THE TUNNEL diode with negative differential resistance

Transcription

1 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 2, FEBRUARY DC Characterization of Tunnel Diodes Under Stable Non-Oscillatory Circuit Conditions Liquan Wang, José M. L. Figueiredo, Member, IEEE, Charles N. Ironside, Senior Member, IEEE, and Edward Wasige, Member, IEEE Abstract A common problem in designing with Esaki tunneling diodes in circuits is parasitic oscillations, which occur when these devices are biased in their negative differential resistance (NDR) region. Because of this, the measured current voltage (I V ) characteristics in the NDR region are usually incorrect, with sudden changes in current with voltage and a plateaulike waveform in this region. Using a full nonlinear analysis of the shunt-resistor-stabilized tunnel diode circuit, we have established the criteria for the range of element values that give stable operation. On this basis, I V measurement circuits can be designed to be free from both low-frequency bias oscillations and highfrequency oscillations. The design equations lead to a direct I V measurement setup in which the stabilization resistor in series with a capacitor can be employed. Experimental results validate the approach, and this is confirmed by second-derivative analysis (d 2 I/dV 2 ) of the measured I V characteristics. Index Terms Parasitic oscillations, resonant tunneling diode (RTD), tunnel diode. I. INTRODUCTION THE TUNNEL diode with negative differential resistance (NDR) was first fabricated in 1958 [1]. Because of the existence of an NDR in the device s current voltage (I V ) characteristic, which can extend from dc to gigahertz frequencies, accurate dc characterization of the NDR region of tunnel diodes is often hindered by parasitic oscillations along the bias lines, making it difficult to correctly determine the static characteristics of these devices in this very critical region [2] [5]. A common method for solving the bias instability problem is to employ a stabilizing resistor directly connected across the tunnel diode [6] [9]. The stabilizing resistor is chosen such that the combined resistance (at dc and low frequencies) is positive when the tunnel diode is biased in the NDR region. The diode characteristic is then indirectly determined. Another previously proposed method uses a large capacitor connected across the device [10], [11], but the inductance of the interconnect be- Manuscript received September 2, 2010; accepted October 26, Date of publication December 13, 2010; date of current version January 21, The review of this paper was arranged by Editor D. Esseni. L. Wang, C. N. Ironside, and E. Wasige are with the Department of Electronics and Electrical Engineering, University of Glasgow, G12 8LT Glasgow, U.K. ( liquan.wang@elec.gla.ac.uk; ironside@elec.gla.ac.uk; ewasige@elec.gla.ac.uk). J. M. L. Figueiredo is with the Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Faro, Portugal ( jlongras@ualg.pt). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TED tween the capacitor and the tunnel diode must be kept very low for this work. The former method yields accurate results so long as the stabilizing resistance value suppresses all oscillations in the circuit. This shunt resistor stabilization method is, to date, the most accurate and robust method for dc characterization of tunnel diodes. It is, however, known that either too large or too small shunt resistor cannot effectively suppress oscillations [6], [9], [12], [13]. The (high-frequency) oscillations, which exist in the circuit also modify the measured I V characteristics. These oscillations can be predicted from the Van der Pol oscillator model, which gives insight to the nature of oscillations and from which circuit stability conditions can be established. Stability conditions can also be established from small-signal analysis of the circuit. Using the developed stability criteria, the dc measurement setup can be designed to be free from oscillations, as will be discussed in this paper. II. DC AND RF STABILITY OF NDR DEVICES A. Tunnel Diode Model Fig. 1(a) shows the typical dc measurement topology of an NDR device such as a tunnel diode or a resonant tunneling diode (RTD). For a large-signal analysis, the NDR device can be modeled as a voltage-controlled current source I(V ) [Fig. 1(b)]. R s is the resistance of the dc supply, the bias line L s is the bias line inductance, and C n is the capacitance of the device when it is biased in the NDR region. If the origin of the axes is shifted to the center of the NDR region, the nonlinear I V characteristics of an NDR device can be represented by a cubic polynomial I(V )= av + bv 3, where a and b are both positive constants [14] [17]. These constants can be related to ΔV and ΔI, which represent the extent of the NDR region. By equating the slope of the I V curve to zero at the peak and valley points, the constants a and b can be determined to be a =(3ΔI)/(2ΔV ) and b =(2ΔI)/(ΔV ) 3. In a small-signal model, the voltage-controlled current source I(V ) is replaced by a small-signal negative conductance G n. At the origin, a = G n. The cubic polynomial provides a simple generic representation of I V characteristics of tunnel diodes or RTDs and has been employed in generic nonlinear analysis of circuits containing these devices [14] [17]. It has, for instance, been widely used in estimating the radio-frequency (RF) output power of actual RTD oscillators [18], [19]. In this paper, it will be used to investigate dc (in)stability to tunnel diodes /$ IEEE

