claiming the most ballistic electrons (Bell, 1986; Eastman, 1986; Heiblum, 1986, 1987 also see Chapter 13). In either case, collisions still play an important role for a significant fraction of the electrpns.

Monte-Carlo Calculations of the Transit Time

Monte-Carlo type simulations have been performed to estimate what the actual velocities and transit times ale for electrons in GaA8 and other semiconductors. In these simulations a number of electrons are followed through the device (one by one). The probabilities for different collision processes,

326 Microwave Semiconductor Devicell

Figure 10.24. Electron velocity ver,u, dilltance in GaAII, after a IItep-like electric field ha, been applied at:ll = O. The purely balliltic calle hBl alIo been included. Adapted /rom RUCH, J.G. (197!). "Electron Dynamic, in Short Channel Field-Effect 7ran.i,tor,," IEEE 7ra7lll. Electron Device" ED-19, 6S!, @197! IEEE.

Figure 10.25. Electron velocity ver,u, di,tance in Si, after a lItep-like electric field hBl been applied at :II = O. Reprinted from RUCH, J.G. (197!). "Electron Dynamic, in Short Channel Field-Effect 7ra7lllilltor" " IEEE 7ran.t. Electron Device., ED-19, 6S!, @197! IEEE.

Chapter 10 327

electron transfer to other valleys, etc. can be estimated as a function of the electron energy, and these processes are allowed to occur randomly according to the above probabilities. The first such simulation for GaAB, by Ruch (1972) yielded a maximum velocity for electrons accelerated in a constant field of 10 kV /cm, of about 4.8 x 107 cm/sec, occuring at an z of about 0.15 micrometers, and for a T = 0.4 psec (see Figure 10.24). This result clearly showed that overshoot velocities are possible when collisions are taken into account correctly. We have plotted the velocity versus distance traveled for the purely ballistic case calculated in the previous section into the same figure, and the difference between purely ballistic behavior and the actual acceleration is also very clear. It is interesting to compare the calculated results for electrons in silicon (see Figure 10.25), which show very little over-shoot velocity. The physical reason for this difference is that the scattering of electrons occurs differently in the two materials. Electrons in GaAs scatter mainly from optical (polar) phonons, which are quantized lattice vibrations which involve movements of neighboring Ga and As atoms with respect to one another (see Chapter 1). Because fairly large electrostatic forces exist between the two atomic species, this lattice vibration is associated with a fairly high energy, about 0.036 eV. The lattice vibration mode can be excited in quanta of this size, which means that an electron which interacts (scatters) off these phonons loses an energy of this amount in most scattering events. Another characteristic of optical phonon scattering is that the direction of the momentum of the electron changes very little in each event (see e.g. Lundstrom (1990)). Also, the change in direction becomes less for scattering of higher energy electrons. The result of these facts is that, if an electron is being accelerated by an electric field of sufficient magnitude that the energy loss of 0.036 e V per scattering event is made up by the energy gained between scattering events from the electric field, then the electron can travel through several scattering events in essentially the same direction, and with a high average velocity. Eventually, the direction of the electron velocity vector will be randomized, and the average velocity will go down. The above phenomena constitute the essential elements in the explanation for how over-shoot velocities occur in GaAs. The scattering processes in Si act to randomize the velocity more quickly.

Some more recent Monte-Carlo simulations show the additional effect of the initial electron energy (Iafrate, 1985). Figure 10.26 first shows a comparison of the velocity versus distance traveled for electrons in GaAs, [nP and Si (constant electric field 0£25 kV /cm). Note the high velocities attained in GaAs and [nP, but not in Si. Figure 10.27 shows a series of curves for electrons in GaAs with the initial (iDjection) energy, Eo, as a parameter. The electric field is a moderate 10 kV /cm. Note that the initial velocity can be maintained at about a constant value over a large distance, in accordance with our discussion above. If the iDjection energy becomes close to the energy required for inter-valley transfer (0.32 eV), however, then the velocity of the electrons will decrease rapidly (curve h). The same decrease of electron velocity occurs if a substantially higher electric field is used, so that the electrons reach the en-


7.0 Electric Field = 25 kVlcm

6.0

'0 (J)

~ 5.0 E 0

I"-0 4.0 :::. ?;-'u 3.0 .2 (J)

> 2.0

1.0

Distance (A) 2000

Figure 10.26. Overshoot velocity enhancement in GaAs, Si and InP, as calculated by Monte Carlo simulation. Electrons are auumed to enter a region with an increased electric field of 25 kV /cm at z = O. Reprinted from IAFRATE, G.J. {1985}. "The Physics of Submicron/Ultrasubmicron Dimensions," in Gallium Arsenide Technology, D.K. Ferry, Editor-in-Chief, Sams: A Division of Macmillan Camp. Publ., Vol. I, Ch. 12, p. 443, with permission.

500 1000

D,slonce (AI

F, 10 ~ ,n <l00)

k,' k" 0 T';,OO"K

1500

•• (?;l Eo(o\Il

o 0 -0.02 0.04 0.03 0.07 0.04 0.11 0.05 0.16 0.06 0.21 0.07 0.27 0.08 0.34

Figure 10.27. Calculated average drift velocity in GaAs versus transit distance, with injection energy as parameter. Reprinted from IAFRATE, G.J. {1985}. "The Physics of Submicron/Ultrasubmicron Dimensions," in Gallium Arsenide Technology, D.K. Ferry, Editor-in-Chief, Sams: A Division of Macmillan Camp. Publ., Vol. I, Ch. 12, p. 443, with permission.

Chapter 10 329

ergy required for inter-valley transfer faster. The ideal conditions thus involve a balance of an injection energy in the right range, and a moderately large electric field. If the conditions of curve I (injection energy of 0.21 eV, field of 10 kV /cm) could be replicated in a real device, with a characteristic length (L) of say 0.1 micrometers, then we would estimate an average velocity of 8 x 107

cm/sec, and a transit time of Tt = L/ < v >= 0.125 psec, with an associated iT of 1,300 GHz!! No such device yet exists, of course, but the estimate shows the reason behind the great interest in developing devices with small dimensions and a suitable injection mechanism. The obstacles to the fabrication of such a device are formidable, but maybe not insurmountable. One must also take other parasitic circuit elements into account, such as Rs, Rg etc. and other capacitances. The development effort which is most clearly following the above path is perhaps that of the hetero-junction bipolar transistor. In this case, the electrons are injected from a hetero-junction between GaAB and another semi-conductor. This injection mechanism results in electrons with a high average energy. Heterojunction bipolar devices will be discussed in Chapter 12. Several other recently investigated ideas also make use of hot-electron injection, see Chapter 13.

In applying the simulation data to MESFETs, one must of course note that the electric field in a real MESFET is anything but uniform. Bernstein and Ferry (1988) performed a Monte Carlo analysis of Ultra-Short-Gate-Length GaAB MESFETs. These authors conclude that actual overshoot (average) velocities (greater than the saturation velocity of 1 x 107 em/sec) only occur for gatelengths less than 0.05 micrometers. The average velocity calculated for a .035 micrometer long gate is 1.5 x 107 em/sec. Quasi-ballistic electron effects thus may never play any large role in practical MESFETs. The best estimate for the average velocity of electrons in typical short gate HFETs is somewhat higher, about 2 X 107 cm/sec, see Chapter 11. In-based HFETs appear to reach average velocities of 3 x 107 cm/sec.

The highest value of iT for MESFETs is presently about 125 GHz (Wang and Feng, 1989). The fact that this device had a 0.25 micrometer gate, and not 0.1 to 0.15 micrometers, which can now be fabricated, indicates that the dependence of IT on the gate length (for very small L9 ) also involves other phenomena than the transit time.

