1.0 THz GaN IMPATT Source: Effect of Parasitic Series Resistance

SRIKANTA PAL

doi:10.1007/S10762-018-0509-Z

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1.0 THz GaN IMPATT Source: Effect of Parasitic Series Resistance

SRIKANTA PAL

Journal of Infrared, Millimeter, and Terahertz Waves

https://doi.org/10.1007/S10762-018-0509-Z

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21 pages

Abstract

The degradation of high-frequency characteristics of a 1.0-THz double-drift region (DDR) impact avalanche transit time (IMPATT) diode based on wurtzite gallium nitride (Wz-GaN), due to the influence of parasitic series resistance, has been investigated. A twodimensional (2-D) large-signal (L-S) simulation method based on a non-sinusoidal voltage excitation (NSVE) model has been used for this purpose. A comprehensive model of series resistance has been developed by considering the influence of skin effect, and the said model has been incorporated in the 2-D L-S simulation for studying the effect of RF power output and DC to RF conversion efficiency of the device. Results indicate 24.2-35.9% reduction in power output and efficiency due to the RF power dissipation in the positive series resistance. However, the device can still deliver 191.7-202.9 mW peak RF power to the load at 1.0 THz with 8.48-6.41% conversion efficiency. GaN IMPATT diodes are capable of generating higher RF power at around 1 THz than conventional diodes, but the effect of parasitic series resistance causes havoc reduction in power output and efficiency. The nature of the parasitic resistance is studied here in the level of device fabrication and optimization, which to our knowledge is not available at present.

Key takeaways
AI

The study reveals a 24.2-35.9% reduction in RF power output due to parasitic series resistance.
The 1.0-THz GaN IMPATT diode delivers 191.7-202.9 mW peak RF power with 8.48-6.41% efficiency.
A comprehensive series resistance model incorporates the skin effect and impacts high-frequency performance.
GaN IMPATT diodes outperform other conventional diodes in THz power generation capabilities.
The research aims to enhance understanding of series resistance in GaN IMPATT diode fabrication and optimization.

1.0 THz GaN IMPATT Source: Effect of Parasitic Series Resistance Arindam Biswas 1 & Sayantan Sinha 1 & Aritra Acharyya 2 & Amit Banerjee 3 & Srikanta Pal 4 & Hiroaki Satoh 3 & Hiroshi Inokawa 3 Received: 9 May 2018 /Accepted: 14 June 2018 /Published online: 4 July 2018 # Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract The degradation of high-frequency characteristics of a 1.0-THz double-drift region (DDR) impact avalanche transit time (IMPATT) diode based on wurtzite gallium nitride (Wz- GaN), due to the influence of parasitic series resistance, has been investigated. A two- dimensional (2-D) large-signal (L-S) simulation method based on a non-sinusoidal voltage excitation (NSVE) model has been used for this purpose. A comprehensive model of series resistance has been developed by considering the influence of skin effect, and the said model has been incorporated in the 2-D L-S simulation for studying the effect of RF power output and DC to RF conversion efficiency of the device. Results indicate 24.2–35.9% reduction in power output and efficiency due to the RF power dissipation in the positive series resistance. However, the device can still deliver 191.7–202.9 mW peak RF power to the load at 1.0 THz with 8.48–6.41% conversion efficiency. GaN IMPATT diodes are capable of generating higher RF power at around 1 THz than conventional diodes, but the effect of parasitic series resistance causes havoc reduction in power output and efficiency. The nature of the parasitic resistance is studied here in the level of device fabrication and optimization, which to our knowledge is not available at present. J Infrared Milli Terahz Waves (2018) 39:954–974 https://doi.org/10.1007/s10762-018-0509-z * Arindam Biswas mailarindambiswas@yahoo.co.in * Hiroshi Inokawa inokawa.hiroshi@shizuoka.ac.jp 1 Department of Electronics and Communication Engineering, Asansol Engineering College, Asansol, West Bengal 713305, India 2 Department of Electronics and Communication Engineering, Cooch Behar Government Engineering College, Harinchawra, Ghughumari, West Bengal 736170, India 3 Research Institute of Electronics, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu 432-8011, Japan 4 Department of Electronics and Communication Engineering, Birla Institute of Technology, Mesra, Ranchi, Jharkhand 835215, India

Keywords Gallium nitride . IMPATT . Large signal . Series resistance . Skin effect . Terahertz 1 Introduction The terahertz (THz) frequency spectrum (0.3–10.0 THz) possesses several advantages over micro- wave (1.0–30.0 GHz) and millimeter-wave (30.0–300.0 GHz) spectrums; the most important advantages of THz waves over microwaves and millimeter waves are a greater resolution and a wider bandwidth. Recent development of semiconductor materials science and advanced lithogra- phy technologies for fabrication of integrated circuits has created extraordinary possibilities and widespread interest in THz technology for various fascinating applications [1]. From ultrahigh-speed wireless communications, biomedical screening [2, 3], non-contact and remote inspection of explosives and concealed weapons [4–6], food diagnostics [ 7], interstellar medium and planetary atmospheres, etc. could be realized with THz technology [8, 9]. Mainly the frequency region ~ 1 THz is important for non-contact and non-destructive sensing as it yields high-resolution images and may analyze the deep interior of materials and biomedical samples as it is non-ionizing because of low photon energies. Some interesting developments have emerged in the THz technology in the last decade, e.g., high-power THz sources [10], room-temperature detector [11–13], real-time imaging [14, 15], etc. However, the present sources and detectors are still insufficient in terms of reliability, sensitivity, and speed of measurements, and an extensive study and development of the sources, detectors, optical elements, and sensing systems are required for commercial and daily life utilization of THz waves. We have reported several and extensive studies on the THz detectors in recent years [16–19]; however, an adequate literature survey did not return a comprehensive information and insights on the development of high-power THz sources at the level of device fabrication and optimization. Some reported efforts on high-power THz radiators are 1.9–2.7 THz cascaded frequency multipliers capable of delivering a few microwatts (μW) of power (output ~ 2–10 μW) [20–24], 0.42–0.97 THz resonant-tunneling-diode (RTD) oscillators (output < 10 μW) [25], etc. Moreover, some solid-state sources such as quantum-cascade lasers (QCLs) [26], high- electron-mobility transistors (HEMTs) [27, 28], heterojunction bipolar transistors (HBTs) [29–33], and impact avalanche transit time (IMPATT) diodes [30–32] have also shown immense potentiality as THz radiators. Among the above-mentioned devices, two-terminal IMPATT diodes based on wide-bandgap (WBG) wurtzite-phase gallium nitride (Wz-GaN) have shown the highest power-delivering capability up to 5.0 THz [34–36]. Simulation results indicate that only GaN IMPATTs are capable of delivering THz power of the order of milliwatts (mW), whereas the power outputs of other solid-state sources mentioned earlier are limited to a few microwatts. However, the generation of THz signal from IMPATT oscillators with appreciable power is a challenging area of research. A schematic illustrating the vertical section of a 1.0-THz Wz- GaN double-drift region (DDR) IMPATT diode designed by Acharyya et al. [34–36] is shown in Fig. 1. The n + -n-p-p + DDR structure as shown in Fig. 1 can be fabricated on single crystal c-plane (1000) sapphire (Al 2 O 3 ) or silicon carbide (SiC) substrate via metalorganic vapor phase epitaxy (MOVPE) or metalorganic chemical vapor deposition (MOCVD) technique [37, 38]. The practical growth conditions may be fixed to (i) chamber pressure, 380 Torr, and (ii) temperature, 1220 °C, and the gaseous-phase sources of gallium (Ga) and nitrogen (N) will be trimethyl gallium (TMG) and ammonia (NH 3 ), respectively [37]. The donor type impurity Si in the form of SiH 4 gas can be introduced with appropriately controlled doses in the reaction J Infrared Milli Terahz Waves (2018) 39:954–974 955