2 344 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 2, FEBRUARY 2011 Fig. 1. (a) Conventional NDR device dc measurement topology. (b) Large-signal model for the NDR device biased in the NDR region. The voltage-controlled current source I(V ) can be modeled by a cubic polynomial if the origin of the axes is shifted to the center of the NDR region. In a small-signal model, the voltage-controlled current source I(V ) is replaced by a small-signal negative conductance G n. Fig. 2. Circuit for direct I V measurement of tunnel diodes or general NDR devices. R s and L s model the resistance and inductance of the dc power supply and the bias line, respectively. Resistor R B and capacitor C B are chosen to achieve both low- and high-frequency stability. C B is omitted and replaced with a short circuit in the conventional indirect method for I V characterization. B. DC Stability Biasing the tunnel diode in the NDR region using the measurement setup of Fig. 1(a) usually leads to oscillations. This is so because the net resistance in the circuit is negative (which is usually the case; note that the series resistance R s is small but increasing this to be numerically larger than the NDR device s negative resistance does not achieve stability but results in bistability [16]). Because of these oscillations, which are usually of low frequency due to the large equivalent inductance L s of the biasing cables, the measured I V characteristic is distorted in the NDR region. It exhibits a characteristic signature in the NDR region variously described as chairlike, N-shaped, double-humped, or plateau [2] [4]. Fig. 2 shows the new direct measurement setup for the I V characteristics of an NDR device in which a shunt resistor R B in series with a capacitor C B is employed. If only the shunt resistor is employed, i.e., C B is replaced with a short circuit, the measurement setup corresponds to the conventional shunt resistor stabilization approach [6] [9]. As will now be shown, the design of this setup directly results from the Van der Pol oscillator model. Consider the conventional circuit first: the inductance L models the connection between R B and the NDR device, whereas R s and L s model the bias line, as earlier stated. The low-frequency stability of this circuit can be determined by considering the real part of the admittance looking into the stabilizing resistor R B, i.e., Re(Y in ).IfRe(Y in ) > 0, the circuit will be stable, and this condition gives R B < 1 (1) G n where the NDR device has been replaced by the small-signal conductance G n, i.e., R B should be chosen to be small Fig. 3. Large-signal RF equivalent circuit of Fig. 2. I 1 is the current through the R B and L branches. This circuit can also represent the low-frequency equivalent circuit but with R B, L,andC n replaced by the elements in brackets R s, L s,andc B + C n, respectively. enough such that the combined dc characteristic of R B in parallel with the NDR device is positive in the NDR region of the tunnel diode or RTD [20], [21]. C. RF stability The dc and low-frequency stability criterion given by (1) is often the only method used to stabilize tunnel diodes. Some diodes, however, could not be stabilized by using this method or any other procedures [9], [13]. The derivation for (1) ignores the inductance L, which, together with the self-capacitance of the NDR device, can lead to high-frequency oscillations in the circuit, thereby introducing errors in the measured I V characteristics. Fig. 3 shows the RF equivalent circuit of Fig. 2. Here, the bias line inductance L s is assumed to be large and so acts like an open circuit at the high frequencies of oscillation, decoupling the dc power supply. This circuit can be described according to Kirchhoff s current law as ( dv I + C n + V L di ) 1 /R B = 0 (2) where I 1 is the current through the R B and L branches of the equivalent circuit and is given by Equation (2) can be rewritten as LC n d 2 V 2 ( ) dv I 1 = I + C n. (3) +(C nr B al + 3bLV 2 ) dv +(1 ar B )V + br B V 3 =0 (4)

3 WANG et al.: DC CHARACTERIZATION OF TUNNEL DIODE UNDER NON-OSCILLATORY CIRCUIT CONDITION 345 and simplified as By substituting d 2 u dτ 2 ε(1 u2 ) du dτ + u + βu3 = 0. (5) I = av + bv 3 τ = 1 arb t LCn 3bL u = V β = R B(aL C n R B ) al C n R B 3L(1 ar B ) ε = al C nr B LCn 1 arb into (4), it can be rewritten as (5). Equation (5) is the Liénard equation and reduces to the classical Van der Pol equation (if β = 0). It describes simple circuits that include NDR components [17], [22]. The type of limit cycle solution depends on ε, which is a scalar parameter that indicates the nonlinearity and the strength of the damping. This equation is structurally stable such that adding higher order terms shall not qualitatively change its oscillatory solution as long as these higher order terms do not lead to bifurcations [15]. If the value of ε is very small (ε 1), the solution to (8) is sinusoidal, and if the value of ε is large (ε >1), the solution is a squarelike (switching) waveform [15]. For negative values of ε, on the other hand, simulations numerical solutions of (5) show