Analytical and simulation modeling of the terahertz photoconductive antennas

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.

Fig. 1.2: Basic schematic diagram of the optoelectronic system as an emitter range) [2, 12].

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].

Fig. 1.4: THz direct detection system block diagram

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.

Fig. 1.7: Illustration of the THz generation from the PCA

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.

Fig. 2.2: Point defect energies distribution as a function of density of states in non-annealed LT-GaAs [90]

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.

Table 2.1: Summary of the simulation studies

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.

Fig. 3.1: Illustration of SRH recombination process

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.

Fig. 3.3: Simulation flow for the PCA in Sentaurus TCAD

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.

Fig. 3.5: Effect of the bias voltage on the current pulse

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.

Fig. 4.5: Flow chart of the analytical calculations 4.3.1.1 Carrier Density

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.

Table 4.2: Parameters Details (at 300 ◦ K) for the circuit modeling

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
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
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.

Fig. 4.34: Net electric field at the gap in the noise free medium

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.

Fig. 5.1: The fields configuration in a PCA

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.

Table 5.1: Parameters details for the near fields calculations

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.

Fig. 6.1: The different fields orientation in a LAPCA

Semiconductor Carrier Dynamics Model

Carrier Densities
Optical Absorption Coefficient
Current Density
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.

Fig. 6.2: Transient behavior of laser pulse, E net , electric field due to polarization (E pol ), and E r at V bias =50 V and P=100 mW

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.

Fig. 6.8: Effect of the external magnetic field on the current density

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.

Fig. 7.1: 3D representation of a PCA with fields directions

Semiconductor Carrier Dynamics

Carrier Densities
Absorption Constant
Carrier Lifetime
Current Density
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.

Fig. 7.2: Approximation of Gaussian pulse using exponential functions

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.

Table 7.1: Parameters Details for the calculation of the radiated fields

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.