paper, the series resistance of the THz DDR GaN IMPATT diode has been modeled from the 2- D L-S simulation method based on the NSVE model; both the influences of the skin effect [44] and depletion width modulation [45, 46] under the L-S condition have been taken into consideration in the present model. 2 Two-Dimensional Modeling of Series Resistance The cross section of the practical THz DDR IMPATT is circular in shape as shown in Fig. 2. However, for simplicity in the modeling of the device, the cross section has been assumed to be rectangular (specifically it is square shaped) instead of circular. This ensures the use of the Cartesian coordinate system which is more convenient than the cylindrical coordinate system (corresponding to the circular cross section). The equivalent 3-D model of the 1.0-THz GaN DDR IMPATT structure having a rectangular (actually square shaped) cross section has been shown in Fig. 3 which is transformed from the 3-D model of the diode having a circular cross section (Fig. 2). The cross-sectional area of different layers of the diode is more important in the present calculations rather than its actual shape; the dimensions of different layers of the diode having a square-shaped cross section along the x-axis and z-axis have been obtained by keeping the cross-sectional area of those equal to the cross-sectional area of the diode having a circular cross section (i.e., d k 2 = πr k 2 → d k = r k √π, where d k and r k are the lengths of the kth layer of the diode having a square-shaped cross section and radius of the kth layer of the diode having a circular cross section respectively; the values of d k and r k are given in Table 1). The absence of any density gradient of impurities along the z direction leads to no variations of the electric field, electric potential, carrier concentration, and current along that direction (all of them are uniformly distributed along the z direction). Therefore, the 3-D model is further simplified into a 2-D model by omitting the z-axis without loss of any generality; the 2-D model is shown in Fig. 4. The notations and values corresponding to the thickness of p + , p, n, n + , and n + buffer layers (along the y direction) and respective doping concentrations have already been provided in Fig. 1; the Fig. 2 The a side view as well as the b top view of the 3-D model of the 1.0-THz GaN DDR IMPATT structure having a circular cross section J Infrared Milli Terahz Waves (2018) 39:954–974 957

notations and values corresponding to the thickness of the metal layers at the anode and cathode have also been given in Fig. 1. The sapphire substrate has been omitted from Fig. 4, since it does not conduct current. The position of the cathode contact layers has been modified in the 2-D model as per the convenience by transforming the dimensions of the n + buffer layer, keeping in mind the current flow from the cathode to the anode along the +y direction under reverse bias. Also, the shape of the cross section of the cathode contact layers has been transformed into a square having each edge length d E3 ¼ ﬃﬃﬃﬃﬃﬃﬃ d 2 E2 p − E2 d 2 E1 E1 = 101.82 μm> W buff , instead of the actual shape of those having inner and outer edge lengths d E1 and d E2 , respectively (see Table 1 and Fig. 3), keeping the same cross-sectional area, i.e., d 2 E3 ¼ E3 d 2 E2 − E2 d 2 E1 E1   . The simplified 2-D doping profile of the diode is given by Nx; y ð Þ¼ N buff −W nþ − d E − d S−1 2   ≤ y < −W nþ ; W buff −d 0 2   ≤ x ≤ W buff þ d 0 2   ¼ N Dþ −W nþ ≤ y < 0; d kþ1 −d k 2   ≤ x ≤ d kþ1 þ d k 2   ; k ∈I 0; S−2 ½  ¼ N D 0 ≤ y < W n ¼ −N A W n ≤ y < W n þ W p   ¼ −N Aþ W n þ W p   ≤ y ≤ W n þ W p þ W pþ   9 = ; ; 0 ≤ x ≤ d 0 ð1Þ where d E =(d E2 + d E1 )/2. Fig. 3 The a side view as well as the b top view of the equivalent 3-D model of the 1.0-THz GaN DDR IMPATT structure having a square-shaped cross section transformed from the circular cross section Table 1 Values of r k and corre- sponding values of d k r k (μm) d k (μm) r 0 = 2.5 μm d 0 = 4.43 μm r S − 1 = 10.0 μm d S − 1 = 17.72 μm r E1 = 40.0 μm d E1 = 70.89 μm r E2 = 70.0 μm d E2 = 124.07 μm r buff = 100.0 μm d buff = 177.25 μm 958 J Infrared Milli Terahz Waves (2018) 39:954–974

∂p ∂t ¼ − 1 q  ∇ ! : J ! p þ G Ap þ G T p −R p ; ð4Þ (iii) Current density equations: J ! n ¼ −q μ n n ∇ ! V −D n ∇ ! n   ; ð5Þ J ! p ¼ −q μ p p ∇ ! V þ D p ∇ ! p   ; ð6Þ where q = 1.6 × 10 −19 C is the unit electronic charge, μ n, p are the mobility, and D n, p are the diffusion coefficients of electrons and holes in the base semiconductor (here GaN). The parameters G An;p x; y ð Þ, G T n;p x; y ð Þ, and R n, p (x, y) are the 2-D avalanche generation rate, band-to-band tunneling generation rate, and Shockley-Read-Hall recombination rate [47] of charge carriers; expressions of these parameters can be obtained from an earlier publication by the authors [48]. The avalanche generation rate of the charge carriers depends on field- dependent ionization rates (α n, p ) and drift velocities (v n, p ) as well as on the carrier concen- trations (n, p), whereas band-to-band tunneling generation rates are strong functions of the electric field [48]. The boundary conditions for solving Eqs. (2)–(6) are given by (i) Electric potential boundary conditions at n + -n and p + -p interfaces: ∂Vx; y; t ð Þ ∂y     y¼0; W n þW p ð Þ ¼ 0 for 0 ≤ x ≤ d 0 ð7Þ (ii) Current density boundary conditions at n + -n and p + -p interfaces: P ! x; y; t ð Þ    y¼0 ¼ 2 J ! p x; y ¼ 0; t ð Þ J ! p x; y ¼ 0; t ð Þþ J ! n x; y ¼ 0; t ð Þ −1  ! P ! x; y; t ð Þ    y¼ WnþWp ð Þ ¼ 1− 2 J ! n x; y ¼ W n þ W p   ; t   J ! p x; y ¼ W n þ W p   ; t   þ J ! n x; y ¼ W n þ W p   ; t   0 @ 1 A 9 > > > > > = > > > > > ; for 0 ≤ x ≤ d 0 ; ð8Þ where the normalized current density parameter is defined by P ! x; y; t ð Þ¼ J ! p x; y ¼ 0; t ð Þ− J ! n x; y ¼ 0; t ð Þ J ! p x; y ¼ 0; t ð Þþ J ! n x; y ¼ 0; t ð Þ  ! : ð9Þ (iii) Space charge boundary conditions at the floating boundaries: ∂ 2 ∂x 2 px ¼ 0; y; t ð Þ−nx ¼ 0; y; t ð Þþ Nx ¼ 0; y ð Þ ½ ¼ 0 ∂ 2 ∂x 2 px ¼ d 0 ; y; t ð Þ−nx ¼ d 0 ; y; t ð Þþ Nx ¼ d 0 ; y ð Þ ½ ¼ 0 9 > > = > > ; for 0 ≤ y ≤ W n þ W p   :ð10Þ Equation (10) is obviously less restrictive than the condition of zero space charge variation proposed by Kurata [49]. The finite difference discretizations of Eqs. (2)–(6) and (7)–(10) have been set up by following the procedure adopted in [49, 50]. The simultaneous solution of the fully coupled Poisson’ s equation, carrier continuity equations, and current density equations 960 J Infrared Milli Terahz Waves (2018) 39:954–974