that oscillations are not sustained and that large negative ε results in faster damping. Note that, if ε is negative, β will also be negative. In addition, the steady-state (non-oscillatory) solution to the Van der Pol in this case is the same as for the Liénard equation but with larger initial transients for β 0. Therefore, ε can be used to choose the stabilizing resistor value R B, which should satisfy al C n <R B < 1 a to make the numerator of ε negative (first inequality) and for ε to be real (second inequality). If direct I V characterization is desired, then capacitor C B can be introduced in the circuit. In this case, the high-frequency analysis is still the same as previously described, and (6) still has to be satisfied. At low frequencies, however, stability can no longer be established via (1) but needs to be reanalyzed. In this case, the inductance L can be assumed to be a short circuit, and R B can be ignored due to large C B, which adds to the device capacitance C n. It turns out that, in this case, Fig. 3 also represents the low-frequency equivalent circuit but with R B, L, and C n replaced by the dominant circuit elements (shown in brackets in Fig. 3) R s, L s, and C B + C n, respectively. In addition to the condition on R B in (6), C B, L s, and R s should satisfy (6) but with C B + C n L, and R B replaced as follows: al s <R s < 1 C B + C n a. (7) (6) Fig. 4. Measured current voltage (I V ) characteristics for tunnel diode 1N3717 with (a) R B = 8 Ω and (b) R B = 15 Ω. Second-derivative analysis confirms that the characteristic in (a) contains oscillations, whereas the other in (b) is free from oscillations. The cubic polynomial (dots), compared to measured data (solid line) in the NDR region, is also shown in (b) and points to how the generic model is to be applied in this case. D. Small-Signal Analysis RF stability for the circuit of Fig. 3 can also be established using small-signal analysis. In this case, the current source is replaced with G n, and from the admittance of the circuit, the characteristic equation as a function of the complex frequency s = σ +jω is given by G n + sc n + 1 = 0. (8) R B + sl The characteristic frequencies of this equation (circuit) fall in the left (stable) half of the complex-frequency plane only when [23] G n L C n <R B < 1 G n. (9) Equations (6) and (9) are identical since diode parameter a is equal with the small-signal conductance G n = a at the point of highest negative differential conductance in the NDR region (which corresponds to the origin of cubic polynomial model for the NDR device). Note that (6) or (9) is not only a highfrequency stability criterion but also includes the conventionally used low-frequency criterion (1). III. EXPERIMENTAL RESULTS Tunnel diodes commercially available from American Semiconductors (1N3717) were used in the experimental work. Initial measurements (without bias stabilization) provided ΔI and ΔV values of 4 ma and 250 mv, respectively. The parameter G n or a was estimated from 1.5ΔI/ΔV. Because of the broad valley region of the actual tunnel diode, the peak-to-valley voltage difference used in the value for a was 125 mv, i.e., a For the experimental tests, a series inductance L of 2 nh (realized from a microstrip line and lead inductance) and a tunnel diode capacitance of 13 pf extracted from RF measurements [24] were used. Therefore, from (6), the shunt stabilizing resistor should satisfy the condition 7.5 Ω <R B < 20 Ω. The measured I V results for these tunnel diodes employing different bias stabilization R B = 8 Ω and R B = 15 Ω are shown in Fig. 4, with smooth oscillation-free characteristics measured for R B = 15 Ω.

4 346 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 2, FEBRUARY 2011 Fig. 5. (a) First and (b) second derivatives of the I V curve of the stabilized 1N3717 tunnel diode [Fig. 4(a)]. Here, R B = 8 Ω. The valley/peak in the second derivative shows the presence of oscillations in the mV range of the NDR region. Accuracy of the values of L and C n is limited for the hybrid microstrip test fixture with packaged tunnel diodes employed in the experimental results described here. The proposed method should prove vital for the on-wafer characterization of RTDs, for which C n can be accurately estimated from the layer structure and L from the layout. In addition, by employing (6), R B and L could be chosen to facilitate RF characterization. For direct I V characterization, bias cables modeled by L s must be kept short, so that a small value for C B can be used to satisfy (7) (since R s, which is the bias cable resistance, is small). Requirements on L s and C B could be relaxed by using an additional larger series resistance R s (but not large enough to cause bi-stability), which is then de-embedded from the measurements. I V characteristics for which (6) or (7) was not satisfied, i.e., R B < 8 Ω and R B > 20 Ω for the 1N3717 tunnel diode, were clearly modified by oscillations in the measurement setup. Fig. 6. (a) First and (b) second derivatives of the I V curve of the stabilized 1N3717 tunnel diode [Fig. 4(b)]. Here, R B = 15 Ω. There are no sharp valleys followed immediately sharp peaks in the second derivative showing no oscillations are present during measurement. For direct I V measurements, a test fixture was built using a series lumped inductance L