Solid-State Electronics 48 (2004) 1569–1577 www.elsevier.com/locate/sse
Silicon carbide TUNNETT diodes V.V. Buniatyan a, V.M. Aroutiounian b,*, K. Zekentes c, N. Camara c, P. Soukiassian d a
d
State Engineering University of Armenia, 105 Teryan Str., 375009 Yerevan, Armenia b Yerevan State University, Al. Manoukian Str. 1, 375049 Yerevan, Armenia c MRG, Institute of Electronic Structure and Lasers, FORTH, GR-71110 Heraklion, Greece Commissariat a l’Energie Atomique, Laboratoire Surfaces et Interfaces de Materiaux Avances associe a l’Universite de Paris-Sud/ Orsay, DSM-DRECAM-SPCSI, B^atiment 462, Saclay, 91191 Gif sur Yvette Cedex, France Received 1 June 2003; received in revised form 1 November 2003; accepted 1 March 2004 Available online 26 April 2004
The review of this paper was arranged by Prof. S. Cristoloveanu
Abstract The theoretical analysis of microwave characteristics of the nþ pþ mnþ TUNNETT diodes made of silicon carbide is carried out. The expressions for the impedance and its active and reactive components as well as expressions for the frequency range, where the negative differential resistance takes place, and the maximal frequency of oscillations are obtained for the TUNNETT diodes made of SiC. After numerical calculations, the conclusion is made that the performance potential of TUNNETTs is better than that of the other transit time devices in very high frequency range. The use of silicon carbide for the manufacture of TUNNETTs can promise better microwave parameters over the range of frequencies 100–500 GHz. 2004 Elsevier Ltd. All rights reserved. PACS: 85.30 Keywords: Transit-time; Microwave diode; TUNNET; Silicon carbide
1. Introduction It is well known that the use of the impact-avalanchetransit-time (IMPATT) diodes [1–7] in millimeter and sub-millimeter ranges of wavelengths is connected with serious difficulties. The avalanche-inducted dispersion effect, time delay and carrier diffusion effects in the IMPATTs limit their high frequency operation. Another well-known transit-time device is the Barrier Injection Transit-Time (BARITT) diode [4,6,8,9], where charge carriers are injected in transit-time space thermally over the potential barrier. As a rule, because of the unfa-
*
Corresponding author. Tel./fax: +374-1-555590. E-mail address:
[email protected] (V.M. Aroutiounian).
vorable injection phase delay, the BARITT diode is operated at lower power and with worse efficiency than the IMPATT diode. Low drift velocity and high diffusivity around the injection point limit high frequency performance of BARITTs. When the thickness of the IMPATT diode becomes narrower (in order to increase the oscillation frequency and decrease the breakdown voltage), avalanche mechanisms weaken and the tunnel injection becomes dominant in reverse biased p–n junction. This, in turns, caused corresponding changes in microwave characteristics of diodes [2–7,10]. The taking into account of physical phenomena, accompanying a hybrid regime between the tunneling effects and avalanche ionization, is also a difficult problem. That is why different approximations are often used for qualitative and quantitative analysis [1–7]. For
0038-1101/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2004.03.004
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example, if the characteristic frequency of the tunneling phenomenon is determined as sffiffiffiffiffiffiffiffiffiffiffi 2q2 xt ¼ Et P x m Eg the tunneling can be assumed non-inertial. Here Et is an average electric field, which is determined by the ‘‘height’’ of the tunneling barrier and effective mass of charge carriers. To reduce the noise and decrease the intrinsic response time in the injection region, the tunneling is used as desirable injection mechanism. Noninertial tunneling phenomenon is less preferable for the microwave generation of power than impact ionization as the phase delay in tunneling structures can be realized at the sacrifice of transit time effects. This leads to lower efficiency and output power in TUNNETTs. But higher oscillation frequency with lower bias voltage and noise level of TUNNETTs will be superior to those of IMPATTs. The growth and processing techniques for silicon carbide, SiC, have tremendously improved last years, which allowed manufacturing high-power and high frequency SiC devices [11–16]. Today this direction in semiconductor electronics is strongly developing and is in the focus of research and development. As material quality and device processing in SiC continue to mature rapidly, it is now possible to fabricate various new semiconductor devices made of SiC epitaxial layers. In particular, IMPATT diodes [17–20], fast resonant tunneling diodes and tunnel emitter transistors [21–24] as well as many other devices made of silicon carbide and having excellent DC and RF performance have been demonstrated. These devices are being developed for microwave power amplifier and oscillator applications. Recently high-quality heterostructures on the base of different SiC polytypes are reported [25]. Possibilities of the use of SiC in microwave technology are especially attractive, in particular, for the manufacture of the BARITT diodes [26–33]. Because the tunneling is the fastest phenomenon observed in semiconductors, the quantum well tunneling structures have recently drawn a great deal of attention, including BARITTs containing the quantum wells in the injection and drift regions [31–33]. The use of SiC is promising because the magnitude of electrical breakdown voltage in SiC is higher in comparison with Si and other semiconductor materials. Here we expected the increase in the amplitude of the microwave signal, all other factors being equal. As it is well known [1–7,26–33], the dynamic negative resistance (NDR) effects can increase in transit-time devices if the phase lag of the modulation component of the current, which is in anti-phase with the local electric field, is increased. In this reason, the use of SiC is promising also owing to the fact that space charge mobility in the SiC
polytypes are rather small, which should lead to an increase in the phase delay between the current and alternating electric field in the microwave range and, hence, to an increase in the absolute magnitude of NDR. As it is noted in [2–4,6], the TUNNETT diode has been evaluated to be a useful device in the frequency range from 100 to 1000 GHz. The high oscillation frequency with a lower bias voltage and a lower noise level of the TUNNETT diode will be superior to those of the IMPATT diode. The GaAs TUNNETT diodes with the pþ –n and pþ –n–nþ structure have been fabricated and pulsed fundamental oscillation frequency up to 338 GHz (k ¼ 0:89 mm) has been obtained from pþ –n–nþ diode [3,6,10]. The aim of this paper is the theoretical analysis of the microwave characteristics of the nþ pþ mnþ TUNNETT diodes made of silicon carbide.
2. Small-signal analysis We have examined the physical processes in the nþ pþ mnþ (pþ nþ ppþ ) structures made of SiC. As the tunneling probability is proportional to expð const Þ, we E can assume that charge carrier tunneling source is located in the plane, where electric field has the maximal value Etm . We shall confine ourselves to the following cases: (A) Left-hand nþ pþ junction biased in forward direction. (B) Left-hand nþ pþ junction is operating in the regime of the reverse bias. In the case A static current–voltage (I–V ) characteristics is the result of three following current components: • the tunneling current It qm p Eg E It ¼ 2 2 exp 1=2 D 2 2 hq xt 2p h • the excess current Ix " # 1=2 4 m es Ix Im exp ðV V v Þ ; 3 N • the thermal current Ith qV Ith ¼ IS exp 1 : kT
ð1Þ
ð2Þ
ð3Þ
R 1=2 In Eqs. (1)–(3) E ¼ 4q3pxhtEt , D ¼ ½Fc ðEÞ Fv ðEÞ
h i Þ dE, m is the effective mass of electrons, 1 expð 2E E
V.V. Buniatyan et al. / Solid-State Electronics 48 (2004) 1569–1577
Fc ðEÞ and Fv ðEÞ are corresponding Fermi–Dirac distri ND bution functions [5], Et0 ¼ ðqVbi2eN Þ1=2 , N ¼ NNAAþN , qVbi is D the built–in potential, ¼ o s , o is the permittivity in vacuum, s is the relative permittivity of SiC, V is the applied voltage, Iv is the valley current density at the valley voltage Vv , IS is the saturation current density. The other parameters are as usual ones. The injection conductance in the case A can be positive, yielding a positive injection resistance, which must be overcome by a drift region negative resistance. The injection conductance can be negative and in this case the resistance of both transit-time region and injection region may be negative. The dependencies of the density of the tunneling current on electric field in the case B are described only by the expression (1) and the injection conductance is positive. We assume for the case A that Jt0 corresponds to the peak of the tunnel dc current. For the alternating component of the conductance height of the tunnel barrier is equal to Jt0 B Jt0 B pEg Et0 rt ¼ 2 ; B¼ 1þ ; Et0 Et0 Et0 2h xt where Jt0 ¼
!1=2
2q2
Et0
m1=2 Eg1=2
qm D B : exp Et0 3p3 h3
For small-signal analysis, after the linearization of the expressions (1)–(3) and using usual technique of calculations for the microwave characteristics of transittime structures developed in Refs. [1–10,26–33], in the cases A and B we have the following expressions for the impedance for the nþ pþ mnþ TUNNETT structure: Jt0 B Jt0 B pEg Et0 rt ¼ 2 1þ ; ; B¼ Et0 2h xt Et0 Et0 !1=2 2q2 qm D B E exp Jt0 ¼ ; t0 1=2 Et0 3p3 h3 m1=2 Eg 8 9 jh hT hM þjh > > = hT þjh U1 V0S T 2 < expðhM Þ þ ðhM jhÞ : Zt hT SI1 jhehM S > ; : h hMjh exp ðhM jhÞ > h jh M
