Temperature dependence of microwave characteristics of n ++ np ++ Si IMPATT diode at X band

Transcription

1 IOS Journal of Electrical and Electronics Engineering (IOS-JEEE) e-issn: -166,-ISSN: , Volume 10, Issue 1 Ver. II (Jan Feb. 01), PP emerature deendence of microwave characteristics of n ++ n ++ Si IMPA diode at band Panka De Deartment of Physics, Gobardanga Hindu College, West Bengal State University, India Abstract: he deendence of both microwave negative resistance () and its ositive series resistance (s) on the rise of diode unction temerature in the range of 100 o C to 0 o C of HP n ++ n ++ Si IMPA [1] diode with flat doing density( x10 1 m -3 ) at band (-1) GHz have been simulated. he studies followed by Gummel- Blue echnique [] show that for a constant exerimental bias current of ma [1], for which the sace charge effect is not rominent, the value of negative conductance and negative resistance degrade taking into account the changes in the ionization rates and drift velocities due to rise of temerature. As a result, it is observed that the series resistance increases with the increase of temerature. Keywords: Negative microwave resistance, IMPA diode, Series esistance, Band I. Introduction he rise of -n unction temerature and its burning roblemare crucial in IMPA ( IMPact ionization Avalanche ransit ime) mode oeration. he inut ower of the diode is artly used for conversion into microwave energy and artly for heating the diode. It is known that the ositive series resistance contributes maor role for the Joule heat dissiation and degrade overall microwave erformance of avalanche transit time diode. As unction temerature increases, the reverse saturation current rises exonentially and leads to thermal runway. Also, the comlete removal of the unction heat is difficult using available good heat sink. herefore, microwave and mm wave ower devices generally oerate at temeratures above the ambient. he increased reverse saturation current roduces a faster build u of the avalanche current and degrades the negative resistance of the device. Intrinsic IMPA oeration deends directly on the temerature and the work of Dalle et al [3] clearly indicates the decrease of F ower with the increase of temerature. he ower loss due to unsweteitaxy can be reduced in unched through structures. Both the electron and hole transort arameters are decreasing functions of temerature[4]. According to ay et al [] deletion layer width, ionization rate and saturation drift velocity are sensitive to the unction temerature. Even in ulse mode the unction temerature and these three arameters vary during the ulse width, resulting in large signal imedance variation within the ulse. his time varying device imedance causes frequency chir in ulsed imatt oscillators []. he value of s basically deends on the width of the undeleted region, which is very difficult to measure under oscillating condition, because the electric field distribution is a function of time, temerature, current density, doing etc. Its direct measurement by a network analyzer is also difficult due to circuit modeling difficulties [6]. he otimum transfer of the emitted F ower to the load circuit deends on the total loss resistance s, which also strongly deends on the choice of both the dc bias current density and the diode area. he ositive series resistance has to be ket to the minimum value to obtain oscillating ower from the device. In 193, Adlerstein et al [] roosed a technique of measuring s from the threshold current and threshold frequency for double drift region GaAs material considering equal ionization rates and drift velocities of the charge carriers. In 1993, Mitra et al [1] calculated s for Si IMPA diode by a choice of multilier to the unequal ionization rates of electrons and holes, where field deendence of the drift velocities and temerature deendence of ionization rates have been neglected. he author [-11] simulated the values of s for Si n ++ n ++ HP band IMPA diode at 100 o C following generalized AC analysis of Gummel and Blue [], where temerature variation have been neglected. But in the resent analysis the author has been able to study the change in the value of s with temerature in the realistic range of o C considering the change in ionization rates and drift velocities [1-13], exerimental threshold current density, eak oerating frequency at band and high multilication factor (10 6 ) [14-1] for electron and hole which corresonds to very low reverse saturation current. II. Numerical Aroach a. Ionization arameters It is found that imact ionization is suressed by increasing temerature because of the increase in honon scattering [16-1]. he imact ionization rocess deends on temerature, largely via scattering from DOI: / Page