has been obtained subject to the given boundary conditions by linearizing the said equations by applying Newton’ s iteration principle [48]. The instantaneous diode voltage excitation (V d (t)) and terminal current response (I d (t)) can be obtained from the field and current density solutions as V d t ðÞ¼ − ∫ x¼d 0 x¼0 ξ x dx− ∫ y¼ Wn þWp ð Þ y¼0 ξ y dy; ð11Þ I d t ðÞ¼ A 0 1 d 0  ∫ x¼d 0 x¼0 J x dx− 1 W n þ W p   ∫ y¼ WnþWp ð Þ y¼0 J y dy 8 < : 9 = ; ; ð12Þ where ξ ! ¼ ξ x ^ x þ ξ y ^ y; J ! d ¼ J ! n þ J ! p ¼ J x ^ x þ J y ^ y and I ! d ¼ A 0 J ! d ; the area of the square-shaped cross section of the diode A 0 ¼ d 2 0 . Here, ^ x and ^ y are the unit vectors along + x and + y directions, respectively. Now, V d (t) and I d (t) may be written as V d t ðÞ¼ V B þ v rf t ðÞ I d t ðÞ¼ I 0 þ i rf t ðÞ  ; ð13Þ where V B ¼ 1 T  ∫ t¼T t¼0 V d t ðÞ dt; I 0 ¼ 1 T  ∫ t¼T t¼0 I d t ðÞ dt here T ¼ 1= f ð Þ: ð14Þ In the non-sinusoidal voltage excitation (NSVE) model of the IMPATT source, a non- sinusoidal voltage waveform v rf (t) is assumed to be used as input excitation to the reverse- biased IMPATT diode via a constant current source (I 0 = J 0 A 0 ; A 0 = πr 0 2 = d 0 2 ). The equivalent circuit for the NSVE model of the IMPATT oscillator is shown in Fig. 5. The excitation voltage having the following form v rf t ðÞ¼ V B ∑ w r¼1 m ð Þ r sin 2πfrt ð Þ; ð15Þ is assumed to be applied across the diode via a coupling capacitor (C c ). Here, m is the voltage modulation factor/index, which should be kept within the range of 50–60% [30, 48]. Fig. 5 Equivalent circuit associated with the NSVE model of the THz IMPATT source J Infrared Milli Terahz Waves (2018) 39:954–974 961

G D ω ð Þ¼ R D ω ð Þþ R S ω ðÞ R D ω ð Þþ R S ω ðÞ ð Þ 2 þ X D ω ðÞ ð Þ 2 ( ) B D ω ð Þ¼ −X D ω ðÞ R D ω ð Þþ R S ω ðÞ ð Þ 2 þ X D ω ðÞ ð Þ 2 ( ) : ð20Þ Now the fundamental component of the peak RF power output is given by P RF ¼ 1 2 mV B ð Þ 2 G D ω ðÞ j j peak ; ð21Þ where |G D (ω)| peak is the magnitude of the peak conductance of the diode corresponding to the optimum frequency f p = 1.0 THz. The DC to RF conversion efficiency is given by η L ¼ P RF P DC   100 % ð Þ; ð22Þ where input DC power P DC = V B I 0 . 2.2 Modeling of Series Resistance An alternating electric current tends to be distributed within a conductor such that the current attains its maximum value near the surface of the conductor and decreases exponentially as the penetration depth in the conductor increases. The depth below the surface of the conductor at which the current density falls to e −1 times of its value at the surface is called skin depth (δ) [51]. The skin depth can be calculated with sufficient accuracy from the approximate relation δ ¼ ﬃﬃﬃﬃﬃﬃﬃﬃﬃ πfμσ p [44, 51], where ε is the electric permittivity, μ is the magnetic permeability, σ is the conductivity, and f is the frequency. A long conductor having a square-shaped cross section has AC resistance given by R ac ¼ 1 σ  W 4δ d−δ ð Þ   for d > 2δ; ð23Þ where d is the length of each edge of the square-shaped cross section. However, the AC resistance of a conductor is equal to the DC resistance value when d ≤ 2δ, i.e., when the skin effect can be neglected. It is given by R ac ¼ 1 σ  W d 2  for d ≤ 2δ ð24Þ The skin depths associated with different semiconducting and metal layers of the DDR structure have been calculated by using the respective values of magnetic mass susceptibility ( χ), density (ρ), and conductivity (σ) at the operating frequency for 1.0 THz, and those are listed in Table 2. It is observed from Table 2 that within p + , p, n, and n + buffer layers the condition d <2δ is satisfied; therefore, the skin effect can be neglected within those layers and Eq. ( 24) can be used to calculate the series resistance associated with those layers. However, all metal contact layers satisfy the d >2δ condition and the skin effect is found to be significant in those layers; thus, Eq. (23) has to be used to calculate the series resistance associated with those layers. Since, the n + layer is tapered conical shaped, according to the dimensions of that layer, the upper portion of that layer satisfies d >2δ (where the skin effect is prominent) and the lower portion satisfies d ≤ 2δ (where the skin effect can J Infrared Milli Terahz Waves (2018) 39:954–974 963

