Comparative Analysis of DDR and DAR IMPATT Diodes for Wide Frequency Band

Transcription

1 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi Coarative Aalsis of DDR ad DAR IMPATT Diodes for Wide Frequec Bad ALEXANDER ZEMLIAK,3, FERNANDO REYES 2, JAIME CID 2, SERGIO VERGARA 2 EVGENY MACHUSSKIY 3 Deartet of Phsics ad Matheatics 2 Deartet of Electroics Autooous Uiversit of Puebla Av. Sa Claudio Rio Verde, Puebla, MEXICO 3 Istitute of Techical Phsics Natioal Techical Uiversit of Uraie UKRAINE azelia@fcf.bua.x Abstract: - The aalsis of Double Drift Regio (DDR) ad Double Avalache Regio (DAR) IMPATT diodes has bee realized o basis of the recise drift-diffusio oliear odel ad secial otiizatio rocedure. DDR IMPATT diode icludes oe avalache regio ad two drift regios ad DAR IMPATT diode icludes two avalache regios iside the diode ad oe drift regios both for electros ad holes. The hase dela which was roduced b eas of the two avalache regios ad the drift regio v is sufficiet to obtai the egative resistace for the wide frequec bad. The adittace ad eerg characteristics of the DAR diode were aalzed i ver wide frequec bad fro 30 u to 360 GHz. Outut ower level was otiized for the secod ad third frequec bads ear the 220 ad 330 GHz. Ke Words: - Ilicit uerical schee, active laer structure aalsis, DDR ad DAR IMPATT diodes. Itroductio The ower geeratio i short art of illieter regio is oe of the iortat robles of oder icrowave electroics. The IMPATT diodes of differet structures are used ver frequetl i icrowave sstes. The sigle drift regio (SDR) ad the DDR IMPATT diodes are ver well ow ad used successfull for the icrowave ower geeratio i illieter regio [-3]. The tical DDR diode structure is show o Fig. b curve, Figure. Doig rofile for two tes of DDR IMPATT diodes: - costat doig rofile; 2- quasi-read-te doig rofile. where N is the cocetratio of doors ad accetors, l is the legth of diode active laer. I this te of diodes, the electrical field is strogl distorted whe the avalache curret desit is sufficietl high. This large sace charge desit is oe of the ai reasos for the shar electrical field gradiet alog the charge drift ath. Because of this field gradiet, the sace charge avalache ruis itself ad cosequetl the otiu hase relatios degrade betwee icrowave otetial ad curret. This factor is eseciall iortat whe the IMPATT diode is fed at the axiu curret desit. The idea to use a colex doig rofile seicoductor structure for icrowave diode was origiall roosed i the first aalsis of IMPATT diode b Read [4]. This roosed ideal structure has ever bee realized till ow. However, a oder seicoductor techolog rovides ew ossibilities for the fabricatio of sub icro seicoductor structures with colex doig rofiles. The other roosed DDR te of IMPATT diode doig rofile is show o the Fig. b the curve 2. This te of seicoductor structure ca be aed as quasi-read-te structure ad this structure rovides a cocetratio of electrical field withi the - juctio. E-ISSN: Issue 6, Volue 2, Jue 203

2 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi Fro the faous aer of Read [4] the ai idea to obtai the egative resistace was defied o the basis of the hase differece beig roduced betwee RF voltage ad RF curret due to dela i the avalache build-u rocess ad the trasit tie of charge carriers. However a IMPATT diode that has double avalache regios ca roduce a avalache dela, which aloe ca satisf coditios ecessar to geerate icrowave ower [5-7]. This diode ca be defied for istace b eas of the structure +v+ i Fig. 2. The DAR diode has two avalache regios aroud + ad + juctios ad oe coo drift regio. This te of diode was suggested i [5]. The characteristics of this diode were aalzed i DC ad RF odes [6-9]. The authors affir that the avalache dela roduced b each of the thi avalache regios becoes earl π /2, aig the total avalache dela equal toπ that is sufficiet to roduce egative diode resistace ad geerates the icrowave ower i illietric regio. Figure 3. Electric field distributio for DDR IMPATT diode with costat doig rofile () ad DAR IMPATT diode (2). 