In modern wireless RF and microwave communications

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1 Frequency Propertes of a Reverse Based Thc Swtchng PIN Dode A revew of PIN dode behavor n a large-sgnal envronment By Loudmla Drozdovsaa llanova Unversty In modern wreless RF and mcrowave communcatons systems, PIN dodes and several types of transstors are used as controlled components for dfferent control devces such as swtches, attenuators, and phase-shfters [1]. In many cases, S or GaAs PIN dodes are the devces of choce because of ther good power-handlng capablty. Forward-based PIN dodes exhbt low mpedance; reverse based ones exhbt hgh mpedance and provde good bandwdth performance. Although PIN dodes have been used wdely n dfferent applcatons for the last 4 years [2, 3], many of ther propertes are not well understood. One of these less understood propertes s the reverse-based state n a large-sgnal envronment. The reverse-bas voltage s used to eep a hgh-mpedance PIN dode n a low-dstorton state. In ths case, the PIN dode has a large RF or mcrowave voltage and a D reverse-bas voltage appled to t. Ths D voltage prevents any detecton effects and, therefore, reduces the harmonc dstortons produced by the PIN dode, especally n an RF or mcrowave hgh-power regme [2 7]. It s very mportant to determne correctly the requred reverse D bas voltage. Ths artcle dscusses expermental data and theoretcal results of the requred D bas voltage estmated by dfferent mathematcal and physcal models. PIN dode under D reverse-bas voltage Expermental data [2, 3, 5, 8] has shown that the appled D reverse-bas voltage depends on the frequency of the nput RF or mcrowave power, as shown n Fgure 1. The frst area (f < f 1 ) s where the mnmum requred D reverse Fgure 1. Mnmum Pn dode D bas voltage versus frequency. bas voltage s the pea RF voltage across the dode m : m. In the second area (f > f 2 ), the mnmum requred D reverse bas voltage may be much smaller compared wth the RF or mcrowave pea across the dode: << m. The low-frequency area (f < f 1 ) s based on the propertes of the classcal detector [2, 3, 6], because the swtchng PIN dode behavor s smlar to t. However, there are dfferent suggestons regardng the second area (f > f 2 ). The frst and smplest explanaton s based on an - regon transt tme of electrons and holes [2, 3, 6]. Ths approach may explan the reducton of the reverse D bas voltage wth the frequency ncrease for the short PIN dodes when the - layer s less than the depleted regon n the nonbased state (above the punch-through). 16 APPLIED MIROAE & IRELESS

2 (a) (b) Fgure 2. Requred D reverse bas voltage versus frequency for PIN dodes wth dfferent - layer thcness. (a) m = 2 ; (b) m = 5. However, for the thc PIN dodes, where the -layer s longer than the depleted regon, ths explanaton s not suffcent [7, 9]. Another explanaton [7, 9] s based on the multlayer mpedance model [1, 11]. Ths model taes nto account the fact that the -regon of the PIN dode below the punch-through conssts of undepleted and depleted regons (for detals of ths model, see the Appendx). Each regon can be represented [1, 11] as the shunt confguraton of resstance and capactance. The propertes of the frequency-dependent mpedance dvder formed by these regons should be taen nto account to explan the characterstc shown n Fgure 1. The depleted regon resstance of the unbased thc PIN dode s much greater than the resstance of the undepleted regon. hen the reverse D voltage s appled to the PIN dode, most of t drops across the depleted regon. At the same tme, appled A voltage s dvded between two regons accordng to the propertes of the frequency-dependent mpedance dvder [1]. At low frequences (f < f 1 ), dvder behavor s defned manly by the depleted regon resstance and the A voltage s across the depleted regon. At the hgh frequences (f > f 2 ), ts behavor s determned by the capactances of both regons. In the case of the thc PIN dode, the depleted regon capactance s greater than the undepleted one and the A voltage s across the undepleted regon at hgh frequences. A voltage appled to the depleted regon causes detecton effects. To prevent t, the D reverse bas voltage s necessary. The requred D voltage value should be at least equal to the ampltude of the A voltage appled to the depleted regon. But the A voltage across the depleted regon decreases wth frequency, so the requred D reverse bas voltage also drops wth frequency (Fgure 1). The transt tme effect provdes the full absence of any detecton effects n PIN dode wth the further frequency ncrease. A program based on the sothermal drft-dffuson model of a semconductor structure was also mplemented for smulaton and determnaton of the requred D reverse bas voltage [12]. Ths program numercally solves one-dmensonal contnuty equatons for electrons and holes, the Posson equaton and the total current equaton. Expermental measurements The measured requred D reverse bas voltage data were taen usng the expermental setup descrbed n [8]. The nput RF sgnal was generated wth a power transponder that was allowed to reach the ampltude of several tens of volts n the waveband of several megahertz. As a devce under tests, the shuntng dfferent PIN dodes wth the return path were used. The D current rectfed by the dode was montored as a measure of mert of the dode nonlnearty. The current value of 1 ma was chosen as the suffcent expermental parameter of the low nonlnearty and low harmonc dstorton when a reverse bas voltage was appled to the PIN dode. The slcon PIN dodes used n the expermental measurements had dfferent -layer thcnesses: = 2 mm, 7 mm and 15 mm. Fgure 2 llustrates the measured mnmum necessary D reverse-based voltage ( o ), eepng PIN dodes n the low nonlnearty and low harmonc dstorton state aganst frequency. The measurements were performed for all types of dodes, wth the RF ampltude across the dode ( m ) of 2 [Fgure 2(a)] and 5 [Fgure 2(b)]. The shapes of the curves are n accordance wth the expermental curve shown n [5] for the thc PIN dode and theoretcal dscussons n [6 9]. Fgure 2 shows that when the -layer thcness ncreases, the area wth the dmnshed requred D reverse bas voltage shfts to the lower frequences. Fgure 3 shows the requred D reverse-bas voltage aganst frequency wth a dfferent nput RF voltage ampltude. The slcon PIN dode wth the -layer thc- 18 APPLIED MIROAE & IRELESS

