OPTOELECTRONIC mixing is potentially an important

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1 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 8, AUGUST HBT Optoelectronic Mixer at Microwave Frequencies: Modeling and Experimental Characterization Jacob Lasri, Y. Betser, Victor Sidorov, S. Cohen, D. Ritter, M. Orenstein, and Gadi Eisenstein, Fellow, IEEE Abstract A heterojunction bipolar transistor (HBT) optoelectronic mixer was studied experimentally and theoretically. A detailed large signal -model and a small signal analysis are described. The frequency dependence of down and up conversion has been analyzed and measured. In terms of conversion gain, the advantage of the down conversion process is clearly demonstrated. The values of parameters employed in the mixing process are also discussed for both large and small signal regimes. I. INTRODUCTION OPTOELECTRONIC mixing is potentially an important function in subcarrier multiplexed (SCM) microwave/optics systems [1], [2]. The use of InP/GaInAs heterojunction bipolar transistors (HBT s) containing an optical access to the base, as an optoelectronic mixer (OEM) is an attractive possibility for use in SCM systems [3]. In order to simulate the optoelectronic mixing of the optical and electrical signals both modulated at radio frequencies (RF s), a large signal model has to be employed. Two known avenues to such a modeling for microwave bipolar transistors are the PSPICE model and the -model equivalent circuit. Both were previously used to identify the origin of the various nonlinear effects in the HBT OEM [3], [4]. While the nonlinear nature of the current gain in an HBT makes it necessary to model the mixer under large signal conditions, it is also useful to develop a small signal model which yields analytical solutions that help to understand the physics behind the device operation. The present paper describes both a large signal -model of an HBT OEM and a small signal analysis of frequency mixing and conversion. Down and up conversion dependencies on frequency were calculated for either large and small signal regime and the mixer nonlinear components were identified. The mixing performance for a modulated optical input signal and an electronic local oscillator (LO) was measured as a function of the signal frequency. The ratio between the measured down and up conversion gains enabled us to identify Manuscript received December 28, 1998; revised May 10, J. Lasri, V. Sidorov, S. Cohen, D. Ritter, M. Orenstein, and G. Eisenstein are with the Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa Israel. Y. Betser was with the Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa Israel. He is now with the Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA USA. Publisher Item Identifier S (99) the mixer nonlinear components. The experimental results are in good agreement with the predictions of the theoretical models. II. THEORY A. Large Signal Model We employed the large signal -model for treating frequency mixing and conversion, assuming that the HBT is subject to a modulation at two different RF frequencies: the LO frequency and the signal frequency. Fig. 1(a) shows a schematic diagram of the large signal -model used for calculating the mixing performance of an HBT OEM at microwave frequencies. The nonlinear input capacitance is, where is the low-frequency ac current gain of the HBT, and are the base-collector and the base-emitter junction capacitance, is the emitter to collector delay time, is the saturation current, is the time dependent base-emitter voltage, and is the thermal voltage, with being the ideality factor of the base-emitter junction, is the Boltzman constant, and the temperature. In order to calculate the performance of the HBT as an OEM, we considered the circuit diagram of Fig. 1(b). The LO signal, connected to the base, was represented as a voltage source:. The input optical signal which impinged on the base served as a current source:. The 50 resistors connected to the LO source and the collector output, represented the LO output impedance and the input impedance of the measurement apparatus (spectrum analyzer), respectively. The capacitance and inductance of the Bias-T are mf and mh. Other symbols represent the following: the voltage at the output of the LO source (after the 50 resistor), voltage at the base port, the base dc bias, the base dc current, the voltage at the collector port, and the collector dc bias. Note that the -model does not take into account saturation effects due to a voltage drop on the 50 load at high collector currents, which results in forward biasing of the base collector junction. This model simulates the HBT in the active mode regime the regime for the best mixing performance [3]. Therefore, only large values and relatively small LO /99$ IEEE

