ECEN 5004, Sprin 2018 Active Microwave Circuit Zoya Popovic, Univerity of Colorado, Boulder LECURE 3 MICROWAVE RANSISOR OVERVIEW AND RANSISOR EQUIVALEN CIRCUIS L3.1. MESFES AND HEMS he ot coonly ued active device at icrowave frequencie are the Metal Seiconductor Field Effect ranitor (MESFE), and it variation, the HEM. he MESFE i a GaA device with a phyical cro ection hown in Fi.L3.1(a), and a typical electrode layout i hown in Fi.L3.1(b). he MESFE i a unipolar device, which ean that there i only one type of carrier. he MESFE ha three terinal: the ource, ate and drain. he ate lenth i the lenth that the electron need to travel between the drain and ource and i uually a fraction of a icroeter. he ate width i in the direction out of the paper referrin to Fiure L3.1(b) and can be hundred of icroeter lon. It deterine the current that can flow throuh the device. he three electrode are depoited on an n-type GaA epitaxial layer which i rown on a eiinulatin ubtrate. he epitaxial layer i on the order of 0.1 thick and the dopin i 16 17 10 10 c -3. he ource and drain are ohic contact (low reitance, uually ade of a olderaniu alloy), and the ate i a Schottky contact. Aociated with the Schottky barrier i a depletion reion which affect the thickne of the conductin channel. he ate i biaed neatively with repect to the ource, and the drain poitively. When the voltae i chaned on the ate, the thickne of the channel chane, and thi control the current between the drain and the ource. (a) (b) Fi.L3.1. A cro ection of a MESFE (a) and photoraph and electrode layout (b). When you buy a MESFE, it can coe in a packae or in chip for. You will alo et eaured -paraeter at a few different bia point for a certain frequency rane. hee -paraeter are eaured uually with the ource terinal rounded and the drain and ate lookin into 50, o they are two-port paraeter. he 21 paraeter correpond to the ain of the device in 1
coon-ource confiuration. he aplitude and the phae of all four paraeter are iven at any dicrete frequencie. Another way to repreent the tranitor i with an equivalent circuit, like you have probably done in your circuit clae. he idea behind equivalent circuit i to odel the device over a rane of frequencie with invariant paraeter. Let u bein with the iplet linear (all-inal) equivalent circuit, for which it i ipler to ue adittance paraeter, iven by I=YV. able L3.1. Converion forula between - and noralized y-paraeter. (fro Microwave Enineerin by D. Pozar.) (a) (b) Fi.L3.2. (a) Low-frequency MESFE odel. (b) Hih-frequency approxiate MESFE equivalent circuit. hee circuit are called the intrinic equivalent circuit becaue additional paraitic fro the packae are not included. 2
he y-paraeter ay be converted to -paraeter uin the forula fro able L3.1. At very low frequencie, ay below 1GHz, the capacitance and inductance aociated with the MESFE are quite all, and we can aue they are neliible. he ae i true for the reitive loe. he reult i a iple low-frequency odel hown in Fi.L3.2(a). hi odel ha an infinite input ipedance and cannot be atched at the input. What i the order of anitude of the eleent of thi circuit? Let u look at a few exaple. he riquint GF2960 device S-paraeter at the lowet 100MHz frequency with VDS = 8V, IDS=100A are: S11= 0.677dB -7.9 10 S21= 20dB -175.75 10-180 S12= -41.9dB 72.47 0 S22= -5.06dB -19.43 0.50 If we wih to find the value of the eleent in the equivalent circuit, we would firt olve for the S-paraeter of the equivalent circuit in ter of the unknown eleent, and then et the expreion equal to the known S-paraeter, thu ettin a yte of equation. Findin the expreion for the S-paraeter of the equivalent circuit can be quite coplicated, and uually the Y-paraeter are found and then converted to S-paraeter. For the low-frequency odel fro Fi.L3.2 (with no capacitor), the Y-paraeter are and the S-paraeter are obtained a follow: 0 0 d S 1 2 1 d 0 1 1 d d. Since you are iven the S-paraeter, you can find the conductance value; note that they are noralized to 1/50=0.02S. he next exaple i an Avao MESFE chip with reaonably tandard paraeter, that at 500MHz with V DS 3V and I DS 20A, ha -paraeter a follow: 11 21 12 22 097. 20 1 50. 1665 0. 029770 052. 1105. 3
For thi device, fro the eaured catterin paraeter, the voltae ain i found to be about A / 1.2and =2.5, d=3. hee conductance value are noralized to 1/50=0.02S. V d Finally, conider the Qorvo (RFMD) FPD HEM device. At 5V and 300A, the lowet available frequency S-paraeter value are at 50MHz: 11 21 12 22 0.946 24 1 36159 36 0.00679 0 0.175 145 0.175 Goin throuh the ae approxiation a for the FE above, we et the paraeter calculated fro the low frequency eaured data to be If you look at the eaured data at f=600mhz for the ae bia point, however, thee are the value: 0.821 144 11 21 12 22 G A d V 0.875S 28.5S 30 10.58798.5 0.03238.2 0.568174.3 Referrin back to the dicuion about the low-frequency tranitor odel, you can ee that the iple equivalent circuit fro before cannot be ued. here are capacitance that are already quite pronounced at 600MHz. he reaon i that the MESFE device ha ain up to uch hiher frequencie (12GHz) and can ive at ot a hundred W of power, while the RFMD HEM i a 1W device for lower frequency operation. he ot baic hih-frequency intrinic equivalent circuit odel i hown in Fi.L3.3. he ae ethod can be ued to calculate the circuit paraeter fro eaured S-paraeter. You will calculate the Y atrix for thi circuit in Project 2. Soe iportant additional paraeter are the ate, ource and drain contact reitance, and thee are eaured uually at DC, thouh their value will chane at hih frequency oewhat due to the kin effect. When the ate, drain and ource+drain are horted, reitance Ra, Rb and Rc are eaured, repectively. he contact reitance can then be found fro: R R R G D S R c R b a R R G G 2 c R R R ( R R ) R c a b a R b 4
