Comparative Analysis of Double Drift Region and Double Avalanche Region IMPATT Diodes

Transcription

1 Comarative Aalysis of Double Drift Regio ad Double Avalache Regio IMPATT Diodes ALEXANDER ZEMLIAK, ROQUE DE LA CRUZ Deartmet of Physics ad Mathematics Puebla Autoomous Uiversity Av. Sa Claudio y 8 Sur, Puebla, MEXICO Abstract: - The comarative aalysis of the well ow DDR (Double Drift Regio) IMPATT diode structure ad the ew + v + structure for the avalache diode has bee realized o the basis of the recise umerical model. The ew tye of the diode was amed as the Double Avalache Regio (DAR) IMPATT diode. This structure icludes the two avalache regios iside the diode. The hase delay, which was roduced by meas of the two avalache zoes ad the drift zoe v is sufficiet for the egative resistace obtai for the wide frequecy regio. The umerical model that is used for the aalysis of the various diode structures icludes all the ricial features of the hysical heomea iside the semicoductor structure. The admittace characteristics of both tyes of the diodes were aalyzed i very wide frequecy regio. Key-Words: - Semicoductor microwave devices, modelig ad simulatio, umerical methods. Itroductio The roblem of the microwave ower geeratio of the sufficiet outut level is the essetial roblem of moder semicoductor electroics. The more owerful semicoductor device is the IMPATT diode of the differet structures. The sigle drift regio (SDR) ad the double drift regio (DDR) IMPATT diodes are very well ow [-3] ad are used successfully for the microwave ower geeratio i millimeter regio. The simulatio ad otimizatio of its arameters [4-9] ca obtai very high outut ower level ad serves as the basis for the techology to roduce the diodes with the extremely characteristics. From the begiig [0] the mai idea to obtai the egative resistace was defied o the basis of the hase differece roducig betwee RF voltage ad RF curret due to the delay i the avalache build-u rocess ad the trasit time of charge carriers. The trasit time delay of both tyes of the diodes is the essetial factor of the ecessary hase coditios fulfillmet to obtai the egative resistace. However a diode that has two avalache regios ca roduce a avalache delay, which aloe ca satisfy the ecessary coditios to geerate the microwave ower. I this case the hase delay of the drift zoe becomes subsidiary. The DDR diode ad the DAR diode ca be defied by meas of the ext two structures (++, +v+) i Fig. (a), (b). (a) (b) Fig.. Doig rofile of DDR - (a) ad DAR - (b) IMPATT diode.

2 The DAR diode has two avalache regios aroud + ad + juctios ad oe commo drift regio. This tye of diode was suggested i []. The characteristics of this diode tye were aalyzed i DC ad RF modes [2-5]. Each of the avalache zoes rovides the hase delay about π ad this is sufficietly to roduce the egative diode resistace. The electric field distributio alog the axis x for both tyes of the diodes ca be aroximate by the Fig. 2. ecessary boudary coditios as for cotiuity equatios ad for the Poisso equatio. The system of the cotiuity equatios iclude two differetial equatios for the carriers cocetratios ad two additioal equatios for the curret desity determiatio: (, ) J ( x, t) x t t (, ) J ( x, t) x t t (, ) (, ) = + J x t + J x t (, ) (, ) = + J x t + J x t () (, ) (, ) J x t = x t V + D (, ) (, ) J x t = x t V D (, ) x t (, ) x t Fig. 2. Electric field distributio for DDR - ad DAR - 2 IMPATT diode There is oe avalache zoe for DDR diode ad two avalache zoes for DAR diode. The authors of the wors [-5] affirm that the drift zoe trasit time delay is ot a critical arameter for DAR diode because of the total avalache delay equal to π. Some advatages of the DAR structure were rogoses due this fact. The aalysis rovided i [- 5] gave the iterestig ad, at the same time very surrised results cocerig the mai features of the DAR diodes. Some of these results were obtaied by meas of the small sigal model [-3]. Others results [4-5] were obtaied o the basis of simlified oliear model. We suose that there is a ecessity to aalyze these structures o the basis of the recise model of the IMPATT diode, which was develoed i some wors of the authors [6-7]. 2 Numerical Model The electrical model which is useful for the recise aalysis of the iteral diode structure describes of all imortat hysical heomea ito the semicoductor device. This model is based o the system of two cotiuity equatios for the electros ad holes, the Poisso equatio for the otetial distributio i semicoductor structure ad the where, are the cocetratios of electros ad holes; J, J are the curret desities;, are the ioizatio coefficiets; V, V are the drift velocities; D, D are the diffusio coefficiets. Ioizatio coefficiets, drift velocities ad diffusio coefficiets are the fuctios of two argumets; the saces coordiate x ad the times coordiate t. The deedeces of the ioizatio coefficiets, o field ad temerature have bee aroximated usig the aroach described i [8]: ( E, T) ( E, T ) 6 [ ( T) / E ] e 5 E < [ ( T) / E ] = e < E < [ (. +. T) / E ] e 5 E > (2) 6 [ ( T) / E ] e < E < = 5 [ ( T) / E ] e E >