3 Fgure 3. Requred D reverse-bas voltage versus frequency of a 15 µm PIN dode wth a dfferent nput RF voltage ampltude. Fgure 4. omputed and expermental results [9]. ness of 15 mm was under test. Fgure 3 clearly shows that the area wth the dmnshed voltage shfts to the hgher frequences whle the appled RF voltage ampltude ncreases. omputer smulaton results and dscusson Three dfferent mathematcal and physcal models were used to estmate the necessary D reverse bas voltage to eep the PIN dode n a low-dstorton state. omputed results based on these models are verfed wth expermental RF performance data. The slcon PIN dode wth p + n n + structure and the -layer wdth of 15 µm was used n smulaton. The other parameters of the dode were: cross-secton of cm 2 ; -layer dopng level of cm 3 ; and electron and hole lfetmes of 1 5 s. The dode dopng profle was assumed to be abrupt, wth acceptor p + and donor n + concentratons of cm 3 and cm 3, respectvely. The dstorton factor was used as a nonlnearty and a dstorton fgure of mert n calculatons wth a drft-dffuson model [7]. The dstorton factor value of 1 4 was chosen as the permssble low level of harmonc dstortons. The effectve threshold voltage t eff of plays the same role n the multlayer mpedance PIN dode model (see the appendx). In both models, t provdes a D current generated by the PIN dode of several mcroamperes. Ths s n agreement wth the expermental parameter of the low nonlnearty and low harmonc dstorton that have been used n the measurements. Fgure 4 compares the measured and computed requred reverse bas D voltage o [9]. The computed results based on the sothermal drft-dffuson model of a semconductor structure (green lne) provde the better agreement wth the expermental data, but the use of ths model requres a lot of tme. omputed data based on the analytcal expressons (red lne) [6], tang nto account only the -regon transt tme, shows qualtatve agreement but overestmates the requred D reverse bas voltage n a wde frequency range. The accuracy of ths expresson s decreased for the PIN dodes wth the -layer thcness exceedng the depleted regon wdth. The multlayer mpedance model, consderng transt tme and effects of the feld dstrbuton nsde the -layer, produces a compromse between the computatonal tme and accuracy. It provdes more precson estmaton (blue lne) than the model [6] and t does not requre sgnfcant computaton tme le the drft-dffuson model [12]. The expressons for the mnmum requred reverse D bas voltage estmatons, usng ths model, are shown n the Appendx. oncluson A reverse-bas state of the PIN dodes wth dfferent -layer thcnesses were under expermental consderaton n ths artcle. Several mathematcal and physcal models were used to estmate the necessary D reversebas voltage to eep PIN dodes n a low-dstorton state. The multlayer mpedance model, consderng the electrc feld dstrbuton nsde the -layer, provdes the trade-off between the computatonal tme and accuracy. It allows engneers and desgners of mcrowave control devces to obtan more precse estmatons of the requred reverse D bas voltage. 11 APPLIED MIROAE & IRELESS

