71D-Ai4i 378 DYNAMIC BEHAV'IOR OF PULSED IMPATT 05CILLRTORS(U) I/iI MICHIGAN UNIV ANN ARBOR DEPT OF ELECTRICAL AND COMPUTERIENGINEERING R K MAINS ET AL. 198± N6@53e-8i-C-0364

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E-eot-rc. -s~2 Iab:ra:-:

-,~~A -:'r, *.

nowiz~rg an' er: Afe i kW

Naa Wea-.onsz Cent-ern ~a 1 al, 9A 3 2 c

,Lt' o,-:'o o f s imulai ing t 11e dvnarn'. ea'- c ir c 2e a

MP.2l oS c .lators it-re sen~te. :t is as~ed t*-at the iiac.

vari alez change slowi-',, with respect. to the RF perifod so ta: te

cu'as-Static approximatior. may be used. A cormoarison of _4_u a-, - n

eei:i:~ exr.er fient a- r e Suts focr an X-b anc eir c,)i S

4-V

approv

13.,ut4tbsOe prv

-4 ulcr~es rd ae !

.4.'ok.a z r.c~t dN v '-C -- a -,l.- :

-KAM~ 2 %.

as::--, a -ry ma::r man vefezt--elx use- to,

*ec S fz. n- f-. r- e,. -r rl*~n n a leoc-Iczoked I

oc_-aot rZ -- F an a'l rn'a-ive --c 11..e t--cns

mezdcrr~u acr:-.ete Ae-vi ce-circ-u::- -rteractior, simulatio

the tim oma-n using- a small ti1me ster due to stability restric-

tiorns on, the device simulatifon. The ouasi-stat4 C metnonreo~re a

comn -Iete sleady-Fseate characteriz:ation of the U-A'Ae-. 4 C e over

the r-an:Je -nprature, bias current denz:-,v an';~

a--,", e na wi. be encountered in i ransient, 7iuain t

is then ass, ed trha-, ts'e simulation uaramet ers hnescw7-: w-t-

-4 es-nect to the --- nerioa so that the- 7A- appears to be ina

I.stead.--staz-e condit.ion at, ani- -,art a-cular i nst.ant of time ts

manner -tn-e z ransfer-L can readily be simulated over the entire Ios e

w ith.

-gure - srL-ws t 'e QoO-:n7 ncro:e -cf th-e GaAs or .:d- 2

C4A? code used 4-.te snulati-n-. '7nar- -ia srctr

1 w~~-as fatri4ca-te-.*:rwv so;ts* ann' vas P'sc uce-

U'in t-e exr---" -n f fett~ w~ o an

!r.aunrnS an,: s-ca,-:, &I- 1W:C:ac~' arsa

wnereln E sz -:~L ta' t- .tC>C Currents ccrsst Cf a d rrusC C aiFui7cs ter, : tol>te and diffusio ncefiiet

U' ~~ex-mrecsec as Iu: :. fte1ca: electric field. Smain

;1c/ orDist"a

- - ~ ~~ ~. . .. 4 .. .j .. . . . .~ %

were carrie- zu-, &Ite-:~e ~ ~ a'K

At each te-cerature, simulations were 4erformed a: iaz curren

densities of -. = h0C, 650 and 100C A/c. For -

combination, a sinusoidal R: voltage at I3 3Hz was a-r!-ed and the

amDlitude was varied from zero tc tne pcin: wher :::e diode efficienc.

dropped si r-nificantly. The information thus obtained s Y f = IC z;

M d % ), the diode admittance in mhno/c=-, and z= H;

J V ) the diode large-signal operatinc voltage. At C.= 0, thedc' F dc

diode is modeled as a depletion capacitance, C = (E '/ ' "F, in series

with a small resistor, Ro=(wu/cA)C, to account for the .Lnde-leted region

(d is the derletion region width and w is the width of the undepleted

region). To obtain the diode characteristics at operating points

other than those simulated, a linear interpolation scheme is used [2].

It is assumed that the circuit admittance Y (s) varies morec

rapidly with frequency than the diode admittance so that YD may be

assumned constant with frequency over the frequency range of interest.

