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Long-wavelength broad band infrared photodetector using four asymmetric quantum wells
ARTICLE IN PRESS
Physica E 39 (2007) 50–52 www.elsevier.com/locate/physe
Long-wavelength broad band infrared photodetector using four asymmetric quantum wells M. Hostut Department of Electrical and Electronics Engineering, Cumhuriyet University, 58140 Sivas, Turkey Received 21 November 2006; received in revised form 15 December 2006; accepted 20 December 2006 Available online 12 February 2007
Abstract A theoretical investigation of GaAs/AlGaAs infrared detector consisting of four asymmetric quantum wells is presented. Each well is designed to yield absorption and a photoresponse at peak wavelengths of 7.9, 9.2, 10.4, and 11.8 mm, respectively. The device operation is based on intersubband bound to bound transition. r 2007 Elsevier B.V. All rights reserved. PACS: 85.60.–q; 07.57.Kp; 85.35.Be; 78.20.Ci Keywords: QWIP; Quantum well; Absorption; Responsivity; Dark current
1. Introduction Quantum well infrared photodetectors (QWIP) for long wavelength infrared detection have been developed rapidly over the past 10 years from the fundamental-physics point of view towards large-area focal plane arrays [1–3]. Due to this progress, high-resolution high-performance large-format focal plane arrays (FPAs) are available [4,5]. On the other hand, sensing a broad range of infrared radiation is highly desirable for a certain application such as spectroscopy. In a standard QWIP structure with bound to bound transition, identical quantum wells are grown successively to achieve a period. Variation from the standard QWIP structure has been recently proposed by us as a singlewavelength bound to bound transition [6] and broadband bound to continuum transition [7] staircase-like detectors working in long-wavelength atmospheric windows. In this proposed structure, four quantum wells of different thickness separated with step-like thin barriers are composed of a unit with thick end barrier. Thus, each unit contains four asymmetric quantum wells that detect four different wavelengths to achieve broadband detector. Thin barriers in the structure were inspired by quantum cascade
E-mail address: [email protected]. 1386-9477/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2006.12.058
detectors (QCD) [8] that have generated a significant photocurrent. The barrier at the end of each unit reduces ground state tunneling. 2. Device structure The device structure reported here involved 20 period repeated layers of GaAs four-QW units. Each unit consists of 50, 53, and two 57 A GaAs quantum wells separated by 23A AlxGa1xAs barriers with Al concentrations of 0.35, 0.31, 0.29, 0.27 and 0.25, respectively. The last barrier thickness is chosen to be 500 A to prevent electron escape from the ground state of the last quantum well. Doping concentration of quantum wells were 1 1018 cm3 and barriers are undoped. Each unit is separated by 500 A GaAs layer with the doping concentration of 1 1018 cm3. The whole period is sandwiched between two 0.5 mm GaAs (1 1018 cm3 Si doping) contact layers. The unit is represented in Fig. 1. 3. Theoretical considerations Potential energy of the system shown in Fig. 1 can be given as V ¼ V G þ V min ,
(1)
ARTICLE IN PRESS M. Hostut / Physica E 39 (2007) 50–52
in free space, kB is Boltzmann’s constant, T is the temperature, y is the angle between the polarization vector and the normal to the quantum well, nr is the refractive index, EF is the Fermi energy which depends on the density of electrons in the well, and linewidth, G ¼ G0 þ Gt (where G0 and Gt are half-width at zero bias and energy-dependent tunneling escape broadening due to tunneling time, tt, respectively [1,9]), is 10 meV. The responsivity of the structure has also been calculated using the formula [1]
Potential Energy (eV)
b
V1
0.25
b V2
b
V3
b
V4
0.2
Vmin
0.15 0.1 0.05
b
b w b w b w b w Z1 Z1 Z2 Z2 Z3 Z3 Z4 Z4 Z5 w w w w V2 V3 V4 V1
0
200
Zmax
400 Z (A)
600
51
800
Fig. 1. Schematic conduction band profile of the structure with relevant parameters.
