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Studies on frequency chirping in optically illuminated α-Gallium Nitride Impatt Diodes at Sub-millimeter wave frequency Soumen Banerjee, Priya Chakrabarti, Riya Baidya and J. P. Banerjee Abstract — The frequency chirping effect under optically illumination of Wurtzite phase of Gallium Nitride (Wz-GaN or α-GaN) based DDR Impatt diodes at 300 GHz or 0.3 Terahertz (THz) has been investigated. Top Mounted (TM) and Flip Chip (FC) structures are chosen and the composition of photocurrent is altered by shining light on the p+ side and n+ side of the device through optical windows. A double iterative computer simulation method based on drift-diffusion model has been used to study the small signal performance and subsequent modification of the small signal parameters owing to optical illumination. The role of leakage current in controlling the dynamic properties is studied by varying the current multiplication factors for electrons (Mn) and for holes (Mp). The simulation studies reveal that these devices are potential sources for generating high power at Terahertz domain. The conversion efficiency is found to be 15.47% at 0.3 THz at an optimum bias current density of 0.5 x 108 A/m2. The output power obtained is 6.23 W at 0.3 THz. The optical illumination reveals that a lowering of Mp causes more upward shift in frequency than a corresponding lowering of Mn. The frequency chirping in α-GaN Impatt is of the order of few GHz. The design results thus indicate the high photo-sensitiveness of α-GaN Impatts at Terahertz domain. Index Terms — Double Drift Impatt diode, Flip Chip structure, Top Mounted structure, Terahertz frequency, Wurtzite phase of Gallium Nitride

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1 INTRODUCTION

S

ub-millimter wave or Terahertz (THz) wave, in today’s scenario, is a very upcoming and developing technological field drawing immense interest among researchers worldwide. The terahertz technology is been used in many areas spanning from applications in food, medical care and security sectors to the studies of fundamental physics and cultural heritage [1]. The ongoing developments in terahertz technology have brought up the possibility of opening up an extra-ordinary range of new markets in the decade [2]. The tremendous versatility of terahertz technology allows it to find extensive applications in aiport screening of passengers for weapons, explosives, drugs or other contraband, secure wireless communication, biological and medical applications, remote sensing, imaging, spectroscopy, monitoring manufacturing processes etc. What is clear is that this terahertz industry as a whole is on the verge of significant growth [3]. To cope with this development, there is tremendous urge observed among scientist worldwide to develop solid state sources that may be employed as high power THz source. Among all the solid state sources, Impatt diodes have already emerged as most powerful solid state source in various civilian and space communication system. These •

• • •

diodes are very powerful solid state sources capable of generating high frequency Power at microwaves, millimeter waves and sub-millimeter waves thereby covering a wide range of frequency spectrum and finding wide applications as solid state transmitters in tracking radars, missile seekers, radiometers, and mmwave communication systems. However the THz region is unapproachable by conventional Si, Ge and GaAs based Impatt devices as because some fundamental limitations in the material parameters of these semiconductors impose restriction on THz frequency operation. The search is on to find new materials for Impatt diodes such that they overcome these limitations and produce high power at higher frequencies. Fortunately, wide band-gap semiconductors such as ІІІ-V GaN and ІV-ІV SiC offer interesting alternatives to traditional Si, Ge, GaAs owing to the possibility of operation with a higher output power resulting from increased critical field, higher band-gap energy, higher saturation velocity and much better thermal conductivity [4], [5]. These wide band gap semiconductors possessing excellent material properties are recently been used as base materials for electronic and opto-electronic devices [6]. GaN (bandgap energy = 3.39 eV at room temperature) ———————————————— supports peak internal electric field about 5 times higher Soumen Banerjee is with the Department of Electronics & Communication than those using Si and GaAs, resulting in higher breakEngg., Hooghly Engineering & Technology College, Hooghly, WB, India. down voltage, which is extremely important for devices Priya Chakrabarti is with the Institute of Engineering & Management, Kolkata, India. handling high power. Hence GaN based Impatts can opRiya Baidya is with the Institute of Engineering & Management, Kolkata, erate at higher voltage at the same operating frequency. India. J. P. Banerjee is with the Institute of Radio Physics & Electronics, Univer- With high value of Ec much higher doping level can be achieved. GaN is less noisy and is chemically very stable sity of Calcutta, Kolkata, India. © 2010 JOT http://sites.google.com/site/journaloftelecommunications/