s of 56 nh (and resistance R s of 1 Ω), and C B = 6 nf to satisfy (7). The stabilizing resistances R B were 8 and 15 Ω, which were the same values used in the indirect I V measurement setup. The measured I V characteristics were practically identical for the two approaches. The generic cubic polynomial has been compared to the measured I V data in the NDR region, as shown in Fig. 4(b). It approximates the crucial NDR region well but does not reproduce the broad valley region. Therefore, in designing the dc test fixture to satisfy (6) or (7), half the actual ΔV from unstabilized measurements is used. IV. DISCUSSION The second derivative of the measured I V curves can be used to detect the presence of oscillations, even when the oscillation frequency is ultrahigh or the oscillation amplitude is very small, e.g., below 10 mv [13]. The first derivative of the I V curve will show a sharp valley/peak, whereas the second derivative curve will show a sharp valley immediately followed by a sharp peak at the onset or quenching of oscillations [13]. Figs. 5 and 6 show derivatives for stabilized tunnel diode I V measurements for the 1N3717 for R B = 8 Ω, and R B = 15 Ω, respectively. The second derivative confirms the presence of oscillations in the measurement shown in Fig. 4(a) (R B = 8 Ω), whereas none for those shown in Fig. 4(b) (R B = 15 Ω). For R B = 8 Ω, only the conventional stability criterion (1) is satisfied (errors in estimating the element values for the test fixture meant (6) was not satisfied and oscillations were present during measurement), whereas, for R B = 15 Ω, (6) is satisfied, and the measurements are free from oscillations. V. C ONCLUSION Design equations for realizing a stable test circuit that can be used in the accurate determination of the current voltage characteristics of tunnel diodes in the NDR region have been derived. The proposed approach eliminates both low-frequency bias oscillations and high-frequency oscillations, which would otherwise distort the measured characteristics. The measured tunnel diode I V characteristics confirm the validity of the design criteria. 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His research interests include understanding RTDdriven laser diode circuits and associated applications, and the development of enhancement mode GaN high-electron mobility transistor technology. José M. L. Figueiredo (M 09) received the B.Sc. degree in physics (optics and electronics) and the M.Sc. degree in optoelectronics and lasers from the University of Porto, Portugal, in 1991 and 1995, respectively. From 1995 to 1999, he was with the Department of Physics, University of Porto, and the Department of Electronics and Electrical Engineering, University of Glasgow, U.K., as a Ph.D. student in co-tutela, working on the optoelectronic properties of resonant tunneling diodes. He is currently with the Department of Physics, University of the Algarve, Faro, Portugal. His research interests include the design and the characterization of electronic and optoelectronic devices and circuits incorporating low-dimensional quantum structures. Charles N. Ironside (M 87 SM 05) received the B.Sc. degree (first-class honors) in physics and the Ph.D. degree from Heriot-Watt University, Edinburgh, U.K., in 1974 and 1978, respectively. His Ph.D. work was on a type of tunable semiconductor laser, the Spin-Flip Raman Laser. From 1978 to 1984, he was a Postdoctoral Research Assistant with the University of Oxford. He was first with the Inorganic Chemistry Department, working on time-resolved spectroscopy of solids and energy transfer mechanisms between luminescent ions. He then moved to the Clarendon Laboratory to work on time-resolved spectroscopy of solids on a picosecond timescale. Since 1984, he has been with the Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, U.K. He has been engaged in a variety of optoelectronic projects that include ultrafast all-optical switching in semiconductor waveguides, monolithic mode-locked semiconductor lasers, broadband semiconductor lasers, quantum-cascade lasers, and optoelectronic integrated chip devices, which concentrated on the integration of resonant tunneling diodes with electroabsorption modulators and semiconductor lasers. Edward Wasige (S 97 M 02) received the B.Sc. (Eng.) degree in electrical engineering from the University of Nairobi, Nairobi, Kenya, in 1988, the M.Sc. (Eng.) degree in microelectronic systems and telecommunications from the University of Liverpool, Liverpool, U.K., in 1990, and the Dr.-Ing. degree in electrical engineering from the University of Kassel, Kassel, Germany, in His doctoral research involved the development of a Si-GaAs quasi-monolithic hybrid technology for microwave and millimeter-wave applications. He was a Lecturer with Moi University, Kenya from and He was also a United Nations Educational, Scientific, and Cultural Organization Postdoctoral Fellow with the Technion-Israel Institute of Technology, Haifa, Israel. Since 2002, he has been with the University of Glasgow, Glasgow, U.K. His current research interests include the reliable design of resonant-tunneling-diode microwave and millimeter-wave oscillators, and the development of new types of gallium-nitride-based heterojunction field-effect transistors for power electronics and high-power microwave applications.