be ignored); therefore, both Eqs. (23) and ( 24) are required to calculate total series resistance associated with n + layer which will be discussed later in this section. The total fixed series resistance arising from Au and Ni layers at p + side (anode metal layers), Ni/ p + -GaN contact (anode metal contact), p + layer, n + layer, n + buffer layer (undepleted GaN layers), Ti/ n + -GaN (cathode metal contact), and Ti, Al, Ti, and Au layers at n + buffer side (cathode metal layers) is given by R S0 ¼ R EA ð Þ Au p ðÞ þ R EA ð Þ Ni p ðÞ   |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} Anode Metal Layers þ R CA ð Þ Ni=p þ   |ﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄ} Anode Contact þ R GaN ð Þ p þ þ R GaN ð Þ n þ þ R GaN ð Þ n þ ‐buff   |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} Undepleted GaN Layers þ R CC ð Þ Ti=n þ ‐buff   |ﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄ} Cathode Contact þ R EC ð Þ Ti n ðÞ1 þ R EC ð Þ Al n ðÞ þ R EC ð Þ Ti n ðÞ2 þ R EC ð Þ Au n ðÞ   |ﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ{zﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄﬄ} Anode Metal Layers ; ð25Þ where the fixed series resistances of metal layers can be calculated by using the following expressions: R EA ð Þ Au p ðÞ ¼ 1 σ Au  W Au p ðÞ 4 δ Au f ðÞ d 0 −δ Au f ðÞ ð Þ   ; R EA ð Þ Ni p ðÞ ¼ 1 σ Ni  W Ni p ðÞ 4 δ Ni f ðÞ d 0 −δ Ni f ðÞ ð Þ   ; R EC ð Þ Ti n ðÞ1 ¼ 1 σ Ti  W Ti n ðÞ1 4 δ Ti f ðÞ d E3 −δ Ti f ðÞ ð Þ   ; R EC ð Þ Al n ðÞ ¼ 1 σ Al  W Al n ðÞ 4 δ Al f ðÞ d E3 −δ Al f ðÞ ð Þ   ; R EC ð Þ Ti n ðÞ2 ¼ 1 σ Ti  W Ti n ðÞ2 4 δ Ti f ðÞ d E3 −δ Ti f ðÞ ð Þ   ; R EC ð Þ Au n ðÞ ¼ 1 σ Au  W Au n ðÞ 4 δ Au f ðÞ d E3 −δ Au f ðÞ ð Þ   9 > > > > > > = > > > > > > ; : ð26Þ The mesa etched n + layer has been approximated as a tapered conical-shaped structure as shown in Fig. 4, which is considered to consist of a number of concentric layers Table 2 Magnetic mass susceptibility, density, permeability, conductivity, and skin depth of different layers [52–54] Layers χ (m 3 kg −1 ) [41] ρ (kg m −3 ) [42] μ = μ 0 (1 + ρχ) (H m −1 ) σ (S m −1 )[43] δ (μm) Calculation of R ac p + layer − 1.39 × 10 −9 6.150 × 10 3 1.25599 × 10 −6 0.1088 × 10 4 15.2622 d 0 <2δ p+ (Eq. 24) p layer − 1.39 × 10 −9 6.150 × 10 3 1.25599 × 10 −6 0.0381 × 10 4 25.7978 d 0 <2δ p (Eq. 24) n layer − 1.39 × 10 −9 6.150 × 10 3 1.25599 × 10 −6 1.0880 × 10 4 4.8263 d 0 <2δ n (Eq. 24) n + layer − 1.39 × 10 −9 6.150 × 10 3 1.25599 × 10 −6 3.2000 × 10 4 2.8142 – (Eqs. 23 and 24) n + buffer layer − 1.39 × 10 −9 6.150 × 10 3 1.25599 × 10 −6 1.6000 × 10 4 3.9798 W buff <2δ n+ - buff (Eq. 24) Ni layer – 8.908 × 10 3 1.26000 × 10 −6 1.40000 × 10 7 0.1343 d 0 >2δ Ni (Eq. 23) Ti layers 4.01 × 10 −8 4.507 × 10 3 1.25686 × 10 −6 2.50000 × 10 6 0.3183 d E3 >2δ Ti (Eq. 23) Al layer 7.80 × 10 −9 2.700 × 10 3 1.25667 × 10 −6 3.80000 × 10 7 0.0816 d c >2δ Al (Eq. 23) Au layers − 1.80 × 10 −9 19.300 × 10 3 1.25659 × 10 −6 4.50000 × 10 7 0.0750 d 0 , d E3 >2δ Au (Eq. 23) 964 J Infrared Milli Terahz Waves (2018) 39:954–974

having a square-shaped cross section, one below the other, each having the same thickness (W n+ /S, where S is the number of those layers (S = 100 has been assumed in the present calculations)), but of increasing edge length from d 0 (topmost layer) to d S − 1 (bottommost layer). Thus, the expression of series resistance due to the n + layer can be formulated as R GaN ð Þ n þ ¼ 1 qN Dþ μ n   ∑ k¼ S−1 ð Þ k¼0 W n þ SA k  ; ð27Þ where A k ¼ 4δ n þ f ðÞ d k −δ n þ f ðÞ ð Þ if d k > 2δ n þ f ðÞ ¼ d 2 k if d k ≤ 2δ n þ f ðÞ  : ð28Þ The fixed series resistances of the p + layer and n + buffer layer are given by R GaN ð Þ p þ ¼ 1 qN Aþ μ p  ! W p þ d 2 0 "# ∵d 0 < 2δ p þ f ðÞ; ð29Þ R GaN ð Þ n þ ‐buff ¼ 1 qN buff μ n   2d E −d S−1 ð Þ 2W 2 buff   ∵W buff < 2δ n þ ‐buff f ðÞ: ð30Þ The contact resistances associated with the Ni/p + -GaN and Ti/n + -GaN contact layers are given by R CA ð Þ Ni=p þ ¼ ρ Ni=p þ A eff ð Þ Ni=p þ 0 @ 1 A ; R CC ð Þ Ti=n þ ‐buff ¼ ρ Ti=n þ ‐buff A eff ð Þ Ti=n þ ‐buff 0 @ 1 A ; ð31Þ where ρ Ni=p þ and ρ Ti=n þ ‐buff are the specific contact resistances of the respective contacts; those are given by [44, 55] ρ Ni=p þ ¼ k B sin π c p k B T   π qA ** p T  ! exp q Φ Ni=p þ Bp ðÞ E p 00 0 @ 1 A ρ Ti=n þ ‐buff ¼ k B sin π c n k B T ð Þ π qA ** n T   exp q Φ Ti=n þ ‐buff Bn ðÞ E n 00 0 @ 1 A 9 > > > > > > = > > > > > > ; ; ð32Þ where k B = 1.38 × 10 −23 JK −1 is the Boltzmann constant, T is the absolute temperature in Kelvin (K), q = 1.6 × 10 −19 C is the unit electronic charge, and A p ** and A n ** are the reduced effective Richardson constants for holes and electrons, respectively. The parameters c p and c n are given by J Infrared Milli Terahz Waves (2018) 39:954–974 965

c p ¼ 1 E p 00  ln 4Φ Ni=p þ Bp ðÞ −Φ fp 0 @ 1 A c n ¼ 1 E n 00  ln 4Φ Ti=n þ ‐buff Bn ðÞ −Φ fn 0 @ 1 A 9 > > > > > > = > > > > > > ; ; ð34Þ where Φ Ni=p þ Bp ðÞ and Φ Ti=n þ ‐buff Bn ðÞ are the Schottky-barrier heights in Ni/p + -GaN and Ti/n + -GaN contacts [44]. The parameters Φ fp and Φ fn are given by Φ fp ¼ k B T q  ln N v N n þ  Φ fn ¼ k B T q  ln N c N buff   9 > > = > > ; ; ð35Þ where N c = 1.4 × 10 20 × T 3/2 m −3 and N v = 8.9 × 10 21 × T 3/2 m −3 are the effective density of states in conduction and valence bands of GaN. The parameters E p 00 and E n 00 are the field emission (FE) parameters (k B T << E p;n 00 ), which are given by [44, 55] E p 00 ¼ qh 4π  N Aþ m * p ε ! 1 2 E n 00 ¼ qh 4π  N buff m * n ε   1 2 9 > > > > = > > > > ; ; ð36Þ where h = 6.62 × 10 −34 J s is Planck’ s constant and m p * and m n * are the effective mass of holes and electrons in valence and conduction bands, respectively. The average effective area of conduction in Ni/p + -GaN and Ti/n + -GaN contacts are given by A eff ð Þ Ni=p þ ¼ 1 2  d 2 0 þ 4δ Ni f ðÞ d 0 −δ Ni f ðÞ ð Þ   ∵d 0 < 2δ p þ f ðÞ; d 0 > 2δ Ni f ðÞ A eff ð Þ Ti=n þ ‐buff ¼ 1 2  W 2 buff þ 4δ Ti f ðÞ d E3 −δ Ti f ðÞ ð Þ   ∵d 0 < 2δ n þ ‐buff f ðÞ; d E3 > 2δ Ti f ðÞ 9 > > = > > ; : ð37Þ It has been already explained by the authors in their earlier report [30] that the thickness of the depletion layers in both n and p epitaxial layers under the L-S condition are functions of time; those are denoted by y Dn (t) and y Dp (t). Thus, the time-varying lengths of undepleted n and p layers are given by (W n − y Dn (t)) and (W p − y Dp (t)) and corresponding time-varying series resistance arises due to time-varying unswept epitaxial layers given by R GaN ð Þ p t ðÞ¼ 1 qN A μ p  ! W p −y Dp t ðÞ d 2 0 " # ∵d 0 < 2δ p f ðÞ; ð38Þ 966 J Infrared Milli Terahz Waves (2018) 39:954–974

