This research covers the different aspects of photoconductive antennas (PCAs) modeling. 6.14 Effect of the angle of incidence of the external magnetic field (from the positive direction of the y-axis) on the radiated electric field in the far zone.

THz Frequency Spectrum

Challenges in the THz Radiation Sources

## THz Sources

### Electronic Sources

These sources include back wave oscillators (BWO) [13], extended interaction klystron [14], gyrotron [15], synchrotrons [16] and traveling wave tubes (TWT) [17]. Sources include Gunn diodes [19], high-frequency transistors [20], frequency multipliers [21], resonant tunneling diodes (RTDs) [22], and IMPATT diodes [23].

### Optical Sources

The principle of operation of vacuum electron sources is based on the interaction between an electron beam and electromagnetic fields. To generate broadband THz radiation from nonlinear crystals, optical routing is one of the most commonly used techniques [29].

### Optoelectronic Sources

The THz generation using non-linear crystals is one of the general methods where crystals with a large second-order sensitivity are used to downconvert the optical power of the lasers. The list of some of the THz sources with their output powers and operating frequencies/bandwidth is shown in Table 1.1.

## THz Detectors

*Coherent THz Detection**Incoherent THz Detection**Optoelectronic THz Detectors**Free Space Electro-Optic Sampling Technique*

This THz wave detection technique uses the linear electro-optical (EO) effect, also known as the Pockel effect, in an EO crystal (non-linear crystal). Birefringence causes a change in the polarization of the probe beam, and its measurement determines the amplitude of THz signals [2, 55].

## Applications of THz Waves

Bio-medical Applications

Pharmaceutical Applications

Security Applications

Polymer Industry Applications

Communication Applications

## Working Principle of the THz PCA as an Emitter

The temporal behavior of the laser pulse, the current pulse and the radiated THz electric field is shown in Fig. The carrier generation rate in the semiconductor material depends on the laser pulse character - TH.

## Research Motivation and the Problem Formulation

There are several factors that limit the efficiency and radiated power of the PCA. Perform analysis to identify the factors that limit the radiated power and efficiency of the PCA. IV).

## Thesis Contribution

The proposed study ignores the effect of the semiconductor substrate on the radiation from the PCAs. It uses the electromagnetic relationships and the effect of the semiconductor substrate material on the radiated fields.

## Thesis Overview

The effect of the parameters related to substrate material, laser and antenna geometry on the PCA performance has been analyzed. Furthermore, a new equivalent electrical circuit of the PCA acting as a detector has been proposed.

## Main Components of a PCA

### Photoconductive Semiconductor Substrate

*Low-Temperature Grown-Gallium Arsenide (LT-GaAs)*

The research [94] found that when the LT-GaAs material undergoes the post-growth annealing process at high temperatures (600-800◦C), the crystallinity of the epi layers is significantly improved. A very small carrier lifetime/relaxation time in the LT-GaAs is a favorable feature. for its THz generation.

### Antenna Geometry

For the first time study reported in [105] investigated the carrier relaxation time and reported a carrier lifetime of 0.4 ps for a material grown at 200◦C and annealed at 600◦C. For LT-GaAs, the carrier mobility has been investigated using various methods such as Hall measurements [112], the time-integrated efficiency of photoconductive switches, and THz spectroscopy.

### Laser Source

In the literature, the PCAs have been divided into three categories based on the gap dimensions: small-aperture PCAs (5–50 µm), semi-large-aperture PCAs (50–100 µm), and large-aperture PCAs (0.1–5 mm) [123] .

## Literature Survey

*Literature Review of the Simulation Studies**Literature Review of the Circuit Modeling Studies**Literature Review of the Near Fields Effect on the Performance of**Literature Review of Performance Enhancement Studies**Literature Review of the Theoretical Analysis of the Radiated Fields 33*

Loata et al.[130] presented a basic equivalent electrical circuit of the PCA as shown in Fig. This study presents the effect of the gap length on the different properties of the PCA.