R ¼ ðe=hvÞZa pe g,
(7)
where g is the optical gain, pe is the hot-carrier escape probability and Za is the unpolarized double-pass absorption quantum efficiency given as [1] Za ¼ ð1 e2al Þ=2,
where VG ¼
4 X
V nG ,
(2)
n¼1
V min ¼ V min Sðz zb5 Þ, 8 b > < V n; n V G ¼ V wn ; > : 0
(3)
zbn ozozwn ; zwn ozozbnþ1 ; elsewhere;
(4)
where S is the step function. The Hamiltonian of the system and wave functions has been given elsewhere [6,7]. In order to calculate the wave functions, we placed quasi-barriers on the left- and righthand sides of the device structure with potential heights, Vb1, as shown in Fig. 1 with bold dashed lines. Thus, we obtain decaying plane waves in this region. We then obtain a 16 16 secular matrix, H16 16, which can be solved by setting Det [H16 16] ¼ 0. The actual energies of the system can be separated from quasi-levels using confined wave functions. The widths of the quasi-wells are chosen so that confinement energies in the wells are not affected. We have also calculated the initial optical absorption coefficient of the structure, which has 451 multipass waveguide geometry, given by a¼
X X pcm kB Te2
ðcos2 yÞjM fi j2 p_2 m20 Lnr w " " #, " ## E F E ðzÞ E F E ðzÞ ðG=2Þ i fi ln 1 þ exp 1 þ exp kB T kB T ð_w E fi Þ2 þ ðG=2Þ2 i
f
ð5Þ with the matrix element ðzÞ Z L=2 m0 ðE ðzÞ i Ef Þ M fi ¼ ff ðzÞzfi ðzÞ dz, i_ L=2
(6)
ðzÞ ðzÞ ðzÞ where, E fi ¼ E ðzÞ f E i ; and E i and E f denote the quantized energy levels for the initial and final states, respectively, P is the permeability, c is the speed of light
(8)
where l is the length of the superlattice, and the factor of 2 in the denominator is a result of the quantum-mechanical selection rules, which only allow the absorption of radiation polarized in the plane of incidence. Total net quantum efficiency Z is expressed as [1] Z ¼ Za pe .
(9)
We use a simple model [10] for field-dependent dark current density, JD, in which we take the ‘‘effective’’ number of electrons n*(F), which tunnel out of the well or are thermally excited out of the well into the continuum states, and multiply by the average drift velocity, n(F), the electron charge q, and A sample area to obtain I D ðF Þ ¼ qnn ðF ÞnðF ÞA, where n ðF Þ ¼
me p_2 Lp
Z
(10)
1
f ðEÞTðE; F Þ dE,
(11)
EF
where f(E) is the Fermi function, LP is length of the active region, and T(E,F) is the tunneling probability through the active region with an applied field of F. The drift velocity is mF nðF Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 1 þ ðmF =vs Þ2
(12)
where m is the electron mobility and ns is the saturation drift velocity. 4. Results and discussion The potential energy profile of the structure and the relevant device parameters are shown in Fig. 1. Height of each barrier decreases from Al mole fraction (x) of 0.35–0.25 by step-like from leftmost to rightmost side of the structure to achieve asymmetric multiquantum wells. Fig. 2 shows the potential profile of the structure with the squared electron wave functions under electric field of 2.5 kV/cm. Electron transition mechanism is based on bound to bound transition. The excited state energy level broadening has been further enhanced due to overlap of
ARTICLE IN PRESS M. Hostut / Physica E 39 (2007) 50–52
52
10-5
Dark Current (A)
Potential Energy (eV)
0.2 0.1 0 -0.1 -0.2
10-7 10-8 10-9
0
200
400 Z (A)
600
0
800
Normalized Absorption
0.8
0.6
0.4
5000
10000
15000
20000
25000
30000
F (V/cm)
Fig. 2. Conduction band profile and squared electron wave functions of the four-quantum-well unit under applied electric field of 2.5 104 V/cm at 77 K.
