Chapter 3 Scattering parameter based Modeling and Simulation of Symmetric Tied-gate InAlAs/ InGaAs DG-HEMT for Millimeter-wave Applications

Transcription

1 cattering parameter based Modeling and imulation of ymmetric Tied-gate InAlAs/ InGaAs DG-HEMT for Millimeter-wave Applications Monika Bhattacharya 8

2

3 3.1 INTRODUCTION uperior ultra-high frequency and low-noise performance reported for the fabricated 1 nm gate-length trenched gate InAlAs/InGaAs DG-HEMT has generated great interest in the device [Vasallo8, Wichmann4]. However, further exploration of the device potential for low-noise microwave integrated circuit design, future military communications, radar and intelligence applications, requires a comprehensive physics based model which can be used for accurate analysis of the device performance at ultra-high frequencies and also forms the basis for the modeling of its noise performance. In the previous chapter, a charge control based analytical model was proposed for the microwave performance assessment of lattice matched 1 nm gate-length symmetric tied-gate geometry InAlAs/InGaAs DG-HEMT [Bhattacharya1]. uperior performance of the DG-HEMT as compared to its single-gate (G) counterpart was established in terms of higher drain current and improved transconductance which occurs due to higher sheet-carrier concentration and better gate control. The significance of optimization of the various device parameters for the extraction of best device performance was also investigated which was found to be even more important for a double-gate structure as compared to the single-gate structure. For designing of low noise microwave active circuits, using these high performance transistors, the knowledge of its scattering () parameters is inevitable. cattering () parameter measurements are in fact the most common microwave measurements used for the characterization of HEMTs. Then, from these parameters measured at a particular bias point, the various elements of the small-signal equivalent circuit are extracted. Therefore, for a more extensive analysis of the performance of InAlAs/InGaAs DG- HEMT for ultra-high frequency applications, an analytical approach for accurate evaluation of its scattering () parameters that correspond well with the device simulation results as well as with the experimental measurements is presented in this chapter [Bhattacharya11]. uch a device model based on -parameter evaluation is inevitable for accurate microwave amplifier circuit design which is optimized for providing the best performance in terms of power gain, stability, maximum frequency of oscillation and minimum noise figure. Monika Bhattacharya 83

4 The present analysis begins with obtaining the intrinsic short-circuit admittance (Y) parameters for a single-gate (G) and symmetric tied-gate geometry double-gate (DG) HEMT using its two-port small-signal equivalent circuit model. The scattering () parameters are then evaluated from the intrinsic Y parameters including the effect of the various parasitic elements associated with the source, gate and drain contacts. The incorporation of the effect of extrinsic elements enables a more accurate evaluation of the parameters and power gain that exhibits better correspondence with the measured results. In addition to this, the results obtained using the analytical model has also been validated with the device simulation results. The extrinsic scattering parameters thus evaluated are in turn used for a rigorous RF performance assessment of the device in terms of the various figures of merit that includes Maximum Unilateral Power Gain (G TUmax ), Maximum table Gain (G ms ) and the Maximum frequency of Oscillation (f max ). The model thus established enables a complete microwave performance characterization of the device for future millimeter wave low-noise amplifier design applications cattering () Parameter Measurement at Microwave Frequencies Devices like a discrete FET, a multi-stage MMIC amplifier or any active or passive circuit when represented as a two-port network shown in Fig. 3.1 can be characterized by the relationships between the input and output currents and voltages. These relations are often given in terms of the short-circuit admittance (Y), open circuit impedance (Z), hybrid (H) or the chain (ABCD) parameters at frequencies below the microwave regime as illustrated in Table 3.1[Ladbrooke89, Gonzalez84, Liao86, Pozar5 and Golio8]. V 1 I 1 Input Port TWO-PORT NETWORK I V Output Port Fig Two Port Network Representation 84 Monika Bhattacharya

5 Table 3.1 Two-port Network Parameters used at frequencies below the microwave regime Open Circuit Impedance (Z) Parameters V1 Z11 Z1 I1 V = Z1 Z I Hybrid (H) Parameters V1 H11 H1 I1 I = H 1 H V hort Circuit Admittance (Y) Parameters I1 Y11 Y1 V1 I = Y1 Y V Chain (ABCD) Parameters V1 A B V I = 1 C D I An attempt to measure the H, Y, Z or ABCD parameters of the device directly at microwave frequencies would require either a short-circuit or open circuit to be presented at the input port and the output port in turn while measurements are made at the other port. uch procedures are inconvenient at microwave frequencies where the provision of obtaining accurate short circuit and especially open circuit is physically difficult as appreciable impedances can result from very small capacitances and inductances. For example a shorting wire or strip across the output terminals of a device will have non-trivial impedance at microwave frequencies. Conversely, an open circuit formed by simply leaving the terminals open can lead to non-trivial capacitance and non-trivial impedance. Also, short or open circuit terminations at microwave frequencies may lead to instability of the device. Therefore, the difficulty in achieving true open and short circuit condition at the terminals of the two-port network and the possibility of the device becoming unstable when their terminals are shorted or open-circuited precludes the use of the H, Y and Z and ABCD network parameters in the microwave regime. Hence, at microwave frequencies, cattering () parameters are the set of parameters that are most commonly used for complete characterization of a linear two-port network. Unlike the Y, Z, H and ABCD parameters in which the terminal voltages and currents are directly measured, the scattering () parameters relate to the travelling waves that are scattered or reflected when a network is inserted into a transmission line of certain characteristic impedance Z o. -parameter measurements require terminations of 5 Ω (or similar), which are comparatively easy to realize. They circumvent the need for Monika Bhattacharya 85