R GaN ð Þ n t ðÞ¼ 1 qN D μ n   W n −y Dn t ðÞ d 2 0 " # ∵d 0 < 2δ n f ðÞ: ð39Þ Therefore, the total time-varying series resistance is given by R S t ðÞ¼ R S0 þ R GaN ð Þ p t ðÞþ R GaN ð Þ n t ðÞ; ð40Þ Fourier transform of R S (t) provides the series resistance of the diode in frequency domain, i.e., R S ω ð Þ¼ ∫ þ∞ −∞ R S t ðÞ e −jωt dt : ð41Þ 3 Results and Discussion The 2-D L-S simulation of the 1.0-THz DDR GaN IMPATT diode has been carried out in order to study the effect of parasitic series resistance on the high-frequency performance of the diode. The material parameters of Wz-GaN such as α n, p , v n, p , μ n, p , D n, p , N c, v , m n, p * , χ, ρ, μ, ε, σ, etc., at room temperature have been taken into account in the simulation from the published literature [52–54, 56–59]. Initially, the 2-D static (DC) simulation has been carried out by keeping voltage modulation factor m = 0, in order to obtain the static current-voltage (I-V) characteristic of the DDR structure under consid- eration. The I-V characteristic is shown in Fig. 7. It is observed that the magnitude of the breakdown voltage (|V B |) increases from 28.79 to 31.21 V with the increase of the bias current from 78.54 to 98.17 mA. After the breakdown voltages for the bias current range under consideration was obtained, the 2-D large-signal simulation was started. The time variations of the diode excitation voltage, peak electric field at the metallurgical junction, and corresponding terminal current response are obtained from the simulation, and a few cycles of those at steady-state oscillation are shown in Fig. 8. A phase shift of around 180° in between the diode voltage and current can be observed from the corresponding waveforms. The 2-D snapshots of the magnitude of the electric field profile at different phases or time intervals of several complete cycles of steady- state oscillation have been obtained from the simultaneous solution of a time- and space- dependent device Eqs. (2)–(6) subject to the boundary conditions (7)–(10). The said snapshots for the bias current of 88.36 mA and voltage modulation factor of 50%, taken at the phase angles ωt = 0, ωt = π/2, ωt = π, ωt =3π/2, and ωt =2π, are shown in Fig. 9a–e. A significant portion of both n and p epitaxial becomes undepleted during the negative half cycles of the V d (t), which indeed contributes to the time-varying series resistance as mentioned in the earlier section. Change in the depletion layer width with time, especially during the negative half cycles of the V d (t), is known as depletion width modulation [33–35]. The time variations of the depletion layer width in both n and p sides for different I 0 are shown in Fig. 10, along with the time variations of corresponding series resistance portions R GaN ð Þ n t ðÞ and R GaN ð Þ p t ðÞ. It is observed that the peak value of R GaN ð Þ p t ðÞ is significantly higher as compared to that of J Infrared Milli Terahz Waves (2018) 39:954–974 967

R GaN ð Þ n t ðÞ. The cause of it can be understood from Eqs. (38) and (39), where the electron mobility is much higher than the hole mobility in GaN (μ n > μ p )[46, 47]. Therefore, all p and p + layers of the DDR structure have greater contribution to total series resistance than the n and n + layers; this can also be observed in Table 3, where the fixed series resistance values of different layers calculated at 1.0 THz are listed. The total fixed series resistance is observed to be R S0 = 1.3374 Ω. Fig. 7 Static I-V characteristics of the 1.0-THz DDR GaN IMPATT diode Fig. 8 Time variations of diode voltage, magnitude of peak electric field, and diode current of the 1.0-THz DDR GaN IMPATT diode for different bias currents 968 J Infrared Milli Terahz Waves (2018) 39:954–974

Figure 11 shows the variations of total series resistance (R S ) of the 1.0-THz DDR GaN IMPATT diode with the bias current. Due to the space charge effect [60, 61], the depletion width modulation phenomenon gets faint at higher bias currents. Therefore, the contribution of R GaN ð Þ n t ðÞ and R GaN ð Þ p t ðÞ decreases as the bias current increases; as a result, R S decreases from 1.7879 to 1.5779 Ω due to the increase of I 0 from 78.54 to 98.17 mA. The RF power output and DC to RF conversion efficiency are obtained from the 2-D L-S simulation as functions of the bias current. Both P RF and η L for different I 0 values have been Fig. 9 2-D snapshots of the magnitude of the electric field profile of the 1.0-THz DDR GaN IMPATT diode for each quarter of one complete cycle of steady-state oscillation, i.e., at a ωt = 0, b ωt = π/2, c ωt = π, d ωt =3π/2, and e ωt =2π, for 88.36 mA of bias current (at 50% voltage modulation) Fig. 10 Time variations of time-varying undepleted n and p layers and corresponding time-varying series resistances of the 1.0-THz DDR GaN IMPATT diode for different bias currents J Infrared Milli Terahz Waves (2018) 39:954–974 969

calculated by considering R S = 0, i.e., by ignoring the effect of series resistance and also by considering R S ≠ 0(R S ∈ [1.7879, 1.7370, 1.6834, 1.6303, 1.5779] Ω for I 0 ∈ [78.54, 83.45, 88.36, 93.27, 98.17] mA), i.e., by taking into account the effect of series resistance. The P RF versus I 0 and η L versus I 0 plots for both R S = 0 and R S ∈ 1:7879; 1:7370; 1:6834; 1:6303; 1:5779 ½  Ω for I 0 ∈ 78:54; 83:45; 88:36; 93:27; 98:17 ½  mA are shown in Fig. 12a, b, respectively. It is observed from Fig. 12a, b that both P RF and η L reduce significantly due to the presence of series resistance. Simulation without Table 3 Fixed series resistances of different layers at f = 1.0 THz Series resistance of different layers Values in Ω R EA ð Þ Au p ðÞ 0.002551 R EA ð Þ Ni p ðÞ 0.000619 R CA ð Þ Ni=p þ 0.613421 R GaN ð Þ p þ 0.174613 R GaN ð Þ n þ 0.100132 R GaN ð Þ n þ ‐buff 0.216518 R CC ð Þ Ti=n þ ‐buff 0.228451 R EC ð Þ Ti n ðÞ1 0.000311 R EC ð Þ Al n ðÞ 0.000276 R EC ð Þ Ti n ðÞ2 0.000213 R EC ð Þ Au n ðÞ 0.000319 Fig. 11 Variation of series resistance of the 1.0-THz DDR GaN IMPATT diode with bias current 970 J Infrared Milli Terahz Waves (2018) 39:954–974