## Semiconductor Physics

*Electrostatic Potential**Continuity Equation**Recombination Process**SRH Recombination Model**Auger Recombination Model**Optical Generation**Metal-Semiconductor Interface**Mobility Models**Arora Mobility Model**Caughey-Thomas Mobility Model*

The mobility models originated from the moment of relaxation time of the carriers in the grid. The doping dependence of carrier mobility is modeled using the Arora mobility model, which is given as.

## Simulation Steps in Sentaurus TCAD

The field dependence of the carrier mobility is modeled by the Caughey-Thomas model and is given as where µlow,n and µlow,p are the low-field mobilities of electrons and holes, respectively, vsat,nandvsat,p are the saturation velocities of electrons, respectively and holes, and is the applied electric field.

LT-GaAs Material Characteristics

## Simulation Setup in the Sentaurus TCAD

The LT-GaAs material is not available in the Sentaurus TCAD material library, so the GaAs material properties were modified according to the information available in the literature of the LT-GaAs. The excitation of the carriers by the laser illumination is resolved using the beam-tracing optical resolver.

## Results and Discussions

*Effect of the Bias Voltage**Effect of the Laser Power**Effect of the Laser Pulse Width**Effect of the Laser Spot Radius**Effect of the Laser Spot Position**Effect of the Antenna Geometry**Effect of the Carrier Lifetime**Effect of the Substrate Temperature**Effect of the Energy Level of the Traps*

The similar behavior of the laser spot radius effect on the current pulse is shown in Fig. The effect of the substrate temperature on the current pulse is shown in Fig.

## Summary

In addition, this chapter also proposes a new electrical equivalent PCA circuit that works as a THz detector. On the basis of the developed circuit model, a comparative study of the PCA detector in noisy and noiseless media is carried out, and the results are presented.

Generation of the THz Radiation from the PCA

## Proposed Equivalent Electrical Circuit Model of the PCA Working as the

### Calculations of the Circuit Parameters

*Carrier Density**Gap Conductance**Capacitive Current**Active Region Capacitance**Screening Voltage**Total Circuit Current**Voltage Across the Gap Capacitance**Effect of the Temperature*

The time-dependent gap conduction (Gp(t)) controls the behavior of the drift current in the active volume. The incremental gap conductance (dGp(t)) for a small thickness dzin the active volume can be calculated as follows: 4.7) where ρ(t) is the time-dependent resistivity, and Lis the length of the active region.

### Results and Discussions

*Effect of the Laser Power and the Bias Voltage**Effect of the Temperature**Effect of the Gap Length and the Carrier Lifetime**Effect of the Antenna Impedance**Effect of the Absorption and the Reflection Coefficients**Different Voltages in the PCA**Gap Conductance**Gap Capacitance*

4.8 & 4.9 show the effect of the laser input power and the bias voltage on the behavior of the current pulse in the PCA. The impact of α and R on the total efficiency of the PCA is shown in Fig.

Detection of the THz Radiation Using the PCA

## Proposed Equivalent Electrical Circuit Model of the PCA Working as the

### Calculations of the Circuit Parameters

*Carrier Density**Gap Conductance**Capacitance Current**Gap Capacitance**Total Circuit Current**Gap Voltage*

Similar to Section 4.3.1.2, the transient conductance in the PCA receiver can be given as:. where µ is the mobility of the carrier, Lr and Wrare respectively the length and width of the gap. The effective mobility of the carriers is calculated using the Caughey-Thomas [145] and Arora [146] mobility models as explained in Section 3.2.6 and given as: .

### Results and Discussions

*Electric Field of the Received THz Signal and Induced**Net Electric Field at the Gap**Total Circuit Current**Gap Conductance*

The net electric field at the gap of the PCA receiver depends on the various parameters as given by (4.40). The behavior of the total circuit current in the PCA receiver is shown in Fig.

