modeling of antennas for thz radiation detectors · 2011-04-12 · em modelling (quickwave 3d ......

Modeling of antennas for THz

radiation detectors

P. Kopyt, W. K. Gwarek

Institute of Radioelectronics

Warsaw University of Technology

Experiment 1 aiming at verifying whether FET detection was sensitive to the

polarization of the incident radiation: a commercially available GaAs/AlGaAs

FET was subject to linearly polarized 100 GHz radiation.

EM modelling (QuickWave 3D) allowed revealing the role of length and

orientation of bonding wires in defining the spatial orientation of the two-lobe

pattern.

a) Device sensitivity measured for 2 values of UGS

b) Far field simulations of the device with bonds

for properly adjusted impedances ZGS, and ZDG.

1 M. Sakowicz, J. Łusakowski, K. Karpierz, M. Grynberg, W. Knap, W. Gwarek, “Polarization sensitive detection of 100 GHz radiation by high mobility field-effect transistors”, JOURNAL OF APPLIED PHYSICS 104, 024519 (2008)

Motivation

100 GHz

radiation

Antenna is a device which should

effectively couple the EM plane

wave propagating in free space to

a lumped element, eg. input impedance Z0 of a receiver.

E-field component (in space)

Z0

A load – lumped

impedance

EM plane wave

Intermediary

element

Antennas

Antenna realizations

Wideband horns

Dielectric resonator antennas

Open quad ridge horns

Antenna parameters 1

Directivity D(θ,φ) of an antenna measures

the ability of the antenna to direct its power

towards a given direction

Radiation intensity U(θ,φ) is the power radiated by an antenna with the P per

unit solid angle.

Radiated power density Pr total power emitted by an antenna per unit area

rE

1∝

rH

1, ∝

UI – same power but radiated

isotropically

U(θ,φ)

UI


Efficiency ηηηη defines all loss mechanisms (e.g. ohmic losses of the currents flowing on the antenna wires or volumetric losses in the dielectric)

Gain G(θ,φ) also measures the ability of the antenna to direct its power towards

a given direction, however the normalization is to power delivered to the

antenna terminals.

ηηηη

For a lossless antenna the efficiency factor will be unity. In the case, there is

no distinction between directive and power gain. In real cases ηηηη < 1 (not all delivered power is radiated)!

ηηηη PT Prad

Power lost to heat in

metal and dielectric

Energy stored in

antenna volume

PRPrad

Power lost to heat in

metal and dielectric

Energy stored in

antenna volume


Effective area A describes the ability of an antenna to extract power from an

incident EM wave.

Diameter(m)

A(m2)

ApertureSize (m2)

Apertureefficiency

0.30

0.45

0.60

0.90

1.20

1.80

0.0375

0.0802

0.1494

0.3121

0.6828

1.3624

0.0707

0.1590

0.2827

0.6362

1.1310

2.5447

0.53

0.50

0.53

0.49

0.60

0.53

The effective area (A) is not equal to the physical

area of an antenna! A is typically a fraction of the

physical area (55–65% for dishes and 60–80% for

horns).


ZA

Input impedance ZA is the antena impedance as seen by a generator feeding

the antenna: ZA = RA + jXA.

where, PT,max and PR,max are available power from the generator or from the antenna respectively

Under impedance matching conditions:

Impedance matching affects the delivered power.


Bandwidth BW range of frequencies within which the performance of the

antenna, with respect to some characteristic, conforms to a specified

standards/requirements.

Impedance bandwidth BWZ range of frequencies within which the antena

reflection coefficient ΓΓΓΓ for its input remains low.

Radiation bandwidth BWR range of frequencies within which the antena

radiation characteristics stays within the desired limit. Typically BWZ < BWR

center

lowerupper

Zf

ffBW

−=

fupper flower

fcenter

Elevation [o]

Antenna analysis methods 1

Analytical methods typically possible for antennas of simple geometries, like

linear antennas, selected horn structures, open-ended waveguides used as

radiating structures.