6 true shorts and opens at the terminations, thus avoiding the accuracy and stability problem. For the measurement of -parameters, the two port network is connected to transmission lines that extend to an impedance termination on the output side and a signal source on the input side as illustrated in Fig. 3.. Fig. 3.. Two Port Network for -Parameters Generally, the impedance seen looking from the terminations into the input and output ports will be different from the characteristic impedance (Z o ) (usually taken as 5 Ω). Consequently, when the signal source is turned on, there will be incident and reflected voltage waves (V + and V - respectively) at the output port and incident and reflected voltage waves (V 1 + and V 1 - respectively) at the input port. Therefore, in terms of these incident and reflected voltage waves, new variables, a 1, a, b 1 and b are defined in which a 1 and b 1 now represent the incident and reflected waves respectively at the input port, and, a and b represent the incident and reflected waves respectively at the output port as illustrated in Fig. 3.. In terms of these newly defined variables, the scattering () parameters for a two port network are defined as: b a1 b = 1 a The physical meaning and significance of the set of four scattering parameters ( 11, 1, 1 and ) is illustrated in Fig Monika Bhattacharya

7 Input Reflection Coefficient ( 11 ) Reverse Transmission Coefficient ( 1 ) 11 b = 1 a 1 a = 1 = b 1 a a = 1 Forward Transmission Coefficient ( 1 ) Output Reflection Coefficient ( ) 1 b = a 1 a = b = a a = 1 Fig cattering Parameters The Input Reflection Coefficient ( 11 ) is defined as the ratio of the wave reflected at input port (Port 1) to the wave incident at the input port with the output port (Port ) terminated with characteristic impedance (Z o ) (i.e. the wave incident at the Port, a = ). With regard to the microwave amplifier design, it is related to the matching of the input port with the source impedance. The Reverse Transmission Coefficient ( 1 ) also regarded as the Reverse Isolation parameter determines the level of feedback from the output of an amplifier to the input and therefore influences its stability (its tendency to refrain from oscillation). Mathematically, it is defined as the ratio of the wave transmitted at the input port (Port 1) to the wave incident at the output port (Port ) when Port 1 is terminated with the characteristic impedance (Z o ),i.e., a 1 =. The Forward Transmission Coefficient ( 1 ) is very important with regard to the microwave amplifier design as it is directly related to the maximum transducer power gain of the device given as 1. Therefore, higher the value of 1, higher is the power gain obtainable from the device and hence higher is the frequency of operation of the device. Mathematically, it represents the ratio of the wave transmitted at the Monika Bhattacharya 87

8 output port (Port ) to the wave incident at the input port (Port 1) with the load impedance (Z L ) matched with the characteristic impedance (Z o ). The Output Reflection Coefficient ( ) is defined as the ratio of the wave reflected at the output port (Port ) for the wave incident at the output port with the input port (Port 1) terminated with characteristic impedance (Z o ) (i.e. the wave incident at the Port 1, a 1 = ). With regard to the microwave amplifier design, it is related to the matching of the output port with the load impedance Microwave Amplifier Design And Power Gains Amplification forms one of the most basic and vital function of a microwave active circuit. As early as in 197s, microwave amplifiers were based on tubes, such as klystrons and travelling-wave tubes or solid-state reflection amplifiers based on the negative resistance characteristics of tunnel or varactor diodes. Due to dramatic improvement and innovations in solid-state technology, modern day RF and microwave amplifiers are based on high performance transistors such as GaAs HBTs and GaAs or InP based HEMTs. The major requirements of modern day microwave amplifiers include [Golio8, Gonzalez84, Liao86]: [i] broad frequency range of operation in excess of 1 GHz [ii] small size [iii] low noise figure [iv] low to medium power capacity Accurate transistor amplifier design relies mainly on the characterization of the terminal characteristics of the transistor which are represented by the scattering () parameters. uch an evaluation of the parameters, in turn, is achieved using an accurate analytical device model. The power gain produced by the microwave active amplifier is then obtained which gives the ultimate measure of ultra-high frequency properties of the device. In the following sections, the various power gains which are derived from the scattering parameter based characterization of a two-port network are discussed. The block diagram of a HEMT based microwave amplifier circuit with input and output matching networks is given in Fig. 3.4 (a). The corresponding -parameter based signal flow graph used for the evaluation of the various power gains is also shown in 88 Monika Bhattacharya

9 Fig. 3.4 (b). Γ IN and Γ OUT represent the input and output reflection coefficients; Γ and Γ L represent the source and load reflection coefficients. (a) Block diagram (b) ignal Flow Diagram Fig (a) Block Diagram of HEMT based Microwave Amplifier Circuit with Input and Output Matching Networks and (b) the equivalent signal flow graph Transducer Power Gain (G T ) It is defined as the ratio of the output power P L delivered to the load Z L over the input power P AV available from the source to the network given as [Gonzalez84, Liao86]: G T P = P L AV where, P L = P AVN (power available from the network) when Γ L = Γ OUT * P AV = P IN (power input to the network) when Γ IN = Γ * (* represents conjugate) From the signal flow graph shown in Fig. 3.4 (b), G T is evaluated in terms of the - parameters and the source and load reflection coefficients (Γ and Γ L respectively) as: G T = ( 1 Γ ) 1 ( 1 ΓL ) ( 1 )( 1 ) Γ Γ Γ Γ 11 L 1 1 L (3.1) Monika Bhattacharya 89