2 1424 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 8, AUGUST 1999 product at, and additional mixing harmonics which are not considered in the present analysis. (a) B. Small Signal Model In general, the nonlinear nature of the differential equations in (1) makes it necessary to solve them numerically. However, a useful analytic solution can be obtained for the case of a small amplitude modulation of both the local oscillator and the optical signal: and. Starting again with the -model (1b) and neglecting (assuming ideal Bias-T) and (which is ), we can model the HBT OEM by the differential equation (3) where c.c. c.c. (3a) (3b) Applying the small modulation approximation, (3) can be simplified by using Taylor s expansion for the exponent. Keeping terms quadratic in, we obtain (b) Fig. 1. (a) HBT large signal -model diagram and (b) schematics of the HBT OEM circuit for large signal simulations. power will be used in order to keep the HBT in the active mode regime ( V). The differential equations describing the model are (1a) (1b) (1c) (1d) With the solution of the form (4) c.c. (5) and the spectral coeffi- (6a) (6b) (6c) (6d) where cients are The output signal of the OEM is the current on the 50 input impedance of the spectrum analyzer. When neglecting the base-collector capacitance, this current is equal to the collector current, and is given by Solving numerically the differential (1), substituting the solution for in (2) and Fourier transforming the result, yields the output spectrum. This spectrum contains the LO component at, the signal component at, the downconversion product at, the up-conversion (2) where and Substituting (5) and (6) into (2) yields expressions for the amplitudes of the output signal at the up- and down-converted

3 LASRI et al.: HBT OPTOELECTRONIC MIXER AT MICROWAVE FREQUENCIES 1425 Fig. 2. Schematic diagram of the epitaxial layer structure and mesa structure of the HBT. The optical window is located on the base mesa. frequencies (7a) (7b) [4], related to large signal operation, which states that the HBT OEM cannot be separated into an ideal input mixing stage followed by an amplifying frequency dependent output stage. Rather, mixing and amplification take place simultaneously and the voltage dependence of the input network is the main nonlinear effect in the HBT OEM. In the asymptotic case, the frequency of the downconversion process is constant at and the frequency of the up-conversion process ( ) varies as. Therefore, in this case, (7) becomes Equations (7a) and (7b) are the most important results of the small signal analysis. An informative characterization of the high-frequency behavior of the mixing scheme is an asymptotic scenario, when the signal and the local oscillator are close in frequency,. The frequency is associated with the RC delay time related to the 50 resistor connected to the LO source and the sum of the diffusion capacitance and the base emitter capacitance. In this asymptotic case, we can describe the HBT OEM performance as a cascade of two transfer functions, which depends on the input signal frequency and which depends on the mixing-product frequency. Both and depend on the frequency, i.e., the input impedance and the nonlinear input capacitance. Cascading and to form the input mixing network results in different currents values for the down and up conversion processes. The input signal passes through, which is a frequency dependent amplification function. Note: this function is not the current gain amplification function of the transistor due to the pole at. Then, the amplified signal passes through the function which is responsible for the different conversion gains of the various mixing products. The later implies that we can model the operation of the HBT OEM as and special amplification stage followed by a mixing stage, however it should be noted that both of these processes are actually simultaneous and taking place at the input network of Fig. 1. This is consistent with one of our previous results (8a) (8b) The result implies that in the small-signal regime, the amplitude of the intermediate-frequency output signal decays as for the down-conversion process and as for the up-conversion process. This frequency behavior makes the use of up-conversion process at low LO power levels (small signal regime) very inefficient at high frequencies. A. The Device III. EXPERIMENTAL The experiments were carried out using an HBT grown on a semi-insulating InP substrate by a compact metalorganic molecular beam epitaxy system [5]. The layer structure of the HBT is shown schematically in Fig. 2 and contained: 400 nm GaInAs ( cm ) and 250 nm InP ( cm ) subcollector, 750 nm undoped GaInAs collector, 50 nm GaInAs ( cm ) base, 150 nm

4 1426 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 8, AUGUST 1999 Fig. 3. Experimental setup for the HBT OEM. InP ( cm ) emitter, and 200 nm ( cm ) GaInAs contact layer. Conventional wet etching and a self-aligned Pt/Ti/Pt/Au one step metallization process were employed to fabricate the devices. Polymide passivation and Ti/Au pads completed the fabrication process. A 5 6 m opening in the base metallization served as an optical window. Small signal of the HBT yielded an and an of 70 and 40 GHz, respectively, at ma and V. B. Measurement System The schematics of the experimental setup are shown in Fig. 3. The on wafer measurements were carried out using 40 GHz GSG probes. An LO source and a dc voltage source were connected via a Bias-T to the base. A DFB laser operating at 1.55 m was externally modulated by an RF source and the optical modulated signal was amplified by an Erbium doped fiber amplifier (EDFA) before being focused onto the optical window of the HBT. The EDFA serves to compensate for various coupling losses in the experimental arrangement. A spectrum analyzer was connected via a Bias-T to the collector which served as the output port. C. Conversion