Microwave Semiconductor Devices || HFETs — Heterojunction Field Effect Transistors

Chapter 11

HFETs - HETEROJUNCTION FIELD EFFECT TRANSISTORS

INTRODUCTION

Heterojunction Field Effect Transistors* (HFETs) have developed very rapidly in the last few years, and rival MESFETs both for microwave and high-speed digital applications. The first report on a working HFET device came as recently as in 1980 (Mimura, 1980). Already in May 1986 did the IEEE Trans. Electron Devices devote an entire special issue to HFETs. The history of the HFET device can be traced to considerably earlier than 1981, however. In 1969, L. Esaki and R. Tsu pointed out that the mobility of the electrons near an interface between two semiconductors of different bandgaps (i.e. a heterointerface) would be enhanced. The time was almost ripe for fabrication of high-quality hetero-interfaces, due to the pioneering work on Molecular Beam Epitaxy (MBE) by A.Y. Cho at AT&T Bell Labs. A physicist working at Bell Labs, Raymond Dingle, was interested in optical spectroscopy of semiconductors, and studied excitons in MBE grown GaAs with good results. To quote Dingle (©1984 IEEE):

Always in the back of our minds was the old question, "What if these layers were so thin that one could see quantization effects; after all, the exciton spectrum of 4000 A of MBE GaAIl was so clear and readily understood?" (reprod uced here in Figure 11.1, top trace).

Dingle initially had trouble seeing the weak optical absorption when the thickness was decreased below 1000 A, but quickly found a solution for this problem:

... Since multiple layers could be readily grown, we simply grew a multilayer (AI, Ga)As/GaAs structure containing 10 or 20 layers interleaved with (AI, Ga)As support layers [note: (AI, Ga)As has a wider bandgap and showed no absorption]. The growth technique was described as "semi-automatic" and consisted of watching the second hand of a darkroom timer and manually rotating a shutter on

* Other names for the same device are: (1) HEMT (High Electron Mobility Transistor), (2) MODFET (Modulation Doped FET), (3) SDHFET (Selectively Doped Heterostructure FET), (4) TEGFET (Two-Dimensional Electron Gas FET). We have chosen HFET to emphasize the similarity with MESFETs.

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

364 Microwave Semiconductor Devices

___ --------------Lt -4OQOA

n·4

n· 3

n· 3

1.515 1.550 1.600 1.650 1.700

ENERGY leV)

Figure 11.1. The original optical.absorption spectra recorded on (Al, GaJAs/GaAs multi-quantum well structures. The GaAs layers had three different thickneues, as noted on the curves. Reprinted from DINGLE, R. (1984). "New High-Speed III- V Devices for Integrated Circuits," IEEE Trans. Electron Devices, ED-31, 1662, @1984 IEEE.

the aluminum effusion oven of the MBE system to initiate and terminate (Al, Ga)As layer growth. In early 1974 a multilayer structure with 200 A-thick GaAs layers and thicker (Al, Ga)As support layers was grown. With the help of Len Kopf, we measured the absorption spectrum at 2K and observed the first direct evidence for size quantization of electron motion in GaAs (the center trace in Figure 11.1). There was great jubilation in my lab - we even danced a bit, as I recall! I began to believe in quantum mechanics!

In order to explain these results, we should refer to the (partial) energy band diagram in Figure 11.2. We assume a "selection-doped" structure, which has n-doped AlGaAs layers, as used in Dingle's later experiments. The material Al"Gal_"As has a larger bandgap than GaAs. Therefore it has a higher conduction band energy than GaAs, see the sketch in Figure 11.2 (b). As the electrons transfer to the lower energy in the conduction band of GaAs, they will stay close to the interface, due to the electrostatic attraction to the donors in the (Al, Ga)As, as indicated in Figure 11.2. The potential energy of the electrons therefore forms a roughly triangular potential well near the interface. An enlarged picture of the energy bands is given in Figure 11.3. The potential well is of the order of only 100 A wide in a typical case, and the electrons are therefore confined to a very small space in the direction perpendicular to the interface. From elementary quantum mechanics, we recognize this as the

Chapter 11 365

well-known potential well problem. The solutions represent discrete quantummechanical states. Since the electrons are now restricted in their motion in the perpendicular direction, one uses the term "two-dimensional electron gas" , abbreviated "2DEG". The electron transitions which give rise to the absorption which Dingle observed, are due to electrons crossing the bandgap, with the discrete states in the potential well as the final state. Note in Figure 11.1 that the wider GaAs layers give rise to a larger number of states which can be observed, as would be expected due to the larger number of discrete states in a well of greater width. (the first experiments were performed on undoped structures which give "square" wells).

The next step toward a practical device was taken when in 1978, Dingle's group measured the mobility of electrons parallel to the layers. In the initial experiments, mobilities of 10,000 to 20,000 cm2 /Vsec were measured at low temperatures, whereas a maximum mobility of 6,000 was common for bulk GaAs. Figure 11.4 shows the rapid progress in terms of increased mobility with the year when the measurements were done as a parameter. Eventually, mobilities as high as 2 x 106 were obtained. Returning to Figure 11.3, the high mobilities occur because essentially all of the electrons transfer from the (AI, Ga)As to the GaAs, which is made very pure. The pure GaAs has very few impurities which can scatter the electrons. The resulting room temperature mobility is about 8,500-9,000 cm2 /Vsec, a value which is typical for pure GaAs at room temperature. At low temperatures, the phonon scattering essentially disappears, and the residual scattering is due to the very few impurities which exist in the GaAs, scattering from interface roughness, and scattering due to long-range electrostatic interaction with the donors in the (AI, Ga)As. These scattering mechanisms are so weak, though, that the mobility rises dramatically.

The device which was designed to utilize the high electron mobility at the interface, the "HFET", has a configuration quite similar to that ofa MESFET, see Figure 11.5. An additional highly doped layer of GaAs is grown next to the source and drain contacts. The high doping under the contacts has to extend to the depth of the GaAs 2DEG "channel", so that a low series resistance path exists to this channel. The crucial region under the gate is entirely in the high-mobility mode, provided that the gate voltage, and the thickness and doping level of the (AI, Ga)As, are such that the AIGaAs is completely depleted. There is usually a thin (20-80 A) un doped buffer layer of AIGaAs close to to the interface, which prevents electrons in the quantum well from being scattered by impurities due to the long-range forces. The HFET current is controlled by the gate voltage in a manner which we will describe in some detail in the following section. We note already, however, that the AIGaAs layer acts like a constant width capacitor - compare this with the case of the depletion region in MESFETs, which changes width in response to the gate voltage. Since the AIGaAs layer is very thin (about 300 A or 0.03 micrometers) one obtains a high transconductance (up to 500 mS/mm at room-temperature). The following sections will discuss the physics of the


(a) Cross-section of layers

(b) Conduction Band

~_}AI'Ga,.,As{

__ } GaAs {

~~}AI'Ga,.,As{

__ } GaAs {

'~?/H'~"=,-,"':"~---,-"---'-'--'-'- } Al,Ga ,.,As {

[J Doped <:) Electrons

[J Undoped ® Ionized Donors

Figure 11.2. (a) A multi-layer structure of (AI,Ga)As/GaAs with modulation doped AlGaAs layers. (b) The conduction band of the material. Adapted from SOLOMON, P. and MORKOC, H. (1984). "ModulationDoped GaAs/AlGaAs Heterojunction Field Effect Transistors (MODFETs), Ultrahigh-Speed Device for Supercomputers," IEEE Trans. Electron Devices, ED-31, 1015, @1984 IEEE.

, , , , ,

Doped -,- Undoped

x = -W2 x 0 d I

AI,Ga, ., As -1- GaAs

e,

Figure 11.3. Energy band diagram of an (AI,Ga)As/GaAs heterojunction. The two-dimensional electron gas is located in the triangular well nezt to the interface. Adapted from DR UMMOND, T.J., MASSELINK, W. T., and MORKOC, H. (1986). "Modulation-Doped GaAs/(AI,Ga)As Heterojunction Field-Effect Transi8tor,: MODFETs," Proc. IEEE, 74, 773, @1986 IEEE.

Chapter 11 367

a

! na ...

! 1DOJIOD t o-'.:.:."~-o--<>-o..-

"'. '171

, .....

u.~~WWL-~~~~-LU S112t1 51 ,DO_.

--[<J Temperolure I K)

Figure 11.4 (a) Mobility of electron. in hetero.tructure., versus temperature, with the time of the measurement as parameter. Reprinted /rom DINGLE, R. (1984), "New High·Speed III· V Device, for Integrated Circuib," IEEE Tram. Electron Device" ED·31, 1662, with permi',ion. (b) 'Typical pre.ent range of electron mobility value, for (AI, Ga)A,/GaA, 2DEG Itructure" ver,u. temperature. The mobility of bulk .ample. of GaA. is al.o indicated. The top curve marked 'bulk' is for a nominally pure .ample. Theoretical curve" are drawn for Polar Optical (Phonon) (PO), Acou.tic Deformation Potential (AP), Piezo·electric (PE), and Ionized Impurity ('NI = 4 X lOU') ,cattering procelle,. Reprinted /rom DRUMMOND, T.!., MASSELINK, W.T., and MORK09, H.(1986). "Modulation.Doped GaA./(AI,Ga)A. Heterojunction Field·Effect Tran,i.tor.: MODFET.," Proc. IEEE, 74, 773, @1986 IEEE.

SOURCE

SELECTIVELY DOPED HETEROSTRUCTURE

DRAIN

~-----------------------SEMI INSULATING

GoAS SUBSTRATE

Figure 11.5. 'Typical croll·,ection of a HFET. Reprinted /rom DINGLE, R. (1984). "New High-Speed III· V Device. for Integrated Circuib," IEEE Tran •. Electron Device., ED.31, 1662, @198-1 IEEE.


HFET in greater detail, as well as the performance which can be obtained in terms of cut-off frequency, noise figure and output power. We will treat several new materials combinations, such as those involving (In, A/)As or (In, Ga)As. HFETs with the new materials have shown drastically improved performance compared with the original GaAs/ AIGaAs system.

DISCUSSION OF THE I-V-CHARACTERISTICS OF A HFET

Energy Bands of Hetero-junctions

This section follows review papers such as (Solomon and Mork<><;, 1984; Drummond et al., 1986; Delagebeaudeuf and Linh, 1981; Lee et al., 1983). We have pictured the energy bands of two semiconductors with different bandgaps in Figure 11.6. The relative levels of the two conduction bands when a heterojunction is made from these two materials are often found by application of Anderson's rule:

ll.t:c = Xl - X2 (11.1)

where ll.t:c is the difference in conduction band energy, as shown in Figure 11.6A, and Xl and X2 are the electron affinities of the two materials. For the (AI, Ga)As/GaAs heterojunction, this energy difference is of the order of:ll eV, where :II is the fraction of aluminum in the formula AlzGal_zAs, i.e. typically 0.2 - 0.3 eV. If we further assume that the AIGaAs is n-type, and the GaAs intrinsic, we find the arrangement of the energy levels, and the Fermi level, as in Figure 11.6H. Some recent evidence suggests that Anderson's rule may not be obeyed all that well in this junction, and we will discuss this later. In any case, the depth of the potential well is considerably greater than the thermal energy at room temperature (about 0.025 eV), so that we can expect the electrons to stay confined in the well.

Energy Levels of the Electrons in the Well

The simplest model for finding the allowed energy eigen-values for the electrons in the well, is to assume that the potential well has triangular shape, i.e. the potential is linear in :II, V = eEsz, and the electric field in the well is constant. From Gauss's law, Es = ens, where ns is the total electron surface concentration (per unit area). The solution to the Schroedinger equation for this potential yields energy eigenvalues of

(11.2)

The electron charge is thus distributed among a number oflevels:

ns = 2:n.o (11.3)

Chapter 11

(a)

(b) N-Doped AlxGa1_xAs

Vacuum Level

, y. ------

369

Figure 11.6. Energy band diagram~ for a heterojunction. (a) Before, and (b) after formation of the junction.

In practise, this form of the eigenvalues can be used, provided that we use an empirically derived value for the constant '"'( in the following equations (only the two lowest energy levels will be taken into account).

