Black phosphorus photoconductive terahertz antenna: 3D modeling and experimental reference comparison

Jose Santos Batista; Hugh O. H. Churchill; Magda El-Shenawee

doi:10.1364/JOSAB.419996

Journal of the Optical Society of America B
Vol. 38,
Issue 4,
pp. 1367-1379
(2021)
•https://doi.org/10.1364/JOSAB.419996

Black phosphorus photoconductive terahertz antenna: 3D modeling and experimental reference comparison

Jose Santos Batista, Hugh O. H. Churchill, and Magda El-Shenawee

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Jose Santos Batista, Hugh O. H. Churchill, and Magda El-Shenawee, "Black phosphorus photoconductive terahertz antenna: 3D modeling and experimental reference comparison," J. Opt. Soc. Am. B 38, 1367-1379 (2021)

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- Photonics
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About this Article
History
- Original Manuscript: January 20, 2021
- Revised Manuscript: March 2, 2021
- Manuscript Accepted: March 9, 2021
- Published: March 31, 2021

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Abstract

This paper presents a 3D model of a terahertz photoconductive antenna (PCA) using black phosphorus, an emerging 2D anisotropic material, as the semiconductor layer. This work aims at understanding the potential of black phosphorus (BP) to advance the signal generation and bandwidth of conventional terahertz (THz) PCAs. The COMSOL Multiphysics package, based on the finite element method, is utilized to model the 3D BP PCA emitter using four modules: the frequency domain RF module to solve Maxwell’s equations, the semiconductor module to calculate the photocurrent, the heat transfer in solids module to calculate the temperature variations, and the transient RF module to calculate the THz radiated electric field pulse. The proposed 3D model is computationally intensive where the PCA device includes thin layers of thicknesses ranging from nano- to microscale. The symmetry of the configuration was exploited by applying the perfect electric and magnetic boundary conditions to reduce the computational domain to only one quarter of the device in the RF module. The results showed that the temperature variation due to the conduction of current induced by the bias voltage increased by only 0.162 K. In addition, the electromagnetic power dissipation in the semiconductor due to the femtosecond laser source showed an increase in temperature by 0.441 K. The results show that the temperature variations caused the peak of the photocurrent to increase by ${\sim}{3.4}\%$ and ${\sim}{10}\%$, respectively, under a maximum bias voltage of 1 V and average laser power of 1 mW. While simulating the active area of the antenna provided accurate results for the optical and semiconductor responses, simulating the thermal effect on the photocurrent requires a larger computational domain to avoid false rise in temperature. Finally, the simulated THz signal generation electric field pulse exhibits a trend in increasing the bandwidth of the proposed BP PCA compared with the measured pulse of a reference commercial LT-GaAs PCA. Enhancing signal generation and bandwidth will improve THz imaging and spectroscopy for biomedical and material characterization applications.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Parameter	Symbol	Value
Laser wavelength	$λ$	780 nm
Average power	$P_{A v e}$	1 mW
Pulse $x$ axis center location	$x_{0}$	0 µm
Pulse $y$ axis center location	$y_{0}$	0 µm
Pulse center location in time	$t_{0}$	0.6 ps
HPBW– $x$ direction	$D_{x}$	2 µm
HPBW– $y$ direction	$D_{y}$	2 µm
Pulse width–time	$D_{t}$	100 fs

Symbol		$σ$		$\hat{ϵ}$ (780 nm)
Description		Conductivity		Relative Permittivity
Units		S/m		1
Au		$2.892 * 10^{7}$	[23]	−25.06−1.60i	[23]
Cr		$7.752 * 10^{6}$	[24]	−2.21−21.07i	[25]
SiO2		$5 * 10^{- 14}$	[26]	2.38	[27]
Si		$4.348 * 10^{- 4}$	[28]	13.623−0.044i	[29]
hBN		$1 * 10^{- 6}$	[30]	4.84	[31]
	$x$	250	[32]	16.0565−1.7283i	[13]
BP	$y$	92.6	[32]	14.763-0.096i	[13]
	$z$	43.5	[32]	8.3	[33]

