# Control of radiative base recombination in the quantum cascade light-emitting transistor using quantum state overlap

**Part of the following topical collections:**

## Abstract

The concept of the quantum cascade light-emitting transistor (QCLET) is proposed by incorporating periodic stages of quantum wells and barriers in the completely depleted base–collector junction of a heterojunction bipolar transistor. The radiative band-to-band base recombination in the QCLET is shown to be controllable using the base–collector voltage bias for a given emitter–base biasing condition. A self-consistent Schrödinger–Poisson Equation model is built to validate the idea of the QCLET. A GaAs-based QCLET is designed and fabricated. Control of radiative band-to-band base recombination is observed and characterized. By changing the voltage across the quantum cascade region in the QCLET, the alignment of quantum states in the cascade region creates a tunable barrier for electrons that allows or suppresses emitter-injected electron flow from the p-type base through the quantum cascade region into the collector. The field-dependent electron barrier in the base–collector junction manipulates the effective minority carrier lifetime in the base and controls the radiative base recombination process. Under different quantum cascade region biasing conditions, the radiative base recombination is measured and analyzed.

## 1 Introduction

The base recombination is key to the operation of a bipolar junction transistor. In the case where a heterojunction bipolar transistor has a direct bandgap base region, radiative band-to-band recombination has been observed and utilized to fabricate light-emitting transistors (LETs) [1, 2, 3] and transistor lasers (TLs) [4, 5, 6, 7, 8, 9, 10, 11] with properties such as high modulation bandwidth, low relative intensity noise (RIN) [12, 13], and improved spurious-free dynamic range (SFDR) [14] that make the devices useful for applications such as optical communications [15, 20]. Fixed structures such as a single quantum barrier at the edge of the base region at the base–collector junction have been shown to affect the effective recombination lifetime and as a consequence modulation bandwidth [21], but as these are structures created during the growth process the resulting parameters are fixed. The QCLET, on the other hand, creates a tunable barrier in the base–collector junction to actively control base recombination through quantum state alignment in the inserted quantum cascade region, and allows more freedom in controlling optical emission in the LETs and TLs.

The concept of the QCLET is illustrated in Fig. 1, which resembles the transistor-injected quantum cascade laser (TI-QCL). The transistor-injected quantum cascade laser (TI-QCL) has been proposed as a three-terminal device that allows independent control of field across and current through a quantum cascade laser (QCL) structure located in the space-charge region of the base–collector junction of a heterojunction bipolar transistor (HBT) in forward-active mode [16, 17, 18, 19]. The QCL is a unipolar semiconductor laser that utilizes electron intersubband transitions for coherent optical emission [22, 23, 24, 25, 26] in which two heavily doped n-type terminals have inserted between them repetitive stages of alternating quantum wells and barriers. When the device is biased, the quantum wells and barriers in each stage define the electron-quantized energy states and wave functions. With band engineering, the process of finetuning the composition and thickness of each layer in the superlattice structure, the upper and lower lasing levels that produce the desired lasing transition are formed for a specific electric field set by the design and determined by the bias voltage. The quantum cascade laser provides a high power and scalable solution for many applications in gas sensing spectroscopy [27, 28, 29, 30, 31], imaging [32, 33, 34], and free-space communication technologies [35, 36]. In the QCLET, an intrinsic quantum cascade region consisting of repetitive stages of quantum wells and barriers is inserted between the p-type base and the n-type collector as illustrated in Fig. 2. The labels \(h\nu _1\), \(h\nu _2\), and \(h\nu _3\) represent the optical output contributed by intersubband transitions in the superlattice, electron–hole radiative recombination process in the bulk base region, and radiative recombination process introduced by injected hole current in the emitter, respectively.