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at high temperatures. Another consequence of higher electric field and higher doping density is the width reduction in the drift region. Thus, not only high power but also the high frequency (THz) operation capability is expected from these wide band gap based devices [7], [8], [9]. Even going by Keyes’ FOM (considering the speed of transistors and their thermal limitations) and Johnson’s FOM (considering the HF and high power capability of devices), the high frequency and high temperature performance of SiC and GaN are much superior as compared to conventional Si and GaAs [10]. Despite all the High Frequency (THz) operating advantages, GaN is yet to hit the main stream owing to the difficulties in growth and device fabrication. Considerable progress in the growth of Nitrides during the last five years makes this material suitable for fabrication of various electronic devices. High quality GaN film can be grown on SiC substrate by MOCVD technique by using a SixNy inserting layer [11]. Hence in the light of maturity of the fabrication technology and the unique material properties, GaN appears to be one of the best choices for development of semiconductor devices, especially in THz region, in the coming decade. To the base of authors knowledge no experimental result on GaN Impatt diodes are available in the literature. However, some studies on GaN Impatts have been reported lately [12], [13], [14], [15], [16], [17]. In the sub-millimeter/THz region, high power Impatt oscillators are extremely useful solid state sources. To satisfy the quest of increasing demand for high power THz sources and to study its optical properties, the authors have designed a symmetrically doped flat profile p+pnn+ Wz-GaN (α-GaN) DDR Impatt at 0.3 THz and have subjected it under optical illumination considering both Top Mounted (TM) and Flip Chip (FC) structure. The DC and small signal properties has been investigated under both unilluminated and illuminated conditions. Impatt oscillators used as THz sources in spacecrafts may be subjected to interstellar radiation that can produce appreciable changes in its performance. The study of frequency chirping under optical illumination is carried out by illuminating the diode by any external radiation. The underlying physics involved is that when a photon of energy hν greater than the bandgap energy Eg of the semiconductor is absorbed at the edge of the reversed bias pn junction of Impatt diode, production of additional e-h pairs takes place within the active region of the device. These photo-generated carriers give rise to photocurrent; thereby enhancing the existing thermal leakage current in the device. This enhanced leakage current alters the avalanche phase delay and subsequently modifies the phase and magnitude of the terminal current in the device oscillator circuit. The present paper aims to explore the potentiality of the devices as probable solid state source at THz frequency and also investigating its optical effects so that the study may be utilised for THz frequency tuning.

2 SIMULATION METHODOLIGIES 2.1 Material Parameters, Design Parameters and Doping Profile The values of the material parameters of WurtziteGaN are taken from recent published papers and electronic archive [18] and they are enlisted in Table-1. The structural parameters of the symmetrically doped p+pnn+ α-GaN DDR Impatt diode are enlisted in Table-2. The operating frequency of Impatt diode essentially depends on the transit time of charge carriers to cross the depletion layer of the diode. Double Drift Region (DDR) structure of Impatt diode are designed and optimized through a generalized double-iterative simulation scheme used for analysis of Impatt action. The prime action underlying Impatt behaviour is Avalanche breakdown caused by high electric field. The main factor is the response time of the charged particles (electrons and holes) which is related to the avalanche multiplication and leads an important role in determining the device characteristics for high frequency performance. If τn and τp be the response times for electrons and holes respectively, then these are expressed as

1 τn = vsn + vsp

WA

x

0

0

∫ exp[−∫ (α − β )dx]dx

(1)

WA

τ p = τ n exp[ ∫ (α − β )]dx

(2)

0

where α and β are the ionization coefficients for α-GaN. The coefficients α and β are expressed as α = An exp (-Bn/E)

and

β = Ap exp (-Bp/E)

The values of An, Ap, bn and bp for α-GaN at low electric field values and Ahn, Ahp, bhn and bhp for α-GaN at high electric field are enlisted in Table-1. When avalanche is initiated by a mixture of electrons and holes then the corresponding response time τ1 is given by WA

τ 1 = τ n [(1 − k ) + k exp{− ∫ (α − β )dx}]−1

(3)

