The impedance of InGaAlAs resonance-tunnel heterostructures used for modulation of optical radiation is experimentally studied in the frequency range from 45 to 18 MHz. The dependence of their equivalent
circuit on the bias voltage is determined. The spectrum of the harmonics of the current in the resistive frequency multiplication in such structures is calculated. The results confirm that these structures are promising as applied to the frequency multiplication. The effect of frequency multiplication is demonstrated experimentally at low frequencies

Aleshkin, V. Ya

Figueiredo, J. M. L.

Ironside, C. N.

Lyubchenko, V. E.

Stanley, C. R.

Journal of Communications Technology and Electronics

Sapientia

 911 Journal of Communications Technology and Electronics, Vol. 45, No. 8, 2000, pp. 911–914. Translated from Radiotekhnika i Elektronika, Vol. 45, No. 8, 2000, pp. 1010–1013.Original Russian Text Copyright © 2000 by Alkeev, Lyubchenko, Ironside, Figueiredo, Stanley.English Translation Copyright © 2000 by  MAIK “Nauka /Interperiodica” (Russia). The tunnel diodes (TDs) created on the basis of two-barrier heterostructures were first proposed in [1]. Theyare characterized by a substantially nonlinear voltage–current characteristic (VCC) with regions of negativedifferential conductance (NDC). In [2], the efficiencyof TDs at frequencies above 2 THz was demonstrated,which shows that these devices are promising for differ-ent microwave applications. In [3, 4], the possibility ofmodulation of light by TDs in the microwave band onthe basis on the Franz–Keldysh effect [5] was demon-strated. The effect of the modulation of light dependson the TD microwave characteristics (impedance),which have been insufficiently studied.In this work, we study the impedance of TDs on thebasis of InGaAlAs structures used in [4]. The structureswere grown on an  n +  InP substrate using molecular-beam epitaxy (Fig. 1a) and consisted of two 2-nm thickAlAs barrier layers separated by a 6-nm thick InGaAsquantum pit. These layers were placed between two500-nm thick layers of doped (Si: 5  ×  10 16  cm –3 )In 0.53 Ga 0.42 Al 0.05 As which served as a core of an opticalwaveguide. The InP substrate and the upper stronglydoped (Si: 2  ×  10 18  cm –3 ) InAlAs layer served as a coat-ing of the optical waveguide directing the light parallelto the barrier layers. The upper  δ -doped InGeAs layerserved for the formation of Au–Ge–Ni ohmic contacts.The rectangular profile of the optical waveguide with awidth 2–6  µ m and mesas on both sides was producedby chemical etching, and the ohmic contacts wereformed along the upper side of the optical waveguideand mesas. The surface of the plate was coated by aSiO 2  film with windows in it that were etched to pro-vide the electric connection between the ohmic con-tacts and the upper bonding areas formed by sections ofthe 50- Ω  coplanar waveguide (Fig. 1b).Figure 2 shows the VCCs of two TD specimens( 1  and  2 ). For the TD active area equal to 200  µ m 2 , thecurrent density  J p  at the VCC maximum was50 kA/cm 2 , the ratio  J p / J v   ≈  3, the difference betweenthe valley and the peak voltages  ∆ U   ≈   0.9 V, and the dif-ference between the current densities of the peak andthe valley  ∆ J  =  J p  –  J v   ≈  35 kA/cm 2 . Following [6], let Superhigh-Frequency Characteristics of Optical Modulators on the Basis of InGaAlAs Resonance-Tunnel Heterostructures N. V. Alkeev, V. E. Lyubchenko, C. N. Ironside, J. M. L. Figueiredo, and C. R. Stanley Received March 3, 2000 Abstract —The impedance of InGaAlAs resonance-tunnel heterostructures used for modulation of optical radi-ation is experimentally studied in the frequency range from 45 to 18 MHz. The dependence of their equivalentcircuit on the bias voltage is determined. The spectrum of the harmonics of the current in the resistive frequencymultiplication in such structures is calculated. The results confirm that these structures are promising as appliedto the frequency multiplication. The effect of frequency multiplication is demonstrated experimentally at lowfrequencies. PHYSICAL PROCESSESIN ELECTRON DEVICES   Window in  SiO 2 LightCoplanar n +  InPAu–Ge–Ni n InGaAlAs n InGaAlAs n +  InP δ InGaAs n +  InAlAs 10 nm Substrate 1000 nm TD (b)(a)SiO 2 Fig. 1.  (a) Scheme of the TD layers and (b) topology of theTD optical modulator.  waveguide 912 JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS        Vol. 45        No. 8       2000 ALKEEV  et al. us estimate the TD switching time  t R  and the critical fre-quency  ω T  = 0.5/ t R  from the static VCC. We have  t R  = 4.4( ∆ U / ∆ J ) C V , where  C V  is the capacitance at the VCCvalley related to the unit area ( C V  =  εε 0 / W ,  ε  = 13 is thepermittivity of the material, and  W  = 0.5  µ m in the TDunder study). We obtain  t R  = 6.6 ps and  ω Τ  = 76 GHz.Note that similar GaAs/AlAs TD structures werestudied in [3]. They have noticeably worse VCC param-eters: lower peak current density  J p , smaller  J p / J v  ratio,smaller  ∆ U  and  ∆ J , and greater switching time. In addi-tion, it should be noted that InAlAs TD optical modu-lators can work in the range of wavelengths from 1.0 to1.6  µ m where the optical fiber has minimum loss andchromatic dispersion.The study of the TD impedance frequency depen-dences for different bias voltages at the diode was car-ried out in the frequency range from 45 to 18 MHz bymeans of an HP-8510 analyzer and a meter producedby the Cascade company. The test signal power did notexceed 200  µ W. For example, Fig. 3 shows the Smithdiagram with the frequency dependences of the TDimpedance (see Fig. 2, specimen  1 ) for different biasvoltages. In order to find the TD equivalent circuit, theobjective function   was constructed, where  Z m ( f i )  and  Z c ( f i )  are, respec-tively, the measured and calculated (for the sought-forequivalent circuit) TD impedances at a frequency  f i  and n  is the number of experimental points in the frequencyrange. By varying the values of the equivalent circuitelements, the minimum of objective function  G  wasdetermined. It turned out that, for any bias voltage, thefrequency dependence of the TD impedance corre-sponds to the equivalent circuit consisting of capacitor C  and resistor  R  connected in parallel and resistor  r connected in series. It should be noted that the value ofthe series inductance, which is usually introduced intothe equivalent circuit of a diode, was negligibly small.For the TD bias voltages varying from  ± 0.7 to  ± 1.6 V,we observed an instability of the TD impedance.Figures 4a and 4b show the curves for  R ( V ), r(V),and C(V). It should be noted that R(U), r(U), and ë(U)substantially depend on the bias voltage, which contra-dicts the results reported in [7].On the basis of the data obtained, one can estimatethe TD critical frequency ωT at which the real part ofthe impedanceof the diode vanishes.We estimate negative resistance R from the gainslope (see Fig. 2) taking capacitance C equal to thecapacitance of the TD under the bias voltages Ub closeto the NDC region. For specimen 2, R ≈ –15 Ω, C ≈1.5 pF, and r ≈ 3 Ω. Then,which is close to the value estimated above. As one cansee, ωT is too small for such diodes in the millimeterwavelength range. In fact, the diode has a large capaci-tance due to its large area (200 µm2).A significant nonlinearity of the VCC and poten-tially high critical frequencies make the TDs verypromising as resistive frequency multipliers. Theoreti-cally, a 100% transformation of the fundamental fre-quency into the nth harmonic can be carried out if thenonlinear element has a VCC in the form of the n-orderChebyshev polynomial [8]. An asymmetric VCC of theTD means that the fundamental frequency can be mostG Zm f i( ) Zc f i( )– 2i 1=n∑=Z r R1 jωRC+-----------------------+=ωT1C R–( )---------------R–( )r----------- 1– 88 GHz,≈=–3 –2 –1 0 1 2 3–100–50050100I, mAU, V12Fig. 2. VCCs of (1, 2) two TD specimens. 3214Fig. 3. Smith diagram of the TD impedance in the frequencyrange from 45 to 18 GHz for different bias voltages Ub =(1) 0.0, (2) –0.5, (3) –0.6, and (4) –2.0 V.JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS      Vol. 45      No. 8      2000SUPERHIGH-FREQUENCY CHARACTERISTICS OF OPTICAL MODULATORS 913efficiently transformed into odd harmonics and espe-cially into the fifth harmonic (at a sufficiently high levelof the input signal). In the earlier studies [9, 10], the fre-quency multiplication was provided by TDs with asmall Jp/Jv ratio; hence, the efficiency η = Pn/P1 of thefrequency transformation was about 1%. Here, Pn is thepower of the nth