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> Energy band gap > GaAs  Al_{x}Ga_{1x}As  In_{x}Ga_{1x}As  
> Refractive index > GaAs  AlAs  Al_{x}Ga_{1x}As  In_{x}Ga_{1x}As  
> Devices > Bragg mirror  SAM  RSAM  SA  SANOS  SOC  Microchip laser  PCA   
PCA  Photoconductive Antenna for THz Applications 

>  Contents  
>  How does a PCA work?  
A photoconductive antenna (PCA) for terahertz (THz) waves consists of a highly
resistive direct semiconductor thin film with two electric contact pads. The film
is made in most cases using a IIIV compound semiconductor like GaAs. It is
epitaxially grown on a semiinsulating GaAs substrate (SIGaAs), which is also a
highly resistive material. 

A short laser puls with puls width < 1 ps is focused between the electric contacts of the PCA. The photons of the laser pulse have a photon energy E = h× n larger than the energy gap E_{g} and are absorbed in the film. Each absorbed photon creates a free electron in the conduction band and a hole in the valence band of the film and makes them for a short time electrical conducting until the carriers are recombined. The PCA can be used as THz transmitter as well as THz receiver.


To get the needed short carrier lifetime, the film must include crystal defects.
These defects can be created by ion implantation after the film growth or alternatively
by a low temperature growth. Low temperature grown GaAs (LTGaAs) between 200 and
400 °C contains excess arsenic clusters. 

>  PCA applications  
As mentioned above, a PCA can be used as a THz emitter or detector in
pulse laser gated broadband THz measurement systems for timedomain spectroscopy. 

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cancer detection and for teeth testing in dentistry. Terahertz waves offers medical benefits:


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>  Frequency and wavelength  
The photoconductive antenna can be considered as a dipole of the length L, which is in resonance with
the electromagnetic wavelength λ_{n}
inside the semiconductor. 

The refractive index n of GaAs at terahertz frequencies is n = 3.4. With this value the first resonant frequency and wavelength of the antenna with the length L can be calculated as follows:  
f (THz)  λ (µm)  L (µm)  
0.3  1000  147  
0.5  600  88  
1.0  300  44  
1.5  200  29.4  
3.0  100  14.7  
>  Escape angle of the THz radiation, PCA without substrate lens  
Because of the high refractive index n ~ 3.4 of the semiconductor PCA the outgoing terahertz waves are strongly diffracted at the substrateair interface. The boundary angle a for the total reflection can be calculated with α = arcsin(n^{1}) ~ 17.1 °Only the THz waves emitted in the solid angle W with 

can escape the substrate. For GaAs with n = 3.4 the escape solid angle is Ω = 0.088 π sr = 0.28 sr. This is only 4.4 % of the forward directed intensity. 

>  Aplanatic hyperhemispherical lens  
To increase the escape cone angle α, a hemispherical lens with the same refractive index n as the PCA can be used. To decrease the divergence in air, a hyperhemispherical lens with a certain distance d from the emitter to the tip of the lens is common. If this distance d is 

then the hyperhemispherical lens is aplanatic, that means without spherical and coma aberration.
For a silicon lens with almost the same refractive index n ~ 3.4 as GaAs at
terahertz frequencies the distance is d = 1.29 R with the lens radius R. The height h
of the aplanatic hyperhemispherical lens is therefore h = d  t with the thickness t of
the semiconductor PCA. 

L = R (n+1) 

For silicon is L = 4.4 R. With this hyperhemispherical lens nearly all the forward directed terahertz intensity can escape the PCA. The collection angle is α = 73.6 ° and the solid angle for the collected THz beam is Ω= 1.43 π sr = 4.51 sr. The problem left is the beam divergence, which requires a further focusing element like a lens or mirror.  
>  Collimating elliptic lens  
With an elliptical lens (truncated ellipsoid) with refractive index n a collimated THz beam can be realized if the following relations are fulfilled: 

Eccentricity  
Focus length  
Conic constant  
Distance d (lens thickness)  
Here R is the radius of curvature at the intersection of the ellipsoid with the optical axis. The lens parameters scales with R.  
The conic constant k = 1/n^{2} is related to the standard equation for an aspheric lens:  
where the optic axis is presumed to lie in the z direction, and z(r) is the sag—the zcomponent of the displacement of the surface from the vertex, at distance r from the axis. 

The antenna is located at the focal point F_{1} on the major axis of the truncated ellipsoid. The ellipse is characterized by the following parameters: 

semimajor axis  
semiminor axis  
The collection angle is  
The solid collection angle is  
The lens diameter is  
For an elliptic collimating silicon lens with n ~ 3.4 the conic constant is k = 0.086, the eccentricity ε = 0.294, the lens diameter D = 2.09 R, the collection angle α = 72.8° and the solid collection angle Ω = 1.41π sr = 4.44 sr. 