Estimated Transit Times and Cut-Oft' Frequencies for Real Devices

An early Monte Carlo simulation by Maloney and Frey (1976) calculated iT for GaAB and InP MESFETs versus gate-length [Figure 10.28]. The measured value of IT for a 1 micrometer GaAB device is about 22 GHz, which is reasonably close to the very much simplified estimate we made earlier. The cut-off frequency for InP is predicted to be higher, basically due to a higher peak velocity for this material. Unfortunately, it is not technically feasible to fabricate a Schottky barrier junction on InP with sufficient barrier height.

330

60,

fT 501

40~ GHz 1

lOt""

20~

! 15~

I GoA.

0.4 0.6 0.8 1.0 2 19. microns


InP

Figure 10.28. Theoretical cut-off frequency (h) as a function 01 gatelength, lor GaAs and InP. Reprinted from MALONEY, T.J., and FREY, J. (1976). "Frequency Limits 01 GaAs and InP Field-Effect Transistors at 300K and 77K with Typical Active Layer Doping, II IEEE Trans. Electron Devices, EDe3, 519, @1976 IEEE.

InGaAs is another material which has a high peak velocity, and thus potentially a high h. This material will be discussed in the next chapter. The data for silicon are from Sze (1981), and show the expected lower value for h.

MESFET technology has undergone continual development in the last few years, and IT-values over 100 GHz have been realized. One successful approach is represented by new versions of self-aligned fabrication (Enoki et al., 1990; Hosogi et al., 1990). The "SAINT" (Self-Aligned Implantation for n+ Technology) process makes it possible to realize a shorter gate length than the pattern size produced by the lithography (Enoki et al., 1990). Substrate current leakage, which has been a problem in some short-gate devices, was suppressed by introduction of a buried p-layer. Gates as short as 0.1 micrometers were fabricated, with effective depletion layer thickness (hg) down to .06 micrometers. Figure 10.29 shows 9m. as a function of gatelength for these devices, and illustrates the leveling off which occurs as the gate-length becomes shorter than 0.25 micrometers. The cut-off frequency, IT, levels off to a value of 93 GHz for a 0.1 micrometer gate length, see Figure 10.30. Enoki et al. (1990) also show that fringing capacitances on either side of the gate actually come to limit IT for very short gatelengths - compare the higher of the two curves in Figure 10.30, which assumes that these capacitances can be neglected. These new data thus point out the error involved in using approximate expressions such as (10.36) and (10.39) above, when the gate length is very short. A major factor which has been invoked to explain the increased 9m and h is the

Chapter 10 331

1000

E a ~ 0 060~m

/ dr E

f~'::~'~!c 00 E

OJ <.I a err ~ O.084~m c

100 ~

t: ::I

"t:I C 0 <.I Vg=O.5-0.6V "' c Vds~ I V ~ ...

Eo-10

.1 10

Gate Length (/lm)

Figure 10.29 The dependence of grn on gatelength for SAINT MESFET!. Reprinted from ENOKI, T., SUGITANI, S., and YAMANE, Y. (1990). "Characteri!tic! Including Electron Velocity Over!hoot for O.l-p.m-Gate-Length GaAs SAINT MESFETs," IEEE TranI. Electron Devices, ED-37, 935, @1990IEEE.

20 L OL.I-_-O'--.2--'---'-O.L.5--,--,-,--,-I.O

Gate Length (I'm I

Figure 10.30. The dependence of IT on the gatelength for the same devices as in Figure 10.29. Clo!ed circles represent measured fT, and open ones the calculated IT, if the fringing capacitances are neglected. Reprinted from ENOKI, T., SUGITANI, S., and YAMANE, Y. (1990). "Charactemtic6 Including Electron Velocity Overshoot for O.l-p.m-Gate-Length GaA6 SAINT MESFETs," IEEE Trans. Electron Devices, ED-37, 935, @1990 IEEE.


increase in average velocity, v" under the gate. Values close to and above 3 x 107 em/sec are obtained for 0.1 - 0.15 micrometer long gates by direct application of (10.36). Although these values are claimed to be consistent with results from Monte Carlo analysis, assuming different (constant) electric fields, as noted in Figure 10.31, this conclusion may need to be re-examined in view of recent work on HFETs with very short gates, which we shall describe in the next chapter. Enoki et a1. (1990) also note that about half the drainsource voltage apparently is wasted in a stationary GUNN domain region at the drain. Golio (1988) examined data for 99 MESFETs, from papers published over 22 years. There is no definite scaling law for the average of these data, but Nd = 1.6 X 1017(cm- 3 )/Lg (p,m) fits fairly well. No definite extrapolation to Lg < 0.1p,m is possible. Sub-O.25 micrometer MESFETs appear to have demonstrated considerable advances in performance, achieving very high average velocities, which are perhaps indicative of velocity over-shoot. Nevertheless, it appears that these devices may have reached their ultimate limit in terms of parameters such as fT. Other devices, such as HFETs described in the next chapter, have reached considerably higher fT's.

THE FUKUI NOISE MODEL FOR MESFETs

The Fukui noise model for MESFETs (Fukui, 1979, 1981) is an empirical model, which assumes particular functional variations of the noise parameters, and finds best-fit values of the associated coefficients. The form of the Fukui expression does correspond to a particular limit for the Pucel-Haus-Statz noise model (to be discussed in the next section). The Fukui expression is reasonably simple, and seems to fit a large number of individual MESFET devices (and even HFETs, see the next chapter) . These features have made it a frequently used tool for analysis and evaluation of MESFET noise performance.

The Fukui model first assumes the somewhat simplified equivalent circuit model shown in Figure 10.32. It also uses the equation for the dependence of the FET noise figure on the source impedance, (8.23), which we repeat here:

(10.45)

Fmin is also often called Fo;

Fukui found that the following empirical relations could be used for the dependence of the noise parameters on certain equivalent circuit elements (impedances (Zs, Zo) are used instead of (Ys, Yo)):

vRg + Rs ka Fmin = 1 + kdCgI ; Rn = -;

gm gm

[ 1 ] k4 Ro = k3 -- + R, + Rs ; Xo = fC ; 4gm gl

(10.46)

Chapter 10 333

~ 5 u

~ ... 4

• This work

0.2 0.5

Gole Lell91h (/Lml

Figure 10.31. Average electron drift velocity as a function of the gate length for the same device, a, in Figure, 10.£9 and 10.30. Solid line, were calculated with Monte Carlo ,imulation, while the points represent values deduced from measuremenb. Reprinted from ENOKI, T., SUGITANI, S., and YAMANE, Y. (1990). "Characteriltic, Including Electron Velocity Over,hoot for 0.1-p.m-Gate-Length GaAs SAINT MESFETs," IEEE Trans. Electron Devices, ED-37, 935, @1990 IEEE.

;r =4klO Rs l>f

~ =4k ToRftI~f

;f =4k ToRf ~f

i154kTOg9nllf

if !!4kTo OClln .o.1

ig.i .... jcRi Figure 10.32. Simplified equivalent circuit used in the noise analysis of MES

FETs. Reproduced from PUCEL, R.A., MASSE', D., and KRUMM, C.F. (1976). "Noise Performance of Gallium Ar,enide Field-Effect Transiltors," IEEE J. Solid-State Circuifl, SC-11, £43, @1976 IEEE.


If! is specified in GHz, and Gg , in pF, the factor in Fmin. should be multiplied by 10-3 .

The factors kl' k2' ka and k4 are the fitting factors, while I is the frequency. The best-fit values for these factors found by Fukui were:

kl = 0.016; k2 = 0.8;

k3 = 2.2; k4 = 160; (10.47)

It was later shown by Pospieszalski and Wiatr (1986) that it is possible in some cases to obtain values of kl through k4 which violate the following inequality, which must be satisfied by any physically realizable two-port:

Fmin -1::; 4N (10.48)

Here, N == ~. These authors recommend that (10.48) be used to establish limits for parameters which are difficult to measure accurately.