Example: half-wavelength dipole :

Antenna analysis methods 2

Numerical methods employed complex radiating geometries based on the

Finite Difference Time Domain – FDTD (QuickWave 3D, CST); Finite Elements

Method – FEM (HFSS) or Method of Moments – MoM (Sonnet, FEKO).

FDTD method implemented in QuickWave 3D, QWED, Poland

Standard FDTD cells:

air dielectric metal

dielectric media interfaces

metal boundaries

Conformal cells in QuickWave 3D:

Classical examples of application 1

Axially symmetrical corrugated horn for satellite communication:

Hφ at 13.75GHz Design & measurements: P. Brachat, IEEE Trans. AP,

April 1994

6 GHz

-40

-30

-20

-10

020

40

60

80

100

120

140

160200

220

240

260

280

300

320

340

Pyramidal horn antenna for military surveillance:

Design & measurements:

Prof. B. Stec,

Technical Military Academy, Poland

------ vertical plane measured

____ vertical plane simulated

------ horizontal plane measured

____ horizontal plane simulated

Classical examples of application 2

Amplitude and phase imbalance

– from the measured (noisy)

and simulated (smooth) results.www.mma.nrao.edu/memos/html-memos/alma278/memo278.pdf

www.mma.nrao.edu/memos/html-memos/alma343/memo343.pdf

WR-10 waveguide quadrature hybrid1 with

six branch lines (S.Srikanth and A. R.

Kerr, National Radio Astronomy

Observatory, Charlottesville, VA 22903,

USA)

The radiation pattern

The dominating E-field

component magnitude (TM00)The impedance matching of the antenna

Numerical antenna analysis

Patch antennas are mostly analysed numerically as analytical approach is

limited to very thin substrates, not applicable to proximity/apperture coupled

antennas.

Example: rectangular patch antenna for 340 GHz

Thickness of the substrate and planar antennas performance

Rectangular patch Circular patch

Impedance bandwidth BWZ

Thickness of the substrate and planar antennas performance 2

The fields distribution under the metalization layer

Instanteneous H-field distribution in the axial-

plane of antenna (f = 300 GHz)

d = 40 µm

(~λ/8)

d = 90 µm

d = 200 µm

Printed dipole on thick

silicon (εr = 11.65) substrate

The substrate supports propagating waveguide modes (simplified 1-D analysis):

• TMn (existence of transverse H-field components and longitudinal E-field in the substrate: Hx, Hz i Ey)

• TEn (existence of transverse E-field components and longitudinal H-field in the substrate : Ex, Ez i Hy).

14

,

−=

r

TETMn

d

ncf

ε, where n = 0, 1, 2, 3, ...;The cut-off frequency is defined as:


The cut-off frequency of substrate modes

vs. substrate thickness

Propagation const.

Im γ for TM0

Propagation const.

Im γ for TE1


A numerical experiment to further investigate

substrate supports propagating waveguide modes (this time 3-D numerical analysis):

• change silicon substrate thickness

• measure the radiated power (into air)

• Compare the value with the power delivered to the antenna

An antenna on thick substrate with a box necessary to calculate power radiated into air

air region

How much power propagates in substrate and never get out into air?How much power in each substrate mode?


The effect employed in Dielectric Resonator Antennas (DRA), where:

• The metal element on the substrate is no longer radiating, but used only to excite proper field distribution within the dielectric

• The dielectric slab of proper dimensions (3-dimensional – thick) radiates from its sides!

An example DRA1 excited through the apperture:

In practice, the substrate under the

printed dipole must end. For thick

substrates supporting propagating modes,

the side of the slab start to radiate. The metal element only excites the fields.

1 K. M. Luk, K. W. Leung, „Dielectric Resonators Antennas”, Research Studies Press, Ltd.

Reciprocity principle states that applying a voltage V to terminals of antenna A,

a current I is measured at the terminals of antenna B. The same current will be

measured at the teminals of antenna A if the voltage V is applied to antenna B.

For linear isotropic medium the reciprocity principle allows to investigate

radiating structures either as a receiving antenna coupling the external radiation

to the receiver or — by reciprocity — as an antenna radiating a particular

pattern when excited at its terminals. In both cases the antenna properties

including the radiation/reception patterns should be the same.

