Resonant Cavity Far Infrared Photo detector based on Self-Assembled InAs/GaAs Quantum Dots.ByC.M. S. Negi1,2*, Dharmendra Kumar2, Saral K. Gupta3 and Jitendra Kumar2

1Department of Electronics, Banasthali University, Rajasthan-304022, India, 2Department of Electronics Engineering, Indian School of Mines, Dhanbad, Jharkhand- 826004, India, 3Department of Physics, Banasthali University, Rajasthan-304022, India1,2*nchandra@banasthali.in

Introduction Objective Device structure and design Quantum dot model Dark current model Results and Discussion Conclusion ReferencesOutline

A medium whose carrier are confined in all three dimensions. 3D confinement

Electronic & optical characteristic of quantum dots are similar to the individual atoms.

Lx, Ly, Lz ldeBroglieDensity of States

Current FIR-detector technologyGa doped Ge based detectors -relatively low absorption coefficient - very low operating temperature

Photodetectors based on quantum coherencein coupled quantum wells

Bolometer - limited by the phonon fluctuations in the device -requires sub-Kelvin cooling

Quantum well infrared photodetector (QWIP) -Unable to detect normal incidence radiation - Low temperature operation

*Quantum dot infrared photodetector (QDIP)

Intersubband transitions allows operation in the FIR regionAdvantage of QDIP Normal incidence operation

Low dark current

Long excited state life time (reduced electron phonon scattering-phonon bottleneck effect)

Bias tunable operation

Thermal imaging, night vision, Chemical spectroscopy Medical diagnostics Fire fighting, Crime Prevention, Forensics Space-based Remote Sensing.biomedical sensingStudies of lattice vibrations in crystals.anti-ferromagnetic resonanceEnergy gap measurements in superconductors .Imaging through fog and imaging through dust.

*ObjectivesDevelop a theoretical model of RCEQDIP based on intervalance subband transitions.Determine the quantum efficiency of RCE QDIP.Calculation of dark current in RCE QDIP due to holes.

*Device structure and design Structure of RCE QDIP The structure consists of InAs/GaAs QDs layer placed in a Fabry-Perot resonant microcavity. The mirrors of resonant cavity consist of 5 pairs of GaAs/AlxGa1-xAs DBR. The area between the QDs is covered by AlGaAs material, due to its large band gap it acts as a blocking layer (BL).The p+ and p regions are made-up of GaAs material and act as QDIP emitter and collector respectively.Advantages of RCE Devices Wavelength selectivity Higher quantum efficiency at the resonant wavelengths Off-resonance wavelengths are rejected by the cavity making device promising for low crosstalk applications. Larger bandwidth.

*QD model A disk shaped anisotropic quantum dot is modeled using a parabolic confinement Vx;y(x, y) in the plane perpendicular to the growth axisThe strain effect will induce change in confinement energy of holesThe strain induced energy shift for the valence band is given by

*Using envelop function approximation the wave function for valence band can be written asThe wave function and electronic structure for valence band can be obtained by numerically solving Luttinger Hamiltonian given byWithout the of diagonal terms solution of the in-plane parabolic confinement potential would be the harmonic oscillator wave function. Using these wave functions as our basis, the matrix element can be written as

*The wave functions obtained after diagonalization of the Hamiltonian as outlined in previous section can be written aswhere an,n are the components of the nth eigenvector with n = (nx,ny,mj) corresponds to the set of quantum numbers characterizing the hole state n. The dipole matrix element of transition between intervalance subband is given by

Here In,n is the overlap integral of valance suband states and is given by

*Absorption coefficient and quantum efficiency

The analytical expression for the absorption coefficient can be obtained by using density matrix approach and can be written as

Mfi is the dipole matrix element of the transition between the valence sub-bands

The Quantum efficiency () of a photodetector placed inside a resonant cavity at wavelength () is given by

*Valance band schematic of InAsGaAs QDIPDark current model A critical parameter in the operation of FIR detectors is the dark currentIt determines the appropriateness of the device to be used in high temperature operation A model is used which includes the thermionic emission of holes from QDs and field assisted tunneling of holes from QDs to describe the dark current.The detailed balanced relation used to equate a rate of hole capture into and hole emission from QDs can be expressed aspc is the capture probability of a hole crossing a QD having BL and can be presented as

*Gth is the rate of hole emission from QDs associated with thermionic emission and can be written asThe field assisted tunneling for one dimensional triangular barrier and can be expressed as Potential barrier height from the uppermost filled quantum dot energy level, and is expressed as

*The analytical expression of N by assuming N< NQD can be obtained from a detailed balance relation and is given byOne can obtain the equation of dark current asWhere

*Luttinger parameters for InAs are 1=20, 2=8.5, 3=9.2.Valance band offset=0.47 eVLe=50nm, Lc=500nm, L=30mm, QD=1014 meter-2, mlh=0.027mo. Go, Got and jmax are used in fitting parameters in the model and are based on [11, 13]. Luttinger Hamiltonian in the presence of strain is numerically solved for different values of rQD and LZ= 5nm

Results and Discussions

Parameter used

Table1-Evaluated parameter

*Quantum efficiency ( ) vs. WavelengthFigure shows oscillatory behavior as a result of resonant cavity structure. of RCE is exceptionally larger than the of conventional QDIP.Conventional QDIP provides roughly constant over a wide wavelength range while RCE QDIP can be design to have significantly enhanced at specific wavelength.Wavelength selectivity property of RCE QDIP can used a background noise reduction factor.Increase in QD radius shows the shift in the peak wavelength.