The values of of the constants are '"'(0

3.2 X lO-12eVm4 / 3 •

(11.4)

2.5 X 1O-12eVm4 / 3 and '"'(1 ==


Density of Electrons in the Well for a Given EF

The density of states function for an "ordinary" three-dimensional electron gas was given in Chapter 1, see (1.10).

( 1 )2 (2m.) j p(E) = 211" h2 VE - E. (11.5)

This function was arrived at by counting the states in a spherical shell in the three dimensions of k-space. If we use the same procedure for the twodimensional k-space of the 2DEG in a hetero-junction quantum-well, we find instead:

1 (2m-) p2D(E) = 211" h2 (11.6)

The energy of an electron in a given quantized state in the quantum well, say Eo, is (z is the direction which is quantized)

1 1i,2(k~ + k~) E=Eo+-·-'--"-_-c"

2 m' (11. 7)

As the energy is incremented by dE, the area in two-dimensional k-space is incremented by 211"k dk, the area of a circular ring, see Figure 11.7. But dE and k dk are proportional to each other, and it then follows that a given energy increment always corresponds to the same number of states in two-dimensional k-space, i.e. the density of states function is independent of the energy. When the energy of the next discrete state is reached, the total density of states will increase abruptly by a factor equal to the degeneracy of that state, as pictured in Figure 11.8. In this sense, the electrons in each discrete state (in the zdirection) actually are in a sub-band in which there is a continuity of energies due to the additional energy from the motion in the y- and z-directions. For our particular case, we shall assume that the constant density of states will be D for energies between Eo and E1, and that the density of states increases to 2D above E1, as shown in Figure 11.8. Neglecting any higher "sub-bands", we can find the total density of electrons by integrating the density of states function times the Fermi-Dirac distribution function, i.e.

ns = D re, dE + 2D roo dE leo l+exp [e,e/t;-:,l] le, l+exp [e,e/t;1rl] (11.8)

Using the standard integral, f dz/l + eZ = -In(1 + e- Z ), we find the result:

kT [ (e,-eol] [ (e .. -e,)] ns=D-;:ln l+ee~ l+ee~ (11.9)

Chapter 11 371

Area = 2 1t kdk

Energye Energy e+ de

Figure 11.7. nlustration for calculation of the density of states of electrons in a £DEG.

P 2D (e)

o I I I I

I

20

Figure 11.S. The density 01 states function lor the 2DEG.

which can also be written

kBT 1 { [EF-Ei]} nS = D-e- t;ln 1 + exp e~

...

(11.10)

The value of D = ~ from (11.6). Numerically, D for GaAs is 3.24 X 1013

cm- 2eV.

In this equation, Eo and El depend on ns (see 11.4». For each value of EF , one must iterate to find the corresponding value ofns. The resulting curve of ns as a function of EF is shown in Figure 11.9. One can see from this


1" 2.0 ~x ..!1~0_12_~_~.----__ .,--_--, u ;: T = 3000 K -~ 1.5

~ ... 1.0 (II ;: ... 1\1 () (II

0.5 u 1\1 1: 0 (II

E -0.2 -0.1 o 0.1 0.2 Fermi Level (Volts)

Figure 11.9. Interface carrier density in a 2DEG in Si and GaAs, respectively, versus Fermi energy. A linear approzimation is also shown. Reprinted from DRUMMOND, T.J., MASSELINK, W.T., and MORK09, H. (1986). "Modulation-Doped GaAs/( AI, Ga)As Heterojunction Field-Effect Transistors: MODFETs,!J Proc. IEEE, 74, 773, @1986 IEEE .

• E-Field I I

Doped : Undoped I

(AI, Ga)As ...... Il-i--I--- --. GaAs I I

-+~----------~--------~--------~x

x=Q

Figure 11.10. Electric field distribution near the heterojunction.

figure that for much of the typical range of values of the surface density, there is a linear relationship between ns and £F. We can write this relationship:

(11.11)

where a£Fo(T) and a are constants (a = 0.125 X 10-12 Vcm2 and a£Fo(T) is equal to 0 at 300K and 0.025 eV at 77K and below. This approximate relation between ns and £F is often accurate enough for practical calculations.

Chapter 11 373

Self-consistent Relation Between ns and [F

The value of the Fermi-energy of course depends on the conditions in the AIGaAs as well, and a self-consistent solution must be found, which satisfies the conditions related to both the electrons in the well and the electrons and donors in the AIGaAs. An approximate model assumes that a portion of the AIGaAs between z = -wa and 0 is completely depleted, while the AIGaAs layer between z = 0 and z = d; is undoped. The geometry is given in Figure 11.4. Poisson's equation/Gauss law show that the electric field varies linearly in the depletion layer, and is constant to the right of this. We can write the following expressions for the electric field (see Fig. 11.10):

eND For - wa < z < 0: Ea(z) = --(z + wa)

£2

eND e and for 0 < z < d;: Ea(z) = --Wa = const. = -ns

£a €

(11.12)

The potential differel!-ce across the AIGaAs layers (Vao = Er -.t1Ec) is found by integrating these electric fields, and the width of the depleted layer can be expressed in terms of this potential difference as follows:

Wa = -d; + d2 2E2 V20 .+--, eND (11.13)

The solutions for the quantum well and the AIGaAs layer are matched by requiring that e/€a times the surface charge, ns, must equal the electric field at the interface of the two regions, i.e.

£aeNDWa . / £2 E a(d;) = = -eNDd; + V e2Nbdl + 2£2VaoeND = ens (11.14)

€2

To find ns as a function of [F, we must obtain a self-consistent solution to equations (11.4), (11.5), (11.9), (11.11) and (11.14). For a more accurate model, one should also take into account that all donors in the AIGaAs are not ionized - this gives a correction 6, which is 25 meV at 300K and 50 meV at 77K. If we use this correction, as well as the linear relation (11.11), we find a more accurate version of Eq. (11.14):

{ 2£2ND [ a[Fo(T) ] 2 2}t ns = -e- V20 - e + 6 + ND(d; + ad) - ND(d; + ad)

(11.15)

The quantity ad = (Ea)/e is about 80 A. The resulting dependence on ns for the Fermi-energy (relative to the conduction band edge at the well side of the interface) is displayed in Figure 11.ll. The position of the two lowest sub-levels in the well can be compared from Figure 11.12 (OOK data). It can be seen that the Fermi energy is of the order of a few ten's of me V above the bottom of the triangular well, and typically between the first and the second sub-band edges. Most of the electron population is in one of the two lowest


-50~1 -----!:----'.--3 -4-!---!-5-----;6--';7~8:-c9~IOX IOU

ns (cm2 )

Figure 11.11. Calculated Fermi energy relative to the conduction band edge at the interface, versus ns. The dashed curve is obtained from the triangular well approzimation. Reprinted from DRUMMOND, T.J., MASSELINK, W. T., and MORK09, H. {1986}. "Modulation-Doped GaAs/{AI,Ga}As Heterojunction Field-Effect Tranllilltorll: MODFET,," Proc. IEEE, 74, 773, @1986 IEEE.

~40 (a) 5 L-_-L------= w20b=:~;:::::::::::~

~ 60t::-~----

(b) 540

0';-1-----!:----'--~4--'----;~'8~IOX10ll ns (cm-2)

Figure 11.12. Calculated values of {a} Co (b) C1 - co, versus density of the f!DEG. Several values have been assumed for the background net acceptor doping denllity in the GaAs, as marked. Reprinted from DRUMMOND, T.J., MASSELINK, W.T., and MORK09, H. {1986}. "Modulation-Doped GaAs/{AI,Ga}As Heterojunction Field-Effect Tranllistorll: MODFETII," Proc. IEEE, 74, 773, @1986 IEEE.

Chapter 11

10" Doping Density (cm-3)

375

Figure 11.13. Interface carrier density versus doping density in the (AI, Ga}As, with the thickneSl of the Alo.sGao.7AB layer as a parameter. The solid lines are obtained from (11.15), and the dotted ones from a numerical solution. Reprinted from SHUR, M. (1987). "GaAs Devices and Circuits," Plenum PrellS, New York, with permillSion.

20XIOll~, __ ~_-~--~_--~--~-~

N 'E 15 u

>

"' ~lO o ~ (;

U 5

'" u -2 :v .s 00

..... -,-,-0300K

.,.,', ... __ .. :--: ;6:

o o

..... ...................................•.

o o

100 200 300 Undoped Loyer Thickness (A)

Figure 11.14. Interface carrier density versus undoped Alo.33Gao.67A" layer thickness for different temperature". Ezperimental point. are for heterostructures with 0.15 ILm of Alo.33Gao.67AB doped with N D = 7 X 1017 cm-3. Solid lines are from (11.15); dotted line using the depletion approzimation and t..d = 0 at 300K. Reprinted from SHUR, M. (1987). "GaAs Devices and Circuita," Plenum Preu, New York, with permi66ion.


sub-bands. The interface carrier density also depends on the doping density in the AIGaAs, and the thickness of the undoped layer, see Figures 11.13 and 11.14. Typically, about 100 A of the A1GaAa will be depleted by the interface, if the doping is 1018 cm-3 (the total thickness of the AIGaAs may be about 300 A).

Charge Control of the Interface Carrier Density Through the Gate Voltage

When a metallic gate electrode is deposited on the AIGaAs, further depletion will in general occur. The conduction band picture for this case is as shown in Figure 11.15. We assume that the entire AlGa As layer is depleted, and integrate Poisson's equation twice to find the potential difference across this layer as:

(11.16)

We may introduce the pinch-off voltage in analogy with the same expression for MESFETs, i.e. VP2 = ~d~. But V2 is also equal to tPb- Va +EF/eIlEc/e, from Figure 11.15, i.e. we can find the interface carrier density (which is still related to the interface electric field) as

£2 ( EF AEc ) ns = VP2 - tPb - - + -- + Va e(dd + d;) e e

(11.17)

If we again use the linear relation between Fermi energy and interface carrier density (11.11), we find a simple expression for ns, which is very accurate except for close to the threshold, see Figure 11.16.

£2 Va - VoJl ns = --; x d + Ad (11.18)

We have introduced VoJJ = V~II + AEFo/e, where V~II = tPb - AEc/e -VP2, and Ad which is as given before, as well as d = dd + d;.

Current Voltage Characteristics for HFETs

The discussion of the J-V -characteristics for HFETs follows very similar lines to that for MESFETs. The interface carrier density would vary along the channel, as predicted by Eq. (11.18), with the actual gate-to-channel voltage at each point inserted. The drain to source current would in general be

(11.19)

where Z is the width of the gate fingers, and v(E) is the drift velocity. Several simplified models have been used for the viE relationship (Shur, 1987): (1) A two-piece linear model similar to that of the PHS model for MESFETs, (2) A three-piece linear model, see Figure 11.17, and (3) approximate analytical

Chapter 11

ec)l +

I I I~

+

Doped (Nd) Undoped I

+ + ++---

++ ++ +

I I I

AlxGa1_xAs

377

GaAs

Figure 11.15. Energ" band diagram for HFET. The (AI, Ga)A, la"er hall been completel" depleted b" application of a negative voltage to the gate. Adapted from SHUR, M. (1987). "GaA .. Device, and Circuit,," Plenum Pre ... , New York, with permillSion.

2El2 ~SUR:::.F.:;.AC=E...:C:::.A".:::=''':.,..:::DE:::.NS::.'TY ___ (=_...:'-.;2 ___ '_--:;,..,.-,, __ _ / .1

/ .'/~

/ /,.

1£12 1----+--~/,,L.,~/4----4----

-// //

·f .S I.S

GATE YDLTAGEM

Figure 11.16. Interface carrier den,it" in a HFET ver,u, the voltage between the gate and the channel. The ,olid line u,ell a ,imple model from DELAGEBEAUDEUF and LINH (1981); the dotted line i, a numerical ,olution, and the da,hed line reprelent' Eq. (11.18). Reprinted from DRUMMOND, T.J., MORKOt;, H., LEE, K., and SHUR, M. (1981). "Model for Modulation Doped Field Effect 7ran,iltor," IEEE Electron Device Lett., EDL-9, 998, @198IIEEE.