10 The three special cases of Power Gain (G T ) evaluated for a microwave amplifier is discussed as follows: (i) Matched Transducer Power Gain (G TM ) is achieved when both the input and output networks are perfectly matched to the source and the load impedance respectively such that Γ = Γ L = which gives: GTM 1 = (3.) Therefore, the forward transmission coefficient ( 1 ) determines the maximum power gain obtainable from a microwave amplifier circuit under perfectly matched conditions. (ii) Unilateral Transducer Power Gain (G TU ) is essentially the forward power gain in a microwave amplifier with feedback, having its reverse feedback power gain set to zero, i.e., The term 1 =, and is expressed as: G TU ( 1 Γ ) 1 Γ 11 ( 1 Γ ) ( 1 Γ L ) = 1 (3.3) 1 Γ 1 Γ 11 1 ΓL (denoted as G ) and the term 1 Γ L ( ) L (denoted as G L ) in the above expression represent the gain or loss produced by the matching or mismatch of the input and output circuits respectively. Therefore, G s represents the degree of matching or mismatch between Γ and 11. It is considered as the input gain block in which decreasing the mismatch between Γ and 11 can be thought of as providing gain. imilarly, G L represents the degree of matching or mismatching between Γ L and and is considered as the output gain block. (iii) Maximum Unilateral Transducer Power Gain (G TUmax ) is obtained when the input impedance (Z IN ) of the active two port network is conjugately matched with the source impedance (Z ) and similarly the output impedance (Z OUT ) of the 9 Monika Bhattacharya

11 active two port network is conjugately matched with the load impedance (Z L ) such that Γ = 11 * and Γ L = *. Then, G TUmax = 1 ( 1 11 )( 1 ) (3.4) where, ( ) 1 represents the maximum increase in gain due to matching of 1 11 the input port, ( ) 1 represents the maximum increase in gain due to 1 matching of the output port and 1 represents the gain contribution of the active network Maximum Available Power Gain (G amax ) and Maximum table Gain (G ms ) The available power gain (G a ) of a microwave amplifier is defined as the ratio of the power available from the network (P AVN ) to the power available from the source (P AV ), expressed as [Gonzalez84, Liao86]: G a 1 Γ AVN 1 1 AV OUT P = = P Γ Γ which is derived from the condition P AVN = P L, when, Γ L = Γ = + * 1 1 OUT 1 11 Γ Γ * Maximum Available Power Gain (G amax ), which occurs for the simultaneous conjugate match at the input and the output port is then evaluated as: G K K ( ) a max = (3.5) 1 where, K = > 1 (for unconditional stability) 1 1 with = < 1 Monika Bhattacharya 91

12 Maximum table Gain (G ms ) is then evaluated as the maximum gain available from the microwave amplifier just before it becomes unstable, i.e., at K=1, given as: G ms 1 = (3.6) 1 For a microwave amplifier to be unconditionally stable, K>1 with <1 Therefore, the physical significance of K which is regarded as the tability Factor is that, it determines the maximum frequency upto which the microwave amplifier is stable. Maximum table Gain (G ms ) forms a very important figure of merit with regard to microwave amplifier design. High value of G ms is desirable in the frequency range of interest for a given application Operating Power Gain (G P ) The operating power gain (G P ) of a microwave amplifier is defined as the ratio of the power delivered to the load (P L ) to the power input to the network from the source (P IN ) as [Gonzalez84, Liao86]: G P 1 1 Γ L 1 IN 1 IN 1 11 P = = (3.7) P Γ Γ which is derived from the condition P AV = P IN, when, Γ = Γ = + * 1 1 IN 11 1 ince, P IN P AV, the operating power gain (G P ) is always greater than or equal to the transducer power gain Maximum Unilateral Power Gain (G U ) It is the highest possible gain that an active port can achieve and is greater than any of the other power gains earlier discussed including the Transducer Power Gain, Operating Power Gain and the Available Power Gain. It is vital figure of merit with regard to the maximum frequency of operation of the microwave amplifier and is often quoted by the transistor manufacturers in the commercial market. It is given as [Kasemsuwan97]: Γ Γ L L * 9 Monika Bhattacharya

13 G U = K Re (3.8) Maximum Frequency of Oscillation (f max ) is evaluated as the frequency at which the Unilateral Power Gain is unity or db. Therefore, it is an indicator of an ultimate frequency limit of the device. With respect to the microwave amplifier design, the maximum power gain obtainable in conjugately matched conditions is more important than the short circuited current gain. This makes Maximum frequency of Oscillation (f max ) as an even more important figure of merit than the Unity-gain cut-off frequency (f T ). 3. CATTERING PARAMETER BAED MODELING APPROACH FOR RF PERFORMANCE AEMENT The modeling approach followed for the evaluation of scattering () parameters and power gains of InAlAs/InGaAs single-gate (G) and symmetric tied-geometry double-gate (DG) HEMT considered in the analysis can be summarized as: Development of a charge control based analytical model which accurately predicts the variation of sheet-carrier concentration (n s ) in the channel with the applied gate-source voltage (V gs ). Evaluation of drain current and the various intrinsic parameters of the smallsignal equivalent circuit including the transconductance (g m ), gate capacitances (C gs and C gd ) and the drain conductance (g d ). The short circuit admittance (Y) parameters which are commonly used for the characterization of two-port networks are then obtained in terms of these equivalent circuit elements. However, at microwave frequencies, experimental investigation of the device generally involves the measurement of scattering () parameters. Therefore, with respect to the device performance analysis at frequencies in the microwave regime and above, characterization of the microwave active Monika Bhattacharya 93