However, the diode cold caDacitance C = (C/w) F/cm 2 (where w = w, + w =D a u

6.95 om' is lumoed into Y (s) sc that the component of the diode

susceptance does vary with frequency. The device area was assumed

to be A = 1.- x 0- 3 cm2 which is the measured value for the diode.

Figure 2 shows the circui- used to model the actual oscillator

circuit, which consists of a 5-x transmission line (represented by

F.) and a low-impedance tran:sfcrner adjacent to the diode package

(represented by Z , £, and E,. The capacitance C is the discontin-

c ruity capacitance between the %-2q transmission line and the

[ .'. ...... _ .... ...... . . . - ... . . -... ... ..-.-. -.- ... . . ..-... . .. ... . , . ... ._ . .. .*.

Pr T -- -m -

-was a-:: e-'ted tc measure e~z roae-c tno cou-v a ent

c ircuit e-,emen- s Land_ C h=,;ever s :n .. ne- _n- rema~re

ccncerning -these vaus etca-l:: 'r the ser-'tS rtac

Thne rorocedure 'was :o use the exrcerimen-.ally dietermined v~~

0.32 cF for and- to det.ermine L. as follows. Thie diode admittance

resulting from the simulatio-n at T = 500'K, do = _5c ~~ bias cr

rent dens-it- use-d experinentallv and V,,, .7 -'ma7xmumefr

-Dcir.-t for thiS rartio_'ular c com.bnatior.' was iranS~'--.-

th r c ur t -; a ca g.-e -7,cn zng e rui va en-t ci4-r cuit 1 to tane r :n

2.L was ~nnchosen so ha this transformed dfitnc was e~ual.

to the exrerircental large-signal ad-mittance measurements a:- T-a

C, is the d~c,7e co.!d canacitance, wh~hi uodf.otec_'r2-uh

rirure T~n~ae a v;era.> pr e,.r

s4 -I a t on . in..'. -a, .I s th a I t a: E c7 eY

frequen~cy the circuit" '--z, 2 a-, 4lar

~s t h e d ce P a :tn ce e er7--*.:: from: ah IaC---

s 1uaao r. , 4;.- e. C. -Urrel.- uSf E. a 'E

e-*ctiOr.--- :r-.e ca2e . tr,~k - ue of :h v 0oa

a- tnE- di*:oe termnals, an os te ~ *'ti ~

to ,.z:.. ant d are r ,..:-.~>.:n

The- c:mp!x freueny .. cI er ene rt r 7 E T~ Cz~ 7- oxr,~

the eouaocn:

P ,

%7

'

+=

and are uT ec ac-crd 4= to

9, - U : .. =...

-"-an!

deC

7,:e diode temrerature : is updated from-P.h p

7 -- - A

dt T T

..... "s the diode thermal resistance in °K/;, _. is the power

dissf-_a- ed in the diode in W, TA is the a=,bient temperature inK

and :'s the therm..al relaxazicn time in seconds.

Tig 3(b], the bias current J_ s assic to r-secc

l-near' from zero to a constant value at turn on, tc maintain this

cornstant va7lue :hrou.hou7 the pulse width, and then to fall l near

to zero at turn off. In principle, the bias circuit co'uld be modeed

and a secornd device-circuit interaction could be solved tc determine

the evo.ut:. of J. with time, however, this was nct done in the

simuatins resente_ here.

For the inlecticn-locked case, it is assumred that 1 is on long

before the bias currnt density J. is switched on at t = 0. Therefore,ac

at t = a substantial -.. voltage existZ across :he diode terminais

ever. thour*, the device is passive at this time.

°,LI. • . . .

. . .'. -.

Figure ;.resents the turn-on and turn-cf-f characteristics

observed for the free-riunning case and rig. (a) shows the behavior over

the entire I.5-us .1se. The diode was f Cd o oscillate at 9.7 G;iz,

the peak outrut -ower was 15.S W, and the diode orerating voltage was

approximately 1C V. Figure 5(b) shows that, for the injecticn-locked

case, the diode turns on faster than for the free-r'nning case. (In

Figs. 4 and 5, an additional 6 ns delay is introduced in the detected EF

waveform relative tc the bias current waveform due to the measurement

setur.)