2 emerature deendence of microwave characteristics of n++n++ Si IMPA diode at band otical honons. his henomenon is conventionally described in terms of coefficients α and β for electrons and holes resectively, which are the recirocal of the mean distance between successive ionization events. he temerature deendence of α reduces with increasing field, essentially because carriers scatter less often during corresonding shorter ionization ath lengths. At a given electric field, the ionization rate decreases with increasing temerature [1]. W. N Grant reorted [1] field deendence of ionization rates of electrons and holes at o C in Si by an exonential form given by n, A n, / B n, ex[ ] E( x) It was also observed that the changes in α n and α with temerature [13] could be incororated by using temerature deendent values of B / n and B /. Where temerature coefficient of B / n and B / are given by / ( B n ) x10 Vm c / ( B ) x10 Vm c hus in the field range of (.4 to.3 )x10 different temeratures using the following exressions, ( E, n ( E, ) 6.x10 [ex{ (1.0x10 ).0x10 [ex{ (1.9x10 For field range between (.3 to. )x10 V m -1 ( E, n ( E, ).0x10 ).6x10 ex[ (9.9x10 ex[ (1.3x10 1.3x10 1.1x10 V m -1, the values of n and are calculated at )) / E}] )) / E}] the ionization rates are given by 1.3x10 1.1x10 )) / E] )) / E] Where is the unction temerature exressed in degree centigrade. b. AC analysis he static roerties of the diode have been obtained following the method of Datta et al [1]. With the static arameters as inut, the satial variation of diode negative resistivity () and the reactivity () in the deletion layer have been obtained solving the following device equations [], [10], [14], [19] and [0] { x x 0 n( ) ( )} r { H} x x v x v v v And x { n } r { H( x)} 0 x v x v v v elacing the diode imedance + by, the total integrated negative resistivity ( ) and reactivity ( ) of the diode at the oerating frequency (f where ω=πf) and temerature can be determined from the numerical integration of the resistivity and reactivity rofiles over the deletion layer as follow- Where W is the deletion layer width of the n ++ n ++ structure. Hence, the diode total negative conductance (G D ) and suscetance (B D ) are obtained as follow- (, W 0. dx (, W 0. dx DOI: / Page

3 emerature deendence of microwave characteristics of n++n++ Si IMPA diode at band G D (, ( ) ( ) BD (, ( ) ( ) Where, G D and B D are functions of F voltage ( V F ) and frequency such that the steady state condition for oscillation is given by [], [], and [10], g L (, GD (, { BD (, } s(, Under the dynamic condition V F is small and s can be calculated by considering the value of load conductance (g L ), which is nearly equal to the diode conductance (G D ) at resonance. III. esults and discussion a. Static roerties he electric field rofiles at breakdown of the n ++ n ++ single drift region (SD) Si diode at different oerating temeratures have shown in Fig.1. It shows that the maximum electric field at the unction and the unch through condition increases with the rise of temerature. As a result, the avalanche region and the effective width of the diode increase with temerature. At 100 o C the diode is ust unch through, which is the required field rofile for otimum erformance [10]. he linear rise of the electric field in the deletion zone indicates that the diode is free from severe sace charge effect at exerimental bias current of ma. he field value in the deletion layer increases as the ionization rate decreases with the rise of temerature. he avalanche region, drift region and the total dc breakdown voltage V A, V D and V B resectively increase with temerature. But the dc to microwave conversion efficiency (η) estimated from the Scharfetter-Gummel formula [1] indicates a minor change with temerature. Fig. 1. Electric field distribution in the deletion layer of band Si n ++ n ++ IMPA diode at different oerating temeratures under same bias current ( ma) he normalized current density difference of hole and electron ( J -J n )/J dc i.e. the P(x) rofile, shown in Fig., indicates the osition of the avalanche center in the deletion zone, where J =J n, i.e P(x)=0; and also the width of the avalanche and drift zone. From the studies of the P(x) rofiles (not shown in Fig.), it is observed that the avalanche region width increases negligibly with temerature, but the increasing electric field in the avalanche zone (as shown in Fig. 1) increases the value of V A and V D with temerature. he dc ower inut (P dc ) and the exected ac outut ower (P ac ) have been calculated from the Sharfetter-Gummel formula [1] and are given in able 1. It is found that the exerimentally observed ac ower as obtained by Mitra et al [1], is of the order of 100 mw, which is nearly one sixth of the resent theoretical result. he resent dc analysis suggests an increase in P dc with the rise of temerature, which is also a usual exectation. DOI: / Page