M
also that in the case of hM ! 0, the expression (4) precisely coincides with the results obtained for the quantum-well transit-time diodes [31–33]. The analysis of the expression (4) showed that the negative magnitude at the low levels of the tunneling can appear over the range of such transit angles, where the following inequality is fulfilled: cos h
hM hT þ h2 hM h hhT
Here hT ¼
rta
d for the case A and ql N
1=2 pE exp½ 2hxgt þ Isd Im 43 mN es ut pEg 2q3 DEt0 rtb 3p
for the case 3 exp½ 2 2 x2 h xt th
2q3 DEt0 3p2 x2t h3
B, hM ¼ xM T ¼ pe A T , S is the area of the device, T is the transit-time. hs ¼ hhT ¼ rxe is the tunneling parameter ta;b depending on the condition and properties of the tunneling contact of the small-signal conductivity rta;b . 0 Note that if rta;b ¼ lJ , the expression (4) coincides with V0s the results obtained for the standard BARITTs [4,8,9,26–30] and quantum well BARITTs [31–33]. Note
sin h > expðhM Þ:
The corresponding angle range is in the range 3:6 < h < 7:2 with the optimum magnitude hop 1:5p for the maximal value of NDR. When hop 1:5p, the frequency 3VS is given by the formula f0 4L . For example, if f ¼ 100 d GHz, Ld 1; 5 lm, f ¼ 300 GHz Ld 0:5 lm, and respectively. As it is exf ¼ 1000 GHz, Ld 1500 A, pected for transit-time devices, there is a specific length of the drift region Ld , which yields the maximal NDR for any given frequency, tunneling conductance, and saturation velocity. The optimum length is found after the solution of the condition oRt =oGt ¼ 0, using Eq. (4). It yields xLd xhS þ xM tg : ms x hS xM When hM ! 0, Eq. (4) coincides with the result obtained for QWITT diodes in Refs. [31–33]. At any given frequency, when hM ! 0, there is an optimal value of conductance ropt , which is obtained from the condition oRt =oGt ¼ 0. This optimal conductance is given by the formula xe =ropt = pffiffiffi : 3 The negative resistance for such an optimized device with 1;ffiffi5p, Vos 8 106 cm/s, parameters hM ! 0, hopt p ffi 4 2 S 10 cm , es ¼ 9; 7, hs 3 is equal to Ropt 9:2
V0s Ld 1014 ðXÞ: fVs
For the hM 1:77 and other parameters, the expression differs by numerical coefficient
ð4Þ rt T , e
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Ropt 12:7
V0s Ld 1015 ðXÞ: fVs
As it is noted in Section 1, the higher oscillation frequency TUNNETTs with lower bias voltage and noise level will be superior to IMPATTs and other transit-time devices. Assume that the most probable sources of the noise in such TUNNETT’s are shot (fluctuation, Ms ) and diffusion (thermal, MT ) noise, we have been also estimated for the above-mentioned structures the noise temperature Tn ¼ ðMs þ MT ÞT0 ,
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pþ –n–pþ SiC BARITT structures are shown for comparison). The use of the 4H–SiC is promising for the manufacturing of the high frequency TUNNETTs due to the fact that after tunneling the charge carriers are moved by their saturation velocities (see Figs. 2–4). The use of SiC makes possible, all other factors being equal, to increase the amplitude of the microwave signal and, consequently, the efficiency and power performance. As it is expected, with the increase in the injection current density It0 and charge velocity mos as well as with the decrease of the electric field Et0 (i.e. with the increase of effective small-signal tunneling conductivity) in the tunneling plane, NDR increases in absolute value and the frequency range, where NDR takes place, becomes larger and is displaced toward higher frequencies (see Figs. 2a,3a,4a). Numerical estimations shown that in the transit-angle ranges when NDR exists, the fluctuation shot-noise measure Ms is always less than diffusion Md one. With the increase in the injection current density It0 as well as with the decrease of the electric field Et0 (i.e. with the increase of effective small-signal tunneling conductivity) in the tunneling plane, noise temperature increased also. The noise measure (temperature) decreases monotonically and in the region, where NDR take place, approximately remains constant, then the noise inevitably increases roughly. In Figs. 3c and 4c analogous calculations of the noise temperature for the SiC BARITTs [31] are shown for comparison. As follows from Figs. 1c,2c,3c, one possible method of a realization of low noise amplification would be to work with increasing space-charge parameter and at the low value of the bias current It0 . The quality factor
where T0 is the normal temperature, T0 ¼ 290 K. Usual technique of the calculations of the noise temperature [31,37] is used. The expression (4) for the impedance of the structure is used.