Table I shows the experimental results for the injection-locked

case as the injection signal power is varied. The injection frequency

vas 10 GH: and the (-eak) bias current was I = C.8L A, or d = 646.~~~ -e. anda doe notr '

A/cm 2 ". F is the (peak) EF power generated by the I1'T_ and does not

include the t, ower delivered by the inection source Fn is the

average junction temrerature calculated from the exper i -entally deter-

mined thermal resistance. It was found exnerimentallv that if the

injecticr. power was reduced below 2 W, the I.FAT did not lock w .th the

injection source.

The thermal resistance was experimentally determined to be R. -tn

5O:/W for the diode and 101:W for the cun,. Sdnce the temiperature in

the mount changes more z~owly than the diode temerature r61, the

10K/W contribution was assumed tc increase the ambient temperature, -.

in (h), from rcom temrerature as follws:

T1 = 30C°K + 6L.7 W x C.24r x 10*:,W = 29oK , (5)

where 64.7 W is thIe peak dissirated power 4!. the d;!de and C.L5 is the

• ' . . , . • - -. . . . -. . -* . -- - .. " .- . " *.- . -W .,'., ' . ...." ' . % " .- '- ",' W.",,'.-""" ."""""%-.- -

%ut? factr. ..e _-.T dicoes were fabr4caied :r. a ud mesa structure;

a. at-rozriate -.herma: relaxaticn ime -.cr tnis arran ement is T = 8 "s

iT (L). Using these values, 1 ilies ,a-., in order for the average

diode temoerature to -e LT 0 w ,see Tatle i, the diode temerature at

the beginninz c' the bias current 'use must le a..rcxima-,ely .. in the

steady state.

'Figure 6(a) shows the start-up behavior obtained from the quasi-

static simulation for the free-running case. For comparison, the corres-

ponding portion of the experimentally observed FF -,ower from FiL. L(a)

is alsc shown. The amplitude of the experimental curve is ncrr'alioed sc

that both the experimental and theoretical curves reach the same maximur.

RF power level. The bias current increases linearly from zero at t = 0

to do 646 A/cm2 at t = 60 ns in Fig. 6 (a). The starting temperature

at t = 0 is 4600K. From Fig. 4(a), the detected F power turns on approxi-

mately 32 ns after the bias current begins to increase (recall the

additional 6-ns delay in the measurement system;; this exre...i.e.tal de'ay

is very close to the delay resulting from the simulation in Fig. 6(a,.

Figure 6(b) shows a plot of the circuit admittance vs. real frequency

(o = G) and srall-signal device ad;ittanc vs. at the start -.-

temperature T = h..K. From I2), v4R_ will nct increase until () is

satisfied for a value c f s su1. that -e{s = > r. :. To. 6(b), the

re:cn tc the right cf th- 4' curve '.,e..v e

such that ReEs ) < C, and the area tc the Ieft t c he -Y f carve co.-

ccTa ins (s' valu es s., ;,_. -ha -.rer.s) ? :. . er: tc

23C . -/c he. a , , vh = es >r,, ,. c r..I..

in~crease. As J.creases further, tlhe > cur'-,,_- .e- trLe

and. . ((,,,ti osee that tVe ou;c 'eicr.an

* - - - - - -_ . . . . . , . _ . •. . ....-r~ ------ *- - - , --,,

._ ." . .. --. - . .

LZ

frequenc:, w- ' ar' a, a.rcx:.-,aty 9. , w:.,c:. -s tre experamentallvo

observed freauency for the free-running case.

Figure 7 shows the R. power simulated during the oscillator

turncf w"ere -t is a5s'med - 7 decreases linearlydc

A/cm 2 at t = C to zero at t = 9c n .. 7 iF result should be

compared with Fig. 4(b), although in the experimen. J departs from thedoc

linear waveform.

Figure 8 shows the start-up transient for the injection-locked

case, with I, = 0.557 A see (1) and Fig. 3(a)] so that the incident power

from the locking source is 2 /8G = L W at 10 GHz. Comparison of Fig.