3 The temerature T is exressed i o C ad the electrical field E is exressed i V/cm. The drift velocities ad diffusio coefficiets were calculated by meas of the aroximatios have give i [9-2]. These aroximatios iclude all of the essetial features of the carrier s mobility i silico semicoductor structure ad give the ossibility to calculate the diode behavior i a wide frequecy regio for the differet regimes. The boudary coditios for this system iclude the cocetratio ad the curret defiitio for cotact oits ad ca be writte as follows: where J ( 0 ) = ( ) D 0 ( 0 ) = A( 0 ) (, ) = ; ( 0, ) =., t N ; l, t N l ; J l t J J t J 0 s s s (3), J are the electro curret ad the s hole curret for iversely 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 layer of semicoductor structure. The electrical field distributio ito semicoductor structure ca be obtaied from 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. Poisso equatio for the above defied roblem has the followig form: 2 (, ) U( x, t) E x t ( ) ( ) (, ) (, ) = 2 = ND x NA x + x t x t where N ( x) N ( x) D A (4), are the cocetratios of doors ad accetors accordigly, U(x,t) is the otetial, E(x,t) is the electrical field. The boudary coditios for this equatio are: M ( 0, ) = 0; ( 0, ) = 0 + m ( + m) U t U l t U U si ω mt ϕ (5) m= where U 0 is the DC voltage o diode cotacts; U m is the amlitude of harmoic umber m; ω is the fudametal frequecy; ϕ m is the hase of harmoic umber m; M is quatity of harmoics. Equatios () - (4) adequately describe rocesses i the IMPATT diode i a wide frequecy bad. However, umerical solutio of this system of equatios is very difficult because of the existig a shar deedece of equatio coefficiets o electric field. Evidet umerical schemes have oor stability ad require a lot of comutig time for good calculatio accuracy obtaiig. It is more advatageous to use o-evidet umerical scheme that has a sigificat roerty of absolute stability. Comutatioal efficiecy ad umerical algorithm accuracy are imroved by alyig the sace ad the time coordiates symmetric aroximatio. After the aroximatio of fuctios ad its differetials, the system () is trasformed to the o-evidet modified Cra-Nicholso umerical scheme. This modificatio cosists of two umerical systems, each of them havig three-diagoal matrix. This system has the followig form: ( a b ) i ( 2a ) i ( a b ) i + ( 2 ) ( ) = a + a + a + b + i i i+ i+ i i ( ) τ V + r D + i+ i ( ) τ V r D i i+ i ( a b ) i ( 2a ) i ( a b ) i+ i ( 2 ) i i+ ( i+ i ) = a + a + a b + ( i+ i ) ( ) τ V r D + i τ V + r D i i =, 2,... I ; i+ i = 0,, 2,... (6) D, where a, = τ V, ; b 2h 2, = τ ; r = τ 4h 2 h ; i is the sace coordiate 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 the ordiary fiite differece scheme at every time ste : ( D i A i i i ) 2 U 2U + U = h N N + i i i+ (7)