Instead of kl' one often uses kF = ~, and the expression for Fmin then becomes:

(10.49a)

Equation (10.49a) can also be expressed in terms of iT by using (10.28):

(10.49b)

Note that IT thus plays an important role in determining the noise performance, just as we earlier found that it determined the high frequency capabilities. We also remind ourselves that iT is related to the transit time under the gate [10.36]. Designing a device for minimum transit time results not only in a high cut-off frequency, but also in good noise performance at a given frequency. Also note that the parasitic series resistances Rs and Rg playa role in determining Ima", , as well as the minimum noise figure.

The constant kF can be regarded as an indication of the quality of the material used in fabricating the FET, and has a value close to 2.5 for typical MESFETs at present. Goronkin et a1. (1985) used (10.49a) for showing the effect of variations in equivalent circuit parameters on minimum noise figure for a number of MESFETs taken from the same wafer. Their result is shown in Figure 10.33.

A slightly different version of Fukui's formula for Fmin was derived by Cappyet al. (1985):

Fmin = 1 + 41rLg x I x . 1_1_(o:Z + {3IDs) X . /(Rs + Rg) V <v > V (10.50)

Here, Lg = gate length, 0: = 2 X 105 pF·cm2 , /3 = 1.25 pF /mA cm, Z = gate width, and < v > = average velocity under the gate.

Chapter 10 335

0.75

/" / ~ ~

'il

0.7

0.65

0.6 'il V

i'V ¥ ~ V 'il

0.55

0.5

4.5 5.0 5.5 6.0 6.5 7.0 7.5

Figure 10.33. Measured dependence of the noise fi9ure of a series of MESFETs on the reduced time-constant. Reprintedfrom GORONKIN, H. GRONDIN, R.O., and FERRY, D.K. (1985). "Low-Noise GaAs Microwave MESFETs," in Gallium Arsenide Technology (David K. Ferry, Editor), Sarns: A Division of Macmillan Camp. Publ., Vol. I, Ch. 5, p. 155, with permission.

It is noteworthy that both Fukui's and Cappy's formulas indicate a dependence of Fmin on the gate width, Z. Thus, MESFETs with the same IT, but different gate width, have different noise figures. In Fukui's formula (10.49) we can deduce this from the fact that grn is proportional to the width. Cappy's expression shows both an explicit dependence on Z, as well as an implicit one due to IDS, both inside a square-root expression, as in (10.49). Low-noise MESFETs do not have to handle large amounts of power, and are consequently made with smaller widths than power MESFETs, typically 50-100 micrometers. At these widths, one typically sees very little dependence of Fmin on Z.

THE PUCEL-HAUS-STATZ NOISE MODEL

We have discussed the Pucel-Haus-Statz model for the equivalent circuit of a MESFET in an earlier section. The same series of papers referred to there also derived a noise model fOI MESFETs which shows very good agreement with experimental results. We can still use the equivalent circuit model in Figure 10.32, and we can refer to this diagram in order to distinguish the extrinsic noise sources (these are due to Nyquist noise in the series resistances, primarily R, and Rs) from the intrinsic ones (noise arising in the MESFET channel). We will first discuss the intrinsic noise.

336 Microwave Semiconductor Device6

There are two main contributions to the intrinsic channel noise of a MESFET, (1) the thermal noise produced in the "ohmic" section of the channel, Region I, and (2) the diffusion noise in the velocity-saturated section of the channel, Region II.

Thermal noise of the same basic type as in Region I of a MESFET was analyzed for the case of a JFET by van der Ziel (1962, 1963). Van der Ziel assumed that the noise was Nyquist noise at the ambient temperature. Pucel, Haus and Statz, however, following among others Baechtold (1971, 1972), took note ofthe fact that the electron temperature increases roughly with the third power of the electric field:

T. ( E )3 -=l+c5x -To E'llt

(10.51)

For the carriers in the velocity-saturated channel, the average drift velocity is constant, and this fact might seem to inhibit noise. The individual carriers still experience random changes in direction and velocity, however. We may thus use a frame of reference which is frozen with respect to the average velocity of the carriers, and sub-divide this moving frame into the type of boxes which were used in the derivation of diffusion noise in Chapter 8. The velocitysaturated carriers will experience about the same type of random exchanges between the boxes as was discussed in this section, and we will assume that the noise which is being produced by the carriers in the channel can be regarded as such diffusion noise. Consequently, we will make use of (8.57) when we calculate the fluctuations in the channel current. Another point to note is that when an electron "jumps" from one box to another, it will produce a dipole with a net negative charge located in the box to which it jumped, and a net positive charge at the box from which it came. Once such a dipole has been produced, it is likely to persist over a time which is typically greater than the transit time for the electron under the gate (of the order ofa few picoseconds). We can see that this is true by realizing that we are primarily interested in noise fluctuations in the frequency band which is being amplified. Since this band is located considerably below IT (which is 1/211"Tt), most fluctuations of interest will persist longer than Tt. The picture we arrive at is one of dipole layers drifting unchanged in shape through the velocity-saturated channel at the constant velocity, V,.

In terms of the equivalent circuit model, we will introduce two noise sources, in" which is the noise induced in the gate due to the electrons in the channel, and inti, which is the noise current which results at the drain output terminal. The two noise sources are partially correlated, and the correlation coefficient is defined as :

(10.52)

Chapter 10 337

Since the gate source arises by capacitive coupling to the gate, we expect the two currents to be approximately 900 out of phase, i.e. C will be a number which is essentially real. Also, ig will vary proportional to the frequency, which means that C should be independent of frequency.

The calculation of the noise sources and their effect on the noise figure is quite involved, and we refer to the papers by PHS for the details. A brief review is given below:

1) First id is calculated. This calculation is easiest to perform by adding the noise powers from the voltage sources along the channel, and converting these to id by using i~ R~, = v3. The channel noise in Region I is calculated following van der Ziel (1962, 1963) with the above-mentioned correction due the increase in electron temperature. One should also note that a noise voltage across Region I will change the length of the unsaturated channel, L 1 , and this will amplify the original voltage across the saturated channel, when it is transferred to the drain.

2) The channel noise in Region II is calculated by finding the rate at which dipole layers are being created at position :1:0 in the saturated channel. Each dipole layer has a strength .~zo, where a:l:o is a characteristic size of the dipole layer, and A is the cross-sectional area of the channel. The rate of generation of dipole layers is l' = (2~nA), which can be seen to be consistent with (8.57). The potential du;o to dipole layers at :1:0 is calculated, and the squared voltages are integrated versus :1:0 for the length of the saturated channel.

3) The noise voltages from the two regions (I and II above) are uncorrelated, i.e. their squares should be added, and converted to a current source as described above under 1).

4) A thermal voltage fluctuation in Region I produces an induced charge aq in the portion of the gate which is adjacent to this region. Effects of changing Ll due to the voltage fluctuation, which again causes a "breathing" of the channel, must be taken into account. The breathing of the saturated channel induces an "indirect" charge in the portion of the gate adjacent to Region I I, of opposite sign. Both of these charges are correlated, since they are caused by the same voltage fluctuation in Region I. The total charge is obtained by integrating the square of the charges due to individual sections of the channel in Region I.

5) The fluctuating dipoles in the saturated channel also induce charges in the gate adjacent to Region I but only indirectly in Region II, and the total charge is found in a similar manner to under 4).

6) The currents corresponding to the fluctuating charges on the gate are found by multiplying the RMS value of the charge by ",2. Given these expressions, one can obtain the correlation coefficient, C.