considering the series resistance (i.e., R S = 0) shows that P RF increases from 252.71 to 316.31 mA and η L decreases from 11.18 to 10.00% with the increase of I 0 from 78.54 to 98.17 mA. However, the same changes are observed to be 191.66–202.85 mW and 8.48– 6.41%, when the effect of series resistance has been taken into account in the simulation. Therefore, in the 1.0-THz DDR GaN IMPATT source, around 24.16–35.87% decrements have been found in both RF power output and DC to RF conversion efficiency due to the influence of series resistance. Earlier, Acharyya et al. reported on the high-frequency performance of the 1.0-THz DDR GaN IMPATT diode by using the 1-D small signal [35, 36] as well as 1-D L-S [34] simulations. Both the small signal [35, 36] and L-S [34] overestimated the peak RF power of around 504 and 300 mW, respectively, since the effect of parasitic series resistance was not considered in both of those calculations. However, 2-D L-S simulation of the device by considering the effect of series resistance presented in this paper predicts much a smaller estimation of RF power output (191.66–202.85 mW) which is expected to be nearer to the practical power output. The simulation results presented in this paper could not be compared with experimental results due to the unavailability of the reported experimental results on 1.0-THz DDR GaN IMPATT sources. However, the device layout, the design parameters, and the simulation results presented in this paper will be extremely useful for the experimentalists to fabricate the DDR GaN IMPATT source operating at 1.0 THz by using the MOCVD or MOVPE technique, which is standard for these kinds of layered devices. 4 Conclusion The effect of series resistance on the high-frequency characteristics of a 1.0-THz DDR GaN IMPATT has been investigated in this paper. A 2-D L-S simulation method based on the NSVE model has been used for this purpose. A comprehensive model of series resistance has Fig. 12 Variations of a RF power output and b DC to RF conversion efficiency of the 1.0-THz DDR GaN IMPATT diode with bias current; both variations have been shown with and without taking into account the effect of series resistance J Infrared Milli Terahz Waves (2018) 39:954–974 971

been developed by considering the influence of skin effect, and the said model has been incorporated in the 2-D L-S simulation for studying the effect of RF power output and DC to RF conversion efficiency of the device. Results indicate around 24.16–35.87% reduction in power output and efficiency due to the RF power dissipation in the positive series resistance. Finally, the device can deliver 191.7–202.9 mW peak RF power to the load at 1.0 THz with 8.48–6.41% conversion efficiency, respectively. From the current study, it is evident that GaN IMPATT diodes are capable of generating high RF power at around 1 THz, higher than conventional Si-, GaAs-, and InP-based IMPATT diodes, but the effect of parasitic series resistance on the THz performance of the device causes havoc reduction in power output and efficiency. The nature of the parasitic resistance is studied here, and the comprehensive understanding on the said topic in the level of device fabrication and optimization, which to our knowledge is not available at present, may lead to the improved performance of the GaN IMPATT devices. Acknowledgements Dr. Arindam Biswas wishes to thank the Science and Engineering Research Board (SERB), India, for providing financial support for carrying out this research work through the Early Career Research (ECR) Award scheme having the grant file number ECR/2017/000024/ES. References 1. P. Martyniuk, J. Antoszewski, M. Martyniuk, L. Faraone, A. Rogalski, New concepts in infrared photode- tector designs, Appl. Phys. Rev. 1, 041102 (2014). 2. R.M. Woodward, B.E. Cole, V.P. Wallace, R.J. Pye, D.D. Arnone, E.H. Linfield, M. Pepper, Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue, Phys. Med. Biol. 47, 3853 (2002). 3. M. Nagel, P.H. Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, R. Buttner, Integrated THz technology for label-free genetic diagnostics, Appl. Phys. Lett. 80 (1), 154 (2002). 4. N. Karpowicz, H. Zhong, C. Zhang, K.I Lin, J.S. Hwang, J. Xu, X.C. Zhang, Compact continuous-wave subterahertz system for inspection applications, Appl. Phys. Lett. 86 (5), 054105 (2005). 5. K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, Non-invasive inspection of c-4 explosive in mails by terahertz time-domain spectroscopy, J. Appl. Phys. 43 (3B), L414 (2004). 6. K. Kawase, Y. Ogawa, Y. Watanabe, H. Inoue, Non-destructive terahertz imaging of illicit drugs using spectral fingerprints, Opt. Express 11 (20), 2549 (2003). 7. C. Joerdens, M. Koch, Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy, Opt. Eng. 47 (3), 037003 (2008). 8. M. Tonouchi , Cutting-edge terahertz technology, Nat. Photonics 1, 97 (2007). 9. P.H. Siegel, Terahertz technology, IEEE Trans. Microwave Theory Tech. 50, 910 (2002). 10. B. S. Williams, Terahertz quantum-cascade lasers, Nat. Photonics 1, (2007) 517. 11. F. Schuster , D. Coquillat , H. Videlier , M. Sakowicz , F. Teppe , L. Dussopt , B. Giffard , T. Skotnicki , W. Knap, Broadband terahertz imaging with highly sensitive silicon CMOS detectors,^ Opt. Express 19, 7827 (2011). 12. Xinghan Cai, et al. Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene, Nature Nanotechnology 9, (2014) 814. 13. L. Liu, J. L. Hesler, H. Xu, A. W. Lichtenberger, R. M. Weikle A broadband quasi-optical terahertz detector utilizing a zero bias Schottky diode, IEEE Microwave Wireless Compon. Lett. 20, 504 (2010). 14. G. C. Trichopoulos , H. L. Mosbacker , D. Burdette , K. Sertel , A broadband focal plane array camera for real-time THz imaging applications, IEEE Trans. Antennas Propag. 61, 1733 (2013). 15. C. M. Watts , D. Shrekenhamer , J. Montoya , G. Lipworth , J. Hunt , T. Sleasman , S. Krishna , D. R. Smith , W. J. Padilla, Terahertz compressive imaging with metamaterial spatial light modulators, Nat. Photonics 8, 605 (2014). 16. A. Tiwari, H. Satoh, M. Aoki, M. Takeda, N. Hiromoto, H. Inokawa, Fabrication and analytical modeling of integrated heater and thermistor for antenna-coupled bolometers, Sensors and Actuators A: Physical 222, 160 (2015). 972 J Infrared Milli Terahz Waves (2018) 39:954–974

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References (60)