F2 Electrical Field

Figure 11.17. Three-piece linear approzimation for the velocity/field characteristic in a HFET. Reprinted from LEE,K., SHUR, M.S., DRUMMOND, T.J., and MORKOr;, H. (1983). "Current- Voltage and Capacitance- Voltage Characteristics of Modulation-Doped Field Effect Transistors," IEEE Trans. Electron Devices, ED-30, f07, @1983 IEEE.

C ~15 -:J

U c o ~lO -

3i c 5-6 Ci

- 3 Piece Made .... 2 Piece Made o Experimental Data

~o -06 -0.4 -02 0 0.2 0.4 06 0.8 10 Gate-To-Source Voltage (Vg,IVJ)

Figure 11.18. IDS/VGS characteristics predicted based on two- and three piece velocity models. Reprinted from LEE, K., SHUR, M.S., DRUMMOND, T.J., and MORKOr;, H. (19BS). "Current- Voltage and Capacitance- Voltage Characteristics of Modulation-Doped Field Effect Transi6tors," IEEE Trans. Electron Devices, ED-30, f07, @1983 IEEE.

Chapter 11 379

expressions, which give a smooth variation of v versus E. Figure 11.18 shows that the three-piece model gives a slightly better fit for the variation of the saturated drain current with gate voltage, while Figure 11.19 shows the reasonable agreement obtained for the entire I-V-characteristic. The smooth velocity function improves the fit for the latter, see Figure 11.20 (Shur, 1987).

TRANSCONDUCTANCE AND CUT-OFF FREQUENCIES FOR HFETs

The maximum saturated drain current is easily obtained as

(11.19)

An approximate expression for the maximum transconductance is also easily seen to be, in analogy with (10.35) and (10.36) for MESFETs,

(11.20)

(11.21)

Note that the gate-length cancels in (11.20) for this simplified model. For short gate-lengths, however, we expect velocity over-shoot effects to become prominent. For this case, we may use the average velocity < v > under the gate instead of V,lle. Equations (11.20) or (11.21) are often used to estimate the average drift velocity from the measured transconductance per unit gate width, or fT. We expect higher values {or 9m in HFETs due to mainly two factors: (1) The effective distance from the gate, at which the electrons are being controlled, (Le. d + ad) is smaller for HFETs, and (2) the velocity over-shoot effects may become more prominent due to the higher initial mobility, which allows electrons to get to the overshoot region faster. The velocity overshoot effects in HFETs are discussed in some detail later in this section. Typical maximum transconductance values {or MESFETs and HFETs are compared in Table 11.1. The transconductance of HFETs increases considerably as the temperature is lowered.


30,----------------------------------,

25

4' EZO

c ~ 15 u

,r/-,-"-'-/-;_,,.._~~_"'-_.=:-_-"'.::---=--.:::---:.:--:.:---=.::.~-:..----:_--~-~ Vg,~OV

tf"---:;c~="----------- -02V

-.-----_ ... --~----------

,r-~~--------------------04V

---~------ .. --6/,"""'-'------------ -O.6V

--------·------------7-------j z

DrOln-To-Source Vcl1ag€ (VdS[VJ)

Figure 11.19. IDs/VDs characteristic for HFET predicted on the basis of the three-piece linear model in Figure 11.17. The dots are measured points. Reprinted from LEE, K., SHUR, M.S., DRUMMOND, T.J., and MORKO(;, H. (1983). "Current- Voltage and Capacitance- Voltage Characteristics of Modulation-Doped Field Effect Transistors," IEEE Trans. Electron Devices, ED-30, 207, @1983 IEEE.

<t 25 E I-~ 20

!E ::> u 15 UJ u 0:: ::> 5l 10

I o lI

Z <i' 0:: <:>

• Measured -- Calculated

. . . . .

. . . . VGS·O.OV

1.0 2.0 3.0

DRAIN-TO-SOURCE VOLTAGE (V)

Figure 11.20. IDs/VDs characteristic for HFET predicted on the basis of a smooth velocity/field characteristic. The dot" are measured points. Reprinted from SHUR, M. {1987}. "GaAs Devices and Circuits," Plenum Press, New York, with permiuion.

Chapter 11 381

Table 11.1

Typical maximum transconductance data for MESFETs and HFETs (quoted from the sources given).

Type of gm,e L, IT Reference Device mS/mm I'm GHz

MESFET 500-600 0.1-0.2 90 Enoki et al. ("SAINT") (1990)

AIGaAB/GaAs HFET,

T= 300K 450 0.3 -80 Zimmermann T=77K 900 0.3 and Salmer (1990)

PHFET 1,100 0.25 120 Fu et al. (1990)

InP-Based HFET 1,200 0.25 190 Fu et al. (1990)

Typical curves of 9m, Cg., IT and Gtl versus V,. are shown in Figure 11.21. One should note that the physical model above yields the intrinsic transconductance, 9m,o. The extrinsic conductance (9m,.) (from the device terminals) has to be measured through Rs, however. The two values are related as follows:

_ 9m,o 9m,.- 1+

9m,o Rs (11.22)

A higher average velocity for electrons in HFETs can be predicted in Monte Carlo simulations, of which Figure 11.22(a) gives an example. This simulation shows quite high over-shoot velocities when the 2DEG electrons are being accelerated by a constant electric field. In actual HFETs, the electric field distribution is of course not uniform at all, as can be seen from Figure 11.22(b), which gives results from simulations of a 0.51-'m gatelength HFET using a simplified model (Salmer et al., 1988). It is noteworthy that the electric field stays fairly low (less than 10 kV /cm) under most ofthe gate length, and that the electron energy also stays below the 0.32 eV necessary for intervalley transfer, until the electrons reach the very edge of the gate. When this happens, the electrons do slow down quickly, but since they have almost traversed the entire length of the gate, the average velocity still stays quite high. Monte Carlo simulations give similar results, and an average velocity of 1.5 x 107 em/sec for a 0.251-'m device (Salmer et al., 1988).

From the above model, we realize that the unprecedentedly high mobility of electrons in HFETs is not the most important feature of the device, although one of the original names for the devices, "High Electron Mobility Transistor (HEMT)" , was chosen because of this feature. Instead, the important property

382

gm (mS)

80

60

40

20

VgS(V)

-.5 0 .5

60 fc (GHz)

Microwave Semiconductor Devices

.4 C gs (pF)

.1

Vgs (V) 0 -1 -.5 0 .5

5 Gd (mS)

4

3

2

Vgs(V)

~1~-----·~.5------~0~----~.5

Figure 11.21. Typical curve6 of gm, Cg" fT' and output conductance, Gil, ver6US gate-to-source voltage, for a 0.5 p,m-gate HFET, with Z = 200 J.l.m, at VDS = 2V. Reprinted from ZIMMERMANN, J., and SALMER, G. (1990). "High-Electron-Mobility Transistors: Principles and Applications," in Handbook of Microwave and Optical Components, K. Chang, Ed., John Wiley & Sons, New York, Vol. 2, Ch. 9, p. -137, with permission.

is the average velocity of the electrons, as they experience very high electric fields under the gate. The mobility actually decreases rapidly as the field is increased, as indicated in Figure 11.23. While low energy electrons have a mobility which is mainly limited by remote scattering due the donors in the A1GaAs, higher energy electrons will lose their momentum (and energy) chiefly by emitting optical phonons, just as the high energy electrons in bulk GaAs do (compare discussions in Chapters 2 and 10). The details in the optical phonon processes differ somewhat, and therefore we find that the viE-curve is similar to, but not identical to, the one for the bulk case. These curves have been measured by Masselink et al. (1988), see Figure 11.24. Note the much higher initial slope of the 2-DEG curve for low fields, and the fact that the maximum velocities and saturation velocities are quite close. In the HFET

Chapter 11

0.8

0.6

0.4

0.2

0

6.0r---...,....-----,----,---.... ----,

~ ;: 3.0

S : :3 2.0 / w >

1.0

FIELD = 10 kV/cm

a T = 77 K

--2DEG ---- BULK GaAs

No = 1 x 1018::-:S---- --------------O.0!-::O----:,:O---~:;_-___;~--7r;__-~

0.0 1.0 2.0 3.0 4.0 5.0 TIME (psec)

t- E kV/cm eV

,-, b , \ , \ V

10 5 m/s 80

v_ 60

40

20

I \ __ E , \

I \ 1.1 \ 1/' \ 'i ! \ f.

r c-; '-., \ ,

\.

\~

4

3

2

383

Figure 11.22. (a) Average drift velocity ver~u~ time for electron6 in a 2DEG and highly doped bulk GaA", respectively, after a uniform electric field of 10 kV/cm has been applied at t = O. Reprinted /rom TOMIZAWA, M., YOKOYAMA, K., and YOSHII, A. (1984). "Hot-Electron Velocity Characteristics at AIGaAs/GaAs Heterostructure6," IEEE Electron Devices Lett., EDL-5, 464, @1984 IEEE. (b) Electric field, electron velocity, and electron energy ver6U. po.ition in a O.5J.£m HFET device. Reprinted from SALMER, G. ZIMMERMANN, J., and FAUQUEMBERGUE, R. (1988). "Modeling of MODFET.," IEEE 1ranl. Microw. Theory Tech., MTT-96, 1124, @1988 IEEE.

device, low-field conditions exist only near the source, and the effect of the high mobility is that the electrons accelerate faster than in bulk GaA., and reach their saturation velocity more quickly - this of course will increase the average velocity, as long as no inter-valley transfer occurs later on. On the basis of this


simple argument, we may expect HFETs to have a somewhat faster transit time than MESFETs, for the same gate length.

The "conventional" HFET, with a GaAs/ A1GaAs heterostructure, has some disadvantages, which eventually became apparent. One of these is that the accelerated electrons may acquire sufficient energy to overcome the potential barrier, and transfer back to the A1GaAs, the "real space (as opposed to momentum space) transfer effect," or RST. These electrons will have a much lower velocity, which results in a decrease of the transconductance, as well as a lower speed of the HFET. At lower temperatures (77 K), these electrons may be captured by traps in the AIGaAs, and cause the 1-V-characteristic to "collapse", since the traps are deep enough that the electrons will not be released from them by thermal energy. Figure 11.25 gives an example of this phenomenon. The electrons may be excited out of the traps by using visible light (a small LED is sufficient). The trap density generally increases with the AI-concentration, and this is therefore usually kept to about 15%. Unfortunately, the bandgap discontinuity also increases with increasing Al content, and one would have liked to increase the aluminum fraction for this reason, in order to minimize real space transfer. It is clear that other material combinations with larger band offsets, and with low trap density, would be superior to AIGaAs/GaAs. These will be introduced in the next section.

As technology advanced, it became possible to grow one or more highly doped (1018 to 10111) thin layers in the AlGaAs, while leaving the remainder lightly doped. This process is known as "planar doping", "spike doping", or "pulse doping". The doped layer may actually be AlAs, which eliminates most of the traps which are characteristic of AIGaAs. The planar doping increases the transconductance by being a more efficient method for supplying electrons to the channel.

Pulse doping can also be accomplished by laying down in the channel of a FET device (MESFET or HFET) an atomic layer of the donor atom (which may be silicon), only. In this case, the positive charge of the donors creates a quantum well, similar to the hetero-junction quantum well we have described for conventional HFETs. The electrons will again be trapped in this well, and will spread over a depth of maybe 100 A. The mobility of electrons in the pulse-doped well is not very high due to the high donor density - the scattering of the electrons by the donors is, however, also decreased by the fact that the electron wavefunction "filling factor" with respect to the donors is rather low (the wavefunction spread is 100 A, say, versus maybe 5 A for the donors). We will return to this question in the next section.

Chapter 11

o 2 Electric Field (kV/cm)

385

Figure 11.23. Electron mobility in Alo.2Gao.sA8/GaA8, at 11K verSU8 electric field. The full line i8 the average mobility, including electrons in the AlGaAs, and the dotted curve the mobility for electrons in the 2-DEG only. Adapted from SHUR, M. (1981). "GaAs Devices and Circuits," Plenum Press, New York, with permission.