3. Discussion and conclusion Results of numerical simulations of real part of impedance, R, quality factor, Q, as well as the noise temperature, Tn , of the SiC TUNNETTs are shown in Figs. 2–4. They have been carried out for the following values of parameters [16,18,34–36]: Vs ¼ 1:9 107 cm/s, 2 m ¼ 1:6m0 , ND ¼ NA 1019 cm3 , ln 400 cm , Vos Vs 6 ð0:6–1Þ 10 cm/s, which are typical for 6H–SiC, and 2 ND ¼ NA 1019 cm3 , ln 880 cm , Vos ð0:6–1Þ 106 Vs 7 cm/s, Vs ¼ 2:2 10 cm/s, m ¼ 0:2m0 , which are typical for 4H–SiC. Here D 0:5–0:8, It0 ¼ 10–100 A/cm2 , the Is 1010 A/cm2 . width of the tunnel barrier d 50 A, For the above mentioned parameters, hs , hT , h and rt are 2 0:0024f Et0 t0 Ld t0 , hT 26:28J , rt 32:6J 2 V 2 Jt0 Et0 Et0 s 0:0628L f d (Ohm cm)1 , h for the 6H–SiC, and hs Vs 2 0:00034f Et0 6:28Jt0 Ld t0 , hT E2 Vs , rt 14:7J (Ohm cm)1 , h 2 Jt0 Et0 t0 0:0628Ld f for the 4H–SiC. Vs
determined as hs
Note that our calculations were shown that the use of 6H–SiC is promising for BARITT’s owing to the fact that the charge mobility value in such a SiC polytype is rather small, which led to an increased phase delay between the current and alternating electric field and, hence, to an increase in the absolute magnitude of NDR [8,9,28,29] (see Fig. 1, where analogous calculations of the negative resistance for the pþ –n–pþ Si and
30
Si
60
100
110
120
130 f,GHz
-10 SiC
4 ×105 V/cm
-20
-30
-40
Et0=3×105 V/cm R,Ohm
2.5 ×105 V/cm
2 ×105 V/cm
Fig. 1. Real part of impedance, R, versus of small-signal frequency, f , for various values of the dc current for the Si and SiC BARITT (left) and SiC TUNNETT diode (right). ld ¼ 1:0 lm, vs ¼ 1 107 cm/s, vs0 ¼ 1 106 cm/s, Et ¼ 4 105 V/cm, S ¼ 104 cm2 , D ¼ 0:5, m 0:092m0 , ln 1450 cm2 /V s (Si), m 1:6m0 , ln 380 cm2 /V s (6H–SiC), doping density in drift region Na 1:25 1014 cm3 , N Na 1019 cm3 . d 50 A,
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Fig. 2. Real part of impedance, R, (a), Q-factor (b) and noise temperature (c) versus of small-signal frequency, f , for various values of the dc current. ld ¼ 1:0 lm, vs ¼ 2:2 107 cm/s, (4H–SiC), vs ¼ 1:9 107 cm/s, (6H–SiC), vs0 ¼ 1 106 cm/s, Et ¼ 4 105 V/cm, Nd Na 1019 cm3 , for the different polytypes S ¼ 104 cm2 , D ¼ 0:5, doping density in drift region Na 1:25 1014 cm3 , d 50 A, of SiC ((- - -) for the 6H–SiC, (––) 4H–SiC). Other parameters are the same as in Fig. 1.
approaches infinity when NDR approaches zero (see Figs. 2b,3b,4b). All these conclusions are in good
agreement with the general principles of the formation of NDR [1–10,26–33,37].