14 circuits in terms of scattering () parameters is more relevant. Therefore, the intrinsic Y parameters evaluated in terms of the equivalent circuit elements are converted into the parameters using standard transformation relations. For more accurate evaluation of the scattering () parameters that matches closely with the experimentally measured -parameters, the effect of the various extrinsic/parasitic elements including the gate-metallization resistance (R g ), source and drain contact resistances (R s and R d respectively), the contact pad capacitances at the gate and drain electrodes (C pg and C pd respectively) and the parasitic inductances at the source, drain and gate electrodes (L s, L g and L d respectively) are also included. These parasitic elements become very significant at ultra-high frequencies, and therefore, must be incorporated in the active device model. In terms of the extrinsic scattering () parameters, the various power gains including the Unilateral Power Gain (G U ) and the Maximum table Gain (G ms ) are evaluated. The results, thereby obtained using the analytical model are also compared and found to correspond well with the experimental measurements as well as with the ATLA device simulation results [ATLA9] Development of mall ignal Equivalent Circuit For ymmetric Tied-Gate Geometry DG-HEMT The extrinsic small signal equivalent circuit model for a conventional single-gate HEMT is shown in Fig. 3.5 [Guru3, Nagatomo93, Eskandarian88]. The elements inside the dashed box represent the intrinsic part of the equivalent circuit comprising of the gate-capacitances (C gs and C gd ), drain conductance (g d ), the drain-source capacitance (C ds ) and the current generator ( y = g exp( jωτ ) ) in which g m is the m transconductance and τ is the transit time of the velocity saturated carriers across the gate-length. R gd is the gate-drain (feedback) resistance which is included in the equivalent circuit model to ensure a smooth transition from cold model to operating m 94 Monika Bhattacharya

15 points in the saturation region because it causes the forward transfer conductance to have a real part (i.e. Re (y 1 ) is not zero). Fig Extrinsic small-signal equivalent circuit model for G-HEMT Most of these elements have already been explained and derived using the charge control based analytical model presented in the previous chapter. In addition to these intrinsic small-signal equivalent circuit elements, the various parasitic extrinsic elements are also shown, the physical significance of each of which can be illustrated as follows [Golio91]: Parasitic Inductances (L s, L d and L g ) associated with the source, drain and gate electrodes respectively arise primarily from the contact pads deposited on the device surface. Therefore, their values are dependent on the surface features of the device. L g and L d are of the order of 5 to 1 ph with L s being smaller with value of around 1 ph. L g is generally the largest of the three. These inductances exist in addition to any parasitic bond wire inductances or parasitic package inductances which must be accounted for in the device model. Parasitic resistances (R s and R d ) associated with the source and the drain represents the ohmic contact resistance as well as any bulk resistance leading up to the active channel. The parasitic resistance (R g ) associated with the gate results from the metallization resistance of the schottky gate-contact. Monika Bhattacharya 95

16 Parasitic capacitances (C pg and C pd ) represent the contact pad capacitances associated with gate and drain electrodes. The following section presents the development of the extrinsic small signal equivalent circuit for a symmetric tied-gate geometry DG-HEMT. Fig. 3.6 shows the resultant equivalent circuit of a DG-HEMT (the elements corresponding to the equivalent circuit of the two heterostructures are differentiated by notations 1 and ). Fig Equivalent circuit of the DG structure with both the gates tied The structure is symmetric (dimensions and doping levels of the corresponding layers in the two heterostructures is the same) and in addition to this the same voltage is applied to both the gate electrodes such that they can be considered to be tied together as illustrated in the figure. As a result of this, the following assumptions can be made: R i1 = R i = R i, C gs1 = C gs = C gs, R gd1 = R gd = R gd, C gd1 = C gd = C gd, g d1 = g d = g d. Also, y m1 = y m = y m. 96 Monika Bhattacharya

17 In addition to this, since the contact properties at both the gates are also the same, L g1 = L g = L g and C pg1 = C pg =C pg ince, the voltage applied to both the gates is equal, the voltage at the corresponding nodes 1 and 1, and, 3 an 3, 4 and 4, 5and 5, 6 and 6 & 7 and 7 are the same. Therefore, the resultant equivalent circuit is obtained as shown in Fig in which R i = R i /, C gs =C gs, R gd = R gd /, C gd = C gd, g d = g d and y m = y m. Considering the extrinsic elements, L g = L g /, R g = R g / and C pg = C gd. Fig Resultant Equivalent circuit assuming symmetric structure with tied-gate geometry Therefore, due to the two gates being tied together, gate metallization resistance (R g ) in a symmetric tied geometry double-gate structure is nearly half of that for a G- HEMT which leads to improved Maximum frequency of Oscillation (f max ). This is because f max which is regarded as the maximum frequency upto which power gain is achievable from a microwave amplifier is essentially extrinsic parameter dependent, given as [Liechti76]: f = T max 1 ( r1 + ft r ) f (3.9) where, f T is Unity Gain cut-off frequency defined in terms of transconductance (g m ) and gate capacitances (C gs and C gd ) as: f T = π g m ( Cgs + Cgd ) (3.1) Monika Bhattacharya 97

18 ; ( ) r = Rg Rs Ri g and r d = π RgC (3.11) gd where, g d is the drain conductance, R i is the input channel resistance and R s and R g are the parasitic resistances associated with the source and gate, Therefore, lower gate metallization (R g ) in a DG structure results in higher f max. In addition to this, the drain-source capacitance (C ds ) which represents the carrier injection into the buffer layer in the equivalent circuit of G-HEMT does not form the part of the equivalent circuit of DG-HEMT. This is because in a DG structure, the buffer layer is not present which leads to the elimination of the injection of carriers into the buffer layer. 3.. Evaluation of hort- Circuit Admittance (Y) Parameters The equivalent circuit model used for the evaluation of intrinsic short circuit admittance (Y) parameters of symmetric tied-gate geometry double-gate HEMT is shown in Fig As shown in the figure, the control voltage (V gs ) is considered to be defined across the gate-source capacitance (C gs ) only as it is found to be more suitable judging from the lower frequency dependence of the equivalent circuit parameters and better agreement between the calculated and measured two port (Y or ) parameters [Yanagawa96] as compared to the Curtice model [Curtice84] in which the control voltage is defined across both C gs and R i. In addition to this, the effect of the gate-drain (feedback) resistance (R gd ) has also been neglected in the evaluation of intrinsic Y parameters. Fig Intrinsic Equivalent Circuit Model for the evaluation of Y parameters 98 Monika Bhattacharya