P. Martyniuk, J. Antoszewski, M. Martyniuk, L. Faraone, A. Rogalski, New concepts in infrared photode- tector designs, Appl. Phys. Rev. 1, 041102 (2014).
R.M. Woodward, B.E. Cole, V.P. Wallace, R.J. Pye, D.D. Arnone, E.H. Linfield, M. Pepper, Terahertz pulse imaging in reflection geometry of human skin cancer and skin tissue, Phys. Med. Biol. 47, 3853 (2002).
M. Nagel, P.H. Bolivar, M. Brucherseifer, H. Kurz, A. Bosserhoff, R. Buttner, Integrated THz technology for label-free genetic diagnostics, Appl. Phys. Lett. 80 (1), 154 (2002).
N. Karpowicz, H. Zhong, C. Zhang, K.I Lin, J.S. Hwang, J. Xu, X.C. Zhang, Compact continuous-wave subterahertz system for inspection applications, Appl. Phys. Lett. 86 (5), 054105 (2005).
K. Yamamoto, M. Yamaguchi, F. Miyamaru, M. Tani, M. Hangyo, Non-invasive inspection of c-4 explosive in mails by terahertz time-domain spectroscopy, J. Appl. Phys. 43 (3B), L414 (2004).
K. Kawase, Y. Ogawa, Y. Watanabe, H. Inoue, Non-destructive terahertz imaging of illicit drugs using spectral fingerprints, Opt. Express 11 (20), 2549 (2003).
C. Joerdens, M. Koch, Detection of foreign bodies in chocolate with pulsed terahertz spectroscopy, Opt. Eng. 47 (3), 037003 (2008).
M. Tonouchi , Cutting-edge terahertz technology, Nat. Photonics 1, 97 (2007).
P.H. Siegel, Terahertz technology, IEEE Trans. Microwave Theory Tech. 50, 910 (2002).
B. S. Williams, Terahertz quantum-cascade lasers, Nat. Photonics 1, (2007) 517.
F. Schuster , D. Coquillat , H. Videlier , M. Sakowicz , F. Teppe , L. Dussopt , B. Giffard , T. Skotnicki , W. Knap, Broadband terahertz imaging with highly sensitive silicon CMOS detectors,^Opt. Express 19, 7827 (2011).
Xinghan Cai, et al. Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene, Nature Nanotechnology 9, (2014) 814.
L. Liu, J. L. Hesler, H. Xu, A. W. Lichtenberger, R. M. Weikle A broadband quasi-optical terahertz detector utilizing a zero bias Schottky diode, IEEE Microwave Wireless Compon. Lett. 20, 504 (2010).
G. C. Trichopoulos , H. L. Mosbacker , D. Burdette , K. Sertel , A broadband focal plane array camera for real-time THz imaging applications, IEEE Trans. Antennas Propag. 61, 1733 (2013).
C. M. Watts , D. Shrekenhamer , J. Montoya , G. Lipworth , J. Hunt , T. Sleasman , S. Krishna , D. R. Smith , W. J. Padilla, Terahertz compressive imaging with metamaterial spatial light modulators, Nat. Photonics 8, 605 (2014).
A. Tiwari, H. Satoh, M. Aoki, M. Takeda, N. Hiromoto, H. Inokawa, Fabrication and analytical modeling of integrated heater and thermistor for antenna-coupled bolometers, Sensors and Actuators A: Physical 222, 160 (2015).
A. Banerjee, H. Satoh, A. Tiwari, C. Apriono, E. T. Rahardjo, N. Hiromoto and H. Inokawa, Width dependence of platinum and titanium thermistor characteristics for application in room-temperature antenna- terahertz microbolometer, Jpn. J. Appl. Phys. 56, 04CC07 (2017).
A. Banerjee, H. Satoh, Y. Sharma, N. Hiromoto, H. Inokawa Characterization of platinum and titanium thermistors for terahertz antenna-coupled bolometer applications, Sensors and Actuators: A Physical, Vol. 273, pp. 49-57, Feb. 10, 2018.
A. Banerjee, Hiroaki Satoh, Durgadevi Elamaran, Yash Sharma, Norihisa Hiromoto, and Hiroshi Inokawa, Optimization of narrow width effect on titanium thermistor in uncooled antenna-coupled terahertz microbolometer, Jpn. J. Appl. Phys., Vol. 57, No. 4S, pp. 04FC09_1-7, Mar. 19, 2018.
J. Ward, E. Schlecht, G. Chattopadhyay, A. Maestrini, J. Gill, F. Maiwald, H. Javadi, and I. Mehdi, Capability of THz sources based on Schottky diode frequency multiplier chains, IEEE MTT-S Digest., pp. 1587-1590, 2004.
S. Heyminck, R. Güsten, U. Graf, J. Stutzki, P. Hartogh, H. W. Hübers, O. Ricken, and B. Klein, GREAT: ready for early science aboard SOFIA, Proc. 20th Intl. Symp. Space THz Techn., Charlottesville, VA., pp. 315-317, 2009.
T. W. Crowe, J. L. Hesler, S. A. Retzloff, C. Pouzou, and G. S. Schoenthal, Solid state LO sources for greater than 2 THz, 2011 ISSTT Digest, 22nd Symposium on Space Terahertz Technology, Tucson Arizona, USA 2011.
T. W. Crowe, J. L. Hesler, S. A. Retzloff, C. Pouzou, and J. L. Hester, Multiplier based sources for frequencies above 2 THz, 36 th International Conference on Infrared, Millimeter and terahertz Sources (IRMMW-THz), pp. 1, 2011.
A Maestrini, I Mehdi, JV Siles, J Ward, R Lin, B Thomas, C Lee, J Gill, G Chattopadhyay, E Schlecht, J Pearson, and P Siegel, First demonstration of a tunable electronic source in the 2.5 to 2.7 THz range, IEEE Trans. Terahertz Science Techn., vol. 3, 2012.
S. Kitagawa, M. Mizuno, S. Saito, K. Ogino, S. Suzuki, and M. Asada, Frequency-tunable resonant- tunneling-diode terahertz oscillators applied to absorbance measurement, Japanese Journal of Applied Physics, vol. 56, pp. 058002-1-3, 2017.
B. S. Williams, Terahertz quantum-cascade lasers, Nature Photonics, vol. 1, pp. 617-626, 2007.
R. Lai, X. Mei, W. Deal, W. Yoshida, Y. Kim, P. Liu, J. Lee, J. Uyeda, V. Radisic, M. Lange, T. Gaier, L. Samoska, and A. Fung, Sub 50 nm InP HEMT device with f max greater than 1 THz, in Proc. IEEE Int. Electron Devices Meeting, 2007, pp. 609-611.
W. Deal, X. Mei, V. Radisic, K. Leong, S. Sarkozy, B. Gorospe, J. Lee, P. Liu, W. Yoshida, J. Zhou, M. Lange, J. Uyeda, and R. Lai, Demonstration of a 0.48 THz amplifier module using InP HEMT transistors, IEEE Microw. Wireless Compon. Lett., vol. 20, no. 5, pp. 289-291, May 2010.
M. Urteaga, M. Seo, J. Hacker, Z. Griffith, A. Young, R. Pierson, P. Rowell, A. Skalare, and M. Rodwell, InP HBT integrated circuit technology for terahertz frequencies, in Proc. IEEE Compound Semicond. Integr. Circuit Symp., 2010, pp. 1-4.
E. Lobisser, Z. Griffith, V. Jain, B. Thibeault, M. Rodwell, D. Loubychev, A. Snyder, Y. Wu, J. Fastenau, and A. Liu, 200-nm InGaAs/InP type-I DHBT employing a dual-sidewall emitter process demonstrating f max >> 800 GHz and f T = 360 GHz, in Proc. IEEE Int. Conf. Indium Phosphide Related Materials, May 2009, pp. 16-19.
M. Seo, M. Urteaga, A. Young, V. Jain, Z. Griffith, J. Hacker, P. Rowell, R. Pierson, and M. Rodwell, 300 GHz fixed-frequency and voltage-controlled fundamental oscillators in an InP HBT process, in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 272-275.