harmonic released in the load and P1is the power supplied to the multiplier from the pump-ing oscillator.In order to demonstrate the TD performance actingas a resistive frequency multiplier with the zero biasvoltage, we calculated theoretically and observedexperimentally the spectrum of the current flowingthrough the TD (specimen 2) generated by a sinusoidalvoltage with the frequency of 50 MHz. In our opinion,the spectrum of the current through the diode uniquelycharacterizes the TD as a frequency multiplier, becausethe transformation efficiency η depends on the circuitsthat match the device with the pumping oscillator andthe load; in the known works, these circuits were differ-ent and the choice was not always optimal.It should be noted that, in the installation for detect-ing the current in the TD, the voltage of the pumpingoscillator was supplied to the TD through a transformerwith n = 2 and 3 in order to avoid instabilities producedby the resistance of the pumping oscillator.The spectrum of the current through the diode wasregistered by means of the Micro-Cap V program. Tothis end, we performed the input of the diode VCC(Fig. 2) and simulated the performance of the circuit ofthe experimental installation. The amplitudes of theharmonics of the current through the diode observedand calculated for different values of voltage Uin of thepumping oscillator are presented in the table.As follows from the data presented in the table, thecalculated and experimental values are in good agree-ment. The results obtained also demonstrate a high effi-ciency of the transformation of the oscillator power intohigher harmonics of the current. According to the table,for Uin = 3 V, the ratio of the amplitudes of the fifth andfirst harmonics of the current is G5/G1 ≈ 12%. This factconfirms that TDs can be applied as resistive frequencymultipliers with the zero shift. However, for applicationin the millimeter wavelength range, which is of practi-cal interest, it is necessary to use specimens with asmaller cross-sectional area and without buffer layers,because the latter cause additional losses. In this case,the contribution of the capacitance as a function of volt-age will be essential. It is also important to prevent themutual compensation of the varistor and varactoreffects.REFERENCES1. Tsu, R. and Esaki, L., Appl. Phys. Lett., 1973, vol. 22,p. 562.–2.0 –1.5 –1.0 –0.5 0 0.5 Ub, cm00.51.01.52.02.5C, pF05101520R, r, Ω4080120160200R, r, Ω(a)(b)RrFig. 4. (a) Resistances R and r and (b) capacitance C of theequivalent circuit vs. bias voltage. Calculated and experimental amplitudes of the harmonics ofthe currentUin , V, µA1 2 3 4 5 6 70.15 – – – – – –0.45 – – – – – –0.75 – – – –1.52.253Note: Figures 1–7 denote the number of the specimen.ExperimentCalculation---------------------------3.164.5---------10.913---------23.126---------0.390.33---------0.150.12---------46.641---------5.4–------4.32.3------3.5–------3.92.5------2.72.7------2.32.3------4951-----5.012------12.510.5---------7.02.8------3.93.0------6.26.1------3.54.7------65.169---------2.7–------6.627------3.514.7---------7.87.6------5.83.9------–4.8------914JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS      Vol. 45      No. 8     2000ALKEEV et al.2. Sollner, T.C.L.G., Goodhue, W.D., Tannenwald, P.E.,et al., Appl. Phys. Lett., 1983, vol. 43, p. 588.3. Figueiredo, J.M.L., Stanley, C.R., Boyd, A.R., et al.,Appl. Phys. Lett., 1999, vol. 74, p. 1197.4. Figueuredo, J.M.L., Stanley, C.R., Boyd, A.R., et al.,Appl. Phys. Lett., 1999, vol. 74, p. 2001.5. McMeekin, S.G., Taylor, M.R.S., Vögele, B., et al.,Appl. Phys. Lett., 1994, vol. 65, p. 1076.6. Brown, E.R., Parker, C.D., Verghese, S., et al., Appl.Phys. Lett., 1997, vol. 70, p. 2787.7. Gering, J.M., Crim, D.A., Morgan, D.G., et al., J. Appl.Phys., 1987, vol. 61, p. 271.8. SVCh-ustroistva na poluprovodnikovykh diodakh (Semi-conductor Diode Microwave Devices), Mal’skii, I.V. andSestroretskii, B.V., Eds., Moscow: Sovetskoe Radio,1969.9. Rydberg, A. and Grönqvist, H., Electron. Lett., 1989,vol. 25, p. 348.10. Neculoiu, D., Dobrescu, D., and Dobrescu, L., CAS-98Proc., 1998, vol. 2, p. 613.

Superhigh-frequency characteristics of optical modulators on the basis of InGaAlAs resonance-tunnel heterostructures

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