Reciprocity principle

Analysis a structure with applying excitation at the antenna terminals:

• Separate calculations of the antenna impedance ZA, and• The antenna gain G,

• Combining the above to obtain responsivity R of the analyzed structure.

V:

)Re()1(4

G 222

TRZR Γ−Π

∝λ

)Re(2, TRRba ZPUR =∝

Responsivity of the structure is proportional to Ua,b at the

load (transistor) terminals.

incR APP =max,

Maximum power delivered by the antenna depends on the

incident wave power Pinc and the effective area A of the

antenna.

Power actually delivered to the load depends on the

impedance matching between antenna and the load.)1(

2

max, Γ−= RR PP

Normalized responsivity of a structure

G, ZA

Excitation of the antenna terminals

Excitation of the antenna terminals 2

A bolometer detector 1-3 modelled using the approach with excitation of the

antenna terminals, obtaning the ZA and G.

The peak responsivity predicted numerically (498

GHz) lies close to the measured one (524 GHz).

hot electron bolometer, Rb = 75Ω

Twin-slot antenna on thick silicon

substrate (1.3 × 1.4 × 0.25 mm3)

1 R. A. Wyss, A. Neto, W. R. McGrath, B. Bumble, and H. LeDuc, “Submillimeter-wave spectral response of twin-

slot antennas coupled to hot electron bolometers,” in Proc. 11th Int. Space Terahertz Technology Symp., Ann

Arbor, MI, May 1–3, 2000, pp. 379–388.2 B. S. Karasik, M. C. Gaidis, W. R. McGrath, B. Bumble, H.G. LeDuc, “A low-noise 2.5 THz superconductive Nb

hot-electron mixer,” IEEE Trans. Appl. Supercond. 7 (2), 3580 (1997).3 B. S. Karasik, private e-mail communication, Nov 2010.

)Re()1(4

G 222

TRZR Γ−Π

∝λ

Analysis a structure using plane wave as an excitation :

• Generate a plane wave incident on a structure;• The structure is loaded with received/detector impedance;

• Observe voltage at the load (FFT necessary to get Uf ).

Responsivity of the structure is proportional to Ua,b at

the load (transistor) terminals.

Since Ua,b is given explicitely, no need to separately

analyze G and ZA.

The difficulty lies in proper definition of ZTR in the

full-wave simulation.

Excitation of antenna with plane wave 1

E-field magnitude in a silicon slab irradiated with planewave

The field distribution within the thick (125 µm) silicon substrate subjected to

THz irradiation (dimensions: 2.20 × 2.25 × 0.125 µm3).

250 GHz 300 GHz 350 GHz

E-field intensity recorded in the location of C14 transistor

Excitation of antenna with plane wave 2

The chip1 consisting of 61 detectors with bow-tie antennas that was subjected

to plane wave irradiation. A simplified version of the metalization planes was

prepared.

Excitation of the multiple detectors with plane wave 1

1 Montpellier university group.

The topology of the metallization planes (layers

shown with colors)

Simplified 1-layer topology with

dicretization

Excitation of the multiple detectors with plane wave 2

The plane wave irradiation revealed a sharp peak of voltage at the C14 antenna

load. Peeling the structure of unnecessary elements allows to point out those

responsible.

Normalized voltage at the C14 antenna load

The stripped-down

structure that still shows

the peak.

Conclusions

• Bonded structures subjected to THz irradiation have antennas (even if

uninteded ones). One needs to take them into account while analysing the behavious of analysed structure.

• The behaviour of planar antennas realized on thick substrates stop to

be governed by sizes of the metal elements (e.g. length of the dipole arms) – the substrate size and its properties start to play a role.

• The numerical analysis may help in understanding the behaviour of detectors integrated with antennas but…

• The more complex the structure the more difficult is its analysis as

multiple effects (e.g. thick substrate, multiple of metalic objects/tracks on the surface) add up like in the case of the 61-detector chip.

Questions ?

modeling of antennas for thz radiation detectors · 2011-04-12 · em modelling (quickwave 3d ......

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