Responsivity (A/W)
10-6
1 0.8 0.6 0.4 0.2 0 6
8
10
12
14
Wavelength (µm)
Fig. 4. Dark current vs. applied electric field at 77 K (sample area is 300 300 mm2).
Eq. (10) at 77 K shown in Fig. 4. Since the structure consists of four asymmetric quantum wells with step like barriers, the contribution to the dark current from each quantum well is different. A quantum well with lower barrier height has higher dark current. Therefore, dark current has been calculated as total dark current of four wells. As the applied field increases, dark current rises rapidly and saturates around 1 106 A due to thermionicassisted tunneling mechanism.
0.2
5. Conclusion 8
10 12 Wavewlength (µm)
14
16
Fig. 3. Overall responsivity vs. wavelength under operating field at 77 K. Inset shows the normalized absorption.
wave functions associated with excited states of quantum wells separated by thin barriers. Since the barrier thicknesses are 23 A, excited electrons easily tunnel through their respective barriers to contribute to the photocurrent. Each unit in the structure consists of four asymmetric quantum wells with different barrier heights and well widths to give raise four absorption peaks that are shown in inset of Fig. 3. The overall responsivity of the structure, given in Fig. 3, has been calculated as Eq. (7). The responsivity spectrum is influenced by absorption coefficient and overlap of wave functions. Quantum wells have peaks at lP ¼ 7.9, 9.2, 10.4 and 11.8 mm, and long wavelengths cutoff are lc ¼ 8.15, 9.6, 11, 12.3 mm (i.e., where R drops to half of its peak value), respectively (at T ¼ 77 K). Thus, this detector covers 8–12 mm long wavelength infrared range (LWIR). The height and thickness of the end barrier have been chosen to be 0.2 eV and 500 A, respectively. The last barrier is taken to be wide enough to avoid electron tunneling into collector under operating bias. Therefore, dark current caused by tunneling probability from the emitter to the collector will be reduced. Dark current has also been calculated by using
The theoretical calculations of four asymmetric quantum well structure are proposed to be used as a photodetector operating in the long wavelength infrared range in the GaAs/ AlGaAs material system. The detection wavelengths are 7.9, 9.2, 10.4, and 11.8 mm, respectively. Thickness of barriers has been chosen to be 23 A to increase photocurrent. References [1] B.F. Levine, J. Appl. Phys. R1 (1993). [2] S.D. Gunapala, H. C. Liu, H. Schneider (Eds.), in: Proceedings of Workshop on Quantum Well Infrared Photodetectors QWIP 2000, 2000. [3] G. Sarusi, A. Carbone, S.D. Gunapala, H.C. Liu (Eds.), in: Proceedings of Workshop on Quantum Well Infrared Photodetectors QWIP 2002, 2002. [4] S.D. Gunapala, S.V. Bandara, J.K. Lui, S.B. Rafol, M. Mumolo, IEEE Trans. Electron. Dev. 50 (2003) 2353. [5] S.D. Gunapala, S.V. Bandara, J.K. Liu, C.J. Hill, S.B. Rafol, J.M. Mumolo, J.T. Trinh, M.Z. Tidrow, P.D. LeVan, Semicond. Sci. Technol. 20 (2005) 473. [6] S.U. Eker, M. Hostut, Y. Ergun, I. Sokmen, Infrared Phys. Technol. 48 (2006) 101. [7] Y. Ergun, M. Hostut, S.U. Eker, I. Sokmen, Infrared Phys. Technol. 48 (2006) 109. [8] L. Gendron, M. Carra, A. Huynh, V. Ortiz, Appl. Phys. Lett. 85 (2004) 2824. [9] Z. Ikonic, V. Milanovic, D. Tjapkin, S. Pajevic, Effectivemassmismatch-induced intersubband absorption line broadening in semiconductor quantum wells, Phys. Rev. B 37 (1988) 3097. [10] S.L. Chuang, Physics of Optoelectronic Devices, New York, 1995.