2 Noliear Model The drift-diffusio odel, which is used for the diode aalsis, cosists of two cotiuit equatios for the electros ad holes, the Poisso equatio for the otetial distributio i seicoductor structure ad ecessar boudar coditios as for cotiuit equatios ad for the Poisso equatio. The ricial equatios ca be reseted i ext for: (, ) J ( x, t) x t t (, ) J ( x, t) x t t (, ) α (, ) + α J x t + J x t x ( ) ( ) + α J x, t + α J x, t x () Figure 2. Doig rofile of DAR IMPATT diode. The electric field distributio alog the axis x for this te of the diode is show i Fig. 3, curve 2. Curve aroxiates the electric field distributio for the DDR with costat doig rofile diode for coariso. The characteristics of this diode were aalzed i [9] b eas of aroxiate odel. The authors affir that the diode active roerties are roduced i a frequec bads for a drift zoe width. Our reliiar aalsis that was obtaied o basis of the sufficietl recise odel [0] cotradicts to the results [9]. We eed aalze the DAR IMPATT diode for wide frequec bad o the basis of this odel ad otiize the diode structure for the secod ad third frequec regios. where (, ) (, ) J x t x t V + D (, ) (, ) J x t x t V D (, ) x t x (, ) x t x, are the cocetratios of electros ad holes; J, J are the curret desities; α, α are the ioizatio coefficiets; V, V are the drift velocities; D, D are the diffusio coefficiets. The ioizatio coefficiets, drift velocities ad diffusio coefficiets are the fuctios of the electric field ad teerature i all oits of seicoductor structure. The deedece of the ioizatio coefficiets o electric field ad teerature ca be aroxiated usig the aroach described i []: E-ISSN: Issue 6, Volue 2, Jue 203

3 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi α α ( E, T) ( E, T) [ ( T) / E ] e 5 E< [ ( T) / E ] e < E< [ (. +. T) / E ] e 5 E> [ ( T) / E ] e < E< [ ( T) / E ] e E> The teerature T is exressed i o C ad electrical field E is exressed i V/c. The drift velocities ad diffusio coefficiets were calculated b eas of aroxiatios give i [2-4]. The boudar coditios for this sste iclude cocetratio ad curret defiitio for cotact oits ad ca be writte as follows: J ( 0, t) N D ( 0) ; ( l0, t) N A ( l0 ) ( l, t) J ; J ( 0, t) J. where J 0 s s s ; (2), J are the electro curret ad the s hole curret for iversel biased - juctio; N ( ) D 0, NA ( l0) are the cocetratios of doors ad accetors at two ed sace oits x 0 ad x l 0 ; where l 0 is the legth of the active laer of seicoductor structure. The electrical field distributio i seicoductor structure ca be obtaied fro the Poisso equatio. As electro ad hole cocetratios are fuctios of the tie, therefore, this equatio is the tie deedet too ad tie is the equatio araeter. The Poisso equatio for the above-defied roble has the followig oralized for: 2 (, t) U( x, t) E x x x 2 N where N ( x) N ( x) D A ( x) N ( x) + ( x, t) ( x t) D A, (3), are the cocetratios of doors ad accetors accordigl, U(x,t) is the otetial, E(x,t) is the electrical field. The boudar coditios for this equatio are: M ( 0, ) 0; ( 0, ) 0 + ( + ) U t U l t U U si ω t ϕ (4) where U 0 is the DC voltage o diode cotacts; U is the alitude of haroic uber i diode cotacts; ω is the fudaetal frequec; ϕ is the hase of haroic uber ; M is the uber of haroics. I this aer we aalze oe haroic regie ol (M) ad