19 Therefore, from two-port network analysis of the above shown equivalent circuit model, the intrinsic short-circuit admittance (Y) parameters are evaluated in terms of the various circuit elements and are given below [Berroth9, Roblin87, Dambrine88, Gonzalez87, hirakawa95]. Input Admittance y 11 ω C R C I1 gs i gs y11 = = + jω + Cgd V1 D D V = (3.1a) Reverse Transfer Admittance y 1 I = = (3.1b) 1 y1 jω Cgd V V = 1 Forward Transfer Admittance y 1 y I g exp( jωτ ) m 1 = = V1 1+ jωc V gsr = i jωc gd (3.1c) Output Admittance y I = = + (3.1d) y gd jωcgd V V = 1 where, D = + C R 1 ω gs i For the computation of various small-signal equivalent circuit elements (in terms of which the Y parameters are obtained), the charge control model proposed in the previous chapter is employed with donor-layer doping concentration, N d =.5 x 1 5 m -3, donor-layer thickness, d a =5 Ǻ, gate-length, L g =1 nm and channel width, Z =1 µm). The other structural and device parameters are the same as considered in the previous chapter. In the evaluation of Y parameters for the G-HEMT, the effect of C ds (drain-source capacitance =.4 pf [Guru3]) is also included which contributes to the output admittance (Y ). In the following section, the frequency dependence of the various intrinsic short circuit admittance (Y) parameters is discussed with comparison between the singlegate (G) and double-gate (DG) HEMT. Monika Bhattacharya 99

20 Fig. 3.9 shows the variation of real and imaginary parts of input admittance Y 11 with frequency for single-gate and double-gate HEMT. For both G as well as DG-HEMT, the real part of Input admittance (Y 11 ) increases parabolically with frequency as shown in Fig. 3.9 (a) which is attributed to its square dependence on the angular frequency (ω). imilarly, as shown in Fig. 3.9 (b), the imaginary part of input admittance (Y 11 ) increases linearly with frequency due to its direct proportionality with ω. In addition to this, a lower value of Re (Y 11 ) is also observed for a higher gate-source voltage from Fig. 3.9 (a) which occurs due to lower value of gate-source capacitance, while, as shown in Fig. 3.9 (b), Im(Y 11 ) is higher for higher gate-source voltage due to higher gate-drain capacitance. Both real as well as imaginary parts of Y 11 are higher for the DG-HEMT as compared to the G-HEMT due to higher value of gate-capacitances. (a).1 (b).18.8 o V gs = V V gs = -.1 V DG Re(Y11).6.4 DG Im(Y11) o V gs = V V gs = -.1 V.6. G Frequency (GHz).4. G Frequency (GHz) Fig Variation of (a) Real part and (b) Imaginary part of Input Admittance (Y 11 ) with frequency at V ds =.1 V (model) The variation of real and imaginary parts of output admittance Y with frequency is shown in Fig From Fig. 3.1 (a), the real part of output admittance (Y ) is observed to be independent of frequency and equal to the drain-conductance (g d ) for both DG as well as G-HEMT. As also shown in the figure, the real part of output admittance (Y ) is higher for a higher gate-source voltage due to higher drainconductance. Im(Y ) which is equal to jωc gd increases linearly with frequency as shown in Fig. 3.1 (b). The imaginary part of output admittance (Y ) is higher for a 1 Monika Bhattacharya

21 higher gate-source voltage due to higher gate-drain capacitance (C gd ). Higher values of Re(Y ) and Im(Y ) for the DG-HEMT as compared to its G counterpart is attributed primarily to higher drain-conductance (g d ) and higher gate-drain capacitance (C gd ) respectively. (a) Re(Y) o V gs = V V gs = -.1 V DG G Frequency (GHz) (b).16 Im(Y) V gs = V o V gs = -.1 DG G Frequency (GHz) Fig Variation of (a) Real part and (b) Imaginary part of Output Admittance (Y ) with frequency (model) Fig (a) shows the variation of imaginary part of reverse transfer admittance (Y 1 ) with frequency. Im(Y 1 ) whose magnitude is equal to admittance associated with the gate-drain (feedback) capacitance increases linearly with frequency. The magnitude of Im(Y 1 ) is observed to be higher for double-gate HEMT as compared to the single-gate HEMT due to higher value of the gate-drain (feedback) capacitance. Fig (a) also shows a higher magnitude of Im(Y 1 ) for a higher gate-source voltage which again results due to higher value of gate-drain capacitance (C gd ). Real part of reverse transfer admittance is zero, i.e., Re(Y 1 )= because the gate-drain resistance (R gd ) has been neglected and not considered in the present equivalent circuit model. Monika Bhattacharya 11

22 (a) -. G Im(Y1) o V gs = V V gs = -.1 V DG Frequency (GHz) (b).16 (c) Re(Y1) o V gs = V V gs = -.1 V DG G Frequency (GHz) Im(Y1) V gs = V o V gs = -.1 DG G Frequency (GHz) Fig Variation of (a) Imaginary part of Reverse Transfer Admittance (Y 1 ), (b) Real part of Forward Transfer Admittance (Y 1 ) and (c) Imaginary part of Forward Transfer Admittance (Y 1 ) with frequency Fig (b) shows the frequency variation of the real part of forward transfer admittance (Y 1 ) for both single-gate and double-gate HEMT. Re(Y 1 ) is higher for the DG-HEMT as compared to the G-HEMT on account of improved transconductance (g m ). Figure also shows lower value of Re(Y 1 ) for a higher gatesource voltage. The variation of imaginary part of forward transfer admittance (Y 1 ) with frequency is shown in Fig (c). The magnitude of Im(Y 1 ) increases linearly with frequency. A higher magnitude of Im(Y 1 ) is obtained at a higher gate-source voltage which occurs due to higher value of g m and C gd. The magnitude of Im(Y 1 ) is 1 Monika Bhattacharya