Physica E 39 (2007) 50–52 www.elsevier.com/locate/physe
Long-wavelength broad band infrared photodetector using four asymmetric quantum wells M. Hostut Department of Electrical and Electronics Engineering, Cumhuriyet University, 58140 Sivas, Turkey Received 21 November 2006; received in revised form 15 December 2006; accepted 20 December 2006 Available online 12 February 2007
Abstract A theoretical investigation of GaAs/AlGaAs infrared detector consisting of four asymmetric quantum wells is presented. Each well is designed to yield absorption and a photoresponse at peak wavelengths of 7.9, 9.2, 10.4, and 11.8 mm, respectively. The device operation is based on intersubband bound to bound transition. r 2007 Elsevier B.V. All rights reserved. PACS: 85.60.–q; 07.57.Kp; 85.35.Be; 78.20.Ci Keywords: QWIP; Quantum well; Absorption; Responsivity; Dark current
1. Introduction Quantum well infrared photodetectors (QWIP) for long wavelength infrared detection have been developed rapidly over the past 10 years from the fundamental-physics point of view towards large-area focal plane arrays [1–3]. Due to this progress, high-resolution high-performance large-format focal plane arrays (FPAs) are available [4,5]. On the other hand, sensing a broad range of infrared radiation is highly desirable for a certain application such as spectroscopy. In a standard QWIP structure with bound to bound transition, identical quantum wells are grown successively to achieve a period. Variation from the standard QWIP structure has been recently proposed by us as a singlewavelength bound to bound transition [6] and broadband bound to continuum transition [7] staircase-like detectors working in long-wavelength atmospheric windows. In this proposed structure, four quantum wells of different thickness separated with step-like thin barriers are composed of a unit with thick end barrier. Thus, each unit contains four asymmetric quantum wells that detect four different wavelengths to achieve broadband detector. Thin barriers in the structure were inspired by quantum cascade
E-mail address: [email protected]. 1386-9477/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2006.12.058
detectors (QCD) [8] that have generated a significant photocurrent. The barrier at the end of each unit reduces ground state tunneling. 2. Device structure The device structure reported here involved 20 period repeated layers of GaAs four-QW units. Each unit consists of 50, 53, and two 57 A GaAs quantum wells separated by 23A AlxGa1xAs barriers with Al concentrations of 0.35, 0.31, 0.29, 0.27 and 0.25, respectively. The last barrier thickness is chosen to be 500 A to prevent electron escape from the ground state of the last quantum well. Doping concentration of quantum wells were 1 1018 cm3 and barriers are undoped. Each unit is separated by 500 A GaAs layer with the doping concentration of 1 1018 cm3. The whole period is sandwiched between two 0.5 mm GaAs (1 1018 cm3 Si doping) contact layers. The unit is represented in Fig. 1. 3. Theoretical considerations Potential energy of the system shown in Fig. 1 can be given as V ¼ V G þ V min ,
(1)
ARTICLE IN PRESS M. Hostut / Physica E 39 (2007) 50–52
in free space, kB is Boltzmann’s constant, T is the temperature, y is the angle between the polarization vector and the normal to the quantum well, nr is the refractive index, EF is the Fermi energy which depends on the density of electrons in the well, and linewidth, G ¼ G0 þ Gt (where G0 and Gt are half-width at zero bias and energy-dependent tunneling escape broadening due to tunneling time, tt, respectively [1,9]), is 10 meV. The responsivity of the structure has also been calculated using the formula [1]
Potential Energy (eV)
b
V1
0.25
b V2
b
V3
b
V4
0.2
Vmin
0.15 0.1 0.05
b
b w b w b w b w Z1 Z1 Z2 Z2 Z3 Z3 Z4 Z4 Z5 w w w w V2 V3 V4 V1
0
200
Zmax
400 Z (A)
600
51
800
Fig. 1. Schematic conduction band profile of the structure with relevant parameters.