he depletion capacitance of the Schottky barrier ate i repreented by C and C d. Uually i uch larer. he reaon i that the poitive voltae on the drain caue the depletion C reion on the drain ide to be wider than on the ource ide. Alo, the eparation between the drain and ate contact i uually about 1 larer than that between the ource and ate. he capacitance between the ource and drain i priarily throuh the ubtrate, and i not neliible becaue of the hih dielectric contant of GaA of 13. he reitance of the ate i inificant becaue the ate contact i lon and thin, and a typical value i 10-15. he uual fiure of erit for the tranitor i the voltae ain AV / d. Since both conductance are proportional to the ate width, the voltae ain doe not depend on the width. hi i iportant in MMIC, where there i coplete control over ate width, but ate lenth are fixed by the fabrication proce. he ate lenth deterine the axiu operatin frequency of the device (directly, the RC tie contant). An experientally obtained forula i 3 3310 f ax Hz, L where L i the ate lenth in eter. Several cutoff frequencie are coonly ued. f i the cutoff frequency when the hort-circuited current ain of the device drop to unity. hi paraeter i often ued, but never eaured, ince a icrowave tranitor tend to ocillate with a hort-circuit load. If the input current for the hih-frequency equivalent circuit i I in then we have I V jc I f in out I I out in i d 2C V 1 C he two ot iportant paraeter for the hih-frequency perforance are therefore and C - lare and all C reult in a hih cut-off frequency. A typical procedure ued to calculate the cutoff frequency i to derive the hort-circuit ain fro the eaured -paraeter, and extrapolate thi curve to the value of the ain equal to 0dB, illutrated in Fi.L3.3. hi ive a iplified 6dB/octave repone, althouh the actual one i obviouly ore coplicated (we ued only approxiate forula). Fi.L3.3. Calculatin the cutoff unity current ain frequency. hi cannot be eaured, becaue the tranitor will ocillate when the drain i horted, due to the feedback capacitance. 5
he axiu frequency of operation i hiher than the cutoff frequency, and i defined a a frequency for which a neative reitance (ocillation) can be produced. he two frequencie are related by f fax, 2 r f r 1 2 where R R R r,and r 2 R C, S i 1 2 Rd d and the different reitance are thoe of the ate and ource contact, the intrinic reitance between ource and ate, and the drain-to-ource reitance. he unilateral tranitor ain a a function of frequency can be expreed in ter of the cutoff frequency a 2 ax f G u f In thi approxiation, the ain i 1 when f fax. he axiu frequency i uually two to three tie hiher than the cutoff frequency. In order to obtain a hih f ax, the cutoff frequency need to be axiized, a well a the ratio of channel reitance to ( R RS Ri), and C d need to be iniized. he tranit tie i decreaed by decreain the ate lenth L, but thi alo reult in a decreae in channel depth in order to aintain a eoetry that ive a hih. In turn, thi ean that the dopin in the channel ut increae, to aintain a low channel reitance. he liit on the dopin i et by the avalanche breakdown in the ate-drain reion which ha the hihet field, and it i about 510 c to ake hih-frequency power device. 17-3. Now it i aybe clear why it i difficult A ethod for reducin the erie reitance in the ource i to rece the ate, by akin a uhroo type tructure for the ate etallization, by elf-alinent. he cutoff frequency can be directly related to the tranit tie of electron under the ate by the followin approxiate aruent. Aue a all poitive chane in the ate voltae v. hi reult in: (1) the ate chare up by q C v ince it i one of the capacitor electrode; (2) the other electrode of the capacitor i the channel, o the ae aount of neative chare ut be drawn into the channel. Neative chare in the channel ean an increae in carrier (electron) denity, o (3) the current throuh the channel ( i d ) increae. he tie that the electron take to tranit the ate reion i found fro q id he current can alo be expreed in ter of the ate voltae a v id C 6