0

where k is the injection ratio, defined as Jps/Js and WA is the avalanche width. If the value of avalanche response time τ1 is found to be smaller than the value of the transit time (τ) of the materials, then only high frequency oscillation can be produced by the diode. The present paper deals with a flat profile p+pnn+ DDR Impatt structure based on α-GaN; where p+ and n+ are highly doped substrate and n and p are epilayer. Computer simulation is carried out at an operating frequency of 300 GHz and the width of the epilayer are accordingly chosen using the transit time formula of Sze and Ryder [19]; which is W = 0.35 vsn/f where W, vsn and

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f are the total depletion layer width, saturation velocity of electrons and operating frequency respectively. Fig. 1 depicts the structure, doping profile and electric field profile of p+pnn+ GaN DDR Impatt diode. The proposed methodology of fabricating the device and the method to study its high frequency and optical properties are dicussed elsewhere [4], [12].

tion layer. The boundary conditions for normalized current density P(x) = (JP – Jn)/J0 (where Jp =hole current density, Jn = electron current density) at the two edges are given by P (-x1) = (2/Mp – 1) and P(x2) = (1 – 2/Mn)

(5)

The necessary device equations have been simultaneously solved [20], [21], [22] satisfying the appropriate boundary conditions mentioned in equations (4-5). The field dependence of electron and hole ionization rates and saturated drift velocities of electron (vs,n) and holes (vs,p) at 300K are made use of in the computation for the profiles of electric field and carrier currents. The conversion efficiency is calculated from the approximate formula [23] η(%) = (1xVd) / (π x VB)

Fig. 1. Electric field and Doping profile of p+pnn+ DDR Wurtzite-GaN Impatt diode.

(6)

where Vd = Voltage drop across the drift region and VB = Breakdown voltage. Avalanche breakdown occurs in the junction when the electric field is large enough such that the charge multiplication factors (Mn, Mp) become infinite. Again, the breakdown voltage is calculated by integrating the spatial field profile over the total depletion layer width, i.e., x2

VB = ∫ E ( x)dx

(7)

x1

2.2 Computer Simulation Techniques The simulation method based on drift-diffusion model starts with DC analysis described in details elsewhere [20],[21],[22]. The following assumptions are made in the computer analysis of DC and small signal behavior of αGaN DDR Impatt diodes; (a) One dimensional model of the p-n junction is treated; (b) The electron and hole velocities are taken to be saturated and independent of the electric field throughout the space charge layer. In this method the computation starts from the field maximum near the metallurgical junction. The distribution of DC electric field and carrier currents in the depletion layer is obtained by the double - iterative computer method, which involves iteration over the magnitude of field maximum (Em) and its location in the depletion layer. A computer algorithm has been developed for simultaneous numerical solution of Poisson’s equation, carrier continuity equations and the space charge equation taking into account the effect of mobile space charge and carrier diffusion in order to obtain the electric field profiles and carrier current profiles. The boundary conditions for the electric field at the depletion layer edges are given by

where –x1 = n – side depletion layer width +x2 = p – side depletion layer width The high-frequency analysis of α-GaN DDR IMPATT diode provides insight into its high frequency performance. The range of frequencies exhibiting negative conductance of the diode can easily be computed by Gummel-Blue method [24]. From the dc field and current profiles, the spatially dependent ionization rates that appear in the Gummel-Blue equations are evaluated, and fed as input data for the small signal analysis. The edges of the depletion layer of the diode, which are fixed by the dc analysis, are taken as the starting and end points for the small signal analysis. On splitting the diode impedance Z (x,ω) obtained from Gummel–Blue method, into its real part R (x,ω) and imaginary part X (x,ω), two differential equations are framed [24]. A double-iterative simulation scheme incorporating modified Runge-Kutta method is used to solve these two equations simultaneously. The diode negative resistance (-ZR) and reactance (-Zx) are computed through numerical integration of the -R (x) and -X (x) profiles over the active space-charge layer. Thus, x2

E (-x1) = 0

and

E (+x2) = 0

(4)

where -x1 and x2 define the p+ and n+ edges of the deple-

− Z R = ∫ − Rdx x1

x2

and

− Z X = ∫ − Xdx x1

The negative conductance (G), Susceptance (B) and the

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quality factor (Q) of the device can be calculated using the following relations:

tron dominated photocurrent that changes the expression for electron current multiplication factor to Mn = J0 / [Jns (th) + Jns (opt)]