25

'" 300K

g 20

~o ,,"',,'--------..... _------15 , ,

>- ,,~ ............ '0 0

" 10 ;> Bulk GaAs c e 2DEG x=0.3 U 5 2DEG x=D.5 OJ UJ

2 3 4 5 6

Electric Field (kV fern)

35

"' 30 E u

~o 25

::- 20 ·0 0

" 15 > c 2 10 U OJ UJ 5

8 0

, I

0

..... 77K

-------------:.:.~."':~---------

Bulk GoAs

2DEG x=0.3

2DEG x=0.5

234 6

Electric Field (kV tem)

8

Figure 11.24. Measured electron velocity in AIGaAs/GaAs heterostructures, ver8US electric field, at two temperatures, 300K and 11K. Reproduced from MASSELINK, W. T. and WRIGHT, S.L. (1988). "Electron Velocity at High Electric Field8 in AIGaA8/GaAs Modulation-Doped Heterostructures," SolidState Electronic8, 31, 331, @1988 Pergamon Press pic.

386

Ids

mAlmm

100

50

'" '"


.., .., "'-,

'" '"

Vgs t

-.8v - ---

-.4v -------

--------~r/~-------------------Ov ------- - ---'" / ---

.... ",,~-- Vds v

.5 15 2

Figure 11.25. 1- V-characteristics for HFET at 77 K. The dashed lines show the "collapse" and were recorded with the device in the dark. Light illumination restores the characteristics, see the fulldrawn lines. Reprinted from ZIMMERMANN, J., and SALMER, G. (1990). "High-Electron-Mobility Transistorll: Principles and Applications," in Handbook of Microwave and Optical CoItlponents, K. Chang, Ed., John Wiley fj Sons, New York, Vol. 2, Ch. 9, p. 437, with permission.

INDIUM-BASED HETEROSTRUCTURES FOR HFETs

Pseudomorphic AlGaA8/InGaAs/GaAs Devices

Several different types of In-based heterostructures have been shown to result in excellent HFETs. The first one of these is the so-called "Pseudomorphic" HFET, or PHFET. The GaA8 in the channel of the conventional HFET is replaced by one grown from In.Gal_.As. As shown in Figure 11.26, this material is not lattice-matched to GaAs (whereas AIGaA8 is). It is still possible to grow a layer of InGaA8 on a GaA8 substrate, provided that the thickness of the layer is below a certain critical value, which depends on the amount of lattice constant mismatch. Below the critical thickness, the InGaA8 is able to adjust its lattice constant to that of the GaAs, and pick up the resulting strain. A typical thickness of InGaA8 in PHFETs is 100-200 A, with z = 0.15. Recently developed PHFETs have increased z to about 0.22 (thickness = 120 A) and 0.35 (thickness 50 A) (Smith et aI., 1990). The bandgap of InA8 is much smaller than that of GaAs, and the bandgap of InGaA8 decreases with increasing 'z' (Figure 11.26). Consequently, we will have a deeper quantum well (conduction band offset 0.3 eV for z = 0.15) at the channel position, and the channel will be able to confine the electrons better (Figure 11.27). The two-dimensional density in a PHFET may be 2 x 1012 cm-2, compared with less than 1 x 1012 for AIGaAs/GaAs. Another potential advantage is

Chapter 11 387

3

ZnSe

0 CdS

AlAs 0

2 0.6

~1.45 E

'" :1 w

0.75 0 Ga47 1n53 As I 2 Ge

I IG~5In65AS

InAs 5 I I 10

0

5.6 5.8 6.0 6.2 a o (A)

Figure 11.26. Energy band gap of different III- V compound semiconductors, versus lattice constant. Reproduced from MISHRA, U.K., BROWN, A.S., DELANEY, M.J., GREILING, P.T., and KRUMM, C.F. (1989). "The AUnAs-GaInAs HEMT for Microwave and Millimeter Wave Applications, JJ

IEEE Trans. Microw. Theory Tech., MTT-37, 1279, @1989 IEEE.

that the peak velocity for electrons in InGaAB is higher than for GaAs, see Figure 11.28. Recent simulation data, reproduced in this figure, show that a substantial advantage in peak velocity only occurs for z~0.5, however.

Pseudomorphic HFETs have been developed during the last five years, and have been demonstrated to be superior to AIGaAs/GaAB HFETs in essentially all respects. In particular, IT and 1m .. ,.. are higher, which means that PHFETs can be employed at much higher frequencies, and with lower noise figures. The process of decreasing the gate length appears to have paid off especially well for PHFETs, down to 0.1 micrometers, and perhaps even shorter. PHFETs have also been shown to be efficient power amplifiers.

As the gate length has been shortened, new phenomena have been uncovered which add to the models which have so far been established for HFETs. An example of a PHFET which shows this particularly clearly is a device with 0.1 micrometer gate length developed by Nguyen et al. (1989). Extrapolation of the measured gain gives values for IT = 152 GHz, and 1m .. ., = 250 GHz. The maximum transconductance is 600-650 mS/mm. This device con-


200A n-GQAs

350A n- Alo I~GOO.1I5 As E ~

I 30A AIo.ls GoOJI5 AS a ::0,

/,///,///////;//,02 OEGW//,//,////;//;7/- ;: 200A Ino.lsGoa 115~

u; ~

\f'm GoAs C Z .

(a) 0

~ 0

n-A!O.lSGoo.ssA5 0

flEe leV) AI Go'_

Figure 11.27. (a) Typical structure of a pseudomorphic HFET. Reprinted from KETTERSON, A.A., MASSELINK, W.T., GYMIN, 1.S., KLEM, 1., PENG, C.-K., KOPP, W.F., MORK09, H., and GLEASON, K.R. (1986). "Characterization of InGaAs/ A lGaAs Pseudomorphic Modulation-Doped FieldEffect Transistors, /I IEEE Trans. Electron Devices, ED-33, 564, @1986 IEEE. (b) Electron density in the 2DEG for pseudomorphic HFETs. Full line - theory; rectan91es - ezperiments. The mole fraction of In varies from o to 0.25. Reprinted from Moll et al. (1988), @1988 IEEE.

2.5

~ 2.0 E

~ 1.5 ~

1.0 .!! ~ 0.5

---11.0.25 unstra;n.d

-- ______ GaAs undroined

---x.O.25 stroined 0.0 O~--""5---'~O---'5--~20

Electric field (kV/cmJ

3.5

_ 3.0

E 2.5 ~

~ 2.0

~ 1.5

] 1.0

~ 0.5

I~

!I",/

1/ I

I I I

___ x.0.78 unslroined

- - _ - - x.0.53 unstrcined

__ x.O 78 strained

b

O.o.l----~--~--~-~ o 5 10 15 20

Electric: field {kV/cm,

Figure 11.28. Calculated steady-state drift velocity for electrons in undoped bulk In .. Gat_ .. A8 a8 a function of electric field, at 300 K. (a) Compared with GaAs, with z = 0.25 for the InGaAs. The strained ca8e assumes that the InGaAs layer is strained as if it had been grown on GaAs (b) z = 0.53 and 0.78. The z = 0.53 case is lattice-matched to InP, and the strained case for z = 0.78 a8sumes that the InGaAs is strained as if it had been grown on InP. Reprintedfrom THOBEL, 1.L., BAUDRY, L., CAPPY, A., BOUREL, P., and FAUQUEMBERGUE, R. (1990). "Electron Transport Properties of Strained In., Gal_lOA., /I Appl. Phys. Lett., 56, 346, with permiS6ion.

Chapter 11 389

sists of a 51 GaAB substrate, with the following epitaxiallayers:(I) 150 A of undoped 1nQ.25Gao.15AB channel, (2) a 50 A undoped Alo.3Gao.1AB spacer, (3) an atomic silicon sheet density of 6 x 1012cm- 2 (planar doping!), (4) 200 A of undoped AIGaAB, and a cap of heavily doped GaAB. The gate area is recessed so that the cap layer is eliminated under the gate. The gate is of the "mushroom" type, presently with a resistance of 600 ohms/mm. 5-parameter measurements established values for the elements in an equivalent circuit model, of the same type as is used for MESFETs. From these an intrinsic value for h was calculated:

h.o = (9 .... 0 ) = 188 GHz 211" C g• + Cd,

(11.23)

The corresponding delay time is T = -2 11 = 0.85 psec. The intrinsic and .,.. T,O

extrinsic values for h differ primarily because of the added time-constant due to the gate pads (compare 10.35!), i.e.

_ Cpad_ Tpad - -- - 0.13 psec.

9 .... 0 (11.24)

This adjusts the extrinsic h, h .• , to 162 GHz, whereas 152 GHz was measured, a reasonable agreement. The relative effect on the delay time of the actual device gate capacitance versus the gate pad capacitance scales with gate width, Z, since the gate pads are always made the same size, as Z is changed. Nguyen et al. (1989) plotted T for devices of different widths, and were thus able to verify that the gate pads did indeed cause the reduction in h. An earlier paper by Moll et al. (1988) introduced similar techniques for identifying different components which contribute to the total delay time, ~:

~ = Tc + Tpad + TelL + T" (11.25)

Here,

TC = transit time*

Tpad - defined above (11.26)

TelL = channel charging time

Ttl = drain delay

Moll et al. (1988) showed that there was a component of ~ which varied linearly with the drain-to-source voltage, and interpreted this as the time delay due to drift through the drain depletion region. This delay is termed Td.

A different plot was made of the total delay time versus the inverse of the current per unit gate width, Z / 1d •. The intercept ofthis curve with the y-axis represents a delay component which disappears when the current is very

* Defined as the "transit time under the gate", in agreement with the definition introduced in Chapter 10.


Table 11.2

Delay times in 0.1 I'm gate length PHFET (quoted from Nguyen et al. (1989), @1989 IEEE).

Component Value Delay psec Tt 0.6 TP4d 0.1 T.h 0.1 Tot 0.2

7'J' 1.0

large, which was called the channel charging time, T.h. By thus finding the remaining components of 7'.r, one can next calculate Tt as follows:

(11.27)

The result for Nguyen et al.'s (1989) device is shown in Table 11.2. Interestingly, the actual transit time is only 60% of the total time delay of 1 psec. The 0.2 I'm gate length devices which Moll et al. (1988) studied showed a total delay time of 1.6 psec., and a transit time which was 0.8 psec. Both articles estimate average velocities under the gate based on the transit time of about 2 x 107 em/sec. Moll et al. (1988) also made devices with the same geometry on AIGaA8/GaA8 material, "conventional HFETs". They concluded in a detailed argument that the higher transconductance of the pseudomorphic devices could not be explained by a higher average velocity under the gate; in fact the transit times were the same for the same gate length in both types of devices! An interesting question is also posed by the results of Chao et al. (1989), who measured and analyzed a PHFET with 0.08 I'm gate, and found a velocity under the gate of 3 x 107 cm/sec., by fitting 9m-data. The higher velocity in this case could be due to the shorter gate. A problem with Chao et al.'s (1989) procedure of obtaining v, from 9m is that the effective distance between the gate and the channel must be known. The analysis by Moll et al. (1988) does not rely on knowing this distance. It clearly would be interesting to perform this analysis for even shorter gate devices, such as the one of Chao et al. (1989).

A new picture thus emerges of the basic speed limitations of HFETs, one in which several different types of time delays have to be minimized in order to obtain the maximum total speed. The simplified model, which stressed the transit time under the gate, clearly was very useful in steering the experimental research effort toward shorter gates and materials with high peak velocities. This process now apparently has been carried so far that other factors have become significant as well. Nguyen et al. (1989) argue that it is especially important to use a high channel density, in order to minimize the channel charging time. This argument appears to also be borne out by the excellent

Chapter 11 391

results obtained with "doped channel" devices, discussed below, which have especially high channel densities. The higher percentage of indium in recent PHFET devices results in a larger band-offset, and thus greater channel density, which appears to be a major reason for the high speed of these devices. Nguyen et al. (1989) also argue that the drain delay time in their device has been made very short by the "virtually self-aligned" gate recess process, and the heavily doped GaAs cap. Now that it has been made clear that essential and meaningful new information regarding delay times in a device can be obtained by experimental means, a challenging task has been set for the theoretical modeling to predict these different time delays. While it may take some time before an established and complete model of this kind emerges, it appears that the above papers have started a breakthrough in our understanding ofthe speed of operation of short-gate PHFETs.