7) Finally, several dimensionless noise coefficients are defined. The noise figure can now be expressed as

F = 1 + lingO + in•o + igo + i dO l2

li,ol2 (10.53)

In this equation, the current components are those which are produced in the short-circuited drain-source path by the four respective noise sources. The quantity i,o is the thermal noise current from the input source load.

8) The noise figure is manipulated to a form similar to (10.48).

Fm;n = 1 + 2 w g, JKg[K. + gm(Rg + Rs)] + order ( C) [higher]

grn terms (10.54)

The PHS paper uses values of 5 = 1.2 in the electron temperature expression (see (10.51)), and E'G! = 2.9 kV fcm. By using these values, PHS were able to obtain the excellent agreement with experimental data, plotted versus normalized drain current, which is shown in Figure 10.34.

For short gate MESFETs, C ~ 1, and K. approaches zero. In this case, we see from (10.54) that the minimum noise figure is on the same form as the Fukui expression (10.48). If we also neglect the parasitic resistances Rg and Rs, then the minimum noise figure becomes

( 2WGg,) ..; 2) Fm ;" = 1 + y;;:-PR(l- C + ... (10.55)

Here, P and R are normalized noise coefficients, which set the strength of the noise sources at the drain and gate terminals respectively:

(10.56a)

and

WI R= 9 4kBToBw2C;,/gm

(lO.56b)

The noise coefficients Kg and K. quoted in (10.54) are functions of P, Rand C, defined and plotted by PHS. The two noise sources can also be represented by noise conductances, defined by

(10.57a)

and

(10.57b)

Chapter 10 339

f '40GHz

- Theory

~ } ~~~~:~~~rnell conf.1973)

o 4.0

3.0

o •

..........~ Intrinsic device .,.....- noise (RQm=R, = 0)

0L---~0~.2~--~0~4~---0!.~6----70.~8----~1~.O~--~1.2

Normalized drain current Idl I dn

Figure 10.34. Theoretical and measured noise figure for a GaAs FET with Lg = 21'm. Reprinted from PUCEL, R.A., MASSE', D., and KRUMM, C.F. (1976). "Noise Performance of Gallium Arsenide Field-Effect Transistors," IEEE J. Solid-State Circuits, SC-ll, 243, @1976 IEEE.

Source-drOW1 "'01100'" 30 ..

~::-:~2Ht -12 -101 ..

O· 3Oc:rntMC

~----~~~--~Q~4----~~--~Q~,----~tO~ Normollzed ~ cUI'.enl J" rol.cl ..

Figure 10.35. Equivalent drain and gate noise conductances (gdn and ggn, respectively) and correlation coefficient (C) as a function of normalized current. Reprinted from STATZ, H., HAUS, H.A., and PUCEL, R.A. (1974). "Noise Characteristics of Gallium Arsenide Field-Effect Transistor.," IEEE Trans. Electron Devices, ED·21, 150, @1974 IEEE.


The noise conductances are displayed as a function of normalized drain current in Figure 10.35. The drain source increases strongly with current, while the gate source is essentially constant.

The approximate expression (10.55) shows very clearly the role of the correlation between the gate and the channel noise - if the correlation were perfect (C = 1) the minimum noise figure would be I! The double role played by the parasitic resistances is also highlighted by the fact that we could only bring the noise figure expression on the form of (10.55) by assuming that Rg and Rs are zero. Finite values for Rg and Rs means that they decrease the correlation, and increase the noise figure in this somewhat indirect manner.

The above review was included to give the reader a flavor for the quite complicated calculation which is necessary in order to derive the noise figure of a MESFET. In discussing the final results from the PHS noise model, we summarize by noting some important general conclusions:

* The optimum drain current is about 0.15 IDss (Figure 10.34)

* The correlation coefficient for the channel noise versus the induced noise in the gate can be quite large (C is about = 0.9, see Figure 10.35). At higher currents, the correlation is not so good, and the noise figure increases. The correlation is also best for a shallow channel (Lja large). It is clear that the near cancellation of the two noise sources in, and inti is the most important factor which explains why MESFETs have so much lower noise figures than e.g. GUNN devices - the latter are also dominated by diffusion noise, but do not have a cancellation mechanism (compare Chapter 6).

* Both the intrinsic noise (primarily diffusion noise from the saturated channel) and thermal noise from parasitic resistances, are important (Figures 10.34 and 10.36). The effect of these resistances is both direct (added thermal noise) and indirect (the correlation is decreased).

* The best fit for the measured noise figure is obtained for a value of the diffusion constant of 35 cm2 jsec, which is a somewhat lower value than expected, but not completely out of line (Figure 10.36).

* Hot-electron noise is used in the PHS model only in the un-saturated Region I.

A few other articles which have extended the theory further have appeared since the PHS papers. The paper by Cappy et a1. (1985) from which the expression in (10.50) was quoted, made some progress. Specifically, it predicted that (Fmin -1) is proportional to the gate length. Goronkin et al. (1985) give an example of measured data of this type, which show an excellent linearity of (F;;;ln) plotted versus L (see Figure 10.37). The situation is more complicated, however, as can be seen if we analyze some ofthe most recent noise figure versus frequency data for MESFETs with the shortest gatelengths. We shall defer a

Chapter 10

7D

6.

~ 5. .. .l

~ 4.

'" i 3.

I L.

:i

a

Drain - SCIUI"Ce voItooe - 3.0 V

Frequency "4.0 GHz

NOise parometer 8:1: 1.2

R, e.o =4.0xlQ-IZHC

------

0.2 0.4

---

0.6

D=50cmi ls.ec

~ ._.____O:::;40Cm 2/5oeC

~.)( O=30cm2 /sec

--- ------

0.8 1.0 1.2

Namohzed drtIin current I II' 1. ..

341

Figure 10.36. Minimum noi8e figure a8 a function of normalized drain current for various diffusion constant!. Reproduced from STATZ, H., HA US, H.A., and PUCEL, R.A. (1974). "Noise Characteristics of Gallium Arsenide Field-Effect Transistors," IEEE Trans. Electron Devices, ED-fl, 150, @1974 IEEE.

discussion of noise theory and experimental noise data for MESFETs for the millimeter wave range to the next chapter, since there have turned out to be interesting similarities between the noise properties of MESFETs and HFETs. A comparison of the noise performance of these two devices will also be given there.

NOISE IN FET OSCILLATORS

The spectra of the noise sources in MESFETs are of two types:

(1) Mostly white noise from the channel/gate and the series resistances

(2) Base-band noise from traps or defects in the channel or an interface.

The functional form of the second component is:

< i: >= F(T) x ra ftl

(10.58)

Typical values are a = 2; f3 = 1 - 2; This noise is similar to other noise processes of the "1/ f " type, which we discuss in Chapter 8. The expression

342 Microwave Semiconductor Devices 1.0 .----------------~ 3.0

0.9 2.8

0.8 2.5

0.7 2.3

~ 0.6 ;:r; 2.0 (ii' a: ::> (/) <{ w 0.5 ::; w

:£ w a:

1.8 ::> Cl u:

(/)

is z 0.4

w (/)

is 1.5 z

1.3

0.3

1.0

«>--10 GHz 0.2 MODFET 0.8

0.5 0.1

!:--~---"l.---__,&-_;:_\,___-,.L;,_--=:I0.3 0.2 0.4 0.6 0.8 1.0

GATE LENGTH (PM)

Figure 10.37. But noise figures achieved at different frequencies in 1985, plotted versus gate length. Reprinted from GORONKIN, H., GRONDIN, R.O., and FERRY, D.K. (1985). "Low-Noise GaA" Microwave ME8FETII," in Gallium Arsenide Technology (David K. Ferry, Editor), Sams: A Division of Macmillan Camp. Publ., Vol. I, Ch. 5, p. 155, with permission.

for the current spectral density of 1/ I-noise due to Hooge (1969), was given in (8.58), and is repeated here:

8;(f) = etH(l? I·N

(8.58)

Here, j and N are averages of the device current and the number of charge carriers in the device, respectively, and I is the frequency.