i this case the hase ϕ ca be defie as 0. Cocrete values of the voltages U 0, U ad frequec ω have bee defied durig the aalsis i sectio 5. Equatios ()-(4) adequatel describe rocesses i the IMPATT diode i a wide frequec bad. However, uerical solutio of this sste of equatios is ver difficult due to existig of a shar deedece of equatio coefficiets o electric field. Exlicit uerical schees have oor stabilit ad require a lot of coutig tie for good calculatio accurac obtaiig [5]. It is ore advatageous to use ilicit uerical schee that has a sigificat roert of absolute stabilit. Coutatioal efficiec ad uerical algorith accurac are iroved b alig the sace ad the tie coordiates setric aroxiatio. After the aroxiatio of the fuctios ad its differetials the sste () is trasfored to the ilicit odified Cra-Nicholso uerical schee. This odificatio cosists of two uerical sstes each of the havig threediagoal atrix. These sstes are defied b for: + + ( a b ) + ( + 2a ) ( a + b ) a i i + ( 2a ) i + a i+ + b ( i+ i ) + α τ V i + r D ( i+ i ) + α τ V r D ( ) i i + i+ i+ i ( a + b ) i + ( + 2a ) i ( a b ) i+ a i + ( 2a ) i + a i+ b ( i+ i ) + α τ V i r D ( i+ i ) + α τ V + r D ( ) i, 2,... I ; i 0,, 2,... i+ i (5) D, where a, τ V, ; b 2h 2, τ ; r τ 4 h 2 h ; i is the sace coordiate curret ode uber; is the tie coordiate ode uber; h is the sace ste; τ is the tie ste; I is the sace ode uber. E-ISSN: Issue 6, Volue 2, Jue 203

4 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi The aroxiatio of the Poisso equatio is erfored usig ordiar fiite differece schee at ever tie ste : i Ui + Ui+ ( N N + ) 2 U 2 h (6) Nuerical algorith for the calculatio of IMPATT diode characteristics cosists of the followig stages: ) the voltage is calculated at the diode cotacts for ever tie ste b forula (4); 2) the voltage distributio is calculated at ever sace oit fro the Poisso equatio (6) b factorizatio ethod [6], the electrical field distributio alog the diode active laer is calculated; 3) the charge carries ioizatio ad drift araeters are calculated i uerical et odes for the curret tie ste; 4) the sste of equatios (5) is solved b atrix factorizatio ethod taig ito accout the boudar coditios (2) ad electro ad hole cocetratio distributios are calculated for the ew tie ste ad the the calculatio ccle is reeated for all tie stes util the ed of the tie eriod; 5) the full curret i exteral circuit is calculated. This rocess is cotiued fro oe eriod to aother util the covergece is achieved b eas of the results coariso for the two eighborig eriods with the ecessar recisio. The all haroics of exteral curret are calculated b the Fourier trasforatio ( J0; J J ex( jφ ) ) ; the adittace is calculated for a haroic uber ( Y J / U ) ad the ower characteristics for all haroics ca be calculated b the followig P 2 forulas: P Re ( Y ) U ; η 2 J U Otiizatio Techique The secial otiizatio algorith that cobies oe id of direct ethod ad a gradiet ethod was used to otiize the outut characteristics of DAR diode. To obtai the better solutio for the otiu rocedure, it is ecessar to aalze N- diesioal sace for N5. The ricial vector of otiizatio araeters cosists of five variables,,,, where the cooets ( ) 2 3 4, 5 will be defied below. The otiizatio algorith ca be defied b ext stes:. Give as iut two differet aroxiatios 0 of two iitial oits ad. 2. At these oits, we start with the gradiet ethod, ad have erfored soe stes. As a Di Ai i i 0 result, we have two ew oits Y ad Y. This rocess is reflected b the ext equatios: 0, +, + Y 0,, 0,,,N- 0 0, N, 0, ( ) δ F,, ( ) δ F, Y, N, (7) where F is the cost fuctio, ad, δ is the araeter of the gradiet ethod. 