4 Numerical algorithm for the calculatio of IMPATT diode characteristics cosists of the followig stages: ) the voltage is calculated at the diode cotacts for every time ste; 2) the voltage distributio is calculated at every sace oit from Poisso equatio by factorizatio method [6], the electrical field distributio alog the diode active layer is calculated; 3) the charge carries ioizatio ad drift arameters are calculated i umerical et odes for the curret time ste; 4) the system of equatios (6) is solved by matrix factorizatio method ad electro ad hole cocetratio distributios are calculated for the ew time ste. After this, the calculatio cycle is reeated for all time stes util the ed of the time eriod. This rocess is cotiued from oe eriod to aother util the covergece is achieved by meas of the results comariso for two eighbor eriods. The all harmoics of the exteral curret; admittace for the harmoic umber m ad ower characteristics ca be foud by the Fourier trasformatio. 3 Numerical Scheme Covergece The umerical scheme (6)-(7) characteristic aalysis for the differet DDR IMPATT diode had bee made some years ago [6]. This aalysis showed a good covergece of the umerical model. The covergece was obtaied durig 6 8 eriods. The aalysis of the umerical model for the ew tye of the doig rofile (Fig.(b)) gave a uexected but uderstadable result. The umerical scheme covergece for this tye of the doig rofile is very slow. The ecessary umber of the cosequet eriods deeds o the oeratig frequecy ad ca chage from for the frequecy regio 5 60 GHz util eriods for GHz. This very slow covergece is stiulated by the asychroies movemet of the electro ad hole avalaches alog the same trasit time regio v. It occurs owig to the differet drift velocities of the carriers. This tye of umerical covergece rovoes a large umber of the ecessary eriods ad a large comuter time. 4 Comarative Aalysis The doig rofile structure for the DDR ad DAR IMPATT diode active layer is show i Fig.. The accurate aalysis for both tyes of the diodes has bee made for the differet values of the, ad v regio legths ad for the differet door ad accetor cocetratios. The aalysis showed that for more or less sigificat legth of the regio v (more tha 0.5 µ m) the active roerties of the diode are ot become. The reaso is the same which for the slow mechaism covergece of the umerical model. The electro ad hole avalaches have the differet trasit velocities but they move alog the same drift regio v. It rovoes the differet time delay for carriers durig the trasit regio movemet. The more legth of the regio v gives the more differece i delay time ad the active roerties are reduced. That is why we eed reduce the legth of the regio v to obtai the ecessary egative admittace. This is the cotrary coclusio to all results of the aers [4-5]. Aother ositive idea cosists of the o symmetric doig rofile utilizatio. This rofile gives some comesate of the asychroies mechaism. Tae ito accout these cosideratios the o symmetric doig rofile diode was aalyzed i a wide frequecy rage. The doig level of the -zoe is equal to cm -3, ad for the -zoe is equal to cm -3. The widths of two these corresodig areas are equal to 0. µ m ad 0.2 µ m accordigly. The width of the each - juctio was give as 0.02 µ m from the techological asects. The legth of the drift zoe v is equal to 0.32 µ m. This tye of doig rofile rovides a cocetratio of electrical field withi the two - juctios. I Fig. 3 ad Fig. 4 the small sigal comlex admittace i.e. the coductace versus suscetace are reseted for the wide frequecies rage for DDR ad DAR diodes ad for the curret desity J 0 = 30 A/cm 2. Fig. 3. DDR diode comlex small sigal admittace (coductace -G versus suscetace B) lots for differet frequecies.

5 Fig. 4. DAR diode comlex small sigal admittace (coductace -G versus suscetace B) lots for differet frequecies. There are some differeces of the DAR diode frequecy characteristics from the classical DDR IMPATT diodes. First of all the ew tye of the diode has three active zoes i the millimetric rage (Fig.4) ad the DDR diode has oly oe zoe (Fig.3). The first active zoe of the DAR diode is very wide ad covers the frequecy regio from 2 to 38 GHz. The secod ad the third zoes give the ersective to use this structure for the high frequecy geeratio ito the millimetric rage. The other differece from the usual diodes is the larger value of the real art of the comlex admittace -G for two more high frequecy zoes. This effect ermits use aother frequecy zoes, at least the secod zoe, for the microwave ower geeratio. The deedecies of the coductace -G as the fuctio of the first harmoic amlitude U are show i Fig. 5 for three frequecy zoes ad for the same value of the curret desity J 0 = 30 A/cm 2. It is clear that the first zoe characteristic (f = 90 GHz) has a better behavior. The maximum value of the coductace -G is a large ad for the small sigal achieves ear the 600 mho/cm 2. The amlitude deedecy for the first zoe is a very soft ad this rovide a sigificat value of the geerate ower. Nevertheless the secod ad third zoes (for 220 GHz ad for 340 GHz) have the ersective too. These characteristics have a more shar amlitude deedecy ad this effect limits the outut ower. However the ossible otimizatio of the diode iteral structure ca imrove these characteristics ad ermits to raise the ower ad the efficiecy. The geerate ower deedecies for two frequecy rages are reseted i Fig. 6 as the fuctios of the first harmoic amlitude. The maximum ower desity is equal to 37 W/cm 2 for the first frequecy Fig. 5. Coductace G deedecy as fuctio of first harmoic amlitude U for three frequecy zoes. Fig. 6. Geerate ower P as fuctio of first harmoic amlitude U for two frequecy zoes. zoe (90 GHz) ad.4 W/cm 2 for the secod oe (220 GHz). The last result ca serves as the start oit for the DAR diode rofile otimizatio to obtai the maximum outut ower geeratio for the suerior frequecy zoes. 5 Coclusio The umerical scheme that has bee develoed for the aalysis of the differet tyes of IMPATT diodes is suitable for the DAR comlex doig rofile ivestigatio. Some ew features of the DAR diode were obtaied by the careful aalysis o the basis of the recise umerical model. First of all we eed to declare that the aalysis of the DAR diode is more comlicated tha DDR because the very slow covergece of the umerical scheme. The ricial results were obtaied by the recise aalysis ad cotradict the data that had bee obtaied o the