In comparison of the QCLET with the conventional QCL, to be compatible with the conventional HBT, which the base–collector interface is formed by a p–n junction instead of an n–n junction (conventional QCL), one n-doped terminal in the conventional QCL structure is replaced with a p-doped layer in QCLET. The detailed structure design of the superlattice structure in the proposed device is based on the one in conventional QCL. In addition, the main difference between the QCLET and TLs is on the mechanism of performing the optical output. Both the QCLET and transistor laser are based on the integration of a conventional transistor with a carrier confined structure aimed to the enhancement of the radiative recombination process. However, the optical output is achieved by spontaneous emission process in QCLET while it is by stimulated emission process in TLs. Also, the TL does not have a barrier at the base–collector junction that is controllable with voltage, through which control of the optical output can be achieved. The QCLET has a similar design but fewer stages are inserted into the base–collector junction. The goal of the QCLET is to allow quantum modulation of the light-emitting transistor direct-gap base recombination while the goal of the TI-QCL is to create a mid-infrared coherent emission source.

## 2 Design of the QCLET

*A*is the cross-sectional area, and \(\phi _n(z)\) is a localized (Wannier) function on site

*n*, are used in the Hamiltonian. The matrix elements of \(H_0\) are \(\langle \mathbf k ,i | H_0 | \mathbf k ,j \rangle = \varepsilon _\mathbf{k ,i}\delta _{i,j}-t_{i,j}\delta _{i,j\pm 1}\). The on-site energy \(\varepsilon _\mathbf{k _i}\) and hopping terms \(t_{i,j}\) can be obtained by associating the matrix with the discretized effective mass Hamiltonian [43]. The device region is assumed to consist of sites \(1,\ldots ,N\). Boundary self-energies which incorporate the coupling to the left and right reservoirs are calculated using Dyson equation [44, 45]:

*z*-direction, which is the growth direction in the QCLET simulation, is given as follows:

*p*and

*n*are the hole and electron density, respectively. In our case, complete ionization is assumed so the ionized donor(acceptor) density is identical with the spatial doping concentration. \(\phi\) is the electrostatic potential corresponding to the given charge distribution and

*q*is the electron charge. The finite difference scheme is then adopted for numerical calculation of Eq.5.