R ¼ ðe=hvÞZa pe g,
(7)
where g is the optical gain, pe is the hot-carrier escape probability and Za is the unpolarized double-pass absorption quantum efficiency given as [1] Za ¼ ð1 e2al Þ=2,
where VG ¼
4 X
V nG ,
(2)
n¼1
V min ¼ V min Sðz zb5 Þ, 8 b > < V n; n V G ¼ V wn ; > : 0
(3)
zbn ozozwn ; zwn ozozbnþ1 ; elsewhere;
(4)
where S is the step function. The Hamiltonian of the system and wave functions has been given elsewhere [6,7]. In order to calculate the wave functions, we placed quasi-barriers on the left- and righthand sides of the device structure with potential heights, Vb1, as shown in Fig. 1 with bold dashed lines. Thus, we obtain decaying plane waves in this region. We then obtain a 16 16 secular matrix, H16 16, which can be solved by setting Det [H16 16] ¼ 0. The actual energies of the system can be separated from quasi-levels using confined wave functions. The widths of the quasi-wells are chosen so that confinement energies in the wells are not affected. We have also calculated the initial optical absorption coefficient of the structure, which has 451 multipass waveguide geometry, given by a¼
X X pcm kB Te2
ðcos2 yÞjM fi j2 p_2 m20 Lnr w " " #, " ## E F E ðzÞ E F E ðzÞ ðG=2Þ i fi ln 1 þ exp 1 þ exp kB T kB T ð_w E fi Þ2 þ ðG=2Þ2 i
f
ð5Þ with the matrix element ðzÞ Z L=2 m0 ðE ðzÞ i Ef Þ M fi ¼ ff ðzÞzfi ðzÞ dz, i_ L=2
(6)
ðzÞ ðzÞ ðzÞ where, E fi ¼ E ðzÞ f E i ; and E i and E f denote the quantized energy levels for the initial and final states, respectively, P is the permeability, c is the speed of light
(8)
where l is the length of the superlattice, and the factor of 2 in the denominator is a result of the quantum-mechanical selection rules, which only allow the absorption of radiation polarized in the plane of incidence. Total net quantum efficiency Z is expressed as [1] Z ¼ Za pe .
(9)
We use a simple model [10] for field-dependent dark current density, JD, in which we take the ‘‘effective’’ number of electrons n*(F), which tunnel out of the well or are thermally excited out of the well into the continuum states, and multiply by the average drift velocity, n(F), the electron charge q, and A sample area to obtain I D ðF Þ ¼ qnn ðF ÞnðF ÞA, where n ðF Þ ¼
me p_2 Lp
Z
(10)
1
f ðEÞTðE; F Þ dE,
(11)
EF
where f(E) is the Fermi function, LP is length of the active region, and T(E,F) is the tunneling probability through the active region with an applied field of F. The drift velocity is mF nðF Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 1 þ ðmF =vs Þ2
(12)
where m is the electron mobility and ns is the saturation drift velocity. 4. Results and discussion The potential energy profile of the structure and the relevant device parameters are shown in Fig. 1. Height of each barrier decreases from Al mole fraction (x) of 0.35–0.25 by step-like from leftmost to rightmost side of the structure to achieve asymmetric multiquantum wells. Fig. 2 shows the potential profile of the structure with the squared electron wave functions under electric field of 2.5 kV/cm. Electron transition mechanism is based on bound to bound transition. The excited state energy level broadening has been further enhanced due to overlap of
ARTICLE IN PRESS M. Hostut / Physica E 39 (2007) 50–52
52
10-5
Dark Current (A)
Potential Energy (eV)
0.2 0.1 0 -0.1 -0.2
10-7 10-8 10-9
0
200
400 Z (A)
600
0
800
Normalized Absorption
0.8
0.6
0.4
5000
10000
15000
20000
25000
30000
F (V/cm)
Fig. 2. Conduction band profile and squared electron wave functions of the four-quantum-well unit under applied electric field of 2.5 104 V/cm at 77 K.