Gain Experiments Both the intrinsic and extrinsic conversion gains are useful figures of merit for OEM s [3], [6]. The intrinsic conversion gain,, is defined as the ratio of the output power (, for down-, up-conversion) to, the primary photo detected RF power. is the photo induced RF electrical power detected by the base collector junction without amplification. It was measured by shorting the base emitter junction of the photodetector transistor. The extrinsic conversion gain,, is defined as the ratio of the output power of the up or down converted signal to the equivalent electrical RF power,, that would have been detected by an ideal photo-diode with an equal load resistance. This ideal power is related to the peak power of the modulated component of the incident optical signal by [6], where is the electron charge, is the photon energy, and 50. Fig. 4. Frequency response of the down- and up-conversion gain. and are related by the external quantum efficiency,, of the base-collector photo-diode, thus. The external quantum efficiency was measured from the DC photo-response of the base-collector junction and was or db. This result agrees with a calculation assuming an absorption depth of 1.5 m, and 30% reflection. The electrical response of the HBT to the modulated optical signal was first measured as a function of the frequency modulation of the optical signal. The electrical frequency response of the base-collector PIN photo-diode served as a reference for calculating the intrinsic signal gain, excluding the effects of the external quantum efficiency of the HBT. Next, the HBT was driven at its optimum bias [3] while the LO power level and the collector emitter bias were held constant at 10 dbm and 2 V, respectively. In both down- and up-conversion experiments, we applied two RF signals (one to the external OE modulator and the other to the HBT base) in the range of GHz, keeping the separation between them at 500 MHz. For each conversion experiment the applied frequency was varied while measuring the amplitude of the converted product. Note that the down-converted product was at a constant 500 MHz and the up-converted product was varied as. The results of the intrinsic down and up conversion gain responses are shown in Fig. 4. The results show that the conversion gain of the downconversion process is larger than that of the up-conversion case for all frequencies. The conversion cut-off frequency (defined as the frequency where the intrinsic conversion gain is 0 db) was 9 GHz for the down-conversion process and 4 GHz for up-conversion process. The measured ratio between the down- and up-conversion gain can be used to identify the dominant nonlinear effects in the OEM operating in the large signal regime. Using the PSPICE model of the HBT, we showed previously [3] that the main nonlinear effect is the exponential dependence of the dynamic emitter resistance,, on the base emitter time dependent bias voltage (i.e., the input network). The

5 LASRI et al.: HBT OPTOELECTRONIC MIXER AT MICROWAVE FREQUENCIES 1427 Fig. 5. The measured ratio between down- and up-conversion gain products. (a) TABLE I VALUES OF THE PARAMETERS USED IN THE LARGE- AND SMALL-SIGNAL MODELS amplitudes and phases of the down- and up-conversion components of differ due to the effect of the input network, and thus, we expect to have a difference between down- and up-conversion efficiencies. Fig. 5 shows the frequency dependence of the measured ratio between the down-conversion and the up-conversion products. One obvious observation is that the absolute efficiency of the down-conversion process is higher than that of the up-conversion process by as much as 3dBat GHz. The applied LO power of 10 dbm was optimized for the 3 GHz RF frequency. This is consistent with LO powers of similar transistors which we examined in detail previously [3]. This 3 db difference is a further proof of the statement made previously regarding the inability to separate the HBT OEM into an ideal mixing stage followed by a frequency dependent amplifying stage. Would this separation be valid, and if we assuming a frequency response of the amplifying stage to be the same as that of the current gain of the HBT, the difference between down- and up-conversion products would be larger than 20 db for a 3 GHz RF signal and 3.5 GHz (b) Fig. 6. Comparison between the experimental and theoretical data for (a) down-conversion process and (b) up-conversion process. LO. Since the measured difference is only 3 db we conclude that this separation is invalid and that the HBT is a distributed mixer and a frequency dependent current amplifier operating simultaneously. D. Comparison to the Model The differential equations in (1), representing the large signal model, were solved numerically using the MAT- LAB/SIMULINK software package for the same biasing and power level conditions used in the experiments. In addition, the conversion gain of the small signal model was calculated from the analytic terms of (7) for large signal conditions. For both models, the values of the HBT parameters used for the calculations were extracted from small-signal -parameter measurements using the technique described in [7]. The values of the model components used for the calculations are listed in Table I. A comparison between the experimental data and the calculated values is shown in Fig. 6.