Epitaxial layer structure of a GaAs-based QCLET

InGaAs | \(n = 2 \times\)10\(^{19}\) cm\(^{-3}\) | 50 nm |

GaAs | \(n = 5 \times\)10\(^{18}\) cm\(^{-3}\) | 50 |

AlGaAs | \(n = 5 \times\)10\(^{18}\) cm\(^{-3}\) | 1000 |

InGaP | \(n = 2 \times\)10\(^{17}\) cm\(^{-3}\) | 50 |

\(p = 1\times\)10\(^{19}\) cm\(^{-3}\) | 50 | |

GaAs | \(p = 5 \times\)10\(^{17}\) cm\(^{-3}\) | 500 |

\(p = 2 \times\)10\(^{16}\) cm\(^{-3}\) | 250 | |

Active region (\(28\times\)) | 1260 | |

GaAs | \(n = 2\times\)10\(^{16}\) cm\(^{-3}\) | 250 |

\(n = 1\times\)10\(^{17}\) cm\(^{-3}\) | 750 | |

AlGaAs | \(n = 6 \times\)10\(^{17}\) cm\(^{-3}\) | 1000 |

GaAs | \(n = 1 \times\)10\(^{18}\) cm\(^{-3}\) |

## 3 Fabrication of a GaAs-based QCLET

## 4 Quantum modulation of the QCLET

### 4.1 Transistor electrical performance

### 4.2 Radiative base recombination measurement

To validate that the base recombination is controlled by the base–collector voltage the quantized electron states in the quantum cascade region under different base–collector biasing conditions are simulated. In Fig. 7, the simulated electron-quantized states in one and a half stages of the quantum cascade region under different biasing conditions are shown. The wave function of each quantum state is shown on its energy eigenvalue. When the base–collector junction voltage is 3 V, the upper and lower lasing levels are separated by 71 MeV. All quantum states are closely located, making it difficult for phonons to depopulate the states to facilitate electron transport. Moreover, the energy states do not have good spatial overlap so the transition probability between states is low. Therefore, the effective impedance for electrons to transition through the quantum cascade region from the base is higher due to the misalignment of the quantized electron states. The quantum barriers of the quantum cascade region thus reject electron flow through the base–collector junction. This results in higher optical output power from the base (enhanced base recombination). As the voltage across the quantum cascade region increases toward the point of creating the designed mid-infrared emission, the electron states are more aligned as in Fig. 7b. The five states in Fig. 7b are from top to bottom: upper lasing level, injection level, lower lasing level, depopulation level and the injection level in the next stage. Electrons are injected from the injection level to the upper lasing level through resonant tunneling. For a TI-QCL, mid-infrared emission occurs when an electron transitions from the upper lasing level to the lower lasing level. In the QCLET, there is no stimulated mid-infrared emission but electrons still transition between the same levels. When \(V_\mathrm{{CB}}\) is 6 V the transition energy between the upper and the lower lasing level is 113 MeV. When transition energy between electron-quantized states is near the longitudinal optical (LO) phonon energy, which is 34 MeV for bulk GaAs, the scattering rate from the state with higher energy to the one with lower energy is largely enhanced due to the resonance tunneling assisted by electron-LO scattering. In other word, in addition to spatially electronic wave function overlap, the electron–phonon interaction introduces an extra path for electron to achieve intersubband transition by producing a phonon with the energy coincident with the transition energy. With the help of electron–LO phonon interaction, electrons are depopulated from the lower lasing level to the depopulation level so that the population inversion rule is satisfied for stimulated emission as the energy difference between the lower lasing level and the depopulation level is 38 Mev from calculation. Electrons then migrate to the injection level of the next stage. The electron wave functions are largely overlapped under this biasing condition. This allows a free flow of electrons into the quantum cascade region thus reducing the base recombination. When the base–collector junction is even more reverse biased at 9 V, the electron states are perturbed by the higher field but the states still have good overlap. The energy difference is 115 MeV. The electron flow through the quantum cascade active region occurs with low-radiative base recombination. The overlap between the upper and lower lasing levels can be used as a metric to gauge the ease with which electrons will flow through the cascade region. Good overlap will facilitate flow, while poor overlap will retard flow. The spatial overlap between the upper and lower lasing state wave functions under different base—collector junction biasing conditions is shown in Fig. 6b. At around 4–5 V, the spatial overlap starts to increase dramatically. This is aligned with the minimum in the base current characteristic. It can be seen that at the base–collector voltage where good overlap is achieved, base recombination and base light output drop. While mid-IR emission is expected, the intensity was too low to be observed. Future work will examine the speed of QCLET base recombination modulation around this transition point.

## 5 Conclusion

With a self-consistent Schrödinger–Poisson Equation solver based on NEGF method, the concept of the QCLET is validated and the design of the QCLET is optimized. A GaAs-based QCLET is fabricated and characterized. Control of the radiative base recombination based upon the QCLET base–collector voltage bias is measured and analyzed, confirming that radiative base recombination is controllable through the alignment or misalignment of electron-quantized states in the quantum cascade region in the base–collector junction. When the quantized states in the base–collector junction are aligned, the transport of electrons in the base is facilitated and the intensity of radiative base recombination is suppressed. When the quantized states in the base–collector junction are misaligned, a strong barrier is formed to effectively inhibit electron flow from the base into the collector and the radiative base recombination is enhanced. The measurement result is validated using the self-consistent model.

## Notes

### Acknowledgements

Funding was provided by National Science Foundation (Grant no: ECCS 1408300).