3. We draw a lie through two these oits, ad erfor a large ste alog this lie. We have a ew s+ oit : s s ( Y Y ) s + s Y + α, s, (8) where α is the araeter of the lie ste. 4. The we erfor soe stes fro this oit b s the gradiet ethod, to obtai a ew oit Y : s, + s s +, Y s, s, ( ) δ F, (9) s s, N. The ste 3 ad 4 are reeated with the ext values of idex s (s 2, 3,). The otiizatio rocess that is reseted above caot fid the global iiu of the objective fuctio, but ol a local oe. To obtai the cofidece that we have the better solutio of the otiu rocedure, it is ecessar to ivestigate N- diesioal sace with differet iitial oits. I that case, it is ossible to ivestigate N-diesioal volue i ore detail. Durig the otiizatio rocess, it is ver iortat to localize the subsace of the N-diesio otiizatio sace for ore detail aalsis. N-diesioal sace volue of ideedet araeters is deteried aroxiatel o the base of silified odel described i [7] for the first stage of otiizatio rocedure. I that case, a Fourier series aroxiatio of ricial fuctios is used ad because of this aroxiate odel, we have a te ties acceleratio. After that, o the basis of the recise odel described i sectio 2 we have aalzed the iteral structure of the differet tes of silico diode. E-ISSN: Issue 6, Volue 2, Jue 203

5 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi 4 Nuerical Schee Covergece The uerical schee for the roble () for the DDR IMPATT diode structures was roduced soe ears ago [6]. The schee aalsis showed a ver good covergece of the uerical odel. The uerical algorith covergece was obtaied durig 68 high frequec eriods. O the other had the careful aalsis of uerical odel for the DAR diode with the doig rofile i Fig.2 shows that the uerical schee covergece for this te of the doig rofile is ver slow ad the uerical trasitio rocess cotiues a eriods to obtai the statioar ode (Fig. 3). Figure 3. Calculated coductace as fuctio of eriod uber N. The ecessar uber of the cosequet eriods deeds o the diode width ad oeratig frequec ad chages fro for the frequec bad 5 60 GHz u to eriods for GHz. This ver slow covergece was stiulated b the aschroies oveet of the electro ad hole avalaches alog the sae drift regio v. It occurs owig to the differet drift velocities of the carriers. This effect rovoes a large uber of ecessar eriods ad large couter tie. This is a secific feature of the aalzed te of diode structure. Figure 4. Colex sall sigal DDR diode adittace (coductace -G versus suscetace B) for differet frequecies. We ca see that DDR IMPATT diode roduces icrowave ower i frequec regio betwee 20 ad 0 GHz. The accurate aalsis for DAR IMPATT diode has bee ade for differet values of, ad v regio width ad the differet door ad accetor cocetratio level. The aalsis shows that the active roerties of the diode racticall are ot dislaed for ore or less sigificat width of the regio v [0]. The sae doig rofile as i [9] gives the egative coductace for ver arrow frequec bad ol as show i Fig. 5 i coductace versus suscetace lot. The aalsis of DAR IMPATT diode rovided soe ears ago show iterestig ad at the sae tie ver surrisig results cocerig ai 5 Results ad Discussio 5. Adittace characteristics of DDR ad DAR diodes The DDR te of IMPATT diode roduces oe frequec bad ol i ractice because a ver strog losses for high frequec bads. The tical sall sigal adittace characteristic of DDR diode is show i Fig. 4. Figure 5. Colex sall sigal DAR diode adittace (coductace -G versus suscetace B) for differet frequecies ad two values of drift laer widths W v. E-ISSN: Issue 6, Volue 2, Jue 203