Excellent performance at 94 GHz has been achieved by using a doped channel PHFET (Smith et al., 1989b). Planar doping layers were located in the AIGaAs just above the undoped AIGaAs spacer, as well as in the middle of the InGaAs channel, which has.., = 0.22, and is 150 A thick. Peak transconductance was 625 mS/mm, and maximum current density 600 mA/mm, with gate break-down voltage of 8 volts. The sheet density was 4.2 x IOu cm- 2 •

In order to increase the current capability of both conventional HFETs and PHFETs, several channels may be grown. For example, a layer of doped AIGaAs may be added below the InGaAs channel layer in the design of Nguyen et al. (1989), see (Smith et al., 1990). Another advantage ofthe pseudomorphic design is the fact that essentially no low-temperature 1-V-collapse, or light sensitivity, can be detected. These features are consistent with the larger band-offset and lower defect density of the InGaAs.

Channel-Doped HFETs

Very high current density can be obtained by actually doping the channel. This turns the original HFET concept around, and ignores the much lower mobility which results due to impurity scattering in the channel. While this may decrease the room temperature mobility for low electric fields to about 5,000 cm2 /Vsec., the electron velocity in high electric fields is not likely to be altered very much. On the other hand, one may obtain sheet densities up to 4 x 1012cm- 2 by using two doped InGaAB channels (Saunier and Tserng, 1989). Current densities up to 1 A/mm, and extrinsic transconductance of 530 mS/mm were also found. Since the break-down voltage is still good (7-8 volts), these are good millimeter wave power devices.

The versatility of present growth technology is evidenced by the many variations possible - devices which may appear to be hybrids between the established types are now arising. One such device is the GaAs MESFET with pulse-doped InGaAIl channel (Kim et al., 1988). A 55 A layer of InGaA8 is grown inside, and near the top of, a standard GaA8 doped epitaxial MESFET


layer. The InGaAB layer has been pulse doped in the middle. The maximum transconductance and current density are considerably higher than for conventional MESFETs - 520 mS/mm and 700 mA/mm, respectively.

MISFETs (Metal Insulator Semiconductor FETs) can be made with a very similar layer structure as the PHFET, except that the AlGaAB layer is left undoped, and acts purely as an insulator (Kim et al., 1989). A doped InGaAs channel again provides a very high sheet density, and about the same current density and maximum gm as the channel-doped PHFET. Devices with doping in the quantum well were found to be much superior to those for which the well was not doped (in the latter case, the charge was supplied from a doped GaAB layer below the InGaAB). The breakdown through the AlGaAB (gate to drain) requires a very high field due to the large bandgap of this material. Instead, breakdown occurs more easily from the drain to the source, and the much lower bandgap InGaAB layer. Several different MISFET structures are discussed by Kiehl (1989). A significant advantage of MISFETs is the ability to achieve an even larger band-offset than for PHFETs. This is possible because the AlGaAB layer on top of the InGaAB channel is undoped, and one may increase the aluminum content to, say, 40%, without causing trapping problems.

There are good results for three different types of devices, PHFETs, InGaAB Pulse-Doped MESFETs, and MISFETs, at frequencies up to 60 GHz at present (1990), and it is impossible to predict which of these that will become predominant in the future. All three devices do have a common feature, however: They utilize planar doping in the channel, and achieve very high electron densities, up to 4 x 1012cm- 2 • High channel density has been shown to be much more important than high mobility in the channel, for both device speed, transconductance, and output power (see below for a discussion of HFET power devices). This is a fundamental discovery which is sure to be utilized in future devices. There are understandably almost no detailed modeling results available at the present time for these effects. All of the above channel-doped devices also have in common the fact that they are grown on SI GaA. substrates - this makes them compatible for integration in GaAB-based MMICs.

AlInAs/GalnAs InP-Based HFETs

GalnAB with a composition of Gaz1nl_"AB, where II: = 0.53, is latticematched to InP (see Figure 11.26), which is available as a substrate for epitaxial growth. Similarly, AlInAs with 48% of aluminum is also matched. The higher fraction of indium at this composition, compared with that used in PHFETs discussed above, translates into a higher (steady state) peak velocity (see Figure 11.28), 2.7x 101cm/sec. It was thus natural to attempt to fabricate HFETs on this material. Successful devices have appeared in the last couple of years only, so the technology is certainly not mature. In that short time, however, AlInAB/GaInAB HFETs have produced the highest values measured

Chapter 11 393

for IT and ImAtIJ so far. The devices have some other problems, such as high gate leakage current and low breakdown voltage, and are not nearly as reliable as, for example, PHFETs. Quite likely these problems will be solved in the future, however.

GaInAs with 21 = 0.53 has a higher mobility and peak velocity than GaInAs with 21 = 0.15 - 0.25, which is used for PHFETs. The actual effect of high peak velocity on device performance is presently a controversial subject, as discussed above. The higher mobility and the ability to form excellent ohmic contacts, demonstrably result in lower parasitic resistances of InP-based HFETs, and thus contribute to higher 1m .... , and lower noise figure, however. Another very important feature is the fact that the band offset is the largest for any of the HFET materials systems, about 0.5 eV between lattice-matched AlInAs and GaInAs (Mishra et al., 1989). If the channel is allowed to be pseudomorphic, by using GaIn As with 21 = 0.62, for example, an even larger band offset will occur. The large band offset and the high doping density possible in AIInAs (1019cm-3 ) allow a high channel density, as high as 4 X 1012cm- 2 • Channel densities of this magnitude are only possible for GaAs-based HFETs by using multi-channels, or doped channels. In the doped channel case, the high density was achieved at the expense of lowered low-field mobility and peak velocity, whereas for InP-based devices an excellent mobility and peak velocity are still maintained. The discussion of GaAs-based HFETs made it clear that a high channel density is more important than the other factors. A plausible conclusion regarding InP-based HFETs is that their very high values for /x and gm are primarily due to the ease with which a high channel density is obtained, and secondarily due to the higher mobility and peak velocity.

A typical AlInAs/GaInA8 HFET structure has the following layers (Mishra et al., 1989): (1) 51 InP substrate (2) Undoped AlInAs buffer (3) Un doped AIInAs/GaInAs supedattice (4) 400 A undoped GaInAs channel (5) 20-50 A undoped AlInAs spacer layer (6) 125 A doped AIInA8 donor layer (7) 200 A undoped AlInAs barrier layer and (8) 50 A n+ GaInAs contact layer. The AlInA II buffer layer appears to give rise to a trap-related "kink" in the 1-Vcurves, for VDS = 300 - 500 mY. Substitution of a GaInAII buffer, with an extra added super-lattice, solves this problem (Mishra et al., 1989).

The highest value of gm at present is 1450 mS/mm (Duh et al., 1990). Maximum intrinsic /x-values are 185 GHz (Duh et al., 1990), and 210 GHz (Mishra et al., 1989) for the lattice-matched and pseudomorphic versions, respectively, of the InP-based HFETs, the highest values for any 3-terminal device. An accurate estimate of Imaz is considerably more difficult to obtain. Values in the range 300-400 GHz have been quoted (Mishra et al., 1989; Smith and Swanson, 1989a). Noise figures will be given in a separate section. Fu et al. (1990) analyzed measured S-parameter data and derived an equivalent circuit from these for 0.25 /Lm devices of (1) conventional (2) pseudomorphic (21 = .2) and (3) InP-based, lattice matched, HFETs. This paper includes a


time-constant which is similar to the channel-charging time constant of Moll et al. (1988). They obtained an average velocity of about 2 x 107 cm/sec for the PHFET, in agreement with the value derived by Nguyen et al. (1989). For the InP-based device, they found < v >~ 3 X l07cm/sec., indicating that the average velocity actually is higher in this case. Further studies will have to elucidate what role high peak (steady state) velocities play in determining device transconductance and cut-off frequency, as discussed in the sections on GaAs-based HFETs.

MICROWAVE EQUIVALENT CIRCUIT FOR HFETs

For microwave applications, we of course need the complete equivalent circuit of the HFET. Weiler and Ayasli (1984) used the charge-control model of Lee et al. (1983) to find gm and ego, and compare this calculation with experimental data from several groups, with good agreement. The source resistance, Rs, was found from a frequently used transmission line model. More recently, Heinrich (1989) has developed a model, which applies to both MESFETs and HFETs. The model includes some distributed effects. For present devices, however, Heinrich (1989) showed that it is unnecessary to include the distributed phenomena, provided that one modifies the equivalent circuit as shown in Figure 11.29. The most important modification is the inclusion of the transit-time dependence of the transconductance. We will discuss this circuit further in relation to noise properties of HFETs.

The total capacitance to the gate can be obtained as the derivative of the surface charge density in the channel with respect to the gate voltage (in the region of Va for which simple charge control applies). A very simple model uses expressions which are similar to those used in SPICE simulations of MOSFETs (Shur, 1987). Reasonable agreement is found with a two-dimensional simulation, see Figure 11.30. A good reference on the determination of equivalent circuit element values from S-parameter data for HFETs is Fu et al. (1990).

NOISE MODELING OF HFETs MESFETs

COMPARISON WITH

The basic noise models developed for MESFETs can be applied for HFETs as well. Fukui's expression, (10.49), generally predicts the correct dependence of Fmin on IT, and since IT can be much higher for HFETs, we expect lower noise figures. Higher IT values have been found as the gate length has been shortened, and as a consequence, noise figures have shown a continuous decline in the last few years. The constant kF in (10.49) often has a somewhat lower value, than for MESFETs, between 1 and 2. There is also general agreement that the basic features of the PHS noise model, i.e. the dominance of diffusion noise in the saturated channel, and the cancellation of a large part of this noise due to correlation between the gate and drain noise sources, respectively, applies to HFETs. In regard to the diffusion noise there is one basic difference -

Chapter 11 395

1 o .• ~

i 0, 2~

\ 125~

1 Cso Cgo

gmo e - jWl \l 9m= 1.jW1 12

Figure 11.29. Equivalent circuit model for HFET according to Heinrich (1989). Reprinted from HEINRICH, W. (1989). "High-Frequency MESFET Modeling Including Distributed Effects," IEEE Trans. Microw. Theory Tech., MTT-37, 836, @1989 IEEE.

2.0 I I

E 15 ~ ..- / l E ,.- ..-"'- / L1.. a. /

/ w 1.0 u z <r .... u - Charge Control Model <r 0.5 <l. --- 2-d Simulation <r u

0 -1.0 -0.5 0 0.5 1.0

GATE VOLTAGE (V)

Figure 11.30. Gate-to-lOurce capacitance versus gate-to-lOurce voltage for HFET. Reprinted from SHUR, M. (1987). "GaAs Devices and Circuits," Plenum Preu, New York, with permiuion.

396 300

c: 100 o .;;; :l

o

" , , ,,' \, , , , ' , '. , , , , , ,

, , ,

10

--


--- ---

E (kV/cm)

20 30 40

Figure 11.31. Diffusion coefficients as a function of electric field at 300 K. The solid line and the dotted line apply to bulk GaAs, remaining lines to an AIGaAs/GaAs heterojunction. Reprinted from ZIMMERMANN, J., and SALMER, G. (1990). "High-Electron-Mobility Transistors: Principles and Applications," in Handbook of Microwave and Optical Components, K. Chang, Ed., John Wiley (j Sons, New York, Vol. 2, Ch. g, p. 437, with permission.

the diffusion constant for the two dimensions parallel to the plane of the channel must be different from the diffusion constant for the perpendicular direction. This difference is due to the fact that the electrons are narrowly confined to a quantized state in the perpendicular direction. Figure 11.31 shows Monte Carlo-calculated results for the two components of D versus electric field.