-G = -ZR /[(ZR)2 + (ZX)2] and B = ZX / [(ZR)2 + (ZX)2] and -Qpeak = (B /-G)at peak frequency It may be noted that both –G and B are normalized to the area of the diode. The avalanche frequency (fa) is the frequency at which the imaginary part (B) of the admittance changes its nature from inductive to capacitive. Again it is the minimum frequency at which the real part (G) of admittance becomes negative and oscillation starts to build up in the circuit. At a resonant frequency of oscillation, the maximum power output PRF from the device can be obtained from the following expression, PRF = V2RF (Gp) A/2

(8)

where, VRF is the amplitude of the RF swing and is taken as VB/2, assuming 50% modulation of the breakdown voltage VB. Gp is the diode negative conductance at the operating frequency and A is the area of the diode, taken as 10-10 m2.

2.3 Effect of optical illumination on Impatt diode The leakage current (Js), entering the depletion region of the reversed biased p-n junction of an IMPATT diode, is normally due to thermally generated electrons and holes [Js = Jns (th) + Jps (th)] and it is so small that current multiplication factor, (9) Mn, p = J0 /[Jns (th) or Jps (th)] [J0 = bias current density] can be considered to be infinitely large. Thus, the enhancement of the leakage current under optical illumination of the devices is manifested as the lowering of Mn,p. The composition of the leakage current (electron versus hole photocurrent) plays a vital role in controlling the microwave properties of the optically illuminated IMPATTs. In a DDR IMPATT structure (p+pnn+ type), the composition of photocurrent may be altered by shining a laser beam selectively on the p+ or n+ side of the device through fabricated optical windows of appropriate diameter, keeping the diode mounted in a microwave cavity. Thus, the electron saturation current and also the hole saturation current may be enhanced separately, which subsequently produce changes in the high frequency performance of the IMPATTs. The effect of shining light from the p+ side in a TM (Top Mounted) IMPATT diode (Fig. 2) is to generate an elec-

(10)

where Jns (opt) = saturation current due to photoelectrons. Thus, the photoelectrons reduce the value of Mn, while the value of Mp remains unchanged. Similarly, the effect of shining light from the substrate side (n+ edge) in a FC (Flip Chip) IMPATT structure (Fig. 3) is to generate a hole dominated photo-current that modifies the expression for hole current multiplication factor to Mp = J0 / [Jps (th) + Jps (opt)]

(11)

where Jps (opt) = saturation current due to photo generated holes. So, the photo generated holes reduce the value of Mp, while the value of Mn remains unchanged. In order to assess the role of leakage current in controlling the dynamic properties of IMPATT oscillator at THz region, simulation studies are carried out by the authors on the effect of Mn (keeping Mp very high ~ 106) and Mp (keeping Mn very high ~ 106) on (i) the small signal admittance characteristics, (ii) the device quality factor (Q), and (iii) the output power, PRF of flat profile α-GaN DDR Impatt diode and the results are reported in the present paper. The details of mathematical calculations based on modified boundary conditions due to enhancement of leakage current is discussed elsewhere [25].

Fig. 2. Wz-Gallium Nitride based Impatt diode under optical illumination (TM diode)

Fig. 3 Wz-Gallium Nitride based Impatt diode under optical illumination (FC diode)

