GaN-Based THz Advanced Quantum Cascade ...

GaN-Based THz Advanced Quantum Cascade Lasers for Manned and Unmanned Systems

A. F. M. Anwar, Tariq Manzur*, Kevin R. Lefebvre** and Edward M. Carapezza‡ Electrical and Computer Engineering, University of Connecticut, Storrs, CT, USA *Naval Undersea Warfare Center (NUWC), DIVNPT, Newport, RI 02841-1708, USA ** Sensis Corporation, 85 Collamer Crossing East, Syracuse, NY 13057, USA ‡DARPA, 3701 N. Fairfax Drive, Arlington, VA 22203-1714, USA

In recent years the use of Unmanned Autonomous Vehicles (UAV) has seen a wider range of applications. However, their applications are restricted due to (a) advanced integrated sensing and processing electronics and (b) limited energy storage or on-board energy generation to name a few. The availability of a wide variety of sensing elements, operating at room temperatures, provides a great degree of flexibility with an extended application domain. Though sensors responding to a variable spectrum of input excitations ranging from (a) chemical, (b) biological, (c) atmospheric, (d) magnetic and (e) visual/IR imaging have been implemented in UAVs, the use of THz as a technology has not been implemented due to the absence of systems operating at room temperature. The integration of multi-phenomenological onboard sensors on small and miniature unmanned air vehicles will dramatically impact the detection and processing of challenging targets, such as humans carrying weapons or wearing suicide bomb vests. Unmanned air vehicles have the potential of flying over crowds of people and quickly discriminating non-threat humans from treat humans. The state of the art in small and miniature UAV’s has progressed to vehicles of less than 1 pound in weight but with payloads of only a fraction of a pound. Uncooled IR sensors, such as amorphous silicon and vanadium oxide microbolometers with MRT’s of less than 70mK and requiring power of less than 250mW, are available for integration into small UAV’s. These sensors are responsive only up to approximately 14 microns and do not favorably compare with THz imaging systems for remotely detecting and classifying concealed weapons and bombs. In the following we propose the use of THz GaN-based QCL operating at room temperature as a possible alternative.

Unmanned/Unattended Sensors and Sensor Networks VI, edited by Edward M. Carapezza, Proc. of SPIE Vol. 7480, 748012 · © 2009 SPIE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.846457

Proc. of SPIE Vol. 7480 748012-1

Quantum Cascade Lasers (QCL) operating at THz frequencies have been demonstrated using GaAs/AlGaAs and InGaAs/InAlAs heterstructures. SiGe/Si heterostructures, being non-polar, also offers an attractive alternative. SiGe/Si with the dominant phonon mode of 64meV offers a larger THz frequency window than its GaAs or InGaAs counterpart with a LO-polar optical phonon energy of 36meV. The rather low LO-phonon energy of 36meV which is comparable to the room temperature thermal energy of 26meV restricts the use of GaAs-material system to low temperatures. With the LO-phonon energy comparable to thermal energy restricts depopulation of the lower lasing state due to thermal excitation of electrons from the ground state to the lasing state. GaN, on the other hand, with LO-phonon energy of 90 meV offers an attractive alternative making possible the realization of QCL operating at room temperatures. Some theoretical work on GaN-based systems has already been reported [1,2]. In this paper we report the different escape times, an understanding of which is critical to evaluate the suitability of this material system as a viable candidate for QCLs operating at room temperatures. The use of GaN-based material system to generate THz radiation has been reported by Sun et al. [1] and Alekseev eta al. [2]. Sun et al. reports the active region design of GaN/Al.15Ga.85N QCL and Alekseev et al. reports THz generation using GaN-based NDR devices. In this paper, we present theoretical calculations comparing the transition times between the lasing states and their respective lifetimes. The determination of electron lifetime in the presence of tunneling and thermionic emissions is discussed. The calculation includes the piezoelectric field induced by the material system, electric field induced redistribution of density of states within a quantum well, the change in the group velocity and the proper partitioning of the total current between tunneling and thermionic components. The calculation of the escape time is achieved by solving Schrödinger equation, through the logarithmic derivative of the wavefunctions, and Poisson’s equation self-consistently. The determination of transition rates between different quantum confined states in AlGaN/GaN/AlGaN hetrostructures is carried out only in the presence of polar optical phonon scattering. The one electron Schrödinger equation under effective mass approximation can be written as [3-4]:

⎡ m ( z)∗ ⎤ d 4 2 G( E z , z ) = − j ⎢ G ( E z , z ) + V( z ) − E z ⎥ h dz ⎢⎣ 2h ⎥⎦

[

(

where G( E z , z) = 2h jm( z)

∗

]

) [ ϕ′(E , z) ϕ(E , z)] is the logarithmic derivative and j= z

z

-1 . V(z) =

Vapp +Vsc(z) +ΔEc +Vpiezo. Vapp is the applied potential, Vsc(z) is the space charge potential, ΔEc is the bandoffset and Vpiezo is the potential due to the piezoelectric field. The calculation of the piezoelectric field is

Proc. of SPIE Vol. 7480 748012-2

based upon Ref. [5] where ξ piezo =

2 ⎞ 2C 33 P 2d 31 ⎛ = ⎜ C11 + C12 − ⎟ u xx and the values for the elastic C 33 ⎠ ε ε ⎝

constants (Cij), the piezoelectric constant (d31) and the strain tensor component (uxx). Also, Ez is the zdirected carrier energy, m*(z) is the effective mass at position z, h is the reduced Planck’s constant, and ϕ(Ez,z) is the envelope function at energy Ez and position z. Vsc(z) is determined by solving Schrödinger and Poisson’s equation self-consistently. The escape rate can be calculated by rearranging the usual current equation (J=qnv=qnL/τ) as [6,7]:

1 = τ

1 τ 2unD

1

β+

(1 − β)

τ 3unD

where τ un ( = qn 2D L w J tu ) is the unweighted tunneling time, τ un ( = qn 3D L w J th 2D

3D

)

is the unweighted

thermionic emission escape time, β ( = n 2 D n tot ) is the partitioning factor, Jth is the thermionic emission current, Jtu is the tunneling current, Lw is the length of the quantum well, q is the elemental charge and n3D , n2D are the carrier concentrations above and below Ec. Following the treatment presented in Refs. [6,7] the total current can be written as:

J Tot

∞ + + ⎤ ⎡∞ dE ⎢ ∫ t ∫ f ( E ) v g ( E z ) D ( E z ) g1D ( E z ) dE z + ⎥ 0 E′ * ⎥ kz>0 qm ⎢ = ⎥ 2 ⎢ 2πh ⎢∞ dE ∞ f ( E ) v − ( E ) D − ( E ) g ( E ) dE ⎥ 1D g z z z z ⎥ ⎢ ∫0 t E∫′ ⎥⎦ kz