8 with Fig. 6(a) shows that the RF power turns on faster for the injection-

locked case than for the free-running case. This is in agreement with

the experimental result shown in Fig. 5(b). This is because there is a

5' substantial RF voltage across the diode at t = 0 due tc the injection

source.

-able 2 presents the simulation results as the injection power

is varied from 2.0 to 6.0 W. Comparison with Table I shows that the

same general RF power variation as observed experimentally is predicted

by the simulation, although the simulation predicts a _wer maxim, at

P.n = h.C W instead of 3.5 W, and the maximum Dower rredicted by the

simulation is 16.56 W instead of 11.6'_ W.

The behavior fndocated in-.abe 2 can be understood Ity ex-a.ininr

the curves in Fig. 9. S nc oe, for in ecion-locking, _ rus- be satis-

fied, the magnitude of the irnjection current source i. mu.t -atisfy

the following relation at the start of the pulse 'af-er -he bia: cur-

rent has reached its maximum value):

IL = V IY (f=10 GHz) + Y (T=L6o°%,j. =6( A/cn2;VRF) (6)F.F c D RF'

5% ~4.5

mani evotare a: .e di de terzEnas a:- Zhe

corresponding ' 2>_ were previously; obtained by the dicie character-

ization process, using the steady-state I-._T simulatio-. rro-'am.

Ecuation (6) matches each V value with a corresponding 7 for

t stead'v-state locking. Also, for each V.7 the r power generated by

the diode is

BF 2 DE 7

where G = Re{Y (V,,)). The exTressions in (6) and (7) are olotted in

Fig. 9. it is see that as i- is varied from 300 A/cm2 .... -L

800 A/cm (1.0k A), the RF power first increases, reaches a maximunm

for L = 450 A/cm2 (0.58" A), and then decreases. (F in Fig. 0 isRF '

the R rower at the start of the pulse, whereas the RF power in Table

2 is the average over the 1.5-s pulse width). Below IL - 285 A/cm2

(0.370 A, F. = 1.76 W), it is anticipated from Fig. 9 that locking

cannot occur except perhaps at very low F__ values. (It must also be 4n_

vestigated whether the operating points in Fig. 9 are stable. -ns

expectation is borne out by the simulation in Fig. 10 for which

. = 1.5 W ( IT = 0.341 A). The diode does not lock untaJ"t !n as

heated up to L7 0K, so that the curves in Tio. 9 are no cnrer aprlicable.

As the diode continues to heat ur the generated RF power gradually

increases to 1l.9 W. This behavior is consistent with the exz.ri...+al

results, since for F. much below 2 W the locking at IC GHz was nc-an

found to be stable.

u.':.T dijo de E J at c... .

it has been shown that a large-sirnal _MT= da 1 ... c ,

program employing the drift-diffusion armrcximation Jn ccn-unc-o.n

LIZ,.

W_ 7. a 77767. ~ .. - - 7 77

w- t a c -c::. f-~h S rarurn C

ex-.er~merta__- c bserveC bePhavicr a-,fee- u-r

andia ~rec:-I _ ockecd cases. 7,ie E!e r c,- ra-. s ma sedefe diode andc

c ircuit des 4. i at '-igfcr e 2~ e- nauee!--ce ..- r

d ff f-4 -1u 1 c-wever, f t-,.,,- e ne _essar-: :: :xxuce n

effects d4Cn; tae 47A Cid inIa n 4-ce~ has been sc.tha-,

-- these effects becom~e Si~n4 ficant at 7low ir7-eter-wave -freouernc-es[7

.

% ' rr r 0rr .vrr.r . - .- . ~ '- N Y b ...b'%.

7-rwaesc 's.a

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::uoka-a,'ln arcio of'cr~ mirwvolid-stat

P. 1tulsed n TMPT ocilatrs art cn- o--ocke marlfn, icc

- The Un~of iveity ofr Michign,AnAroFb19.