4 emerature deendence of microwave characteristics of n++n++ Si IMPA diode at band Fig.. Normalized current density difference i.e. (J -J n )/J dc or P(x) rofile in the deletion region of band Si n ++ n ++ IMPA diode. able 1: he dc roerties of n ++ n ++ Si band IMPA diode at bias current ma with diode cross sectional area.x10-9 m and at different temeratures. emerature V A V D V B η Inut Outut dc ower ac ower ( o C) (V) (V) (V) % (Watt) (Watt) b. Dynamic roerties he negative resistivity rofiles in the active region of the diode under the same oerating bias current ( ma) and frequency (10 GHz), but at different temeratures have been lotted in Fig. 3. he satial distribution of the negative resistivity in the deletion layer gives a clear insight regarding the microwave ower generation in the avalanche and drift region which is the significant characteristics of the AC analysis of Gummel and Blue [].he rofiles indicate that the drift region contribute maximum negative resistance comared to its avalanche zone. he diode yields maximum negative resistance at 100 o Cand the same decreases with the rise of temerature. It is also observed from Fig. 3 that the substrate-eitaxy (nn ++ ) interface region contributes lowest value of negative resistance (). As the temerature increases from 100 o C to 00 o C, the value of negative resistance decreases from -11.6Ω to -.Ω, as given in able. able : he small signal roerties of n ++ n ++ Si band IMPA diode at bias current ma and oerating frequency 10 GHz, but at different temeratures. emerature (-G) B (-) s g L ( o C) mho.m - mho.m - Ohm ohm mho.m DOI: / Page

5 emerature deendence of microwave characteristics of n++n++ Si IMPA diode at band Fig. 3. Negative resistivity rofiles in the deletion layer of band n ++ n ++ Si IMPA diode at different temeratures. he frequency deendence of negative conductance (G) and ositive suscetance (B) at a constant bias current of ma but at different temeratures had shown in Fig. 4. It shows that the maximum (center) negative conductance and the corresonding center frequency (f c ) decrease with the increase of temerature as exected, which is defined as the frequency chir [] in avalanche transit time devices. he decrease of center frequency is due to the widening of the effective deletion width as a result of increasing temerature. he Fig. 4 also suggests that the resent SD diode with active layer doing x10 1 /m 3, oerating at ma dc bias current and ambient temerature 100 o C oerate exactly at band, with center frequency at 11 GHz. he resent decrease in the center frequency due to rise of temerature is in contrary with the ublished data [10], where the higher field value in the nn ++ (substrate-eitaxy) interface indicating higher unched through and lower field value at the ++ n unction due to lower active zone doing result uward shift in the center frequency. he decrease of negative conductance with temerature has been lotted in Fig.. he rate of decrease is more in the range 100 o C to 130 o C. Fig.4. Admittance (Conductance-Suscetance) characteristics at different oerating temeratures of band Si n ++ n ++ IMPA diode. DOI: / Page

6 emerature deendence of microwave characteristics of n++n++ Si IMPA diode at band he diode yields higher negative resistance (-10 Ω) comared to the series resistance (1.-.1 Ω), which is the required condition for sustained oscillation. Fig. 6, indicates an aroximate linear rise of s with device temerature within the realistic limit of Ω for band IMPA diode [1]. Fig.. emerature variation of negative conductance of band Si n ++ n ++ IMPA diode. Fig. 6. emerature-series esistance rofile of band Si n ++ n ++ IMPA diode IV. Conclusions he resent studies indicate an overall degradation in the microwave roerties of negative resistance and negative conductance of IMPA diode in the band due to rise in the oerating temerature at a constant bias current and under slight unched through. As a result, the ositive series resistance increases with the increase of temerature that may cause an increase in the Joule heat dissiation at higher oerating bias current (> ma) leading to thermal instability and burnout of the diode. he study also coincides with the earlier results regarding the decrease of oerating frequency with the rise of temerature leading to frequency chir. Acknowledgement he author acknowledges University Grants Commission, India, for aroval of Minor esearch Proect. eferences [1]. M.Mitra, M. Das, S. Kar, and S. K. oy, A study of the electrical series resistance of Silicon IMPA diodes, IEEE rans Electron Devices, 40, 1993, []. H. K. Gummel, and J. L. Blue, A small signal theory of avalanche noise in IMPA diodes, IEEE rans. Electron Devices,14, 196, [3]. C. Dalle, P. A. olland, and G. Lleti, Flat doing rofile double drift silicon IMPA for reliable CW high ower, high efficiency generation in the 94 GHz window, IEEE rans.electron Devices, 3, 1990, -36. DOI: / Page

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