## Summary

A high conductance value supports a high amplitude current in the circuit, which effectively increases the sensitivity of the PCA receiver. This chapter presents an analysis of the effect of near-field radiated fields on the LAPCA radiated power.

## Relationship Between the Near-Zone Fields and the Current Density

In addition to these limiting factors, near-site radiated fields also affect radiation power [134] and have not been adequately addressed in the literature. Electromagnetic boundary conditions as well as semiconductor carrier dynamics are used to account for the effect of near-field fields on the behavior of various parameters.

## Semiconductor Carrier Dynamics

*Carrier Densities**Surface Current Density**Carrier Velocities**Net Electric Field**Carrier Polarization**Radiated THz Electric Field*

Similarly, the total number of holes in the active area can be written as:. where lp is the diffusion length for the holes and can be calculated from,lp = p. is the diffusion coefficient of the holes. So the average carrier densities are calculated for the volume corresponding to the diffusion lengths of the carriers and are given as:

## Results and Discussions

*Effect of the Near-Zone Fields on the Net Electric Field**Effect of the Near-Zone Fields on the Carrier Velocities**Effect of the Near-Zone Fields on the Current Density**Effect of the Near-Zone Fields on the Radiated THz Electric Field . 91*

The effect of the near-field electric field on the current density in the gap is shown in the figure. The behavior of the near-field electric field with Vbias and P is shown in Figure 10.

## Summary

The reduction in the amplitude of the current density due to the near-zone field effect can be overcome by using an external magnetic field, which also increases the radiated power of the PCA. The effect of the external magnetic field on the current density, the amplitude and the polarity of the radiated reconciled electric field is calculated and presented.

## Boundary Conditions

The current density characteristics at the gap are strongly dependent on the net electric field at the gap. 6.1, the net electric field consists of the DC bias electric field, the radiated near-zone electric field, and the field associated with the polarization of the carrier waves.

## Semiconductor Carrier Dynamics Model

*Carrier Densities**Optical Absorption Coefficient**Current Density**Net Electric Field**Carrier Polarization**Carrier Velocities**Effect of the Magnetic Field of the Carrier Densities**Radiated THz Electric Field*

The change in the absorption coefficient causes a change in the dielectric constant value of the semiconductor material. The increase or decrease in carrier density depends on the orientation of the external magnetic field (positive or negative y-axis direction).

## Results and Discussions

### In the Absence of the External Magnetic Field

It can be seen from (6.48) that the amplitude of the radiated far electric field depends on the rate of change of carrier velocity and carrier density. Thus, by changing the dimensions of the gap, it is possible to increase the amplitude of the radiated electric field of the remote area.

### In the Presence of the External Magnetic Field

This shows that the amplitude and the orientation of the radiated far-zone electric field strongly depend on the same of the applied magnetic field as shown in Fig. The amplitude of the radiated far-zone electric field from the PCA increases with the applied magnetic field as shown in Fig.

## Summary

Among all the studies, very few are related to the analytical analysis of the radiated fields from PCA, as discussed in Chapter 2. In addition, an improved semiconductor carrier dynamics is proposed to calculate the current density, which helps in the analysis of the PCA radiation behavior.

## Derivation of Radiated Fields from a PCA

Since the first study done in the field of THz generation using a PCA, several experimental, simulation and circuit modeling studies have been reported in the literature. The proposed carrier dynamics first accounts for the transient temperature variation of the substrate, which further helps in incorporating the temperature dependence of various parameters.

## Semiconductor Carrier Dynamics

*Carrier Densities**Absorption Constant**Carrier Lifetime**Current Density**Net Electric Field**Carrier Polarization**Carrier Velocities**Radiated THz Fields*

The total current density can be given by adding the current densities of the electrons and the holes. 7.40) where vn(t) and vp(t) are the time-dependent velocities of the electrons and the holes, respectively.

## Results and Discussions

*Effect of the Laser Power on the Substrate Temperature**Effect of the Bias Voltage and the Laser Power**Effect of the Laser Pulse Width**Effect of the Gap Length*

The laser beam power increases the temperature of the semiconductor substrate which varies with time. The analytically calculated results of the laser beam power and the bias effect on the radiated electric field are compared with the reported experimental results in [169] and [174], respectively.