and fro the definition of tranconductance, the followin can be written 1, C where the left-hand ide i the inificant ratio for the cutoff frequency that we derived earlier. We can therefore expre the cutoff frequency in ter of the tranit tie a follow: 1 vat f, 2C 2 2L where vat i the carrier aturation velocity. So, thi ive a very iple rule: if you wih to ake a device with a hih cutoff frequency, you need to increae the aturation velocity and decreae 7 the ate lenth. he aturation velocity in bulk GaA i liited to about 10 c/, and to overcoe that the eiconductor aterial under the ate ut be odified. hi i done i Hih Electron Mobility ranitor (HEM). If you wih to ake a device with a hih cutoff frequency, you need to: - increae the aturation velocity of electron in the channel and - decreae the ate lenth of the device. It i oewhat obviou what iue need to be olved in decreain the ate lenth and that they are purely technoloical, i.e. require better photolithoraphy. o increae the aturation carrier velocity, however, require a new device dein. What i the liit in aturation velocity in a GaA MESFE? If no colliion occur, electron in GaA are accelerated by the electric field and follow Newton econd law, with the a replaced by the effective a *: dv F * a ee dt ee v t, * where e i the electron chare. At roo teperature, the ean free path for the electron can be etiated fro the eaured obility, and the value of about 0.1 i reaonable. If the electron tart at x=0, then at tie it ha travered the entire ate lenth L,a nd the followin can be written: ee 2 L vdt. 2 * 0 If an averae electron with a ean free path before the firt colliion of 0.1 i choen, the value for i found to be 2 * L 14 8.7 10 0.1p, ee 4 for a value of E 10 V/c. herefore, the axiu velocity that the electron can acquire i iven by 2eEL 7 vax a 7.3 10 c/. * 7
Since the peak teady-tate velocity of electron in GaA i in the rane of 7 7 1.510c/ - 210c/, the axiu velocity derived above i an overhoot velocity that an electron acquire when in a very hort ate reion with a lare electric field. Keepin in ind the cro-ection of a MESFE, conider a device that ha a cro-ection a in Fi.L3.3. In thi Hih Electron Mobility ranitor (HEM), GaA i not the only aterial that i ued. here are a nuber of o-called hetero-junction, i.e. eiconductor junction between different aterial. he ot iportant one in ter of device operation i that between the ilicon-doped AlGaA and the undoped GaA. Due to the hiher band-ap of AlGaA copared to GaA, free electron diffue fro the AlGaA into the GaA forin a two-dienional electron a at the interface. hee electron are confined to a very thin heet becaue of the built-in potential barrier. It i eay to undertand qualitatively why the tranport propertie of electron in thi reion are uperior to thoe in the channel of a MESFE: the MESFE channel ut be doped to have current, and the electron catter off the dopant ion. In the thin layer of electon in the a HEM, there are no ion to catter off, o the electron can ain very hih velocitie, i.e. their obility i very hih. hi i oewhat of a ubtle point: initially it wa thouht that the excellent propertie of HEM are due to the hih obility of electron (thu the initial nae), but later it becae clear that it i in fact the averae hih electron velocity that enable hih frequency operation with uperior noie fiure. Fi.L3.4. Sketch of the cro-ection of a HEM device, with approxiate dienion of the different layer rown by MBE. Fro Fi.L3.4 one can ee that the layer of different eiconductor are extreely thin. echnoloy wa not ature enouh to enable uch aterial tructure until Molecular Bea Epitaxy (MBE) wa invented in Bell Lab in the 1970. he proble in rowin uch tructure are aociated with lattice iatche between different eiconductor crytal. he firt heterotructure were rown to invetiate optical pectrocopy by a phyicit fro Bell Lab, R. Dinle. He wrote:...ince ultiple layer could be readily rown, we iply rew a ultilayer AlGaA/GaA tructure containin 10 or 20 layer interleaved with AlGaA upport layer. he rowth technique wa decribed a ei-autoatic and conited of watchin the econd had of a darkroo tier and anually rotatin a hutter on the aliinu effuion oven of the MBE yte it initiate and terinate AlGaA layer rowth. In early 1974 a ultilayer tructure with 200 A- thick GaA layer and thicker AlGaA upport layer wa own. With the help of Len Kopf, we eaured the aborption pectru at 2K and oberved the firt direct evidence for ize quantization of electron otion in GaA. here wa reat jubilation in y lab we even danced a bit, a I recall! I bean to believe in quantu echanic! What wa in effect oberved wa electron otion in the 2-D electron a. A 8
obility of 10,000-20,000c 2 /V wa firt eaured at low teperature, while the coon bulk GaA obility wa 6,000c 2 /V. Eventually, a hih a 2,000,000 wa obtained at low teperature and 8,500-9,000c 2 /V at roo teperature. When one look throuh FE device pecification, one often run into the acrony PHEM. he P tand for peudoorfic and what it ean i that, in order to iprove the perforance of a HEM, the two-dienional electron a i confined to a thin layer of InGaA intead of GaA. hi allow for even hiher heet chare denity of the 2-D electron a, and therefore hiher tranconductance. he cro-ection of a typical PHEM, alon with a SEM photo of the 0.15 -ate tructure i iven in Fi.L3.5. (a) (b) Fi.L3.5. (a) Cro-ection of a typical PHEM, and (b) SEM photo of the 0.15 -ate etal on top of a HEM channel. 9