Both noise sources cause FM-modulation of the oscillator frequency, as described in Chapter 6. Pucel and Curtis (1983) show how the main mechanism

Chapter 10 343

for up-converting the base-band noise to frequencies near the carrier is via modulation of the source-gate capacitance due to the trap-generated noise in the channel. These authors measured the base-band noise spectrum and found it to be close to 1/1, see Figure 10.38. This figure also compares the calculated up-converted noise near the carrier to the actual measured near carrier FM noise (expressed as RMS frequency deviation), and very good agreement is obtained. The dependence of the near carrier RMS frequency deviation on the deviation frequency is also 1/1. As we showed in Chapter 6, the corresponding noise-to-carrier power ratio should vary as 1/ p. This is also shown in the figure.

The "corner-frequency" at which the FM noise changes from 1/1 to white noise is quite high, often in the range 10 - 100 MHz. This is a basic disadvantage of MESFETs used as oscillators, when near carrier noise is important, such as in Doppler radar applications. While most other characteristics of MESFETs have improved drastically since the earliest devices were introduced, the corner frequency for typical devices has stayed almost unchanged. Comparing the MESFET FM noise with that quoted in Chapter 6 for GUNN devices (about 10 Hz in a 1 Hz bandwidth, at a deviation frequency of 10 kHz, or an N /C ratio of - 70 dB in a 1 Hz bandwidth, some other data go as low as - 80 dB in a 1 Hz BW), we find that the FM noise measured by Pucel and Curtis (1983) is quite comparable. The corner frequency still appears to be as high as a few MHz. These data were taken on a specially fabricated FET oscillator, however. More typical values for the N/C are about 20 dB higher. A recent paper by Hughes et al. (1987) demonstrates corner frequencies less than 1 MHz in GaAs FETs. The epitaxial layer was grown with the help of MBE, and a much reduced trap concentration was obtained, which in turn lowered the corner frequency for the "input" 1/1 noise (see Figure 10.39). The noise level measured was only a few dB higher than that predicted from the quantum theory of 1/ I-noise (see Chapter 8). No measured near-carrier FM noise was quoted. They also showed that theoretically the limiting noise power is proportional to h, so that FETs with high h, and consequently good high-frequency performance, have higher near-carrier noise. This theory also has a bearing on the difference between Si and GaAB with regard to 1/1 noise: Si-devices are predicted to have lower 1/ I noise due to the larger effective mass for carriers in Si. Of course, the larger effective mass also makes Si devices generally much inferior in terms of available gain at high microwave frequencies.

The typical MESFET oscillator shows much larger 1/ I-type near-carrier noise than was measured by Pucel and Curtis (1983), or Hughes et al. (1987), however. Several mechanisms have been suggested to explain this noise, and at least some of these have been eliminated in particular experiments, while others look plausible (Stennes, 1989):

* Trap noise from the free surface. This may have been a factor in some earlier MESFETs. Su et al. (1983) varied the drain-source spacing with

344 Microw/Jve Semiconductor Devices --;;,.

8269!11&1-L.

P, ',-IOGtlr

10' I , ~~IftO\'ICGIy~ V,·5" ~,e'

UC!-~I'OIM I '70'"

I .'.; I ", ) .. '","" . "

'c' ;,: .. :-" .', t>_

c '. -C--'" ... ' ...... • .,' -! <I .... : .. ..' ...... ~_t;O'. ",

~ "'.. .... i!' - ", 'i "'. ro' .,' -;; ".,

~- ..... . ' f'IOiIe 1' .....

" ',.

4<> ., '\ "' .. -

I, ..

---, I , .,. .,. 10' .,. 10'

FRE~ OFJ'SET CIA M5OWC) FREOUEHCY t.

Figure 10.38. Baseband and Oscillator FM noise as a function of frequency for a MESFET device. Reprinted from PUCEL, R.A., and CURTIS, J. (1983). "Near-Carrier Noise in FET Oscillators," IEEE Intern. Microw. Symp. Digest, 282, @1983 IEEE.

-90.----------------------------------------,

-100

w -110 (!) <l: >-- -120 ...J

~ ~-130 w -(/) > 6 ro- 140 z '0

>-- -150 ::0 Q.

~

-170

100 10' 10 2 103 10' 10 5 106 10 7

FREQUENCY (Hz)

Figure 10.39. Measured input voltage spectra (baseband) of two GaAs FET devices. The top curve is for a standard ion-implanted device, the lower curve for one fabricated on MBE-grown material. The estimated quantum limit for the 111-noise is also shown. Reprinted from HUGHES, B., FERNANDEZ, N.G., and GLADSTONE, J.M. (1987). "GaAs FETs with a Flicker-Noise Corner Below 1 MHz," IEEE Trans. Electron Devicelf, ED-34 , 793, @1987 IEEE.

Chapter 10 345

fixed gate length, and saw no change in the 1/ I-noise. They concluded that the free surface region did not contribute significantly.

* Bulk trap noise. This is a possible mechanism if one assumes that there is a temperature gradient in the channel, which changes the characteristic energy of the traps, as discussed in Chapter 8. In many cases, trap noise with a peak at a specific frequency (Le. generation-recombination noise) is also detected.

* It was shown by Su et al. (1983) that the 1/1 noise varied with the gate length as 1/"jL,. This is yet another indication that high speed devices have higher 1/ I-noise!

Undoubtedly, some improvements will occur in the 1/ I-noise characteristics of MESFETs, mainly due to new fabrication technology. One should note the ultimate quantum 1/ I-noise limit, which is rather high for GoA" however.

It is possible to improve the FM noise performance of a given MESFET oscillator by optimizing the loading at low frequencies, as shown by Prigent and Obregon (1987). Another method of designing a low-noise oscillator is to employ a MESFET amplifier in a feedback loop configuration (Lusher and Hardy, 1989).

POWER-FREQUENCY LIMITATIONS IN MESFETs

In order to evaluate the power-frequency limitations of MESFETs, we start from the I-V-characteristics, and a typical load line, see Figure 10.40. The maximum sinusoidal output power is obtained at the maximum currentvoltage swing (the voltage swing at the high end is limited by the break-down voltage, VB). In order to optimize the output power, one must optimize the doping in the channel. If one increases N D, then the maximum current goes up. Increasing ND also decreases the break-down voltage, however. There is therefore roughly a constant VB X 1m ... for a device with a given gate-length. The situation is similar to that for two-terminal devices, and an electronic power-limitation, i.e. P varying as 1/ p, seems to dominate, if one plots data for maximum power output versus frequency, see Figure 10.41 (DiLorenzo and Wisseman, 1979). Some typical numbers are 1m.",. of about 350 mA/mm gatewidth. The break-down occurs between the drain and the gate, the region with the highest fields. The drain to gate voltage is related to the maximum drain-source voltage at breakdown as follows:

(10.59)

346

100

10


NORMALLY - ON n-CHANNEL

~ __________ ~~~ ________ ~~<O

~--____ -L __________ -L __________ -L ____ -.Vo o v,

Figure 10.40. I-V characteristic of a power MESFET. Reprinted from DILORENZO, J. V., and WISSEMAN, W.R. (1979). "GaAs Power MESFETs: Design, Fabrication and Performance," IEEE Trans. Microw. Theory Tech., MTT-27, 367, @1979 IEEE.