6 1428 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 17, NO. 8, AUGUST 1999 In general, the large signal simulation results are in good agreement with the experimental data with only minor deviations. The reason for the deviations is mainly due to calibration errors and to nonideal behavior of the Bias-T we used. Regarding the small signal calculated results, a good match to the experimental data was obtained only at high frequencies where the LO power levels ( 10 dbm) are in fact in the small signal modulation range. Indeed, in the highfrequency regime, the dependence of the experimental data on frequency agrees with the small-signal theoretical predictions of (8). In the asymptotic case, (which is about 10 GHz), the efficiency dependence on frequency varies as for the down-conversion process and as for the up-conversion process. IV. CONCLUSIONS We have demonstrated large and small signal models of an HBT OEM. The models were confirmed by experimental results for both down- and up-conversion processes. In terms of conversion gain, the down-conversion process was found to be more efficient. The conversion cut-off frequency, when both the optically modulated signal and the local oscillator were close in frequency, was 9 GHz for the down-conversion and 4 GHz for the up-conversion process. The input network, i.e., the input impedance and the sum of the nonlinear diffusion capacitance and the base emitter capacitance acts as the main nonlinear mechanism of the HBT OEM. The asymptotic frequency dependence of the HBT OEM at low LO power levels was found and confirmed experimentally to be for the down-conversion process and for the up-conversion process. REFERENCES [1] T. E. Darcie, Subcarrier multiplexing for multiple-access lightwave networks, J. Lightwave Technol., vol. LT-5, pp , Aug [2] R. Olshansky, V. A. Lanziera, and P. M. Hill, Subcarrier multiplexed lightwave systems for broad-band distribution, J. Lightwave Technol., vol. 7, pp , Sept [3] Y. Betser, D. Ritter, C. P. Liu, A. J. Seeds, and A. Madjar, A single-stage three-terminal heterojunction bipolar transistor optoelectronic mixer, J. Lightwave Technol., vol. 16, pp. 1 5, Mar [4] Y. Betser, J. Lasri, V. Sidorov, D. Ritter, M. Orenstein, G. Eisenstein, A. Seeds, and A. Madjar, An integrated heterojunction bipolar transistor cascode opto-electronic mixer, to be published. AU: Please update if possible ED. [5] R. A. Hamm, D. Ritter, and H. Temkin, A compact MOMBE growth system, J. Vacuum Sci. Technol., vol. A12, pp , [6] C. P. Liu, A. J. Seeds, and D. Wake, Two-terminal edge-coupled InP/InGaAs heterojunction phototransistor optoelectronic mixer, IEEE Trans. Microwave Guided Wave Lett., vol. 7, pp , Mar [7] S. J. Spiegel, D. Ritter, R. A. Hamm, A. Feygenson, and P. R. Smith, Extraction of the InP/GaInAs heterojunction bipolar transistor small signal equivalent circuit, IEEE Trans. Electron. Dev., vol. 42, pp , June Jacob Lasri was born in Haifa, Israel, on February 22, He received the B.A. degree in physics and the M.Sc. degree from the Electrical Engineering Department, Technion Israel Institute of Technology, Haifa, in 1995 and 1998, respectively. He is currently working towards the Ph.D. degree at the Technion. His current research interests are in the field of microwave photonics and fiber optics communication systems and devices. Y. Betser, photograph and biography not available at the time of publication. Victor Sidorov received the M.Sc. honors degree in chemistry from Voronezh University, Russia, in He is currently working towards the D.Sc. degree in chemical engineering at the Technion Israel Institute of Technology, Haifa. Since 1995, he has been employed as a Senior Research Assistant at Microelectronics Research Center, Technion, where his primary responsibilities involve microwave and optoelectronic devices and circuits manufacturing based on III V semiconductors processing. Prior to this, he held an Engineer Researcher position at Mizur Micromechanics Technologies Ltd., responsible for microsensors manufacturing and micromachining. His current research interest is III V semiconductor surface coatings and passivation. S. Cohen, photograph and biography not available at the time of publication. D. Ritter, photograph and biography not available at the time of publication. M. Orenstein, photograph and biography not available at the time of publication. Gadi Eisenstein (M 80 SM 90 F 99) received the B.Sc. degree from the University of Santa Clara, Santa Clara, CA, in 1975 and the M.Sc. and Ph.D. degrees from the University of Minnesota, Minneapolis, in 1978 and 1980, respectively. In 1980, he joined AT&T Bell Laboratories, where he was a Member of Technical Staff in the Photonic Circuits Research Department. His research at AT&T Bell Laboratories was in the fields of diode laser dynamics, high-speed optoelectronic devices, optical amplification, optical communication systems, and thin-film technology. In 1989, he joined the faculty of the Technion Israel Institute of Technology, Haifa, where he is a Professor of Electrical Engineering and the Head of the Barbara and Norman Seiden Advanced Optoelectronics Center. His current activities are in the fields of fiber-optic systems and components for such systems, dynamics of quantum-well lasers, nonlinear semiconductor optical amplifiers, and compact short-pulse generators. He has published over 200 journal and conference papers and regularly lectures in all major fiber optics and diode laser conferences and serves on numerous technical committees. Dr. Eisenstein is an Associate Editor of the IEEE JOURNAL OF QUANTUM ELECTRONICS