More and more, recent papers regarding FET noise have come to primarily treat HFET noise, and regard MESFETs as a special case. Cappy (1988) reviews FET noise theory, and measurement techniques. His expression for Fmin is basically the same as that of the PHS model, discussed in Chapter 10. It was derived in an earlier paper (Cappy et al., 1985). Figure 11.32 gives the variation of the noise coefficients R, P, and C, for a 0.5 J.l.m gate device. In comparing theoretically calculated minimum noise figures at 12 GHz with measured values, Cappy (1988) uses typical values of P = I, R = 0.5, and C = 0.9. A few of these comparisons are quoted in Table 11.3. Quite good agreement can be obtained. Cappy (1988) also gives expressions for gn == 1/ Rn, and Zapt:

Chapter 11

P

3

2

R

0.3

0.2

0.1

c

0.8

0.4

L-______ ~--------~-------L--~O o 2 3

drain-to-source voltage V

397

Figure 11.32. Evolution of the noise coejJicientl R, P, and C verSU8 VDS ,

at VGS = -0.5 V for a typical HFET. Reprinted from CAPPY, A. (1988). "Noi8e Modeling and Mea8urement Technique8," IEEE Tran8. Microw. Theory Tech., MTT-36, 1, @1988 IEEE.

gn = gm (f; r x J P + R - 2C./RP (11.28)

(R R ) PRC1-C') gm S + , + R+P-2C'IRP 1 ------=~~~=--x--

P + R - 2C.fPii wCg, Zopt=

(11.29)

1 (p -c.fPii ) +---x jWC" P + R - 2C.fPii

One should note that the noise conductance, gn, is inversely proportional to (1x)2. Since HFETs generally have higher lx's, it follows that gn is lower. This facilitates finding the optimum matching conditions for lowest noise.

It is difficult to predict accurate values of P, R and C for particular devices. However, Cappy (1988) notes that both P and R are likely to be quite similar for MESFETs and HFETs under low-noise operating conditions. The correlation coefficient, C, primarily depends on the ratio L,la, which


Table 11.3

Calculated and measured noise figures at 12 GHz for HFETs (quoted from Cappy (1988), @1988 IEEE).

Device I III V Geometry (}Lm) 0.25 x 150 0.35 x 62 0.5 x 200

9m(mS/mm) 570 330 220 Rg(O) 0.9 1.6 2.1

R.(O mm) 0.5 0.19 0.65 G A (dB) - 13 10.3 iT (GHz) 50 26 29 Fm;n (dB) 0.83 1.1 0.95 FeA/e• (dB) 0.8 1.2 1.2 FeA/e• (dB) (intrinsic) 0.6 1.08 0.98

is smaller for a given Lg for HFETs than for MESFETs due to the thinner epitaxial layer used under the gate. Typical values of C for short-gate devices are then 0.7-0.8 for MESFETs and 0.8-0.95 for HFETs.

An illuminating experimental and theoretical analysis of noise in HFETs has been published by Joshin et a1. (1989). These authors measured the drain noise current directly, from 100 to 900 MHz. They assumed that the dra.in current spectral density is frequency-independent, and could thus use the measured values to predict noise figures at microwave frequencies, and compare these with measured noise figures. Actual dra.in noise current spectral densities were found to be essentially the same for MESFETs and HFETs, when using the same dra.in (DC) currents, and the same VDs. The dra.in noise currents were then normalized with respect to the intrinsic transconductance, as follows:

'2 Q = < t A• >

4kBT 9m.oB (11.30)

Joshin et al., (1989) calculated the contributions to the dra.in current caused by different sections of the channel, see Figure 11.33. Most of this noise is caused by the region of the channel nearest the source, where the electron energy, also shown in Figure 11.33, is lower for the MESFETs. The HFET dra.in noise current has a larger peak, because it is amplified more due to the larger 9m,o for this device. When < i~. > is normalized with respect to 9m, however, a smaller value of Q is obtained for the HFET. Joshin et al. (1989) attribute the lower value of Q for HFETs to the slower heating of the electrons under the gate in HFETs, as indicated in Figure 11.33.

Joshin et al. (1989) could also estimate the correlation coefficient, C, values for both noise figure and dra.in noise current, and found C = 0.8 - 0.9. They calculated the contributions of different sections ofthe channel for devices

Chapter 11 399

Source Gate Drain

n r--. I I'

~ ·11

(x 10 )

1.2 0.8 :> ::s __ HEMT ~

1\ 1.0

'0 0.6 ·v 0.8 " E

0.6 0.4 >-

~ !:» Q)

::J c: <.> 0.4 Q) Q)

0.2 (;; <J> ·0 0.2 ." c: ro c: 0 .~ 0.0 0 0.2 0.4 0.6 0.8 1.0

Normalized distance

Figure 11.33. Electron energy and contribution to the drain noise current from a particular "ection of a HFET and a MESFET, versus normalized distance through the device. The gate length is 0.5 JLm in both cases. Reprinted from JOSHIN, K., ASAI, S., HIRACHI, Y., and ABE, M. (1989). "Ezperimental and Theoretical Noise Analysis of Microwave HEMTs," IEEE Trans. Electron Devices, ED-36, 2274, @1989 IEEE.