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Fig. 3. Real part of impedance, R, (a), Q-factor (b) and noise temperature (c) versus of small-signal frequency, f , for various values of the electric field Et0 at the tunneling plane. ((- - -) for the 6H–SiC, (––) 4H–SiC). Other parameters are the same as in Figs. 1 and 2.
4. Conclusions • Possibilities and advantages of the silicon carbide as a working material for design of TUNNETT diodes have been discussed.
• Theoretical analysis of the microwave characteristics and noise of the nþ pþ mnþ TUNNETT diodes made of silicon carbide is carried out. The expressions for the impedance and its active and reactive components as well as expressions for the frequency
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Fig. 4. Real part of impedance, R, (a), Q-factor (b) and noise temperature (c) versus of small-signal frequency, f , for various values of the charge velocity in the injected (tunneling) plane vs0 . ((- - -) for the 6H–SiC, (––) 4H–SiC). The other parameters are the same as in Figs. 1 and 2.
range, where the negative differential resistance takes place, and the maximal frequency of oscillations
are obtained for the TUNNETT diodes made of SiC.
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• After numerical calculations the conclusion is made that the performance potential of TUNNETTs is better in very high frequency range than that of the other transit time devices. The use of silicon carbide for the manufacture of TUNNETTs can promise better microwave parameters over the range of frequency 100–500 GHz. Acknowledgements V.B. and V.A. carried out investigations in the framework of the ISTC A-322 grant. V. B. carried out investigations in the framework of the grant supported by the Ministry of Education and Science of Republic Armenia No. 0664. References [1] Misawa T. Multiple uniform layer approximation in analysis of negative resistance in p–n junction in breakdown. IEEE Trans Electron Dev 1967;14(9):795–801. [2] Aladinsky VK, Gradinov PG. On tunnel-transit-time diode output characteristics. Russ J Radioeng Electron 1972; 17(2):376–80. [3] Motoya K, Mishizawa JT. Int J Infrared Millimeter Waves 1985;6(7):483–95. [4] Tager AS. Field-injection transit-time diodes with negative dynamic impedance. Izv VUZ-ov Radioelectron 1974;17:3– 18 (in Russian). [5] Tager AS, Val’d-Perlov VM. Impatt diodes and its applications in microwave. Moscow: PH Soviet Radio; 1968 (in Russian). [6] Sze SM. Physics of Semiconductor Devices. second ed. New York: Wiley & Sons; 1981. [7] Mehdi I, Haddad GI, Mains RK. Microwave and millimeter-wave power generation in silicon carbide avalanche devices. J Appl Phys 1988;64(3):1533–40. [8] Aroutiounian VM, Buniatyan VV, Soukiassian P. Microwave characteristics of BARITT diodes based on silicon carbide. Solid-State Electron 1999;43(3):343–6. [9] Aroutiounian VM, Buniatyan VV, Soukiassian P. Microwave characteristics of BARITT diodes based on silicon carbide. IEEE Trans Electron Dev 1999;46(3):585–8. [10] Yeh S. A unified treatment of the impedance of transit-time devices. IEEE Trans Electron Dev 1985;28(3):117–24. [11] Harris GL, editor. Properties of silicon carbide. London: INSPEC; 1995. [12] Casady JB, Johnson RW. Status of silicon carbide as a wide-bandgap semiconductor for high-temperature applications. Solid-State Electron 1996;39(1):1409–22. [13] Baliga BJ. Trends in power semiconductor devices. IEEE Trans Electron Dev 1996;43(10):1717–31. [14] Weitzel CE, Palmour IW, Carter CH, et al. Silicon carbide HIGH-power devices. IEEE Trans Electron Dev 1996; 43(10):1732–9. [15] Pensl G, Choyke WI. Electrical and optical characterization of SiC. Physica B 1993;185:264–83.
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