J. Hacker, M. Seo, A. Young, Z. Griffith, M. Urteaga, T. Reed, and M. Rodwell, THz MMICs based on InP HBT technology, in IEEE MTT-S Int. Microw. Symp. Dig., May 2010, pp. 1126-1129.
M. Seo, M. Urteaga, J. Hacker, A. Young, Z. Griffith, V. Jain, R. Pierson, P. Rowell, A. Skalare, A. Peralta, R. Lin, D. Pukala, and M. Rodwell, InP HBT IC technology for terahertz frequencies: fundamental oscillators up to 0.57 THz, IEEE Journal of Solid-State Circuits, vol. 46, no. 10, pp. 2203-2214, 2011.
Aritra Acharyya, Aliva Mallik, Debopriya Banerjee, Suman Ganguli, Arindam Das, Sudeepta Dasgupta and J. P. Banerjee, IMPATT devices based on group III-V compound semiconductors: prospects as potential terahertz radiators, HKIE Transactions, vol. 21, issue 3, pp. 135-147, 2014.
Aritra Acharyya and J. P. Banerjee, Prospects of IMPATT devices based on wide bandgap semiconductors as potential terahertz sources, Applied Nanoscience, Springer, vol. 4, pp. 1-14, 2014.
Aritra Acharyya and J. P. Banerjee, Potentiality of IMPATT devices as terahertz source: an avalanche response time based approach to determine the upper cut-off frequency limits, IETE Journal of Research [India], vol. 59, issue 2, pp. 118-127, March-April 2013.
V. A. Dmitriev et al., SiC a(3)n alloys and wide band gap nitrides grown on SiC substrates. Inst Phys Conf. Ser., vol. 141, pp. 497-502, 1995.
Y. V. Melnik, I. P. Nikitina, A. S. Zubrilov, A. A. Sitnikova , Y. G. Musikhin, V. A. Dmitriev, High-quality GaN grown directly on SiC by halide vapour phase epitaxy, Inst Phys. Conf. Ser., vol. 142, pp. 1996.
Adesida et al. Dry and wet etching for group 111 nitrides, MRS Internet J. Nitride Semiconductor Res. 4S1, G1.4, 1999.
C. F. Chu, C.C. Yu, Y.K. Wang, J.Y. Tsai, F.I. Lai and S.C. Wang, Low-resistance ohmic contacts on p-type GaN using Ni/Pd/Au metallization, Appl. Phys. Lett., vol. 77, pp. 3423-3425, 2000.
J. Burm, K. Chu, W.A. Davis, W.J. Schaff, L.F. Eastman and T.J. Eustis, Ultra-low resistive ohmic contacts on n-GaN using Si implantation, Appl. Phys. Lett., vol. 70, pp. 464, 1997.
T. Al-Attar, and T. H. Lee, Monolithic integrated millimeter-wave IMPATT transmitter in standard CMOS technology, IEEE Trans. on MTT, vol. 53, no. 11, pp. 3557-3561, 2005.
M. Gilden, and M. E. Hines, Electronic tuning effects in Read microwave avalanche diode, IEEE Trans. on Electron. Devices, vol. ED-13, pp. 169-175, 1966.
Aritra Acharyya, Suranjana Banerjee and J. P. Banerjee, Influence of skin effect on the series resistance of millimeter-wave of IMPATT devices, Journal Computational Electronics [USA], Springer, vol. 12, issue 3, pp. 511-525, 2013.
W. Harth, Large-signal series resistance of IMPATT-diodes, Arch. Elektron. Uebertragungstechnik, vol. 33, pp. 502-504, 1979.
Aritra Acharyya, Suranjana Banerjee and J. P. Banerjee, A proposed simulation technique to study the series resistance and related millimeter-wave properties of Ka-Band Si IMPATTs from the electric field snap-shots, International Journal of Microwave and Wireless Technologies, vol. 5, no. 1, pp. 91-100, 2013.
S. M. Sze, Physics of semiconductor devices, 2nd edn Wiley,New York, 1981.
Partha Banerjee, Aritra Acharyya, Arindam Biswas and A. K. Bhattacharjee, Effect of magnetic field on the RF performance of millimeter-wave IMPATT source, Journal of Computational Electronics [USA], Springer, vol. 15, pp. 210-221, 2016.
M. Kurata, Numerical analysis for semiconductor devices, Heath, Lexington, 1982.
H. H. Heimeier, A two-dimensional numerical analysis of a silicon n-p-n transistor, IEEE Trans. Electron Dev., vol. 20, pp. 708-714, 1973.
W. Hayt, Engineering electromagnetics. 4th edn McGraw-Hill, New York, 1981.
Mass magnetic susceptibility of the elements. http://periodictable.com/Properties/A/MassMagneticSusceptibility. v.log.html (Last accessed on: November 2017).
Electrical conductivity of the elements. http://periodictable.com/Properties/A/ElectricalConductivity.v.log. html (Last accessed on: November 2017).
F. A. Padovani, R. Stratton, Field and thermionic-field emission in Schottky barriers, Solid-State Electron., vol. 9, pp. 695-707, 1966.
K. Kunihiro, K. Kasahara, Y. Takahashi, and Y. Ohno, Experimental evaluation of impact ionization coefficients in GaN, IEEE Electron Device Letter, vol. 20, no. 12, pp. 608-610, 1999.
S. C. Shiyu, and G. Wang, High-field properties of carrier transport in bulk wurtzite GaN: Monte Carlo perspective, Journal of Applied Physics, vol. 103, pp. 703-708, 2008.
The Ioffe Institute, Electronic archive: new semiconductor materials, characteristics and properties, Available from: http://www.ioffe.ru/SVA/NSM/Semicond/index.html (Last accessed on: November 2017).
B. V. Zeghbroeck, Principles of semiconductor devices, Colorado Press, USA, 2011.
M. Sridharan, and S. K. Roy, Computer studies on the widening of the avalanche zone and decrease on efficiency in silicon X-band symmetrical DDR, Electron Lett., vol. 14, pp. 635-637, 1978.
M. Sridharan, and S. K. Roy, Effect of mobile space charge on the small signal admittance of silicon DDR, Solid State Electron., vol. 23, pp. 1001-1003, 1980.

FAQs

What causes the reduction in RF power output in GaN IMPATT diodes?add

The study indicates a 24.16-35.87% decrease in RF power output due to parasitic series resistance.

How does series resistance affect the conversion efficiency of 1.0 THz GaN IMPATT diodes?add

The research shows that series resistance reduces DC to RF conversion efficiency from 11.18% to 10.00%.

What is the peak RF power output of the 1.0-THz GaN IMPATT source?add

Simulation results predict a peak RF power output of 191.66-202.85 mW at 1.0 THz.

What modeling approach was used to study series resistance in GaN IMPATT diodes?add

The paper employs a 2-D large-signal simulation method considering the influence of skin effect.

Why is GaN preferred over conventional materials for IMPATT diodes in THz applications?add

GaN IMPATT diodes show higher RF power generation capability compared to Si, GaAs, and InP-based diodes.

1.0 THz GaN IMPATT Source: Effect of Parasitic Series Resistance

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