Source Gate Drain

~~~ LD-'---'-~~-'-~~...LD--, vl v

c: 0.4

~

~ 0.2

"g ~

L,' -02Sllm

------ 2.0 11m

~ 0.0 f--t---\''"'''*-----i

~ ·0.2

~ :0. 1.0

A 0.8

" ·v 0.6

C ~ 0.4 a m 0.2 "g

0.0 c .~

a Normalized distance

Figure 11.34. Distribution of drain and induced gate noise currents along the channel in HFETs with 0.25 and 2.0 JLm gate length, respectively. VDS = 2 V, and IDS = 10 mAo Reprinted from JOSHIN, K., A SA I, S., HIRACHI, Y., and ABE, M. (1989). "Ezperimental and Theoretical Noise Analysis of Microwave HEMTs," IEEE Trans. Electron Devices, ED.36, 2274, @1989 IEEE.

400 Microwave Semiconductor Device6

with 0.25 and 2.0 p.m. channel lengths, respectively, see Figure 11.34. The 0.25 p.m gate device has only one major peak in the gate noise current. This gate current noise also exits the input of the device, and is reflected back with a phase which depends on the source impedance. If the phase is adjusted correctly, the resulting gate noise can be made to cancel the drain noise. In the 2 p.m gate device, there are two peaks in the gate noise, one negative and one positive, and it is impossible to make the gate and drain noise cancel as effectively. The model presented by Joshin et al. (1989) thus appears to predict the essential reasons for lower noise figures in short-channel HFETs.

There is some disagreement in the recent literature concerning the applicability of Fukui's equation up to the highest frequencies (noise measurements have been performed up to 94 GHz). Heinrich (1989), and Cappy and Heinrich (1989), have extended the earlier noise models. Heinrich (1989) included distributed effects, i.e. waves were introduced which propagate in the direction of the gate fingers. Distributed effects can be neglected in present low-noise devices, Heinrich concluded. Both lumped element and distributed models predict lower Fmin for very wide gates, but this case was known to result in higher noise and lower gain, according to the older models, anyway. Heinrich (1989) also introduced a frequency dependent factor for the transconductance:

gm = g~.o x e-j"'TIl 1 + 1WTI2

(11.31)

In Heinrich's example 0.25 p.m MESFET, Til = 1.9 ps and TI2 = 0.1 ps. A frequency-dependent gm has, of course, been used to calculate the gain in conventional models, but had not been included in the PHS noise model.

In a further development, Cappy and Heinrich (1989) propose a new formulation for the impedance field. A local small-signal equivalent circuit (Fig. 11.35) is first introduced for a small section of the channel, and the Y-parameters for this section are derived. The impedance field (Z) and a gate-noise coefficient (A) can then be derived with the help of these local Yparameters. The result is that there is an intrinsic frequency dependence of the noise sources, due to the fact that the local equivalent circuit includes a capacitance. The frequency dependence is in such a direction that the noise figure decreases as the frequency goes up, relative to for example the PHS noise model. We refer to Cappy and Heinrich (1989) for detailed expressions.

The noise figures predicted by the new theories of both Heinrich (1989) and Cappy and Heinrich (1989) differ from those predicted based on conventional noise theories only for very high frequencies, as shown in Figure 11.36, which applies to a 0.25 micrometer gate HFET. One may also note that the expressions for Fmin in both conventional theories and that of Heinrich (1989) can be expressed in terms of a power series, where the expansion variable is basically 1/ IT. Based on the series expansions, one may expect that the Fukui expression, which is essentially the first order term in the expansion based on the PHS model, would work quite well at frequencies below h. This may at least partly explain the results of the GE group, who are able to fit their

Chapter 11

<aJ

Gat. IlZIZZIIZZZZZZZZ?II????

depleted layer

401

Figure 11.35. A local small-signal equivalent circuit for a FET. Reprinted from CAPPY, A., and HEINRICH, W. (1989). "High-Frequency FET Noi8e Performance: A New Approach," IEEE Trans. Electron Devices, ED-36, ,403, @1989 IEEE.

NFmin [db]

Q.n~-Qat. MESFET laccard.ng 10 dolo of FI9 21

20 30

3db I

~ ______________ ~2db

- Ihl" work _ dlstflbuted lumped

40 I/GHz - -

Puetl ., at 151 FukuI I 'ill KF' 1 ]

SO 60 80 ldb

Figure 11.36. Fmin for 0.25 p.m gatelength MESFETs ver8U8 frequency. Full lines: Distributed model; line8 with long dashe8: lumped model; lines with short dashe8: PHS model; dotted line8: Fukui ezpression with kF = 2.3. Reprinted from HEINRICH, W. (1989). "High-Frequency MESFET Modeling Including Distributed ElJect8," IEEE Tran8. Microw. Theory Tech., MTT-37, 836, @1989 IEEE.


measured noise figures versus frequency up to 94 GHz, to the Fukui expression (Smith and Swanson, 1989a). The real need for a revised noise theory for FETs thus has not quite arrived - even the Fukui expression serves well to explain data in most cases. Measurements at frequencies of about 100 GHz, and eventually higher, will have to be pursued, in conjunction with further theoretical work. We may note that the modeling of fT, referred to above in conjunction with PHFETs, introduced several new time-constants beyond the conventional transit time (Nguyen et al., 1989). A theory which combines these new features for both h and noise modeling, is undoubtedly a few years from completion.

A different perspective on noise properties of FETs is obtained from direct measurements of the noise parameters (Pospieszalski, 1989). From such data, Pospieszalski (1989) has developed a model which requires knowledge of only two parameters, plus the normal small signal equivalent circuit, to predict all four noise parameters. The PHS model requires three noise quantities (P, R, and e), as discussed above. The difference is, of course, that the PHS model involves a priori calculations, based on the physics of the device. The noise equivalent circuit for the intrinsic device, used by Pospieszalski (1989) is shown in Figure 11.37. The magnitude of the two noise sources in the gate and drain circuit, respectively, are determined from the Nyquist thermal noise expression by using equivalent temperatures, Tg and Ta. In this circuit, ego and ia• are assumed to be uncorrelated. The four noise parameters are derived to be (with equivalent circuit parameters as in Fig. 10.33):

where

Tmin = 2 ~ gd.R.;TgTd + (~) 2 R!g~.Tl

+ 2 (L r R.;gd.Td

1 Xopt =-we,.

(11.32a)

(11.32b)

(11.32c)

(11.32d)

Tn = Tm•n + To ~: IZs - Zoptl 2 (1l.32e)

corresponds to (8.23). Here, h is defined as h = gm/27reg.' Note that for f « h, (11.32a) predicts that Tmin is proportional to flh, in agreement with the Fukui expression. The above relations should be very useful since the noise parameters need only be measured at a single frequency, whereupon (11.32) can be used to predict values for other frequencies. Another interesting point is the fact that for the experimental data which are available so far, the

Chapter 11 403

gate source temperature, Tg , is found to be close to the physical temperature of the device. One should note that Tg represents a different type of source than the gate noise source in the PHS model, which is found to be strongly correlated to the drain source. Future investigation is needed to clarify the physical origin of the gate source in Pospieszalski's (1989) model. This paper also gives a detailed description of the procedures used for de-embedding of measured S-parameter data, and the measurement of noise parameters. A CAD-program for this purpose has been described by Rohde et al. (1988).

REVIEW OF NOISE DATA FOR HFETs and MESFETs

When Liechti (1976) reviewed FET amplifiers in the mid-1970's, he quoted a best noise figure at 12 GHz of about 4 dB. The actual noise figure for the entire amplifier (i.e. including the contributions from the following stages, see Chapter 8) was about 1 dB higher. The shortest gates for MESFETs at that time were 1 p.m. In 1988, the best noise figure at 18 GHz was 0.5 dB (Smith and Swanson, 1989a). This was obtained with a 0.25 I'm gate length InPbased HFET. The development of HFET noise figures at 18 GHz between the years 1984 and 1988 is illustrated in Figure 11.38. Perhaps even more striking is the fact that noise figures of about 1 dB at 60 GHz (Mishra et al., 1989; Duh et al., 1990) and 1.4 dB at 94 GHz (Duh et al., 1989), have been measured. Both of the latter numbers are for InP-based HFETs, which is expected since these devices so far how the highest values for fT. PHFETs are not far behind, however, with Fmin = 2.5 dB at 94 GHz (Duh et al., 1990). The best noise figure for a three-stage amplifier at 94 GHz is 3.3 dB (Duh et al., 1990). Based on published data for laboratory devices, we can then draw the curves of Fmin and associated gain versus frequency, shown in Figures 11.39 and 11.40. Commercial devices are available for use up to the 30-40 GHz range, and higher frequency devices will no doubt become available in the near future. Extremely low noise temperatures have also been achieved by cooling HFETs to temperatures in the 10-20 K range, see Figure 11.41 (Pospieszalski et al., 1990). Data for cryogenically cooled and room-temperature HFETs and MESFETs are compared.

HFET POWER AMPLIFIERS

The limitations on the output power of HFET amplifiers can be derived in the same manner as was done for MESFETs in Chapter 10, i.e. the main requirements are high current density and large break-down voltage. Initially, it was thought that the current density was generally going to be inferior to that of MESFETs, but as HFETs developed, the reverse turned out to be true. The methods used to accomplish the high current density are (1) improved carrier confinement due to higher band offsets, (2) multi-channel geometry, (3) planar doping, and (4) channel doping, all of which were reviewed above. Break-down voltages between the drain and the gate tend to be fairly high due to the larger


Figure 11.37. Noise equivalent circuit of an intrinsic FET chip. Reprinted from POSPIESZALSKI, M. W. (1989). "Modeling of Noise Parameters of MESFETs and MODFETs and Their Frequency and Temperature Dependence," IEEE Trans. Microw. Theory Tech., MTT-37, 1340, @1989 IEEE.

w 1.5 a: :J ~~o_ HE ... (!J

u:: 1.0 w en i5 z 0.5 InP-BASm

HEUT N :I: CJ

0 CO ,... 1984 1985 1986 1987 1988 1989

Figure 11.38. Development of Fm;n for HFETs at 18 GHz, for the time period 198-4 - 1988. Reprinted from SMITH, P.M., and SWANSON, A. W. (1989). "HEMTs - Low Noise and Power Transistors/or 1 to 100 GHz," Applied Microw. Mag., Vol. 1, May 1989, p. 63, with permission.

bandgap of AIGaAs. Planar doping can increase the breakdown voltage, since in this configuration a sizeable fraction of the path through which breakdown may occur is made up of material with very low doping.

HFET power amplifiers have been developed primarily for the millimeter wave range, where the unique advantage of high iT-values had the largest

Chapter 11

CD '0

405

3.5~---T----~----r----T----~

3 MESFET

2.5

2

1.5

0.5

oL---~----~----L---~----~ o 20 40 60 BO 100

Frequency. GHz

Figure 11.39. Bellt valuell of Fmi .. for three-terminal device" ver,ulI frequency - 1990.

18

16

m "0 1 .. C ... 1\1 12 I!I

II ... 10 D 1\1 ... ... 1\1 8 >

"' 6

4 0 20 40 60 80 100

Frequency. 6Hz

Figure 11.40. Typical allilociated gain. for HFET amplifier., with Fmin all in. Figure 11.39.


'" 10' • HESFt:T. 300K-->

,; <.

" .. " <-II Q e II I- 15K--> .. ! 0 z

<--HFET. RX.

15K <--IIfET. DEVICE. 15K

1%. ---'----'------'--'~O~

Frequancy.GHz

Figure 11.41. Best value8 of noise temperature of MESFET and HFET amplifiers, versus frequency, at 15 K as well as at room temperature. Adapted from several sources. A representative 07le is POSPIESZALSKI, M. W. (1990). "Cry0genically-Coolable Amplifiers in the 1 to 40 GHz Range," IEEE Intern. Microw. Symp. Dige6t, 1253, @1990 IEEE.

effect. Power densities of up to 1 W /mm have been demonstrated up to 60 GHz, whereas with MESFETs this is only possible up to about 20 GHz. Similar data have been obtained from both a double-channel, doped channel, 0.25 IJ-m gate PHFET (Saunier and Tserng, 1989; Smith et aI., 1989a), a 0.15 p.m double heterojunction PHFET with an InGaAB channel (Smith et aI., 1990), and from an InGaAB, doped quantum well channel, MISFET (Kim et aI., 1989). It is of course not possible at present to predict which type of device that will turn out to be optimum, but one can note that all three devices have features such as a doped channel with very high (4 X 1012cm- 2) carrier density. These devices also have much higher PAEs at 60 GHz than conventional HFETs and MESFETs (30-40%). At 94 GHz, about 0.4 W /mm has been measured, with 23% PAE, in a 0.15 x 50 p.m. double-heterojunction PHFET (Kao et al., 1989). It is also possible that the higher gain and efficiency of HFETs and similar devices can be employed at lower frequencies (below 20 GHz), where MESFETs are now well established as the pre-eminent power amplifier (Smith et aL, 1990). Figures 11.42 and 11.43 show the best values for PAE and power density, versus frequency.

Chapter 11

cy GE PM HEMT' ," HPPM HEMT' , • n, PM :HEMT' :0 TfFET"!' • AVANTEK' FET'

o

x ROCKWELL HBT"

• o X

OL-______ ~IL-______ L----L-L~~------~

10 20 40 60 100 200

FREQUENCY (GHz)

407

Figure 11.42. Highest reported power-added efficiencies (PAE) for threeterminal amplifier devices in the 20 to 94 GHz frequency range. Reprinted from SMITH, P.M., CHAO, P.C., BALLINGALL, J.M., and SWANSON, A. W. (1990). "Microwave and mm- Wave Power Amplification Ulling Pseudomorphic HEMTs," Microw. J., Vol. 33, May 1990, p. 71, @1990 Horizon Houlle-Microwave, Inc.

1.1 .. 1

e e 0.9 ... ...... :E O.B . ...

>- 0.7 f-H 0.6 Ul z ILl 0.5 c a:: 0.4 ILl

MESFET--> :E 0

0.3 0.

0.2 .......... 0.1

10·

FREIlUENCY - 6Hz

Figure 11.43. Highest power densities obtained with three-terminal amplifier devices, versus frequency. Based on SMITH, P.M., CHAO, P.C., BALLINGALL, J.M., and SWANSON, A. W. (1990). "Microwave and mmWave Power Amplification Using Pseudomorphic HEMTs," Microw. J., Vol. 33, May 1990, p. 71, @1990 Horizon House-Microwave, Inc.