Responsivity (A/W)
10-6
1 0.8 0.6 0.4 0.2 0 6
8
10
12
14
Wavelength (µm)
Fig. 4. Dark current vs. applied electric field at 77 K (sample area is 300 300 mm2).
Eq. (10) at 77 K shown in Fig. 4. Since the structure consists of four asymmetric quantum wells with step like barriers, the contribution to the dark current from each quantum well is different. A quantum well with lower barrier height has higher dark current. Therefore, dark current has been calculated as total dark current of four wells. As the applied field increases, dark current rises rapidly and saturates around 1 106 A due to thermionicassisted tunneling mechanism.
0.2
5. Conclusion 8
10 12 Wavewlength (µm)
14
16
Fig. 3. Overall responsivity vs. wavelength under operating field at 77 K. Inset shows the normalized absorption.
wave functions associated with excited states of quantum wells separated by thin barriers. Since the barrier thicknesses are 23 A, excited electrons easily tunnel through their respective barriers to contribute to the photocurrent. Each unit in the structure consists of four asymmetric quantum wells with different barrier heights and well widths to give raise four absorption peaks that are shown in inset of Fig. 3. The overall responsivity of the structure, given in Fig. 3, has been calculated as Eq. (7). The responsivity spectrum is influenced by absorption coefficient and overlap of wave functions. Quantum wells have peaks at lP ¼ 7.9, 9.2, 10.4 and 11.8 mm, and long wavelengths cutoff are lc ¼ 8.15, 9.6, 11, 12.3 mm (i.e., where R drops to half of its peak value), respectively (at T ¼ 77 K). Thus, this detector covers 8–12 mm long wavelength infrared range (LWIR). The height and thickness of the end barrier have been chosen to be 0.2 eV and 500 A, respectively. The last barrier is taken to be wide enough to avoid electron tunneling into collector under operating bias. Therefore, dark current caused by tunneling probability from the emitter to the collector will be reduced. Dark current has also been calculated by using
The theoretical calculations of four asymmetric quantum well structure are proposed to be used as a photodetector operating in the long wavelength infrared range in the GaAs/ AlGaAs material system. The detection wavelengths are 7.9, 9.2, 10.4, and 11.8 mm, respectively. Thickness of barriers has been chosen to be 23 A to increase photocurrent. References [1] B.F. Levine, J. Appl. Phys. R1 (1993). [2] S.D. Gunapala, H. C. Liu, H. Schneider (Eds.), in: Proceedings of Workshop on Quantum Well Infrared Photodetectors QWIP 2000, 2000. [3] G. Sarusi, A. Carbone, S.D. Gunapala, H.C. Liu (Eds.), in: Proceedings of Workshop on Quantum Well Infrared Photodetectors QWIP 2002, 2002. [4] S.D. Gunapala, S.V. Bandara, J.K. Lui, S.B. Rafol, M. Mumolo, IEEE Trans. Electron. Dev. 50 (2003) 2353. [5] S.D. Gunapala, S.V. Bandara, J.K. Liu, C.J. Hill, S.B. Rafol, J.M. Mumolo, J.T. Trinh, M.Z. Tidrow, P.D. LeVan, Semicond. Sci. Technol. 20 (2005) 473. [6] S.U. Eker, M. Hostut, Y. Ergun, I. Sokmen, Infrared Phys. Technol. 48 (2006) 101. [7] Y. Ergun, M. Hostut, S.U. Eker, I. Sokmen, Infrared Phys. Technol. 48 (2006) 109. [8] L. Gendron, M. Carra, A. Huynh, V. Ortiz, Appl. Phys. Lett. 85 (2004) 2824. [9] Z. Ikonic, V. Milanovic, D. Tjapkin, S. Pajevic, Effectivemassmismatch-induced intersubband absorption line broadening in semiconductor quantum wells, Phys. Rev. B 37 (1988) 3097. [10] S.L. Chuang, Physics of Optoelectronic Devices, New York, 1995.