23 also observed to be higher for the DG-HEMT over the G-HEMT which is again attributed to higher transconductance (g m ) and higher gate-drain capacitance (C gd ) Evaluation of Extrinsic cattering () Parameters The characterization of two port active networks in terms of the scattering () parameters is more relevant at frequencies in the microwave regime and above which forms the foundation of microwave active circuit design and the evaluation of its power gain and stability performance. Experimental measurement of -parameters can be performed with great accuracy at frequencies even greater than 6 GHz due to the availability of sophisticated network analyzers. The accuracy of the measurements, however, largely depend on the ability to calibrate the system. For the purpose of microwave active circuit design, an analytical physics based device model which is reasonably accurate in the desired frequency bandwidth is still desirable, so that the scattering parameters and power gains evaluated using the model correspond well with the measured results. uch a model enables optimization of the structural and material parameters of the active device in order to obtain the best power gain and high-frequency performance and also cater to the principle concerns regarding the design of small-signal microwave active integrated circuits which can be summarized as: stability (tendency to oscillate) frequency response (unity gain cut-off frequency(f T ) and power gain cutoff frequency (f max ) ) power gain input and output reflection coefficient over a specified bandwidth minimum noise figure The following section presents a procedure for the evaluation of the extrinsic scattering () parameters for symmetric tied-geometry DG-HEMT incorporating the effect of the various extrinsic elements including the contact resistances associated with the source and drain electrodes (R s and R d respectively), metallization resistance of the gate contact (R g ), parasitic inductances associated with the source, gate and drain electrodes (L s, L g and L d respectively) and the contact pad capacitances Monika Bhattacharya 13

24 associated with the gate and drain electrodes (C pg and C pd respectively). The corresponding extrinsic equivalent circuit model for the device is also shown in Fig. 3.1 and the values of the various extrinsic elements used in the model are given in Table 3.. Fig Extrinsic mall ignal Equivalent Model of ymmetric Tied Geometry InAlAs/InGaAs DG-HEMT Table 3. Values of Extrinsic Elements for InAlAs/InGaAs DG-HEMT (for channel width Z=1 µm) ELEMENT R g R s R d L s, L d & L g VALUE [Vasallo7, Mahon9] 1.7 Ω 5.8 Ω 3. Ω., 67.5 and. (ph) respectively C pg and C pd.9 and.95 (ff) respectively For the evaluation of the extrinsic - parameters, a number of steps are followed, the complete flow chart of which is summarized in Fig [Dambrine88]. 14 Monika Bhattacharya

25 Intrinsic y to Intrinsic s s 11int s s 1int s 1int int Intrinsic s to Extrinsic z z 11int+R s+r g+jωl s z 1int+R s+jωls z 1int+R s+jωl s z int+r s+r d+jωls Extrinsic z to Extrinsic y y 11ext +jωc pg y1ext y y +jωc 1ext ext pd z 11ext +jωl g z1ext z z +jωl 1ext ext d Extrinsic y to Extrinsic z G G C pg L g C pg G Intrinsic tep 1 D tep G D R g R d R L R g R L R d tep 3 D C pd tep 4 R g R d L d Extrinsic C pd R D Extrinsic z to Extrinsic s L Fig Flow chart for the conversion of intrinsic (Y) parameters to extrinsic () parameters The intrinsic y-parameters are first converted into scattering () parameters. parameters are then converted into open circuit impedance (Z) parameters for the incorporation of the effect of source, gate and drain contact resistances (R s, R g & R d respectively) and the source parasitic inductance (L s ) as shown in step of the flow chart. The resultant extrinsic Z-parameters are then converted into short circuit admittance (Y) parameters to include the effect of gate and drain contact pad capacitances (C pg and C pd respectively) as shown in step 3 of the flow chart These extrinsic Y parameters are then again converted back to Z parameters, also including the effect of the gate and drain parasitic inductances (L g and L d respectively) as shown in step 4. The final step involves conversion of the resultant extrinsic Y parameters to extrinsic parameters. The conversions between the Y, Z and parameters are performed using the conversion table given in [Gonzalez84]. Monika Bhattacharya 15

26 The following section illustrates the frequency dependence of the set of four extrinsic () scattering parameters, namely, Input Reflection Coefficient ( 11 ), Reverse Transmission Coefficient ( 1 ), Forward Transmission Coefficient ( 1 ) and Output Reflection Coefficient ( ). The analytical results are compared and observed to show good agreement with the device simulation results in the considered frequency range. (a) Re( 11 ) Im( 11 ) Frequency ( GHz ) (b) Re( ) Im( ) Frequency ( GHz ).1 line-model symbol-simulated Frequency ( GHz ).1 line-model symbol-simulated Frequency ( GHz ) Fig (a) Variation of Re( 11 ) and (inset) Im( 11 ) with frequency, (b) Variation of Re( ) and (inset) Im( ) with frequency at V ds =.1 V and V gs = V [Bhattacharya11] Figure 3.14 (a) shows the frequency variation of real and imaginary parts of Input Reflection Coefficient ( 11 ). The magnitude of input reflection coefficient 11 is related to the mismatch at the input port. The variation of real and imaginary part of output reflection coefficient ( ) with frequency is also shown in Fig (b). The magnitude of the output reflection coefficient indicates the degree of mismatch at the output port. The frequency variation of real and imaginary parts of Reverse Transmission Coefficient ( 1 ) is shown in Fig (a). The magnitude of Reverse Transmission Coefficient 1 is related to the reverse power gain indicative of the feedback. Fig (b) shows the frequency dependence of the real and imaginary part of the Forward Transmission Coefficient ( 1 ) which is the main contributor to the maximum power gain achievable from the device. The maximum unilateral transducer power gain that can be obtained from the device when the input and output 16 Monika Bhattacharya