## Summary

The effect of the different parameters on the current pulse behavior was analyzed and discussed. It analyzes the radiated near-zone fields effect on the behavior of the different parameters of the PCA.

## Suggestions for the Future Work

The FDM is used to solve ordinary differential equations where conditions are imposed at the boundary instead of at the starting point. In this thesis, the central difference scheme is used to solve the differential equations.

## Solution of the Heat Equation

For 2τ l ≤ t< ∞

## Expansion of Eqs. (7.64) and (7.65)

*The electromagnetic frequency spectrum**Basic schematic diagram of the optoelectronic system as an emitter**THz coherent detection system block diagram**THz direct detection system block diagram**Optoelectronic system as a detector**Block diagram of free space EO sampling technique**Illustration of the THz generation from the PCA**Temporal behavior of the laser pulse and the current pulse**Temporal behavior of the current pulse and the radiated THz electric field 12**A basic structure of a PCA**Point defect energies distribution as a function of density of states in non-**Point defect energies distribution as a function of density of states in an-**Different PCA Structures**First proposed Electrical Equivalent circuit of a PCA**Second proposed Electrical Equivalent circuit of a PCA**Third proposed Electrical Equivalent circuit of a PCA**Fourth proposed Electrical Equivalent circuit of a PCA**Comparison of the total circuit current at P in =10 mW**Comparison of the screening voltage at P in =10 mW**Comparison of the conductance values**Illustration of SRH recombination process**Simulation geometry of PCA**Simulation flow for the PCA in Sentaurus TCAD**Parameters affecting the behavior of the current pulse generated in the PCA 45**Effect of the laser power on the current pulse**Effect of the laser pulse width on the current pulse**Effect of the laser spot radius on the current pulse**Effect of the laser spot position on the current pulse**Voltage distribution profile in the comb structured PCA**Voltage distribution profile in the interdigitated structured PCA**Voltage distribution profile in the Hertzian dipole PCA**Comb structured PCA gap**Interdigitated structured PCA gap**Peak amplitude of the current pulse in the comb structured PCA**Peak amplitude of the current pulse in the interdigitated structured PCA . 49**Effect of the temperature on the current pulse**Effect of the traps energy levels on the current pulse**An equivalent circuit of the PCA in dark condition**An equivalent circuit of the parallel plate plasma**An equivalent circuit of the PCA in transient illumination state**Proposed equivalent electrical circuit of a PCA working as a THz source . 56**Comparison of the optical-to-electrical (η e ), the matching (η m ), and the**Current pulse behavior at the different laser powers**Current pulse behavior at the different bias voltages**The average radiated power at different V bias**Efficiency of the PCA at different V bias**Current pulse dependence on the temperature**Dependence of the average radiated power on the temperature**Dependence of the PCA efficiency on the temperature**Current pulse for different L and τ c**Dependence of the average radiated power on L**Dependence of the PCA efficiency on L**Dependence of the average radiated power on τ c**Dependence of the PCA efficiency on τ c**Dependence of the average radiated power on Z a**Dependence of the PCA efficiency on Z a**The total efficiency of the PCA at the different absorption coefficients**The total efficiency of the PCA at the different reflection coefficients**Transient behavior of the voltages in the PCA**Transient behavior of the conductance at different laser powers**Transient behavior of the conductance at different bias voltages**Transient behavior of the capacitance at different laser powers**Transient behavior of the capacitance at different bias voltages**Proposed equivalent electrical circuit of the PCA working as a THz receiver 73*

Mourou, “Ultrafast carrier dynamics in III-V semiconductors grown by molecular beam epitaxy at very low substrate temperatures,” IEEE J. Kopcsay, “Broadband microwave measurements with transient radiation from optoelectronically pulsed antennas,” IEEE Trans.