6 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi features of the DAR diodes. Oe of the iortat coclusios of these wors cocers of the drift zoe width v ifluece to the diode frequec characteristics. It is oted that the diode active roerties are roduced racticall for a drift zoe width ad this width has a ifluece o the uber of the frequec bads. The larger drift zoe rovoes ore uber of frequec bads. Soe of these results were obtaied b eas of the sall sigal odel [5-7]. Other results [8-9] were obtaied o the basis of silified oliear odel. We suose that it is ecessar to aalze this diode b eas of recise odel described i sectio 2. The DAR diode doig rofile was defied the sae as i aer [9] for riar aalsis to rovide the adequate coariso betwee results which were obtaied b two differet aroaches. The the accurate aalsis for DAR IMPATT diode has bee ade for differet values of, ad v regio width ad the differet door ad accetor cocetratio level. The aalsis showed that the active roerties of the diode racticall are ot dislaed for ore or less sigificat width of the regio v. The sae doig rofile as i [9] gives the egative coductace for ver arrow frequec bad ol as show i Fig. 5 i coductace versus suscetace lot. The solid lie of this figure gives deedec for drift laer width W v 0.6 µ ad the dash lie for W v.5 µ. First deedec dislas the diode active roerties for oe arrow frequec bad fro 50 GHz u to 85 GHz. Secod adittace deedec for W v.5 µ gives ver arrow oe frequec bad fro 40 GHz u to 62 GHz with a ver sall value of egative coductace G. I geeral the adittace behavior has a da oscillatio character but ol first ea lies i egative sei lae. The egative coductace disaears coletel for W v >.5 µ. All these results have bee obtaied i assutio of a sufficietl sall value of a series resistace R s Oh. c 2. This value was used for all further aalsis too. The ai reaso of obtaied characteristics behavior is the sae as for the slow echais covergece of the uerical odel. The electro ad hole avalaches have differet trasit velocities but the ove alog the sae drift regio v. It rovoes differet tie dela for the carriers durig the trasit regio oveet. The larger width of the regio v aes dela tie ore differet ad the active roerties are reduced. That is wh we eed to reduce the width W v to obtai ecessar egative adittace. This coclusio is cotrar to results of the aers [8-9]. The ai results obtaied b these authors showed the DAR diode active features resece i soe frequec bads for differet values of v regio widths fro 0.5 µ to 2.0 µ. Our results disla the active features of the DAR diode the sae rofile for soe frequec bads i case whe the v-regio width less tha 0.5 µ ol. The obtaied differece could be exlaied robabl b eas of aroxiate uerical odel used i aer [9]. Oe odified Ruge-Kutta ethod was used to atheatical odel solve as show i this aer. However it is ow that a exlicit uerical ethod lie Ruge-Kutta does ot have the ecessar stabilit to solve the sufficietl difficult roble for cotiuit equatios () with a ver shar deedec of ioizatio coefficiets. The ai reaso of this effect is a oschroize echais of carriers oveet alog the drift regio. This coclusio is cotrar to results of the aer [9]. Our results obtaied i this aer disla the active features of the DAR diode the sae rofile for soe frequec bads whe the width of the v-regio of the diode less tha 0.5 µ ol. Oe ositive idea to icrease egative adittace of the diode cosists i utilizatio of the o-setric doig rofile too. This rofile gives soe coesatio to the aschroies echais which aears ito the structure. Taig ito accout these cosideratios o-setric doig rofile diode was aalzed i a wide frequec bad. Oe of the ersective diode structures that was aalzed detail is defied b eas of followig araeters: the doig level of the -zoe is equal to c -3, the doig level of the -zoe is equal to c -3, the