While excellent efficiencies have been obtained in the millimeter wave range, most of these devices have had a relatively small width, and thus low total power. The process of developing wider devices is under way. The techniques employed are similar to what we described for MESFET power devices in Chapter 10. The present state of the art in terms of output power for single three-terminal devices is compared with the predicted future performance of wider devices in Figure 11.44 (Smith et al., 1990). These power levels are not too much lower than what can be achieved with two-terminal devices (see Chapter 5), and it is likely that a large number of application areas will be able to benefit from the availability of millimeter wave devices of this type in the future. HFETs will be much easier to adapt to various circuits by virtue of being three-terminal devices. They generally operate at much lower temperatures than the two-terminal devices, with a typical calculated temperature rise of 45°C for a 1.6 mm 20 GHz HFET (Smith et al., 1990), which will translate into longer life-time (> 106 hours). Power-combining, for applications which require even higher powers, tends to be easier for three-terminal devices, as well. HFETs may be more nonlinear than MESFETs due to the steeper dependence of gm on the gate voltage, and thus have a lower input power threshold for third order intermodulatiQn, but the gm/Vg, characteristic is considerably flatter when planar doping and multiple channels are employed (Chao et al., 1989). Finally, we may note that the experience with monolithic versions of MESFETs is that they tend to have similar output power as do hybrid devices, in the millimeter wave range (see (Shih and Kuno, 1989); this is not true for frequencies of 10 GHz or below, see Chapter 10). Monolithic millimeter wave circuits, which include HFETs for both low-noise and power active devices, thus look very attractive. Applications in space-based systems can benefit from their excellent efficiency, while millimeter wave phased arrays may be developed based on the predicted good yields of HFET MMICs.

HFET OSCILLATORS

HFET oscillators can be designed using techniques similar to those used for MESFETs. While MESFET oscillators suffer from high near-carrier 1/1-type noise, this phenomenon is much less prominent in certain HFETs. It is generally accepted that the 1/ I-noise originates in traps (Loreck et al., 1984). Conventional HFETs under large signal conditions often develop a substantial current component in the A1GaA8. When this happens, it is found that the 1/ I-noise is high, while the output conductance and the transconductance become frequency dependent (Reynoso-Fernandez and Graffeuil, 1989). The frequency-dependence of especially the output conductance is similar to the same phenomenon in MESFETs, which has been related to deep, long timeconstant, traps (see Chapter 10, and (Golio et al., 1989)). Often, a "bulge" can be seen in the frequency-dependence of the noise, indicative of a single time-constant for the recombination-generation through the trap. Methods for minimizing this noise are still an area of active research (see Chau et al., 1989). There is evidence that the low-frequency noise is correlated with 1-

Chapter 11

0.1

0.01

0.001

5

<> ..................

+ ..... ~ ............. <> .. o ....

~ ...... , .~

" GE PM HEM 4.18 • TI PM HEMT6 '" Avantek FET 8.19 <> Toshiba FET 20.21

+ TI HBT22

x Rockwell HBT 9

10 20 40

Frequency (GHz)

x

60 100

409

Figure 11.44. State of the art for single transistor output power. The dalhed line represents the power ezpected from wider PHFETs. Reprinted from SMITH, P.M., CHAO, P.C., BALLINGALL, J.M., and SWANSON, A. W. (1990). "Microwave and mm- Wave Power Amplification Using Pseudomorphic HEMTs," Microw. J., Vol. 33, Ma1l1990, p. 71, @1990 Horizon House-Microwave Inc.

10' 102 to· Frequency (Hz)

Figure 11.45. Equivalent gate noise voltage spectra for (a) Conventional HFET and (b) PHFET. Reprinted from LIU, S.-M.J., DAS, M.B., PENG, C.-K., KLEM, J., HENDERSON, T.S., KOPP, W.F., and MORKOy, H. (1986). "Low-Noise Behavior of InGaA, Quantum- Well-Structured ModulationDoped FETs from 10-2 to 108 Hz," IEEE Trans. Electron Devices, ED-33, 576, @1986 IEEE.


V-collapse and light-sensitivity at low temperatures (Dieudonne et al., 1986). Since InGaAs devices typically show no such low-temperature effects, due to the lower trap density, and larger band offset, they are expected to be superior to conventional AIGaAs/GaAs HFETs in terms of low-frequency noise. This was confirmed by measurements of Liu et a1. (1986), see Figure 11.45.

OVERVIEW

The concept of a heterojunction FET arose out of fundamental studies of the optical properties of electrons in quantum wells. The development of HFETs has since taken somewhat of a zig-zag path. The high mobility of the electrons moving along the quantum well channel initally was thought to lead to much faster devices than MESFETs. Later developments have emphasized the attainment of a high density of electrons, well confined in the channel, and situated at a short distance from the gate, so that a high transconductance, and a high iT result. The most important feature for achieving a high density is the use of heterojunctions with large band-offsets, best illustrated by the InGaAs devices with a high In content. The HFETs thus developed have turned out to be quite close to ideal FET devices, with high 1T and 1m.42 ,

and low noise figures all the way up to 100 GHz. The lowest noise devices probably take advantage of a high peak velocity, as well as a high channel density, while for power devices the latter feature dominates. Given the very rapid development of several different versions of HFETs or similar devices, it will be exciting, indeed, to follow these devices in the next few years. Our basic understanding of very short gate devices has advanced, but a theoretical model of these may take years to complete.

Problems, Chapter 11

1. A HFET has the following parameters:

d; = 5011;

ND = 1018cm- 3

Use correction factors for 300K, as given in this chapter. Find a selfconsistent solution to (11.11) and (11.15) by using iteration. (a) Calculate ns and fF for this structure. (b) Find the depletion depth, W 2 • (c) Calculate the position of the first two energy levels in the quantum well (fl and fo). (d) Check the consistency of your results by inserting your calculated values in (11.10).

2. Assume dd = 30011, and other parameters as in Problem 1. (a) Calculate and plot ns as a function of the gate voltage, VG. Use a typical value for <Ph on GaAs, and ll.fc as given in text after (11.1), assuming z = 0.25; also give VolJ. (b) Calculate the saturated maximum drain current for VG = 0, assuming a typical value for vs, and Z = 100~m. Also assume

Chapter 11 411

the ns-value which you calculated in (a) (which will be valid at the ,ource end for the channel). (c) Find approximate values for gm,m ... , gm,m ... /Z, G," '7't and IT, if the gate length is 0.25J.£m.

3. Find the solution to the Schroedinger equation for a "triangular" potential well (see (11.2)).

4. Calculate the value of the constant k p in Fukui's noise formula for the three HFETs with parameters given in Table 11.3.

5. Plot the curve of ns versus ep for a HFET with an In"Gal_ .. A, channel with z = 0.53. First find the density of states, D. Then find an iterative solution to (11.10), using four levels in the quantum well. Use (11.2) to obtain e, in terms of ns. The effective mass is m· = 0.032mo'

6. Cappy (1988) gives the following expression for Fmin:

Fmin = 1 + 2-/ P + R - 2G..fiiR x -/;

PR(l- G2) X gm(R, + R,) + v'RP .

R+P-2G RP

Calculate F .... n for the devices given in Table 10.1, assuming typical values for P, Rand G given in the text in Chapter 11.

REFERENCES

CAPPY, A., VANOVERSCHELDE, A., SCHORTGEN, M., VERSNAYEN, C., and SAL MER, G. (1985). "Noise Modeling in Submicrometer-Gate TwoDimensional Electron Gas, Field-Effect Transistors," IEEE 7ran.. Electron Device., ED-32, 2787.

___ , (1988). "Noise Modeling and Measurement Techniques," IEEE Tran,. Microw. Theory Tech., MTT-36, 1.

___ , and HEINRICH, W. (1989). "High-Frequency FET Noise Performance: A New Approach," IEEE Tran •. Electron Device., ED-36, 403.

CHAO, P.-C., SHUR, M.S., TIBERIO, R.C., DUH, K.H.G., SMITH, P.M., BALLINGALL, J.M., HO, P., and JABRA, A.A. (1989). "DC and Microwave Characteristics of Sub-O.l-J.£m Gate-Length Planar-Doped Pseudomorphic HEMTs," IEEE 7rans. Electron Device" ED-36, 461.

CHAU, H.-F., PAVLIDIS, D., CAZAUX, J.-L., and GRAFFEUIL, J.(1989). "Studies of the DC, Low-Frequency, and Microwave Characteristics of Uniform and Step-Doped GaA./AIGaA8 HEMTs," IEEE 7ran •. Electron Device., ED-36, 2288.


DELAGEBEAUDEUF, D., and LINH, N.T. (1982). "Metal-(n)AIGaAsGaAs Two-Dimensional.Electron Gas FET," IEEE'1hms. Electron Devices, ED-29,955.

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DUH, K.H.G., CHAO, P.C., HO, P., TESSMER, A., LIU S.M.J., KAO, M.Y., SMITH, P.M., and BALLINGALL, J.M. (1990). "W-Band InGaAs HEMT Low Noise Amplifiers," IEEE Intern. Microw. Symp. Digest, 595.

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GOLIO, J .M., MILLER, M.G., MARACAS, G.N., and JOHNSON, D.A. (1989). "Frequency-Dependent Electrical Characteristics of GaAs MESFETs," IEEE Tran8. Electron Device6, ED-37, 1217.

HEINRICH, W. (1989). "High-Frequency MESFET Noise Modeling Including Distributed Effects," IEEE Trans. Microw. Theory Tech., MTT-37, 836.

JOSHIN, K., ASAI, S., HIRACHI, Y., and ABE, M. (1989). "Experimental and Theoretical Noise Analysis of Microwave HEMTs," IEEE Trans. Electron Device8, ED-36, 2274.

KAO, M.-Y., SMITH, P.M., HO, P., CHAO, P.-C., DUH, K.H.G., JABRA, A.A., and BALLINGALL, J.M. (1989). "Very High Power-Added Efficiency and Low-Noise O.15-p,m Gate-Length Pseudomorphic HEMTs," IEEE Electron Device Lett., EDL-12, 583.

KIEHL, R.A. (1989). "Single-Interface and Quantum-Well Heterostructure MISFETs," IEEE Trans. Microw. Theory Tech., MTT-37, 1304.

KIM, B., MATYI, R.J., WURTELE, M., BRADSHAW, K., KHATIBZADEH, M.A., and TSERNG, H.Q. (1989). "Millimeter-Wave Power Operation of AIGaA8/InGaAs (on GaAs) MODFETs," IEEE Trans. Electron Devices, ED-36, 2236.

Chapter 11 413

LEE, K., SHUR, M.S., DRUMMOND, T.J., and MORKOQ, H. (1983). "Current-Voltage and Capacitance-Voltage Characteristics of Modulation-Doped Field-Effect Transistors," IEEE Trans. Electron Devices, ED-30, 207.

LIECHTI, C.A. (1976). "Microwave Field-Effect Transistors -1976," IEEE Microw. Theory Tech., MTT-24, 279.

LIU, S.-M.J., DAS, M.B., PENG, C.-K., KLEM, J., HENDERSON, T.S., KOPP, W.F., and MORKOQ, H.(1986). "Low-Noise Behavior of InGaAs Quantum-Well-Structured Modulation-Doped FETs from 10-2 --+ 108 Hz," IEEE Trans. Electron Devices, ED-33, 576.

LORECK, L., DAEMBKES, H., HElME, K., PLOOG, K., and WEIMANN, G. (1984). "Deep Level Analysis in (AIGa)AB - GaAB 2-D Electron Gas Devices by Means of Low-Frequency Noise Measurements," IEEE Electron Device Lett., EDL-5, 9.

MASSELINK, W.T., BRASLAU, N., LATULIPE, D., WANG, W.I., and WRIGHT, S.L. (1988). "Electron Velocity at High Electric Fields in AIGaAB/ GaAB Modulation-Doped Heterostructures," Solid-State Electronics, 31, 337.

MIMURA, T., HIYAMIZU, S., FUJII, T., and NANBU, K. (1980). "A New Field-Effect Transistor with Selectively Doped GaAB/n - AI., Gal_zAB Heterojunctions," Japan J. Appl. Phys., 19, L225.

MISHRA, U.K., BROWN, A.S., DELANEY, M.J., GREILING, P.T., and KRUMM, C.F. (1989). "The AIInAB - GaInAB HEMT for Microwave and Millimeter-Wave Applications," IEEE Trans. Microw. Theory Tech., MTT-37, 1279.

MOLL, N., HUESCHEN, M.R., and FISCHER-COLBRIE, A. (1988). "PulseDoped AIGaAB/InGaAtJ Pseudomorphic MODFETs," IEEE Trans. Electron Devices, ED-35, 878.

NGUYEN, L.D., TASKER, P.J., RADULESCU, D.C., and EASTMAN L.F. (1989). "Characterization of Ultra-High-Speed Pseudomorphic AIGaAB/InGaAB (on GaAs) MODFETs," IEEE Trans. Electron Devices, ED-36, 2243.

POSPIESZALSKI, M.W. (1989). "Modeling of Noise Parameters ofMESFETs and MODFETs and Their Frequency and Temperature Dependence," IEEE TrantJ. Microw. Theory Tech., MTT-37, 1340.

--, GALLEGO, J.D., and LAKATOSH, W.J. (1990). "Broadband, LowNoise, Cryogenically-Coolable Amplifiers in 1 to 40 GHz Range," IEEE Intern. Microw. Symp. Digest, 1253.

REYNOSO-HERNANDEZ, J.A., and GRAFFEUIL, J. (1989). "Output Conductance Frequency Dispersion and Low-Frequency Noise in HEMTs and MESFETs," IEEE Tran". Microw. Theory Tech., MTT-37, 1478.


ROHDE, U.L., PAVIO, A.M., and PUCEL, R.A. (1988). "Accurate Noise Simulation of Microwave Amplifiers Using CAD," Microw. J., 31, No. 12, 130.

SAUNIER, P., and TSERNG, H.Q. (1989). "AlGaAs/InGaAs Heterostructures with Doped Channels for Discrete Devices and Monolithic Amplifiers," IEEE Trans. Electron Devices, ED-36, 2231.

SHUR, M. (1987). "GaAs Devices and Circuits," Plenum Press, New York, Chapter 10, p. 513.

SMITH, P.M., and SWANSON, A.W. (1989a). "HEMTs - Low Noise and Power Transistors for 1 to 100 GHz," Appl. Microw. Mag., 1, No.1, 63.

__ , LESTER, L.F., CHAO, P.C., HO, P., SMITH, R.P., BALLINGALL, J.M., and KAO, M.Y. (1989b). "A 0.25 Micron Gate Length Pseudomorphic HEMT with 32 mW Output Power at 94 GHz," IEEE Electron Device Lett., EDL-10, 437.

__ , CHAO, P.C., BALLINGALL, J.M., and SWANSON, A.W. (1990). "Microwave and mm-Wave Power Amplification Using Pseudomorphic HEMTs," Microw. J., 33, No.5, 71.

SOLOMON, P.M., and MORKOQ, H. (1984). "Modulation-Doped GaAs/AI GaAB Heterojunction Field-Effect Transistors (MODFETs), Ultrahigh-Speed Device for Supercomputers," IEEE Trans. Electron Devices, ED-31, 1015.

TAN, K.L., DIA, R.M., STREIT, D.C., HAN, A.C., TRINH, T.Q., VELEBIR, l.R., LIU, P.H., LIN, T., YEN, H.C., SHOLLEY, M., and SHAW, L. (1990). "Ultralow-Noise W-Band Pseudomorphic InGaAs HEMTs," IEEE Electron Device Lett., EDL-ll, 303

TOMIZAWA, M., YOKOYAMA, K., and YOSHII, A. (1984). "Hot-Electron Velocity Characteristics at AIGaA8/GaAB Heterostructures," IEEE Electron Device Letters, EDL-5, 464.

WEILER, M.H., and AYASLI, Y. (1984). "DC and Microwave Models for AI2Gal_.A8/GaA8 High Electron Mobility Transistors," IEEE Trans. Electron Devices, ED-31, 1854.

FURTHER READING

PEARTON, S.J., and SHAH, N.J. (1990). "Heterostructure Field-Effect Transistors," in High Speed Semiconductor Devices, S.M. Sze, Ed., John Wiley & Sons, New York.

SALMER, G., ZIMMERMANN, J., and FAUQUEMBERGUE, R. (1988). "Modeling of MODFETs," IEEE Trans. Microw. Theory Tech., MTT-36, 1124.

Chapter 11 415

SHUR, M. (1987). "GaAs Devices and Circuits," Plenum Press, New York, cited above.

TU, C.W., HENDEL, R.H., and DINGLE, R. (1985). "Molecular Beam Epitaxy and the Technology of Selectively Doped Heterostructure Transistors," in GaAs Technology (D.K. Ferry, Ed.), Howard W.Sams, Inc., Indianapolis, IND., Chapter 4, p. 107.

ZIMMERMANN, J., and SALMER, G. (1990). "High-Electron-Mobility Transistors: Principles and Applications," in Handbook of Microwave and Optical COlDponents (K.Chang, Ed.), John Wiley & Sons, New York, Volume 2, Chapter 9, p. 437.

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Microwave Semiconductor Devices || HFETs — Heterojunction Field Effect Transistors