6 basis of the aroximate models of the DAR diode. These results show that the diode do ot have the active roerties for the sufficietly large itrisic regio. To obtai the egative coductace we eed to reduce the itrisic regio. Nevertheless the diode has a widely first frequecy zoe geeratio ad the two suerior frequecy zoes with the sufficiet outut ower level. The DAR tye of the IMPATT diode ca be used for the outut ower geeratio i more widely frequecy regio tha well ow DDR diode. Acowledgmet This wor was suorted by the Uiversidad Autóoma de Puebla, uder roject VIEPIII05G02. Refereces: [] Edited by Kai Chag, Hadboo of Microwave ad Otical Comoets, Joh Wile & Sos, N.Y., Vol. 2, 990. [2] M. Curow, Proosed GaAs IMPATT Devices Structure for D-bad Alicatios, Electro. Lett., Vol. 30, 994, [3] M. Tscheritz ad J. Freyer, 40 GHz GaAs Double-Read IMPATT Diodes, Electro. Letters, Vol. 3, No. 7, 995, [4] K.V. Vasilevsii, Calculatio of the Dyamic Characteristics of a Silico Carbide IMPATT Diode, Sov. Phys. Semicod., Vol. 26, 992, [5] R.P. Joshi, S. Patha ad J.A. Mcadoo, Hot- Electro ad Thermal Effects o the Dyamic Characteristics of Sigle-Trasit SiC Imact- Ioizatio Avalache Trasit-Time Diodes, J. Al. Phys., Vol. 78, 995, [6] H.J. Kafa ad K. Hess, A Carrier Temerature Model Simulatio of a Double- Drift IMPATT Diode, IEEE Tras. Electro Devices., Vol. ED-28, No. 7, 98, [7] A.M. Zemlia ad S.A. Zicheo, No-liear Aalysis of IMPATT Diodes, Vesti K.P.I., Radiotechia, Vol. 26, 989, [8] C. Dalle ad P.A. Rollad, Drift-Diffusio Versus Eergy Model for Millimetric-Wave IMPATT Diodes Modellig, It. J. Numer. Modellig, Vol. 2, 989, [9] V. Stoiljovic, M.J. Howes ad V. Postoyalo, Noisothermal Drift-Diffusio Model of Avalache Diodes, J. Al. Phys., Vol. 72, 992, [0] W.T.Read, A Proosed High-Frequecy Negative Resistace Diode, Bell Syst. Tech. J., Vol.37, 958, [] B. Som, B.B. Pal ad S.K. Roy, A Small Sigal Aalysis of a IMPATT Device havig two Avalache Layers Itersaced by a Drift Layer, Solid-State Electro., Vol. 7, 974, [2] D.N. Datta ad B.B.Pal, Geeralised Small Sigal Aalysis of a DAR IMPATT Diode, Solid-State Electro., Vol. 25, No. 6, 982, [3] D.N. Datta, S.P. Pati, J.P. Baerjee, B.B. Pal ad S.K. Roy, Comuter Aalysis of DC Field ad Curret-Desity Profiles of DAR IMPATT Diode, IEEE Tras. Electro Devices, Vol. ED-29, No., 982, [4] S.P.Pati, J.P.Baerjee ad S.K.Roy, High Frequecy Numerical Aálisis of Double Avalache Regio IMPATT Diode, Semicod.. Sci. Techol. Vol. 6, 99, [5] A.K. Pada, G.N. Dash ad S.P. Pati, Comuter-Aided Studies o the Wide-Bad Microwave Charactyeristics of a Silico Double Avalache Regio Diode, Semicod. Sci. Techol., Vol. 0, 995, [6] A. Zemlia, S. Khotiaitsev ad C. Celaya, Comlex Noliear Model for the Pulsed- Mode IMPATT Diode, Istrumetatio ad Develomet, Vol. 3, No. 8, 997, [7] A. Zemlia ad R. De La Cruz, A Aalysis of the Active Layer Otimizatio of High Power Pulsed IMPATT Diodes, Comutació y Sistemas, Edició Esecial, Diciembre 2002, [8] W.N. Grat, Electro ad Hole Ioizatio Rates i Eitaxial Silico at High Electric Fields, Solid-State Electroics, Vol.6, No.0, 973, [9] C. Jacoboi, C. Caali, G. Ottaviai ad A. Alberigi Quarata, A Review of Some Charge Trasort Proerties of Silico, Solid-State Electro., Vol. 20, 977, [20] C. Caali, C. Jacoboi, G. Ottaviai ad A. Alberigi Quarata, High Field Diffusio of Electros i Silico, Al. Phys. Lett., Vol. 27, 975, [2] F. Nava, C. Caali, L. Reggiai, D. Gasquet, J.C. Vaissiere ad J.P. Nougier, O Diffusivity of Holes i Silico, J. Al. Phys., Vol. 50, 979,. 922.