20 POul (2;; cons1

10 e

~

J I

0.8 en 06 -RCA o. o BELL LABS

6. FUJITSU

o NEe 02

-0.1 4 6 8 10 20 40

FREQUEI\ICY (GHz)

Figure 10.41. Power output 0/ GaAs MESFET device .. ver .. u .. frequency in 1979. Reprinted from DILORENZO, J. V., and WISSEMAN, W.R. (1979). "GaAs Power MESFETs: Design, Fabrication and Performance," IEEE Tran6. Microw. Theory Tech., MTT-27, 367, @1979 IEEE.

Chapter 10 347

Typical numbers again are VDG = 30Vj Vp = 5V (magnitude )j V1 = 2Vj l.e. vffs = 30 - 5 = 25 volts. The estimated maximum output power then is

(P) ~ (IDl - ID2)(VB - V1 ) _ 350~ x (30 - 5 - 2) ~ 1W/ -~- 8 - 8 - ~

(10.60)

This approximate calculation agrees remarkably well with actual achieved performance, at least up to 20 GHz (See (DiLorenzo and Wisseman, 1979)) (Figure 10.42). The power for a single device still varies as 1/ F, because (1) the impedance level goes down as the width of the gate is increased (2) it becomes difficult to uniformly feed a very wide device, and (3) it is crucial to keep the total source inductance down as the width is increasedj for example a plated heat-sink design due to TI uses 4 chips, and source grounding between chips. Consequently, at higher frequencies, the devices are in general of less width, and produce less power. The maximum total width versus frequency is also given in Figure 10.43. The layout of a typical device is illustrated in Figure 10.44.

The insert shows a typical via-hole cross-section. For a substrate thickness of 0.1 mm, Pucel (1985a) calculates an inductance of 38 pH, or wL = 2.40 at 10 GHz. This reactance can affect the gain noticeably, when placed in the source connection, as is typical for power FETs.

In somewhat greater detail, the factors which determine the optimum geometry of the layout are (Figure 10.45):

(1) The unit gate width (Z) of anyone of the gate fingers can not be too largej The limiting factors are the attenuation of the microwave signal traveling along a gate finger, as well as the fact that the finger must not be an appreciable fraction of a wavelength long, in order for the entire signal to be amplified in phase. Typical values are 50-100 micrometers for 20-40 GHz operation, and 200 micrometers at 10 GHz.

(2) The other dimension of the active device area is 'l' (Figure 10.45). Hirachi et al. (1984) developed a rule of thumb according to which l = >./16. For the configuration with two source pads, which was used in this paper (and in Figure 10.45), the maximum deviation in phase shift to any gate finger will then be 7r/32. If the layout can be made as compact as possible within the constraints on the total area given by (1) and (2), the output power will be maximized.

(3) The total width is L = n x Z, where n is the number of gate fingers used. This is the L which was referred to in Figure 10.43. Even though a design may observe criteria (1) and (2), L can not be increased arbitrarily, since then the input impedance will be too low, as discussed above.

If the above criteria are exceeded, the power will still increase as L is increased, but more slowly than linearly with L, i.e. the power per unit width


20,------------------------,

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~ 0::: 0.4 w ~ o Q.

I-~ 0.2

'"

. -0 __ 0_ .----.

a BTL 0. FUJITSU

• TI

FREQUENCY (GHII

f -z p-

Figure 10.42 Best power/width for GaAs FET amplifiers, at 3-4 dB gain, as a function of frequency. Reprinted from DILORENZO, J. V., and WISSEMAN, W.R. (1979). "GaAs Power MESFETs: Design, Fabrication and Performance," IEEE Trans. Microw. Theory Tech., MTT-27, 367, @1979 IEEE.

20 ....

E \ ~ 10 \

~ e \ 6 \

~ \ .; w- ,-2 z \ ::; \

" '-~ \ 0: \ 0 \

"" "'. I 1 \ I- 0.8 \ 0

\ ~ 0.6 ,. \ :::> 04 \ !

x

" ,. 0.2

4 6 e 10 20 40

fREOUENCY(GHz)

Figure 10.43. Mazimum total width of MESFET power devices for scaling, as a function of frequency. The mazimum width is defined as the width at which the output power "cale" with the width, starting with a small-signal device, to within 30% . Reprinted from DILORENZO, J. V., and WISSEMAN, W.R. (1979). "GaAs Power MESFET,,: Design, Fabrication and Performance," IEEE Trans. Microw. Theory Tech., MTT-27, 367, @1979 IEEE.

Chapter 10 349

VIA HOLt: AND GROUND PLAN!" PLATING

Figure 10.44. Layout of a typical GaA6 FET power device. The node .. marked are (1) Gate (2) Drain and (7) 60urce. Reproduced from HUNG, H.-L., SMITH, T., and HUANG, H.-C. (1990). "FET .. : Power Application6," in Handbook of Microwave and Optical Components, K. Chang, Editor, John Wiley fJ Sons, New York, Vol. 2, Ch. 10, p. 479, with permiuion. The imert shows the crou-6ection of a typical via hole, reproduced from PUCEL, R.A. (1985). "Technology and Design Consideration .. of Monolithic Microwave Integrated Circuit&," in Gallium Arsenide Technology, (David K. Ferry, Editor), Sam,: A Division of Macmillan Compo Publ., Vol. I, Ch. 6, p. 189, with permission.

will become less than about 1 Watt/mm. In this case, the gain will go down, and the power-added efficiency (PAE) will also decrease. The PAE is defined as:

P AE = 1]D x (1 - ~) (10.61 )


1.4

E .§. 1.2 -J til 1.0 QI ... « QI

0.8 > ti « QI 0.6 .c --0

0.4 .c -C) C QI 0.2 -J

0.0

Frequency (GHz)

Figure 10.45. Design chart for the length i of the active area of power FETs. The RF signal propagates perpendicular to the dimension marked i, and W is the width of one finger. In Region I, the device output power scales with total width, and all elements operate in phase. In region 9, scaling does not apply and special techniques must be used to properly phase the different cells on the chip. Region 2 is an intermediate region, with smaller gain degradation. Reprinted from HIRACHI, Y., TAKEUCHI, Y., IGARASHI, M., KOSEMURA, K., and YAMAMOTO, S. (1984). "A Packaged 20-GHz 1- W GaAa MESFET with a Novel Via-Hole Plated Heat Sink Structure, II IEEE Tran.t. Microw. Theory Tech., MTT-32, 309, @1984 IEEE.

Here, 1JD is the drain efficiency, i.e. the microwave output power at the drain divided by the total DC power dissipated.

Maximum power out and the maximum total width for single MESFET devices have not increased greatly in the last ten years since the curves in Figures 10.41 and 10.43 were published by DiLorenzo and Wisseman (1979). The above general discussion makes it plausible that this should be so, i.e. the limitations involved a:e quite fundamental. Some modest increase has indeed occurred, however, and we show the state-of-the-art for MESFET single device power output in Figure 10.46. One design technique which has evolved is that of constructing via holes for the source connection. Figure 10.47 shows the layout of a recent FET (actually an HFET) which employs individual via holes under each source finger. The earlier technique was to position the via holes outside the active area under the source pads, as shown for comparison in the figure. Typical via hole fabrication has involved chemical etching, which limits the minimum size to about 50 micrometers, whereas the new fabrication techniques employ either a plated heat sink with extremely thin GaAs substrate

Chapter 10 351

C~ OUTPUT POWt,R - MESFErs & MMICs lOa --'--------, ._ .. r -- I---r-'---'-'--'--I-----r--,.--'---,

en 10' ~.

>-« :.:

cr .u :.: 0 Q.

>-=> Q.