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3 RESULTS AND DISCUSSIONS The material parameters of α-GaN is enlisted in Table-1 and the structural parameters of symmetrically doped αGaN based DDR Impatt diode at 0.3 THz is enlisted in Table-2. Fig. 4 depicts the plot of electric field profile of αGaN based DDR Impatt diode at 0.3 THz and at an optimum bias current density of 0.5 x 108 A/m2. The peak electric field obtained is very high (~ 18 x 108 V/m). A very small punch through is observed from the electric field profile. The simulated results of the DC and high frequency (small signal) properties of α-GaN DDR Impatt diode are given in Table-3. From the DC properties of the device, it is observed that GaN based Impatts has a very high breakdown voltage of 110.26 V at 300 GHz with a conversion efficiency of 15.47%. The output power generated by the device is 6.23 W at 300 GHz. As GaN is a wide bandgap semiconductor with bandgap energy of 3.39 eV, hence from the data reflected from Table-3 it is quite evident that α-GaN based DDR Impatt diode is a high current and high power device. Hence from practical application point of view, Impatts based on α-GaN is favoured owing to its capability of generating higher efficiency and much higher power at THz domain. At 0.3 THz, the peak negative conductance for α-GaN Impatt is 0.41 x 108 S/m2 at a bias current density of 0.5 x 108 A/m2. Fig. 5 depicts the plot of Conductance vs. Susceptance at 0.3 THz for αGaN based DDR Impatt diode under unilluminated condition. The simulation has been carried out by varying the bias current density (J0) and at an optimum value of J0 = 0.5 x 108 A/m2, the peak frequency (300 GHz) obtained is exactly equal to the design frequency (300 GHz) under consideration. The Q-factor determines the growth rate and stability of oscillation. Less Q-factor means better device performance. The Q-factor in case of this device is found to be 3.5. The avalanche response time (τ1) in case of α-GaN is obtained as 2.47 x 10-16 s and its transit time (τ) is 1.33 x 10-16 s. Hence the value of τ1 is less than τ thereby indicating the capability of producing oscillations at higher frequencies. The results obtained are very encouraging and portrays the strong potentiality of α-GaN Impatt diode as a powerful oscillator for Terahertz communication. The effect of electrons and holes generated photocurrent on the high frequency properties of α-GaN DDR Impatt diode are shown in Table-4. The optimized design parameters of the unilluminated α-GaN DDR Impatt diode for which both Mn and Mp are large (=106) are already mentioned earlier. Fig. 6 depicts the conductancesusceptance plot of illuminated α-GaN DDR Impatt diode for both TM and FC structure at a bias current density of 0.5 x 108 A/m2. The G-B plot has been carried out by varying the value of Mn and Mp. For a decrease in the value of Mp, keeping Mn constant, there is a decrease in the value

of both conductance |-Gp| and output power PRF. The same is observed in case of lowering of Mn, keeping Mp fixed. The optimum frequency of oscillation shifts upwards from 300 GHz to 302 GHz for the TM structure and hence the frequency chirping for the TM diode is 1-2 GHz. For the FC structure, the frequency shifts upwards from 300 GHz to 300.5 GHz and hence the frequency chirping is found to be of the order of 0.5 GHz. Thus the effect of photo illumination on frequency chirping is found to be more pronounced in FC diode than in TM diode in case of α-GaN DDR Impatt diode operating at 300 GHz. It is thus expected that this device can be employed as a promising switching tool at THz regime.

TABLE 1 MATERIAL PARAMETERS OF α-GAN Parameters

α-GaN

Band gap energy (eV)

3.39

Thermal conductivity (W/cm K)

1.30

An (108 /m)

3.65

bn (108 V/m)

0.99

Ap (108 /m)

6.44

bp (108 V/m)

1.57

Ahn (108 /m)

3.65

bhn (108 V/m)

0.99

Ahp (108 /m)

6.44

bhp (108 V/m)

1.57

vsn (105 m/s)

2.0

vsp (105 m/s)

0.70

µn (m2/Vs)

0.055

µp (m2 /Vs)

0.051

Permittivity

(10-9 Fm-1)

0.108

An, Ap, bn, bp : Ionization coefficient of electrons and holes resp. at low fields Ahn, Ahp, bhn, bhp : Ionization coefficient of electrons and holes resp. at high fields vsn,vsp : Saturation drift velocity of electrons and holes resp. µn ,µp : Mobility of electrons and holes resp.

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TABLE 2 STRUCTURAL PARAMETERS OF SYMMETRICALLY DOPED α-GAN BASED DDR IMPATT DIODE AT 300 GHZ Structural Parameters

α-GaN

Width of n epilayer Wn (nm)

575 nm

Width of p epilayer Wp (nm)

570 nm

Doping conc of n region ( m-3) -3

Doping conc of p region ( m ) 2

Current Density (A/m )

1.5 x 1023 1.5 x 1023 0.5 x 108

-3

Substrate Doping Conc (m )

1 x 1026

Area of the diode

1 x 10-10

Fig. 4. Electric Field profile of p+pnn+ DDR Wurtzite-GaN based DDR Impatt diode at 300 GHz.