Parameter	Symbol	Units	Black Phosphorus
Doping profile	$N_{A}$	$1 / {c m}^{3}$	$2 * 10^{15}$	[32]
Electron mobility	$μ_{n}$	${c m}^{2} / V \cdot s$	1,500	[17]
Hole mobility	$μ_{p}$	${c m}^{2} / V \cdot s$	5,000	[18]
Bandgap	$E_{g}$	$V$	0.3	[15]
Electron affinity	$χ$	$V$	4.4	[15]
Electron lifetime	$τ_{n}$	$p s$	0.360	[16]
Hole lifetime	$τ_{p}$	$p s$	0.360	[16]
Electron saturation velocity	$v_{n, s a t}$	$c m / s$	$1.0 * 10^{7}$	[38]
Hole saturation velocity	$v_{p, s a t}$	$c m / s$	$1.2 * 10^{7}$	[38]
Effective density of states, conduction band	$N_{C}$	$1 / m^{3}$	$5.933 * 10^{25}$	[40]
Effective density of states, valence band	$N_{V}$	$1 / m^{3}$	$1.052 * 10^{23}$	[40]

Symbol		$κ$		$ρ$		$C_{p}$
Description		Thermal Conductivity		Density		Heat Capacity Constant Pressure
Units		$W / m K$		$k g / m^{3}$		$J / k g K$
Au		318	[41]	19300	[41]	129	[41]
Cr		93.7	[41]	7150	[41]	450	[41]
SiO2		1.4	[42]	2200	[43]	703	[44]
Si		150	[42]	2329	[44]	700	[44]
hBN		390	[45]	2279	[45]	818.18	[46]
	$x$	25.29	[47]	2420	[48]	695.5	[49]
BP	$y$	48.79	[47]
	$z$	4.00	[50]

	Solved Models	Mesh Elements	DOF (Unknowns)	Required Memory (GB)	CPU Time (hours, minutes)	Platform
Optical Response	Case 1–Fig. 9	6 159 517	39 188 546	288.4	5 h,39 m	AHPCC–2 x Intel Xeon Gold 6126 CPU at 2.60 GHz. (2 sockets–24 cores)
	Case 2–Fig. 9	7 704 717	49 002 884	372.37	8 h,34 m	AHPCC–2 x Intel Xeon Gold 6126 CPU at 2.60 GHz. (2 sockets–24 cores)
	Case 3–Fig. 9	9 329 505	59 321 684	463.07	11 h,40 m	AHPCC–2 x Intel Xeon Gold 6126 CPU at 2.60 GHz. (2 sockets–24 cores)
	Case 4–Fig. 2, 9	11 822 474	75 151 948	617.34	18 h,52 m	AHPCC–2 x Intel Xeon Gold 6126 CPU at 2.60 GHz. (2 sockets–24 cores)
	Case 5 (Largest Case)	49 328 365	313 252 784	3 202.98	25 h,6 m	XSEDE Bridges–16 x Intel Xeon CPU E7-8880 v3 at 2.30 GHz. (16 sockets–24 cores)
Electrical Response	Case 4–Fig. 3	311 958	5 000 711	36.16	6 h,51 m	4 x AMD Ryzen Threadripper 2990WX CPU at 3.00 GHz. (4 sockets–32 cores)
	Case 5 (Largest Case)–Fig. 5	2 544 387	25 480 658	146.49	25 h,47 m	AHPCC–2 x Intel Xeon Gold 6130 CPU at 2.10 GHz. (2 sockets–24 cores)
THz Response	$Δ_{max} = 35 µ m$ –7	114 674	800 016	6.06	3 h,47 m	4 x AMD Ryzen Threadripper 2990WX CPU at 3.00 GHz. (4 sockets–32 cores)
	$Δ_{max} = 20 µ m$ –7	554 407	3 713 386	18.56	15 h,16 m	4 x AMD Ryzen Threadripper 2990WX CPU at 3.00 GHz. (4 sockets–32 cores)
	$Δ_{max} = 15 µ m$ –7	1 293 643	8 552 746	40.64	72 h,10 m	4 x AMD Ryzen Threadripper 2990WX CPU at 3.00 GHz. (4 sockets–32 cores)
Temperature	Case 5 (Largest Case) Figs. 4, 5 (Joule Heating)	2 544 387	25 480 658	147.96	40 h,58 m	AHPCC–2 x Intel Xeon Gold 6130 CPU at 2.10 GHz. (2 sockets–24 cores)
	Case 5 (Largest Case) Figs. 4, 5 (Laser Heating)	2 544 387	25 480 658	148.98	24 h,14 m	AHPCC–2 x Intel Xeon Gold 6130 CPU at 2.10 GHz. (2 sockets–24 cores)

Abstract

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Equations (8)

Journal of the Optical Society of America B