!::; 10· 0

10-' '----~'---- L--1.~'___1_JL..L..L.J'___ ___ I __ .l._-'_L_.'__L_LLJ

10. 10' 10·

FREQUENCY - 6HZ

Figure 10.46. Mazimum output power of GaAs MESFET devices, versus frequency - 1990. A separate curve is included for MMICs. Data have been compared from a number of sources. A typical one is HUNG, H.-L., SMITH, T., and HUANG, H.-C. (1990). "FETs: Power Applications," in Handbook of Microwave and Optical Components, K. Chang, Editor, John Wiley fj Sons, New York, Vol. 2, Ch. 10, p. 479.

(Hirachi et al., 1984), or reactive ion etching (Smith et al., 1990). The latter method can produce a minimum size of 20 micrometers in a 50 micrometer thick substrate. The accepted maximum power density of 1 Watt/mm still holds for the new devices, but the best designs have increased the maximum power which can be obtained at a given frequency. It has become increasingly difficult to define what should be counted as a single device, however, since power-combining and internal matching are often performed directly on the chip, or by combining two chips in a compact package. In plotting Figure 10.46, we have counted only the power for one single chip. Power-combining of MESFETs and other devices is discussed in Chapter 7.

The highest power devices invariably push the total width (L) beyond the point at which about 1 Watt/mm is obtained. For example, a recent Toshiba device delivered about 6 Watts per chip (and 12.3 Watts with two chips combined) at 14.25 GHz, with a total width of 16 millimeters, i.e .. 375


Watts/mm. Smaller devices can produce 0.8 Watts/mm up to 30 GHz, see Figure 10.48, whereas 0.4-0.5 Watts/mm is more typical at that frequency (Shih and Kuno, 1989). Above 30-40 GHz, the output power falls faster than 1/ p, but future development is likely to produce a continuation of the 1/ pcurve up to higher frequencies.

In many applications the power-added efficiency is more important than the maximum power output. A good example is amplifiers used in communication satellites and other space-based applications, in which it is imperative to make the most efficient use possible of the limited DC power available. It should be clear from the above discussion that the amplifiers which have the largest output power are not the most efficient ones. Another approach for increasing the power, that of power-combining, also involves inevitable losses in the combiner circuit. Also, power amplifiers with very large output tend to be highly tuned - there is thus a further trade-off between power and the bandwidth desired. By observing these trade-offs, in a recent design, Boesch and Thompson (1990) demonstrated average PAEs of 65% at 600 m W power level, 52% at 1 Watt, and 45% at 2 Watts, employing a basic device with L = 1.2 mm, and power-combining 2 and 4 devices, respectively. The bandwidth was unusually wide - 20% at X-band. A short was also provided at the second harmonic frequency, a well-known method for improving the efficiency. Bahl et al. (1989) measured a PAE of 70% at a power level of 1.7 Watts from 5 to 6 GHz, in a monolithic device. PAE achieved with MESFET amplifiers at present (1990) has been plotted versus frequency in Figure 10.49.

Monolithic power amplifiers, based on MESFETs, have attracted considerable attention. Generally, it has not been possible to reach as high powers with monolithically integrated amplifiers, as with discrete devices, mainly because any large gate width device would take up too much of the space on the MMIC chip. Figure 10.46 includes a curve for the monolithic case as well. Interestingly, the power output of monolithic and discrete devices become more similar the higher the frequency is. At these frequencies, the discrete devices have smaller widths, comparable to those used in MMICs. It is also worth noting that the monolithic circuit has much lower parasitics, which makes it easier to match. In terms of power density, the monolithic amplifiers have comparable performance to the discrete ones.

MESFET power amplifiers have received competition from HFET devices in the last few years, primarily in the millimeter wave range. HFETs will be covered in the next chapter, while a comparison of the power output versus frequency for several three-terminal devices can be found in Chapter 13.

We saw earlier that the break-down voltage is one of the limiting factors in the power-output of MESFETs. The details of the break-down process in MESFET devices has been studied recently, in an attempt to improve the power capability. Zaitlin (1986) concluded that the use of a gate recess and an n+ layer under the drain contact (which decrease the series resistance, as discussed earlier) reduce VB: the n+ layer-to-gate distance (de) should be

Chapter 10 353

(a) (b)

Figure 10.47. Layout of a 1.6 mm total width FET device with (a) wet-etched via holes and (b) reactive ion etched vias. Reproduced from SMITH, P.M., CHAO, P.C., BALLINGALL, J.M., and SWANSON, A. W. (1990). "Microwave and mm- Wave Power Amplification Using Pseudomorphic HEMTs," Microwave J., Vol. 33, no. 5, 71, @1990 Horizon House-Microwave, Inc.

'.2

x '.0

E • ~

0.8 x

• x x

~ • .. 0.6 l: 0>

w'" 0 D~ ~ <:>'< 0>

0.4 x ~ V Avantek

VXD 0 B::-D 0 o COMSAT Il. o GE

0 • Hughes x 0.2 • RCA x TI • '" Toshiba

0 , I , 3 10 30 100

Frequency (GHz)

Figure 10.48. Power density for GaA .. MESFET amplifiers - 1989. Reprinted from SHIH, Y.C., and KUNO, H.J. (1989). "Solid-State Sources from 1 to 100 GHz," in State of the Art Reference, Supplement to Microw. J., Vol. 32, September 1989, 1,.5, @1989 Horizon House-Microwave, Inc.

354

w <I: n.


100.-----------------------, 'V Avantek

80

60

40

20

3

o

10

o COM SAT • Hughes • Mitsubishi o Raytheon

• RCA x TI Il Toshiba TNTT

30

x x

Frequency (GHz)

100

Figure 10.49. Power added efficiency (PAE) achieved by GaAs FET amplifiers, ver"u" frequency. Adapted from SHIH, Y.C., and KUNO, H.l. (1989). "Solid-State Source" from 1 to 100 GHz," in State of the Art Reference, Supplement to Microw. J., Vol. 32, September 1989, 145, with permis"ion.

several tenths of a micrometer. Another possible method is to use a spacer layer under the gate of AlGaA8, which has a lower ionization rate. In an earlier paper, Wemple et al. (1980) concluded that the gate recess depth should be about equal to the depth of the surface depletion region.

Power GaAs MESFETs also suffer from gradual degradation of the gate fingers which occurs when the device is used for a long time at a high power level. Aluminum gates electromigrate into the GaAs so that eventually only a fraction of the gate remains. The electromigration occurs when gate current flows at the peak of the cycle. The Schottky barrier interface also is modified chemically, resulting in a change in barrier voltage. Gate fingers made from gold suffer from rapid diffusion of the gold metal at higher temperatures.

To minimize thermal limitations on the power output, one must be careful not to use a too thick substrate, since the heat must be transmitted through the substrate, except in "flip-chip" devices. A typical value for the thermal resistance on a 2-mil thick substrate on a gold-plated heat-sink, and a gate-togate spacing of 36 micrometers, and power output of 1 W jmm, is 30 degrees C x mmjW. Typical temperature increases in MESFETs at full power are less than for two-terminal devices. This is one factor which makes the average lifetime of MESFETs excellent.

An important area for MESFET amplifier and oscillator design is that of large-signal modeling of the device. We shall not go into this topic here, except

Chapter 10 355

to mention that there are many contending methods, or variations of methods, for large-signal modeling. Recent papers which show the present state of the art are the ones by Hwang and Itoh (1987), and by Curtice (1987), as well as the special issue ofIEEE Trans. Microw. Theory Tech. of February, 1988. The paper by Curtice (1987) applies not only to single device amplifiers, but also to distributed amplifiers and FET mixers (see also (Maas, 1986) and (Vendelin et al., 1990».