27 ports are conjugately matched is given as 1. Therefore, higher 1 indicates higher achievable power gain. (a). line-model symbol-simulated (b) -.4 line-model symbol-simulated Re( 1 ) Im( 1 ) Frequency ( GHz ) Frequency ( GHz ) Re( 1 ) Im( 1 ) Frequency ( GHz ) Frequency ( GHz ) Fig (a) Variation of Re( 1 ) and (inset) Im( 1 ) with frequency, (b) Variation of Re( 1 ) and (inset) Im( 1 ) with frequency at V ds =.1 V and V gs = V [Bhattacharya11] The frequency variation of the various power gains which are extracted in terms of these extrinsic -parameters is analyzed in this section. Fig shows the dependence of Unilateral Power Gain (G U ) which is regarded as the highest possible gain that an active port can achieve at a particular frequency. The frequency variation curve of G U obtained using the analytical model shows a steep exponential decrease from the peak value of 35 db to a value as low as 7 db at 5 GHz beyond which the rate of fall of G U with frequency decreases significantly followed by the tail region in which the magnitude of G U stays above but close to db. This tail region was numerically computed to extend till 65 GHz which forms the highest frequency up to which the power gain can be obtained from the device. A similar trend is observed in the frequency variation curve obtained using device simulation in which also G U initially decreases exponentially from the peak value of around 37.5 db down to 6. db at 5 GHz after which the decrement of G U with frequency slows down. The tail region for the simulated curve is extrapolated to db ( G U = 1) which gives us the value of the Maximum Frequency of Oscillation (f max ) equal to 59 GHz. The value of f max obtained from the analytical model is around 65 Monika Bhattacharya 17

28 GHz which matches closely with the value of 59 GHz obtained using the device simulation. Unilateral Power Gain (GU) (db) GU (db) V gs = V V ds =.5 V line-model symbol-experimental [Vasallo7 ] Frequency (GHz) V gs = V V ds =.1 V line-model symbol-simulated Frequency (GHz) Fig Variation of Unilateral Power Gain (G U ) with frequency at V gs = V and V ds =.1 V and (inset) at V ds =.5 V with experimental verification [Bhattacharya11] Fig (inset) shows the variation of the Unilateral Power Gain (G U ) with frequency (log scale) at V ds =.5 V which is compared and observed to be in good agreement with the experimental results further validating the proposed model. The frequency variation of Maximum table Gain (G ms ) obtained using the proposed analytical model is shown in Fig (a) which is also compared and found to show good agreement with that obtained using device simulation. As shown in Fig (a) (inset), the peak value of G ms obtained analytically is 15 db, while, that obtained through device simulation is 13.8 db. From both the frequency variation curves, obtained analytically as well as that obtained through simulation, a steep decrease in G ms is observed for low frequencies up to around 1 GHz. Thereafter, the decrement of G ms with frequency occurs at a much slower rate maintaining its value to much greater than db for frequencies even greater than 1 GHz. This indicates good stability performance exhibited by the device making it suitable for RF and low-noise amplifier applications. 18 Monika Bhattacharya

29 (a) 1 16 Maximum table Gain (db) Gms (db) line-model symbol-simulated Frequency ( GHz ) Frequency ( GHz ) (b) 1 Max. Unilateral Transducer Power Gain (db) GTUmax (db) line-model symbol-simulated Frequency ( GHz ) Frequency ( GHz ) Fig Variation of (a) Maximum table Gain (G ms ) and (b) Maximum Unilateral Transducer Power Gain (G TUmax ) with frequency at V gs = V and V ds =.1 V [Bhattacharya11] Fig (b) shows the variation of the Maximum Unilateral Transducer Power Gain (G TUmax ) with frequency. The frequency variation of G TUmax obtained using the analytical results shows a high peak value of around 41 db which matches closely with the peak value of 37 db obtained from device simulation. The incorporation of the various parasitic elements in the equivalent circuit model has resulted in accurate evaluation of scattering () parameters and power gains that exhibit good agreement with the device simulation results as well as with the experimental measurements. Monika Bhattacharya 19

30 3.3 UMMARY The evaluation of the scattering () parameters for symmetric tied-gate geometry InAlAs/InGaAs DG-HEMT is presented in this chapter which is followed by a comprehensive RF performance assessment of the device in terms of the major figures of merit including Unilateral Power Gain which determines the maximum power gain achievable from the device, Maximum Frequency of Oscillation which determines the ultimate frequency limit of the device and the Maximum table Gain (G ms ) in terms of which the stability performance of the device is judged. In the equivalent circuit model employed for the analysis, the effect of the various extrinsic elements including the parasitic resistances associated with the source, gate and drain electrodes which become significant at ultra-high frequencies has also been incorporated. Better correspondence between the results obtained using the analytical model with the device simulation results as well as with the experimental measurements has established the validity of the proposed analytical model incorporating various extrinsic elements. uch a physics based model, thereby enables a complete analysis of the device performance in terms of power gain and stability which is inevitable for the exploration of its potential for low noise microwave amplifier design. This accurate scattering parameter based model is followed by a comprehensive charge control based approach for the noise performance assessment of the device which is very important for low noise millimeter-wave frequency applications. 11 Monika Bhattacharya