widths of the two corresodig areas are equal to 0. µ ad 0.2 µ, accordigl, the width of the drift v- regio is equal to 0.32 µ, the width of each - juctio was give as 0.02 µ fro the techological asects. This structure rovides cocetratio of electrical field withi the two - juctios ad aschroies echais is ot dislaed drasticall et. I Fig. 6 the sall sigal colex adittace i.e. the coductace versus suscetace is reseted for the wide frequecies bad for DAR diode ad for the curret desit J 0 30 A/c 2. The DC voltage U 0 is equal to V with a sall variatio fro oe frequec to other to obtai this value of curret desit. The first haroic voltage alitude is equal to 0. V. E-ISSN: Issue 6, Volue 2, Jue 203

7 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi Figure 6. Colex sall sigal DAR diode adittace for differet frequecies ad W v 0.32 µ. There are soe differeces of the DAR diode frequec characteristics fro the classical DDR IMPATT diodes (Fig. 4). First of all the DAR diode te has three active bads i the illieter rage (Fig.6) ad the DDR diode has ol oe bad. The first active bad of the DAR diode is ver wide ad covers frequec regio fro 2 to 38 GHz. The secod ad the third bads ear 220 GHz ad 340 GHz give the ersective to use this structure for the high frequec geeratio i the illieter rage too. We ca decide that two suerior bads aear fro the ositive coductace G sei lae (loo Fig. 5) as a result of the secial coditios aig for these bads. This effect gives ossibilit to use suerior frequec bads, first of all the secod ad the third bads, for the icrowave ower geeratio of the sufficiet level. The deedeces of coductace -G as the fuctio of the first haroic alitude U are show i Fig. 7 for three frequec bads ad for the sae value of the curret desit J 0 30 A/c 2. We ca decide that two suerior frequec bads aear as a result of soe secial coditios aig for these bads. This effect gives us the ossibilit to use the secod ad the third frequec bads for the icrowave ower geeratio of the sufficiet level. It is obviousl that the first frequec bad characteristic (f 90 GHz) has a better behavior. The axiu value of the coductace -G is large ad achieves earl the 600 ho/c 2 uder the sall sigal. The alitude deedec for the first bad is ver soft ad this rovides a sigificat value of the geerated ower. Figure 7. Coductace G deedece as fuctios of first haroic alitude U for differet frequec bads. Nevertheless the secod ad the third bads (for 220 GHz ad for 340 GHz) have the ersective too. The outut ower deedeces for two frequec bads are reseted i Fig. 8 as fuctios of the first haroic alitude. Figure 8. Outut ower P deedece as fuctios of first haroic alitude U for differet frequec bads. The axiu ower desit is equal to 37 W/c 2 for the first frequec bad (90 GHz), ad.4 W/c 2 for the secod oe (220 GHz). Oe ricial liit of outut ower for secod ad third bads is based o the shar alitude deedec as show i Fig. 7. However the ossible otiizatio of the diode iteral structure for selected frequec bad ca irove these characteristics ad erits raise the ower ad the efficiec. The DAR diode iteral structure otiizatio has bee rovided below for the secod frequec bad ear 220 GHz ad for the third frequec bad ear 330 GHz searatel. E-ISSN: Issue 6, Volue 2, Jue 203