TABLE 3 DC AND SMALL SIGNAL ANALYSIS OF α-GAN BASED DDR IMPATT DIODE AT 300 GHZ α-GaN

Structural Parameters Peak electric field, Ec (V/m)

18.17 x 107

Breakdown voltage, VB (V)

110.26

Peak frequency (THz)

0.300

Peak Conductance (S/m2)

-0.41 x 108

Quality Factor, -QP

3.5

Efficiency (%)

15.47

Output power, PRF Avalanche response time (sec)

6.23 W 2.47 x 10-16

Transit time (sec)

1.33 x 10-16

Fig. 5. Conductance-Susceptance plot of unilluminated α-GaN based DDR Impatt diode at 300 GHz

TABLE 4 MODIFIED HIGH FREQUENCY PARAMETRS OF α-GAN BASED DDR IMPATT DIODE FOR DIFFERENT VALUES OF CURRENT MULTIPLICATION FACTOR (UNDER OPTICAL ILLUMINATION) Mn

Mp

fp (GHz)

Gp 108 S/m2

B 108 S/m2

-Q

PRF (W)

300

R 10-8 Ωm2 -0.19

106

106

-0.41

1.43

3.49

6.23

106

100

301

-0.18

-0.40

1.39

3.48

6.078

106

50

302

-0.17

-0.39

1.42

3.64

5.93

100

106

300.1

-0.19

-0.41

1.43

3.48

6.23

50

106

300.5

-0.18

-0.40

1.43

3.48

6.078

Fig. 6. Conductance-Susceptance plot of α-GaN based DDR Impatt diode (TM and FC structure) under optical illumination at 300 GHz and bias current density of 0.5 x 108 A/m2.

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4 CONCLUSION The simulation of the DC and high frequency properties of α-GaN based DDR Impatt diode reveals a strong potentiality of the device as a powerful source at Terahertz frequency. The study on the photo-illuminated properties shows that the optical modulation of the FC structure is more pronounced than the TM counterpart at 300 GHz. This study will be very helpful for the optical control of α-GaN DDR Impatt diode in applications like sub-millimeter wave communication systems, missile guidance, solid state terahertz transmitters, radar tracking etc.

ACKNOWLEDGMENT The authors wish to thank Institute of Radio Physics & Electronics, University of Calcutta for the support of the research work.

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Prof. Soumen Banerjee is Professor and Head of the Department of Electronics & Communication Engineering at Hooghly Engineering & Technology College, West Bengal, India. He obtained B. Sc degree with honours in Physics from the University of Calcutta and both B.Tech and M.Tech degrees from the Institute of Radio Physics & Electronics, University of Calcutta, India. He is pursuing research work on Millimeter wave and THz devices for Ph.D degree in the Institute of Radio Physics & Electronics, University of Calcutta. His research interests are microwave & millimeter-wave semiconductor devices & systems. He is working with wide band gap semiconductor based Impatt diodes design, fabrication and characterization in D-band, W-band and THz frequencies for many years. He has published many papers related to Impatt diodes in Int. Journal and International/National Conferences. He is also associated with the Centre of Millimeterwave Semiconductor Devices & Systems (CMSDS), University of Calcutta, for research activities. Prof. Banerjee is a member of IET (UK), IETE (New Delhi, India) and IE (India).

Priya Chakrabarti is pursuing B. Tech Course in Electronics & Communication Engineering from Institute of Engineering & Management, Kolkata, India. Her areas of interest are solid state devices, microwave, millimeter wave & opto-electronic devices and communication systems.

Riya Baidya is pursuing B. Tech Course in Electronics & Communication Engineering from Institute of Engineering & Management, Kolkata, India. Her areas of interest are solid state devices, microwave, millimeter wave & opto-electronic devices and communication systems.

Prof. J. P. Banerjee is a Senior Professor at the Institute of Radio Physics & Electronics, University of Calcutta and also the Director of Centre of Millimeterwave Semiconductor Devices & Systems (CMSDS), Kolkata, India. He received B.Sc, M.Sc and Ph.D degrees from the University of Calcutta, India. He has been in teaching and research for more than three decades at the University of Calcutta. His research interests are microwave, millimeter-wave & opto-electronic semiconductor devices & systems. He has published more than 100 research papers in peer-reviewed International & National Journals most of which are highly cited. He is the recipient of Indian National Science Academy award and Griffith Memorial prize of the University of Calcutta. He is a Senior Member of IEEE and a Fellow of IETE.