*Dark current density as a function of applied voltage at different temperature. As expected the dark current increases with the increase in temperature and the bias voltage. The main mechanism producing the dark current in lower applied bias region is thermionic emission and at higher bias is the field assisted tunneling process of the holes in the QDs.

*Dark current density vs. applied voltage for different QD radiusDark current density vs. applied voltage for QDIP with or without BL. Figure display large dark current density for small rQD.. This can be attributed to the small value of ionization energy for rQD=3 in comparison with the rQD=6 as given in table 1.

Figure clearly indicates the AlGaAs layer used in the active region of RCE QDP acts as blocking layer for the dark current and reduces dark current by a greater extent in comparison with the RCE QDIP without BL.

*Summary We have investigated QE and characteristics of dark current in FIR RCE QDIP.

Valance subband structure of QDs embedded in the device is evaluated by numerical digonalization of Luttinger Hamiltonian.

QD radius has the effect of shifting the peak wavelength of the photodetector.

We find prominent effect of QD radius on dark current density.

Blocking layer inserted between QDs in the active region of the device significantly reduces dark current density of QDIP.

*References[1] M. F. Kimmitt, Far-Infrared Techniques, Pion Limited, London, 1970.[2] A. G. U. Perera, S. G. Matsik, H. C. Liu, M. Gao, M. Buchanan, W. J.Schaff, and W. Yeo, GaAs/InGaAs quantum well infrared photodetector with a cutoff wavelength at 35 m Appl. Phys. Lett., Vol. 77, No.5, pp.741-743, 2000.[3] A. K. Wojcika, F. Xiea, V.R. Chagantia, A. Belyanina an J. Konom, Mid/far-infrared photodetectors based on quantum coherence in coupled quantum wells, Journal of Modern Optics Vol. 55, No. 1920, pp. 33053317, 2008.[4] J. Wolf and D. Lemke, Infrared Phys. 25, 327, 1985. [5] S. J. Xu, S. J. Chua, T. Mei, X. C. Wang, X. H. Zhang, G. Karunasiri, W. J. Fan, C. H. Wang, J. Jiang, S. Wang, and X. G. Xie, Characteristics of InGaAs quantum dot infrared photodetectors, Appl. Phys. Lett., Vol. 73, No. 21, pp 3155-3177, 1998.[6] J. W. Kim, J. E. Oh, S. C. Hong, C. H. Park, and T. K. Yoo, Room temperature far infrared (8-10mm) photodetectors using self-assembled InAs quantum dots with high detectivity, IEEE Electron Device Lett., Vol. 21, pp. 329-331, 2000. [7] V. Ryzhii1, I. Khmyrova, M. Ryzhii and V. Mitin, Comparison of dark current, responsivity and detectivity in different intersubband infrared photodetectors, Semicond. Sci. Technol, Vol. 19, pp. 816 2004.[8] J. Kumar, S. Kapoor, S.K. Gupta and P.K. Sen, Theoretical investigation of the effect of asymmetry on optical anisotropy and electronic structure of Stranski-Krastnov quantum dots, Phys. Rev. B, Vol. 74, pp. 115326(1-10), 2006.

*[9] G. H. Wang, and Q. Guo, and K. X. Guo, Refractive Index Changes Induced by the Incident Optical Intensity in Semiparabolic Quantum Wells, Chin. J. Phys., Vol 41, pp. 296-306, 2003.[10] M. Selim lhiiia and S. Strite, Resonant cavity enhanced photonic devices J. Appl. Phys., Vol. 78, No. 2, 1995, pp. 607-639. [11] V. Ryzhii, Physical model and analysis of quantum dot infrared photodetectors with blocking layer, J. Appl. Phys., Vol. 89, No. 9, pp. 5117-5124, 2001.[12] P. Martyniuk and A. Rogalski, Insight into performance of quantum dot infrared photodetectors, Bulletin of the Polish Academy of Sciences Technical Sciences,Vol. 57, No. 1, , pp. 103-116, 2009.[13] A. D. Stiff-Roberts, X. H. Su, S. Chakrabarti, and P. Bhattacharya, Contribution of field-assisted tunneling emission to dark current in InAsGaAs quantum dot infrared photodetectors , IEEE Photonics Technology Letters, Vol. 16, No.3, pp.867-869. 2004.

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