8 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi 5.2 DAR diode otiizatio for 220 GHz The DAR diode iteral structure otiizatio has bee rovided for the secod frequec bad ear 220 GHz for the feedig curret desit 30 A/c 2. The cost fuctio of the otiizatio rocess was selected as outut ower level for the frequec 220 GHz. The set of the variables for the otiizatio rocedure was coosed fro five techological araeters of the diode structure: two doig levels for ad regios ad three widths of, ad v regios. The otial values of these araeters were foud: doig levels of ad zoe are equal to c -3 ad c -3 accordigl, the widths of the two corresodig areas are equal to 0. µ ad 0.2 µ, ad the width of the drift v- regio is equal to 0.34 µ. The results of the colete aalsis of sall sigal adittace for ver wide frequec bad ad for three curret desit values lie 30, 50 ad 70 A/c 2 are show i Fig. 9. Figure 0. Coductace G deedec as fuctio of first haroic alitude U for 220 GHz. Figure 9. Colex sall sigal DAR diode adittace otiized for secod frequec bad for differet value of feedig curret. It is clear that the active diode roerties for two first bads ca be iroved whe the feedig curret desit icreases. More ositive effect was obtaied for the frequec 220 GHz because we rovided the structure otiizatio for this frequec exactl. The characteristics obtaied for 220 GHz uder a large sigal serve as the ai result. The alitude characteristics for the coductace ad the outut ower geerated b the diode for this frequec are show i Fig. 0 ad Fig. accordigl. These results have bee obtaied for three values of the feedig curret desit. Figure. Outut geerated ower P deedec as fuctio of the first haroic alitude U for 220 GHz. We ca state that a sufficiet iroveet of ower characteristics is observed for this diode structure i coariso with o otiized structure. The axiu values of geerated ower are equal to 3.3 W/c 2 for J 0 30 A/c 2, 6.0 W/c 2 for J 0 50 A/c 2 ad 7.5W/c 2 for J 0 70 A/c 2 accordigl. 5.3 DAR diode otiizatio for 330 GHz The results of the diode structure otiizatio are reseted below for frequec 330 GHz ad feedig curret desit 50 A/c 2 ad 70 A/c 2. The sall sigal adittace otiizatio for third frequec bad is show i Fig. 2 for two values of curret desit: 50 ad 70 A/c 2. E-ISSN: Issue 6, Volue 2, Jue 203

9 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi Figure 2. Colex sall sigal DAR diode adittace otiized for third frequec bad for two values of feedig curret. The cost fuctio of the otiizatio rocess was selected as real art of the colex adittace. The set of the otiized variables for the otiizatio rocedure was coosed fro five techological araeters of the diode iteral structure: two doig levels for ad regios ad three widths of, ad v regios. The otial values of these araeters are ext: doig levels of ad zoe are equal to c -3 ad c -3 accordigl, the widths of the two corresodig areas are equal to 0.09 µ ad 0.8 µ, ad the width of the drift v-regio is equal to 0.32 µ. The active diode roerties for all frequec bads are iroved whe the curret desit icreases. More ositive effect was obtaied for the frequec 330 GHz because the otiizatio for this frequec. The alitude characteristics of the coductace for this frequec are show i Fig. 3 for two values of the curret desit 50 A/c 2 ad 70 A/c 2. The coductace characteristic is softer for the curret desit 50 A/c 2 because the diode structure otiizatio was rovided for this curret exactl. The characteristics for other feedig curret desit 70 A/c 2 are sharer but corresod to the larger coductace G. The outut ower deedecies as a fuctio of the first haroic alitude U for the frequec f 330 GHz ad for two values of the feedig curret desit are show i Fig. 4. These alitude characteristics show the ossibilit to obtai a sufficiet level of outut ower of the diode ear the 4 W/c 2. Figure 3. Coductace G deedec as fuctios of first haroic alitude U for f 330 GHz ad for two values of feedig curret desit. Figure 4. Outut geerated ower P deedec as fuctios of first haroic alitude U for f 330 GHz ad for two values of feedig curret desit. 6 Coclusio The uerical schee that has bee develoed for the aalsis of the differet tes of IMPATT diodes is suitable for the DAR colex doig rofile ivestigatio too. The additioal roble that aears for the DAR diode structure aalsis is the slower covergece of the uerical odel i coariso with the DDR diode aalsis. Soe ew features of the DAR diode were obtaied b the aalsis o the basis of oliear odel o coarig with DDR diode. The ricial obtaied results cotradict to the data that were obtaied before o the basis of the aroxiate E-ISSN: Issue 6, Volue 2, Jue 203

