Comparative Analysis of DDR and DAR IMPATT Diodes Frequency Characteristics

Transcription

1 Recet Researches i Automatic Cotrol ad Electroics Comarative Aalsis of DDR ad DAR IMPATT Diodes Frequec Characteristics ALEXANDER ZEMLIAK,3, FERNANDO REYES 2, JAIME CID 2, SERGIO VERGARA 2 EVGENIY MACHUSSKIY 3 Deartmet of Phsics ad Mathematics 2 Deartmet of Electroics Autoomous Uiversit of Puebla Av. Sa Claudio Rio Verde, Puebla, MEXICO 3 Istitute of Techical Phsics Natioal Techical Uiversit of Uraie UKRAINE azemlia@fcfm.bua.mx Abstract: - The aalsis of DDR ad DAR IMPATT diodes has bee realized o basis of the recise driftdiffusio oliear model. The admittace ad eerg characteristics of the DAR diode were aalzed i ver wide frequec bad from 30 u to 360 GHz ad had bee otimized for two high frequec bads ear the 200 ad 300 GHz. Ke Words: - Imlicit umerical scheme, active laer structure aalsis, DDR ad DAR IMPATT diodes. Itroductio The ower geeratio i short art of millimeter regio is oe of the imortat roblems of moder microwave electroics. The IMPATT diodes of differet structures are used ver frequetl i microwave sstems. The sigle drift regio (SDR) ad the double drift regio (DDR) IMPATT diodes are ver well ow ad used successfull for the microwave ower geeratio i millimeter regio [- 2]. The tical DDR diode structure is show o Fig. b curve, where N is the cocetratio of doors ad accetors, l is the legth of diode active laer. The other roosed DDR te of IMPATT diode doig rofile is show o the Fig. b the curve 2. This te of semicoductor structure ca be amed as quasi-read-te structure. This te of doig rofile rovides a cocetratio of electrical field withi the - juctio. From the famous aer of Read [3] the mai 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 time of charge carriers. However a IMPATT diode that has double avalache regios (DAR) ca roduce a avalache dela, which aloe ca satisf coditios ecessar to geerate microwave ower [4-7]. This diode ca be defied for istace b meas of the structure +v+ i Fig. 2. Figure. Doig rofile for two tes of DDR IMPATT diodes: - costat doig rofile; 2- quasi-read-te doig rofile. Figure 2. Doig rofile of DAR IMPATT diode. ISBN:

2 Recet Researches i Automatic Cotrol ad Electroics The characteristics of this diode were aalzed i [7] b meas of aroximate model. The authors affirm that the diode active roerties are roduced i ma frequec bads for a drift zoe width. Our relimiar aalsis that was obtaied o basis of the sufficietl recise model [8-9] cotradicts to the results [7]. We obtaied three active frequec regios for roosed diode. We have bee otimized the DAR IMPATT diode for the secod frequec bad ear 200 GHz ad for the third frequec regio ear 300 GHz. 2 Noliear Model The drift-diffusio model, 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 semicoductor structure ad ecessar boudar coditios as for cotiuit equatios ad for the Poisso equatio. The ricial equatios ca be reseted i ext form: (, ) J ( x, t) x t t (, ) J ( x, t) x t t where (, ) α (, ) = + α J x t + J x t x (, ) α (, ) = + α J x t + J x t x (, ) (, ) 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 deedeces of the ioizatio coefficiets o field ad temerature ad charge trasort roerties have bee aroximated usig the aroach i [0-3]. The boudar coditios for this sstem 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. 0 s s ; (2) where J s, J are the electro curret ad the hole s curret for iversel biased - juctio; N, N l are the cocetratios of doors D ( ) ( ) 0 A 0 ad accetors at two ed sace oits x = 0 ad x = l 0 ; where l 0 is the legth of the active laer of semicoductor structure. The electrical field distributio i semicoductor structure ca be obtaied from the Poisso equatio. As electro ad hole cocetratios are fuctios of the time, therefore, this equatio is the time deedet too ad time is the equatio arameter. The Poisso equatio for the above-defied roblem has the followig ormalized form: 2 (, ) U( x, t) E x t = 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 + m ( + m) U t U l t U U si ω mt ϕ (4) m= where U 0 is the DC voltage o diode cotacts; U m is the amlitude of harmoic umber m i diode cotacts; ω is the fudametal frequec; ϕ m is the hase of harmoic umber m; M is the umber of harmoics. I this aer we aalze oe harmoic regime ol (M=) ad i this case the hase ϕ m ca be defie as 0. Cocrete values of the voltages U 0, U ad frequec ω have bee defied durig the aalsis i sectio 4. Equatios ()-(4) adequatel describe rocesses i the IMPATT diode i a wide frequec bad. However, umerical solutio of this sstem of equatios is ver difficult due to existig of a shar deedece of equatio coefficiets o electric field. Exlicit umerical schemes have oor stabilit ad require a lot of comutig time for good calculatio accurac obtaiig [4]. It is more advatageous to use imlicit umerical scheme that has a sigificat roert of absolute stabilit. Comutatioal efficiec ad umerical algorithm accurac are imroved b alig the sace ad the time coordiates smmetric aroximatio. After aroximatio of fuctios ad its differetials the sstem () is trasformed to the imlicit modified Cra-Nicholso umerical ISBN:

3 Recet Researches i Automatic Cotrol ad Electroics scheme. This modificatio cosists of two umerical sstems each of them havig threediagoal matrix. These sstems are defied b form: ( 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 umber; is the time coordiate ode umber; h is the sace ste; τ is the time ste; I is the sace ode umber. The aroximatio of the Poisso equatio is erformed usig ordiar fiite differece scheme at ever time ste : U ( N N + ) 2 i 2 U i + Ui+ = h Di Ai i i (6) Numerical algorithm for the calculatio of IMPATT diode characteristics cosists of the followig stages: ) the voltage is calculated at the diode cotacts for ever time ste b formula (4); 2) the voltage distributio is calculated at ever sace oit from the Poisso equatio (6) b factorizatio method [5], the electrical field distributio alog the diode active laer is calculated; 3) the charge carries ioizatio ad drift arameters are calculated i umerical et odes for the curret time ste; 4) the sstem of equatios (5) is solved b matrix factorizatio method taig ito accout the boudar coditios (2) ad electro ad hole cocetratio distributios are calculated for the ew time ste ad the the calculatio ccle is reeated for all time stes util the ed of the time eriod; 5) the full curret i exteral circuit is calculated. This rocess is cotiued from oe eriod to aother util the covergece is achieved b meas of the results comariso for the two eighborig eriods with the ecessar recisio. The all harmoics of the exteral curret, admittace for the harmoic umber m ad ower characteristics ca be calculated b the Fourier trasformatio. 3. Otimizatio Techique The secial otimizatio algorithm that combies oe id of direct method ad a gradiet method was used to otimize the outut characteristics of DAR diode. To obtai the better solutio for the otimum rocedure, it is ecessar to aalze N- dimesioal sace for N=5. The ricial vector of otimizatio arameters cosists of five variables =,,,, where the comoets ( ) 2 3 4, 5 will be defied below. The otimizatio algorithm ca be defied b ext stes:. Give as iut two differet aroximatios of 0 two iitial oits ad. 2. At these oits, we start with the gradiet method, ad have erformed some stes. As a 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 =, F 0, ( ) δ,, ( ) δ F, Y, N =, (7) where F is the cost fuctio, ad, δ is the arameter of the gradiet method. 3. We draw a lie through two these oits, ad erform 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 arameter of the lie ste. 4. The we erform some stes from this oit b s the gradiet method, 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, ). ISBN:

4 Recet Researches i Automatic Cotrol ad Electroics This otimizatio algorithm caot fid the global maximum of the cost fuctio, but ol a local oe. To obtai the better solutio of the otimum rocedure, it is ecessar to aalze N- dimesioal volume with differet iitial oits. Durig the otimizatio rocess, it is ver imortat to localize the subsace of the N-dimesioal otimizatio sace for more detailed aalsis. The this subsace ca be aalzed carefull. 3 Numerical Scheme Covergece The umerical scheme for the roblem () for the DDR IMPATT diode structures was roduced some ears ago [6]. The scheme aalsis showed a ver good covergece of the umerical model. The umerical algorithm covergece was obtaied durig 6 8 high frequec eriods. O the other had the careful aalsis of umerical model for the DAR diode with the doig rofile i Fig.2 shows that the umerical scheme covergece for this te of the doig rofile is ver slow ad the umerical trasitio rocess cotiues ma eriods to obtai the statioar mode (Fig. 3). 4 Results ad Discussio 4. Admittace 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 small sigal admittace characteristic of DDR diode is show i Fig. 4. Figure 4. Comlex small sigal DDR diode admittace (coductace -G versus suscetace B) for differet frequecies. The accurate aalsis for DAR IMPATT diode has bee made 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 more or less sigificat width of the regio v [9]. The same doig rofile as i [7] gives the egative coductace for ver arrow frequec bad ol as show i Fig. 5 i coductace versus suscetace lot. Figure 3. Calculated coductace as fuctio of eriod umber N. The ecessar umber of the cosequet eriods deeds o the diode width ad oeratig frequec ad chages from for the frequec bad 5 60 GHz u to eriods for GHz. This ver slow covergece was stiulated b the aschroies movemet of the electro ad hole avalaches alog the same drift regio v. It occurs owig to the differet drift velocities of the carriers. This effect rovoes a large umber of ecessar eriods ad large comuter time. This is a secific feature of the aalzed te of diode structure. Figure 5. Comlex small sigal DAR diode admittace (coductace -G versus suscetace B) for differet frequecies ad two values of drift laer widths W v. ISBN:

5 Recet Researches i Automatic Cotrol ad Electroics The solid lie of this figure gives deedec for drift laer width W v = 0.6 µ m ad the dash lie for W v =.5 µ m. First deedec dislas the diode active roerties for oe arrow frequec bad from 50 GHz u to 85 GHz. Secod admittace deedec for W v =.5 µ m gives ver arrow oe frequec bad from 40 GHz u to 62 GHz with a ver small value of egative coductace G. I geeral the admittace behavior has a dam oscillatio character but ol first ea lies i egative semi lae. The egative coductace disaears comletel for W v >.5 µ m. The mai reaso of this effect is a oschroize mechaism of carriers movemet alog the drift regio. This coclusio is cotrar to results of the aer [7]. Our results disla the active features of the DAR diode the same rofile for some frequec bads whe the v-regio width less tha 0.5 µ m. Oe ositive idea to icrease egative admittace of the diode cosists i o-smmetric doig rofile utilizatio. This rofile gives some comesatio to the aschroies mechaism. Oe of the ersective diode structures that was aalzed detail is defied b meas of followig arameters: the doig level for ad zoe is equal to cm -3 ad cm -3, accordigl, the widths of the two corresodig areas are equal to 0. µ m ad 0.2 µ m, the width of the drift v- regio is equal to 0.32 µ m. I Fig. 6 the small sigal comlex admittace i.e. the coductace versus suscetace is reseted for the curret desit J 0 = 30 A/cm 2. It is clear that we ca obtai larger value of the coductace icreasig the curret desit. We ca decide that two suerior bads aear from the ositive coductace G semi lae (loo Fig. 5) as a result of the secial coditios maig for these bads. This effect gives ossibilit to use suerior frequec bads, at least the secod bad, for the microwave ower geeratio of the sufficiet level. We ca decide that two suerior bads aear as a result of the secial coditios maig for these bads. This effect gives ossibilit to use the secod ad the third bads for the microwave ower geeratio of the sufficiet level. 4.2 DAR diode otimizatio for 220 GHz The DAR diode iteral structure otimizatio has bee rovided for the secod frequec bad ear 220 GHz for the feedig curret desit 30 A/cm 2. The cost fuctio of the otimizatio rocess was selected as outut ower level for the frequec 220 GHz. The set of the variables for the otimizatio rocedure was comosed from five techological arameters of the diode structure: two doig levels for ad regios ad three widths of, ad v regios. The otimal values of these arameters were foud: doig levels of ad zoe are equal to cm -3 ad cm -3 accordigl, the widths of the two corresodig areas are equal to 0. µ m ad 0.2 µ m, ad the width of the drift v- regio is equal to 0.34 µ m. The results of the comlete aalsis for three curret desit values 30, 50 ad 70 A/cm 2 are show i Fig. 7. The active diode roerties for two first bads are imroved whe the curret desit icreases. More ositive effect was obtaied for the frequec 220 GHz because the otimizatio for this frequec. Figure 6. Comlex small sigal DAR diode admittace for differet frequecies ad W v = 0.32 µ m. Figure 7. Comlex small sigal DAR diode admittace otimized for secod frequec bad for differet value of feedig curret. ISBN:

6 Recet Researches i Automatic Cotrol ad Electroics The characteristics obtaied for 220 GHz uder a large sigal serve as the mai result. The amlitude characteristics for the coductace ad the outut ower for this frequec are show i Fig. 8 ad Fig. 9 accordigl, for three values of the curret desit. curret desit 50 A/cm 2 ad 70 A/cm 2. The small sigal admittace otimizatio for third frequec bad is show i Fig. 0 for two values of curret desit: 50 ad 70 A/cm 2. Figure 8. Coductace G deedec as fuctio of first harmoic amlitude U for 220 GHz. Figure 9. Outut geerated ower P deedec as fuctio of first harmoic amlitudeu for 220GHz. We ca state that a sufficiet imrovemet of ower characteristics is observed for this diode structure i comariso with o otimized structure. The maximum values of geerated ower are equal to 3.3 W/cm 2 for J 0 =30 A/cm 2, 6.0 W/cm 2 for J 0 =50 A/cm 2 ad 7.5W/cm 2 for J 0 =70 A/cm 2 accordigl. 4.3 DAR diode otimizatio for 330 GHz The results of diode structure otimizatio are reseted below for frequec 330 GHz ad feedig Figure 0. Comlex small sigal DAR diode admittace otimized for third frequec bad for two values of feedig curret. The cost fuctio of the otimizatio rocess was selected as real art of the comlex admittace. The set of the variables for the otimizatio rocedure was comosed from five techological arameters of the diode structure: two doig levels for ad regios ad three widths of, ad v regios. The otimal values of these arameters are ext: doig levels of ad zoe are equal to cm -3 ad cm -3 accordigl, the widths of the two corresodig areas are equal to 0.09 µ m ad 0.8 µ m, ad the width of the drift v- regio is equal to 0.32 µ m. The active diode roerties for all frequec bads are imroved whe the curret desit icreases. More ositive effect was obtaied for the frequec 330 GHz because the otimizatio for this frequec. The amlitude characteristics of the coductace for this frequec are show i Fig. for two values of the curret desit. The coductace characteristic is softer for curret desit 50 A/cm 2 because the diode structure otimizatio was rovided for this curret. The characteristics for 70 A/cm 2 are sharer but corresod to the larger coductace G. The outut ower deedecies as a fuctio of first harmoic amlitude U for f = 330 GHz ad for two values of feedig curret are show i Fig. 2. These amlitude characteristics show the ossibilit to obtai a sufficiet level of outut ower ear the 4 W/cm 2. ISBN:

7 Recet Researches i Automatic Cotrol ad Electroics some frequec bads for the sufficietl large drift regio. To obtai the egative coductace for some frequec bads we eed to reduce the drift laer widths to obtai W v lesser tha 0.5 µ m. Nevertheless the diode has a wide first frequec bad geeratio ad two suerior frequec bads with sufficiet outut ower level. The diode structure otimizatio gives the ossibilit to icrease the outut ower level for high frequec bads. This level ca be exceedig b the secial diode structure otimizatio taig ito accout ecessar feedig curret desit. Figure. Coductace G deedec as fuctios of first harmoic amlitude U for f = 330 GHz ad for two values of feedig curret desit. Figure 2. Outut geerated ower P deedec as fuctios of first harmoic amlitude U for f = 330 GHz ad for two values of feedig curret desit. 6 Coclusio The umerical scheme that has bee develoed for the aalsis of the differet tes of IMPATT diodes is suitable for the DAR comlex doig rofile ivestigatio too. The additioal roblem that aears for the DAR diode structure aalsis is the slower covergece of the umerical model i comariso with the DDR diode aalsis. Some ew features of the DAR diode were obtaied b the aalsis o the basis of oliear model o comarig with DDR diode. The ricial obtaied results cotradict to the data that were obtaied before o the basis of the aroximate models of the DAR diode. These results show that the diode does ot have the active roerties i Acowledgemet This wor was suorted b the Autoomous Uiversit of Puebla b the roject VIEP ZEEA/EXC/2-G. Refereces: [] G.I. Haddad, P.T. Greilig, ad W.E. Schroeder, Basic riciles ad roerties of avalache trasit-time devices, IEEE Tras. Microwave Theor Tech., MTT-8, 970, [2] Chag K. (Ed.), Hadboo of microwave ad otical comoets, Joh Wile & Sos, N.Y., 990. [3] W.T. Read, A roosed high-frequec egative resistace diode, Bell Sst Tech. J, Vol. 37, 958, [4] B. Som, B.B.Pal, ad S.K.Ro, A small sigal aalsis of a IMPATT device havig two avalache laers itersaced b a drift laer, Solid-State Electro., Vol. 7, 974, [5] D.N. Datta, B.B.Pal, Geeralized small sigal aalsis of a DAR IMPATT diode, Solid-State Electro, Vol. 25, No. 6, 982, [6] S.P. Pati, J.P. Baerjee, ad S.K. Ro, High frequec umerical aalsis of double avalache regio IMPATT diode, Semicod Sci Techol, No. 6, 99, [7] A.K. Pada, G.N. Dash, ad S.P. Pati, Comuter-aided studies o the wide-bad microwave characteristics of a silico double avalache regio diode, Semicod Sci Techol, No. 0, 995, [8] A. Zemlia, ad R. De La Cruz, Comarative aalsis of double drift regio ad double avalache regio IMPATT diodes, WSEAS Tras. o Commuicatios, Vol. 3, No., 2004, ISBN:

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