.. R. . -. z.ainas art G. . addad, "IM-wpATTf~ dvce imulatio'c~ ncan

rropber - -ice, !E- Elcton aeics, vl ol. D2vicpe.s, L

Orc, =-2ne 1?"?.Fe.15C

7. R. K. Mains and G. . :'Haddad, "Properlties of high -ffT diodc s

z275%c5n Labraryan TheUnvrity ofnsr eqichian," nn98o, WOCSE ll.:

volf. San7 "itnic L3- "eb.-ar 19 .

4g 5%

'iN . C.& *7 OW ' w VI'V -2X% 4r nu w w rw E7 ey f r. a-t ,is .- -- -. -- - .

op N

_-267cm = 0.1 r an-R 5

Fig. 3 >(aZ'RF circuite o:d !'b ba c ci used in t he theore, tia 44o

beavorfo nv restratznsz c e are 7. 6 t /'c.c--

wiopt 1.5 -,s an ru~ -yc fl

Fig. 6e usaSarti eavior fr e sintatior is simuatio

) = 0.13 n , C _ (t =3 6B, n = 6Q, q/m ,

cc CII

ad T .5 ;s and duty cycltae zlo of5YCvl

4%4

tu rn-onf cnaracteristicfo 'hiect fre qun aeny=T

Fig. 6 (a erStaruph behavior foed reerrning tsiuain

C' C) = 0 I J tH 6c ns: 6L46 A/cm 2 r% - i

a.±~ A 4T W and f 1ita 0 rio o Y (R 0

-mltd and je-nandd RVpowr v

Big.dii. T and C chrcersi for the, re-unic case1./cF2

1.d3K x C = m 6 n6 A/ T2 J.(t= 0 s)= ad =8

Big. RB owerfortheinjetio-loced tar-u; ranien

'it-.

I F~ig. 10 -- ;cwer for th e iz~jectior-oz'ke5 case -= ,=,

i-cc2-. . . =0.L . : n n =

-, %''

i-.°o

..-.:.,

#v4°,

w* .

- o-4

'p-."So

• --

.4-- p

-' . -, . - • , . . ' " • . . . .,, - ! " I . . ,, - , , " , ,t 4 " -

'4,. ,.4 ,. ,,-'". ,' ," -. " ." " " -" ".' " "" " '.-" / "- "'- ,, " ,," ,,- ''" e . . ., ,", ,- " - '

l4

ELI

.1,_i able I inljecticn-locked resultIs bserved expDeri mentally as a funct'on

o.f ,4e -ea'e (f 10 GHz, J,=6 A/cr.2, -us widt

5 -s and d, - factor= .

A, Table 2 Results f the uasi-static simulation for "he inecicn-

. locked case. (j- = 646 A/cm, = 8 vs, f = 10 GHz,GC 05ulse width 1!5 Vs and duty factor =4,"'. P is averaged

- " " EF

over the tulse width.)

.. ,[

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Table i

Injection-locked results observed experimentally

as a function cf in.ected nower

f_0- ...6 2, w,. = I us and duty factor = 1,55)

1D Added Average T,. Efficiency V"in "F " dV(w, peak) (W, -peaK) (OV)() v

2.00 14.77 49. 17.9 98.0

2.50 16.28 472.8 20.0 97.0

3.00 17.4 1472.0 21.2 98. 0

3.50 17.63 471.4 21.4 98.0

3.75 17.39 472.1 21.1 98.0

4.00 16.51 474.5 20.1 98.C

4.50 16.12 1475.6 19.6 98.0

5.00 15.88 476.2 19.3 98.0

-u

ios:

4°...

-4-.. , " "-;4. v ~ - . .$: .,

.* .]

Resultz of t*-e mias-static S 41-,; a-tic. for -the ireto-o'~case

(Ja C. .... , - = c .s, C = !GHz, pulse w dth 1.5 . andCc -c--

duty factcr = -- S. F s averazea over the pulse width."

(W) Pr (W, poeak)

C- .39-' 2.0 15.50

So L6 2.5 16.30

3.0 16.41

0.521 3.5 16.53

C. 557 4.o 16.56

0.59-1 . C3

C.C2: 5.0 16.11

. 5.15.87

c. o.6,_ 6 .0 15.56

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