10 WSEAS TRANSACTIONS o COMMUNICATIONS Alexader Zelia, Ferado Rees, Jaie Cid, Sergio Vergara, Evge Machussi odels of the DAR diode. These results show that the diode does ot have the active roerties i soe frequec bads for the sufficietl large drift regio. To obtai the egative coductace for soe frequec bads we eed to reduce the drift laer widths to obtai W v lesser tha 0.5 µ. Nevertheless the diode has a wide first frequec bad geeratio ad two suerior frequec bads with sufficiet outut ower level. The otiizatio of the diode structure gives us the ossibilit to icrease the outut ower level for high frequec bads. This level ca be exceedig i future b eas of the secial diode structure otiizatio taig ito accout ecessar feedig curret desit. Acowledgeet This wor was suorted b the Cosejo Nacioal de Ciecia Tecologia, Mexico uder research roject CONACYT Refereces: [] G.I. Haddad, P.T. Greilig, ad W.E. Schroeder, Basic riciles ad roerties of avalache trasit-tie devices, IEEE Tras. Microwave Theor Tech., MTT-8, 970, [2] Chag K. (Ed.), Hadboo of icrowave ad otical cooets, Joh Wile & Sos, N.Y., 990. [3] M. Tscheritz, ad J. Freer, 40 GHz GaAs Double-Read IMPATT Diodes, Electro. Lett.,Vol. 3, No.7, 995, [4] W.T. Read, A roosed high-frequec egative resistace diode, Bell Sst Tech. J, Vol. 37, 958, [5] B. So, B.B.Pal, ad S.K.Ro, A sall sigal aalsis of a IMPATT device havig two avalache laers itersaced b a drift laer, Solid-State Electro., Vol. 7, 974, [6] D.N. Datta, B.B.Pal, Geeralized sall sigal aalsis of a DAR IMPATT diode, Solid-State Electro, Vol. 25, No. 6, 982, [7] D. N. Datta, S. P. Pati, J. P. Baerjee, B. B. Pal, ad S. K. Ro, Couter aalsis of DC field ad curret-desit rofiles of DAR IMPATT diode. IEEE Tras Electro Devices, Vol. ED- 29, No., 982, [8] S.P. Pati, J.P. Baerjee, ad S.K. Ro, High frequec uerical aalsis of double avalache regio IMPATT diode, Seicod Sci Techol, No. 6, 99, [9] A.K. Pada, G.N. Dash, ad S.P. Pati, Couter-aided studies o the wide-bad icrowave characteristics of a silico double avalache regio diode, Seicod Sci Techol, No. 0, 995, [0] A. M. Zelia, S. Cabrera, Nuerical Aalsis of a DAR IMPATT diode, J Cout Electro, Vol. 5, No. 4, Deceber 2006, [] W.N. Grat, Electro ad hole ioizatio rates i eitaxial silico at high electric fields, Solid-State Electro., Vol. 6, No. 0, 973, [2] C. Jacoboi, C. Caali, G. Ottaviai, A review of soe charge trasort roerties of silico, Solid-State Electro, Vol. 20, 977, [3] C. Caali, C. Jacoboi, G. Ottaviai, High field diffusio of electros i silico, Al Phs Lett, Vol. 27, 975, [4] F. Nava, C. Caali, L. Reggiai, D. Gasquet, J.C. Vaissiere, ad J.P. Nougier, O diffusivit of holes i silico, J Al Phs, Vol. 50, 979, [5] A.M. Zelia, Differece schee stabilit aalsis for IMPATT-diode desig, Izv. VUZ Radioelectroia, Vol. 24, No. 8, 98, [6] A. Zelia, S. Khotiaitsev, ad C. Celaa, Colex oliear odel for the ulsed-ode IMPATT diode, Istruetatio ad Develoet, Vol. 3, No. 8, 997, [7] A. Zelia, C. Celaa, R. Garcia, Active laer araeter otiizatio for high-ower Si 2 ulsed IMPATT diode, Microwave Ot. Techol. Lett., Vol. 9, No., 998, E-ISSN: Issue 6, Volue 2, Jue 203