4 Acnowledgements The author wshes to than Prof. I.. Lebedev as a scentfc advser, Prof. A.S. Shntnov for helpful dscussons and Dr. N.I. Flatov for the permsson to use the computer software ISTO. References 1..J. esman, Essental Gude to RF and reless, Upper Saddle Rver, NJ: Prentce Hall, R.. Garver, Mcrowave Dode ontrol Devces, Norwood, MA: Artech House, J.F. hte, Mcrowave Semconductor Engneerng, New Yor: an Nostrand Renhold, H.M. Olson, Desgn alculatons of Reverse Bas haracterstcs for Mcrowave PIN Dodes, IEEE Trans., 1967, ol. ED-14, No. 8: M. aulton, et.al., PIN Dodes for Low Frequency Hgh Power Swtchng Applcaton, IEEE Trans., 1982, MTT-3, No. 6: R.H. averly and G. Hller, Establshng the Mnmum Reverse Bas for a PIN dode n a Hgh-power Swtch, IEEE Trans., 199, MTT-38, No. 12, I.. Lebedev, et.al., Mnmal Reverse Bas oltage of the Hgh-power PIN dode Swtch, Radoelectroncs and ommuncatons Systems, ol. 38, No. 1, 1995: L.M. Drozdovsaa and N.. Drozdovs, Expermental Exploraton of a Reverse Based Thc Slcon PIN dodes, Proceedngs of the Power onverson, Intellgent Moton & HFP onference, Appendx Toyo, Japan, Aprl 15 17, 1998: L.M. Drozdovsaa, RF Frequency Propertes of a Reverse-based Thc Swtchng PIN dode, Proceedngs of the 2 IEEE Rado and reless onference, September 1 13, 2, Denver, O: I.. Lebedev, Nonlnear Propertes and haracterstcs of Mcrowave PIN dodes, Radoeletrona (Izv. UZ), 1992, ol. 3, No. 11: P.R. Hercfeld, et al, Optcally ontrolled Mcrowave Devces and rcuts, RA Revew, ol. 46, 1985: A.S. Shntnov and N.I. Flatov, Mcrowave Lmter Dode Performance Analyzed by Mathematcal Modelng, Sold-State Electroncs, 1991, ol. 34, No. 1: Author nformaton Loudmla Drozdovsaa receved a Dploma n Electrcal Engneerng n 1984 and the anddate of Techncal Scence Degree n Mcroelectroncs n 1997, both from the Moscow Power Engneerng Insttute (Techncal Unversty), Moscow, Russa. She has authored and co-authored 1 ournal papers, about 2 conference presentatons and holds 6 patents. Her man research nterests are RF and mcrowave control devces and semconductor components, especally S and GaAs PIN dodes. She can be contacted at EE Department, llanova Unversty, 8 Lancaster Ave., llanova, PA 1985; Tel: ; E-mal: ldrozd@ece.vll.edu. The mpedance multlayer model of a PIN dode [7, 1] s based on the noton that the -regon of the dode below punch-through conssts of undepleted and depleted regons (Fgure A1). The depleted regon wdth and capactance of a reverse-based PIN dode are defned usng the expressons: where = 1+ = 1+ (1) (2) 2 = ε en S = ε (3) (4) Fgure A1. Multlayer model of the PIN dode. contnued on followng page 112 APPLIED MIROAE & IRELESS

5 = depleted regon wdth of non-based dode, = bult-n potental, = D reverse bas voltage, e = sngle charge, N = -layer dopng level, ε = slcon delectrc permttvty, S = dode cross-secton area. The value of depleted regon resstance R was assumed to be about 1 to 2 Mohms. The undepleted regon capactance and resstance R are S = ε R = ρ S ( ) (5) (6) where ρ = 1 eµ N ( ) r = -layer bul resstance, = -layer wdth, m = the maorty carrer moblty. The equvalent crcut of the dode accordng to ths model s shown n Fgure A2. There are also parastc elements such as nductance L s, contact or passve regons resstance R s and pacage capactance (n the case of pacaged PIN dode). Ths model also taes nto account the transt tme effect. It leads to the reducton of the voltage across the depleted regon n 1/F(θ ) tmes. Here, F(θ ) s the emprcal functon of the non-zero carrer transt tme threw depleted regon. Ths depends on dode geometry, semconductor materal propertes, RF or mcrowave nput power and appled D reverse bas voltage [1]. hen the dode s under D zero or reverse bas voltage, R >> R. Therefore, D voltage across the PIN dode s appled drectly to the depleted regon (to p + n uncton). Appled A voltage s dvded between two regons n an -layer accordng to the propertes of (7) Fgure A2. Equvalent crcut of a PIN dode. the frequency-dependent mpedance dvder formed by depleted and undepleted regons. It was assumed that p + n uncton does not produce harmonc dstortons when the total voltage across the depleted regon s less than the effectve threshold voltage t eff. Ths value was assumed to be about.1.2. Ths condton s wrtten as [7]: t eff (8) Fnally, we can estmate requred reverse bas D voltage (for L s, and R s ) as: R 1+ 2π f R = m F( Θ ) 1+ R 1+ 2π f R where f s the operatng frequency, m s the RF or mcrowave ampltude across the dode. Tang nto account Equatons (1) and (2), we can see that Equaton (9) s the nonlnear equaton, wth : = F( ), and should be solved teratvely. 1 t eff (9) 114 APPLIED MIROAE & IRELESS