31 3.4 REFERENCE [ATLA9] ATLA Device imulator, ILVACO International, 9. [Berroth9] M. Berroth, R. Bosch, Broad-band determination of the FET small-signal equivalent circuit, IEEE Transactions on Microwave Theory and Techniques, Vol. 38, no. 7, pp , 199. [Bhattacharya1] M. Bhattacharya, J. Jogi, R.. Gupta and M. Gupta, Impact of Doping concentration and Donor- layer thickness on the dc characterization of symmetric Double-gate and ingle-gate InAlAs/InGaAs/InP HEMT for nanometer gate dimension-a comparison, IEEE TENCON 1 Conference Proceedings, pp , 1. [Bhattacharya11] M. Bhattacharya, J. Jogi, R.. Gupta and M. Gupta, cattering parameter based modeling and simulation of symmetric tied-gate InAlAs/InGaAs DG-HEMT for millimeter-wave applications, olid tate Electronics, Vol. 63, no. 11, pp , 11. [Curtice84] [Dambrine88] [Eskandarian88] [Golio8] [Golio91] W. R. Curtice and R. L. Camisa, elf-consistent GaAs FET Models for Amplifier Design and Device Diagnostics, IEEE Transactions on Microwave Theory and Techniques, Vol. 3, no. 1, G. Dambrine, A. Cappy, F. Heliodore and E. Playez., A new method for determining the FET small-signal equivalent circuit, IEEE Transactions on Microwave Theory and Techniques, Vol. 36, no. 7, pp , A. Eskandarian, Determination of the small signal parameters of an AlGaAs/GaAs MODFET, IEEE Transactions on Electron Devices, Vol. 35, no.11, pp , M. Golio, RF and Microwave Passive and Active Technologies, CRC Press, 8. J.M. Golio, Microwave MEFETs and HEMTs, Artech House,1991. Monika Bhattacharya 111

32 [Gonzalez84] [Gonzalez95] [Guru3] [Kasemsuwan] [Ladbrooke89] [Liao86] G. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design, Prentice Hall, T. Gonzalez and D. Pardo, Monte Carlo determination of the intrinsic small-signal equivalent circuit of MEFETs, IEEE Transactions on Electron Devices., Vol. 4, no. 4, pp.65-67, V. Guru, J. Jogi, M. Gupta, H.P. Vyas, R.. Gupta, An improved intrinsic small-signal equivalent circuit model of delta-doped AlGaAs/InGaAs/GaAs HEMT for microwave frequency applications, Microwave and Optical Technology Letters, Vol. 37, no. 5, pp , 3. V. Kasemsuwan and M. A. El Nokali, "A microwave model for high electron mobility transistors", IEEE Transactions on Microwave Theory and Techniques, Vol. 45, no. 3, pp. 4-47, P.H. Ladbrooke, MMIC Design: GaAs FETs and HEMTs, Artech House, London, Y. Liao, Microwave Circuit Analysis and Amplifier Design, Prentice Hall, [Liechti76] C. A. Liechti, Microwave Field-Effect Transistors-1976, IEEE Transactions on Microwave Theory and Techniques, Vol. 4, no. 6, pp. 79-3, [Mahon9].J. Mahon, D.J. kellern and F. Green, A Technique for Modelling - parameters for HEMT tructures as a Function of Gate Bias, IEEE Transactions on Microwave Theory and Techniques, Vol. 4, no. 7, pp , 199. [Nagatomo93] K. Nagatomo, Y. Daido, M. himizu and N. Okubo, GaAs MEFET Characterization Using Least quares Approximation by Rational Functions, IEEE Transactions on Microwave Theory and Techniques, Vol. 41, no., pp , Monika Bhattacharya

33 [Pozar5] D.M. Pozar, Microwave Engineering, John Wiley & ons, Inc., 5. [Roblin87] [hirakawa95] P. Roblin,. Kang, A. Ketterson and H. Morkoc, Analysis of MODFET Microwave Characteristics, IEEE Transactions on Electron Devices, Vol. 34, no. 9, pp , K. hirakawa, H. Oikawa. T. himura, Y. Kawasaki, Y. Ohashi, T. aito and Y. Daido, An Approach to Determining an Equivalent Circuit for HEMT s, IEEE Transactions on Microwave Theory and Techniques, Vol. 43, no. 3, pp , [Vasallo7] B.G. Vasallo, N.Wichmann,. Bollaert, Y. Roelens, A. Cappy, T. Gonzalez, D. Pardo, and J. Mateos, Comparison Between the Dynamic Performance of Double- and ingle- Gate InP Based HEMTs, IEEE Transactions on Electron Devices, Vol.54, no. 11, 7. [Vasallo8] B.G. Vasallo, N.Wichmann,. Bollaert, Y. Roelens, A. Cappy, T. Gonzalez, D. Pardo, and J. Mateos, Comparison Between the Noise Performance of Double- and ingle- Gate InP Based HEMTs, IEEE Transactions on Electron Devices, Vol.55, no. 6, pp , 8. [Wichmann4] N. Wichmann,I. Duszynski,. Bollaert, X. Wallart, J. Mateos and A. Cappy, 1nm InAlAs/InGaAs Double-Gate HEMT using transferred substrate, IEEE International Electron Devices Meeting, pp , 4. [Yanagawa96]. Yanagawa, H. Ishihara and M. Ohtomo, Analytical Method for Determining Equivalent Circuit Parameters of GaAs FET s, IEEE Transactions on Microwave Theory and Techniques, Vol. 44, no. 1, Monika Bhattacharya 113