OVERVIEW

MESFETs are undoubtedly the most versatile microwave device at present. We have emphasized their fundamental physical operation, and the equivalent circuit which follows from this. Much of our present understanding of the MESFET stems from studies performed in the 1970s, while the important applications arose in the 1980s. The earlier results have held up well despite the large changes which have occurred in the fabrication technology, especially the shortening of the gate length. We can anticipate that MESFETs will still remain useful as they develop further. We will also see in the next chapter that there are many similarities in the circuit models for MESFETs and HFETs , despite Bome rather striking new features which have to be introduced in the physical description of the HFET. There are already some variations which have been introduced in the physical structure of FETs, which we have not covered, such as pulse-doped MESFETs (the doping is concentrated in a thin layer), the MISFET, etc. Modern semiconductor growth and micro-fabrication technology is capable of realizing many new structural ideas, and many of these will undoubtedly be attempted. Nevertheless, we expect that for quite some time there will be devices which are recognizably related to the basic MESFET which we have described in some detail in this chapter.

One orthe ways in which MESFET and HFET modeling have converged, is in the noise area. We have chosen to delay the treatment of the newest noise models to the next chapter.

In terms of circuit configurations of MESFETs, we have neglected some major types. Distributed amplifiers, for example, can now be designed to operate over bandwidths which are nothing short of incredible from the point of view of technology only ten years ago (basically "DC to 100 GHIII", see (Majidi-Ahy et al., 1990». MESFETs are also heavily used as control elements: Phase-shifters and switches, etc. The most important aspect of MESFET circuits, however, must be their suitability for being built into integrated circuits, MMICs. Because of the availability of excellent recent reviews of this area «Pucel, 1985a, 1985b, 1985c), we have not gone into this topic in any detail, except for a few references to differences between hybrid integrated (with "discrete" devices) and MMIC implementations.


Problems, Chapter 10

1. Assume a MESFET with the parameters given in the Table below, and apply the Pucel-Haus-Statz model. The objective is to verify how well this model works for this particular MESFET. The measured points which you should compare your results with are given in Figure 10.12.

Table of equivalent-circuit parameters for a Low-noise GaAs MESFET with a 1 microm. x 500 microm. gate {Pucel et al., 1975, with permiuion}.

ND = 6.5 X 1016cm- 3 }Vp = 5.65V a = 0.351Lm

Z = 500ILm

Lg = 1ILm

Vs = 1.3 X 107 cm/ sec}E - 289kV/ . - 1957 IL = 4, 500cm2 /V sec .at -. em, Z - •

R. = 6.50}S F' 10 15 Rtl = 11.30 ee Igure .

Neglect R;. and Rg

a) Set the values of IDs = 74 rnA and VDS = 4 volts, which is one of the measured points in Figure 10.12, but assume that you do not know VGS

or VGG. Find 1£<,1£1, and L 1 , such that the correct values are obtained for IDs and VDS • Then find the gate voltage from 1£1, and compare with the measured value in Figure 10.12. Hint: The measured voltages are VGG

and VDD, with respect to ground (the source is grounded). Find VGS and VDS from these, using the equivalent CiICl~!t (Fig. 10.15), where VGS and VD 5 are the intrinsic values "inside" the device.

b) Sketch the cross-section of the channel using the results from a) with reasonably accurate proportions for the depletion layer.

c) Change the drain current from 74 to 64 rnA without changing the drain voltage. Find the new channel dimensions, and the new VG • Estimate the extrinsic and intrinsic 9m from the data in a) and c). Compare Fig. 10.13.

d) An expression for 9m which is reasonably accurate for short-channel MESFETs is the following:

Is ( 1 ) 9mo::::-, 2Vp 1- IDs/Is

Calculate 9m,o from this expression and compare with the value from c).

e) Now assume the value for VGG which you found for IDS = 74 rnA, and change the drain voltage in steps to 3,2 and 1.5 volts, recalculating the channel parameters and finding the new values for the drain current at

Chapter 10 357

these drain voltages with constant gate voltage. Plot IDs versus VDS , and compare with the measured points in Figure 10.12.

f) Estimate R DS from the curve you plotted in e). Compare this value with the one found from the following approximate expression from Pucel, Haus and Statz (1975):

RDS ~ 11" Vp X VDS x (1 - IIDsS) ; aE,at Is

g) Pucel, Haus and Statz (1975) give an expression for the capacitance CGs:

Use this expression to find CGS, and compare with the value given in Figure 10.13. Also estimate the cut-off frequency IT from CGS and gm.

h) Use the above IT and the values in the table to calculate Imax. Estimate the unilateral gain at 5 GHz.

i) Compare Is/VGS with (10.20)-(10.22).

[Optional; If you write a computer program for the above procedure, then you can plot the I-V-curves].

2. Calculate IT and Imax for the 0.25p.m MESFET in Table 10.1. Assume Rs = 20.

3. (a) Calculate Fmin from Fukui's noise model for the two MESFET devices given in Table 10.1. Assume that kF = 2.5. Plot Fmin versus frequency.

(b) Use Cappy's expression to calculate Fmin for the 1p.m MESFET device in Table 10.1. Compare the result with that in (a).

4. Show that the generation of "dipole layers" in a MESFET due to the diffusion noise mechanism is r = 2flA, where f>.Xo is the characteristic size of a dipole layer. Start with (8.57).

5. Calculate the thermal resistance of a power MESFET device on a substrate which is 0.1 mm thick. Use thermal data for GaAB from Chapter 5. If the device has a power output of 1 W /mm, with 25% drain efficiency, how large is the temperature rise?

6. Calculate IT for a MESFET with Lg = O.lp.m, and v, = 1 X 107cm/sec. Explain why no devices reach this high iT. Discuss the possible iT of a device with Lg = 0.05p.m.


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Chapter 10 359

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___ , (1963). "Gate Noise in Field-Effect Transistors at Moderately High Frequencies," Proc. IEEE, 51, 461.

WANG, G.W., and FENG, M. (1989). "Quarter-Micrometer Gate Ion-Implanted GaAs MESFETs with an IT of 126 GHz," IEEE Electron Dev. Lett., EDL-10, 386.

WEMPLE, S.H., NIEHAUS, W.C., COX, H.M., DiLORENZO, J.V., and SCHLOSSER, W.O. (1980). "Control of Gate-Drain Avalanche in GaAs MESFETs," IEEE Trans. Electron Devices, ED-27, 1013.

ZAITLIN, M. (1986). "Reverse Breakdown in GaAs MESFETs," IEEE Trans. Electron Devices, ED-33, 1635.

ZHOU, H., and PULFREY, D.L. (1989). "A Criterion for Stationary Domain Formation in GaAs MESFETs," IEEE Trans. Electron Devices, ED-36, 872.

FURTHER READING

DiLORENZO, J.V. and KHANDELVAL, D.D. (Editors) (1982). "GaAs FET Principles and Technology," Artech House, Dedham, MA.

FUKUI, H. (Editor) (1981). "Low-Noise Microwave Transistors & Amplifiers," IEEE Pre8ll, New York.

GOLIO, J .M. (1990). "Large-Signal Analog Circuit Simulation," in Gallium Arsenide Technology, (David K. Ferry, Editor), Howard W. Sams, Indianapolis, IND., Volume II, Chapter 1,1.

HUNG, H.-L.A., SMITH, T, and HUANG, H-C. (1990). "FETs: Power Applications," in Handbook of Microwave and Optical Components, (K. Chang, Editor), John Wiley & Sons, New York, Volume 2, Chapter 10, 479.

MIDFORD, T. (1990). "FETs: Low-Noise Applications," in Handbook of Microwave and Optical Components, (K. Chang, Editor), John Wiley & Sons, New York, Volume 2, Chapter 11,550.

VENDELIN, G.D., PAVIO, A.M., and ROHDE, U.L. (1990). "Microwave Circuit Design, Using Linear and Nonlinear Techniques," John Wiley & Sons, New York.

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Microwave Semiconductor Devices || MESFET Devices