## References

- 1.M. Feng, N. Holonyak Jr., W. Hafez, Appl. Phys. Lett.
**84**, 151 (2004)ADSCrossRefGoogle Scholar - 2.M. Feng, N. Holonyak Jr., B. Chu-Kung, G. Walter, R. Chan, Appl. Phys. Lett.
**84**, 4792 (2004)ADSCrossRefGoogle Scholar - 3.M. Feng, N. Holonyak Jr., R. Chan, Appl. Phys. Lett.
**84**, 1952 (2004)ADSCrossRefGoogle Scholar - 4.G. Walter, N. Holonyak Jr., M. Feng, R. Chan, Appl. Phys. Lett.
**85**, 4768 (2004)ADSCrossRefGoogle Scholar - 5.R. Chan, M. Feng, N. Holonyak Jr., G. Walter, Appl. Phys. Lett.
**86**, 131114 (2005)ADSCrossRefGoogle Scholar - 6.G. Walter, A. James, N. Holonyak Jr., M. Feng, R. Chan, Appl. Phys. Lett.
**88**, 232105 (2006)ADSCrossRefGoogle Scholar - 7.N. Holonyak Jr., M. Feng, IEEE Spectr.
**43**, 50 (2006)CrossRefGoogle Scholar - 8.F. Dixon, M. Feng, N. Holonyak Jr., Y. Huang, X.B. Zhang, J.H. Ryou, R.D. Dupuis, Appl. Phys. Lett.
**93**, 021111 (2008)ADSCrossRefGoogle Scholar - 9.M. Feng, N. Holonyak Jr., H.W. Then, C.H. Wu, G. Walter, Appl. Phys. Lett.
**94**, 041118 (2009)ADSCrossRefGoogle Scholar - 10.F. Dixon, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**96**, 241103 (2010)ADSCrossRefGoogle Scholar - 11.H.W. Then, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**94**, 013509 (2009)ADSCrossRefGoogle Scholar - 12.F. Tan, R. Bambery, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**101**, 151118 (2008)ADSCrossRefGoogle Scholar - 13.F. Tan, W. Xu, X. Huang, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**102**, 081103 (2013)ADSCrossRefGoogle Scholar - 14.P. Lam, J.M. Dallesasse, G. Walter, in
*Digest of Papers 2014 International Conference on Compound Semiconductor Manufacturing Technology*(2014), p. 91Google Scholar - 15.F. Tan, R. Bambery, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**99**, 061105 (2011)ADSCrossRefGoogle Scholar - 16.J. Dallesasse, M. Feng, US Patent 8,948,226, filed August 2, 2013, issued February 3, 2015Google Scholar
- 17.K. Chen, J.M. Dallesasse, in
*Digest of Papers 2014 International Conference on Compound Semiconductor Manufacturing Technology*(2004), p. 75Google Scholar - 18.K. Chen, F.-C. Hsiao, B. Joy, J.M. Dallesasse,
*Proceedings SPIE 10123*(Photonics West, Novel In-Plane Semiconductor Lasers XVI, 2017), p. 1012318Google Scholar - 19.K. Chen, J.M. Dallesasse, in
*55th Electronic Material Conference*(2014)Google Scholar - 20.R. Bambery, F. Tan, M. Feng, J.M. Dallesasss, N. Holonyak Jr., IEEE. Photon. Technol. Lett.
**25**, 859 (2013)ADSCrossRefGoogle Scholar - 21.R. Bambery, C. Wang, J.M. Dallesasse, M. Feng, N. Holonyak Jr., Appl. Phys. Lett.
**104**, 081117 (2014)ADSCrossRefGoogle Scholar - 22.J. Faist, F. Capasso, D.L. Sivco, C. Sirtori, A.L. Hutchinson, A.Y. Cho, Science
**264**, 553 (1994)ADSCrossRefGoogle Scholar - 23.M. Beck, D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, H. Melchior, Science
**295**, 301 (2002)ADSCrossRefGoogle Scholar - 24.C. Sirtori, P. Kruck, S. Barbieri, P. Collot, J. Nagle, Appl. Phys. Lett.
**73**, 3486 (1998)ADSCrossRefGoogle Scholar - 25.H. Page, C. Becker, A. Robertson, G. Glastre, V. Ortiz, C. Sirtori, Appl. Phys. Lett.
**78**, 3529 (2001)ADSCrossRefGoogle Scholar - 26.C. Gmachl, F. Capasso, D.L. Sivco, A.Y. Cho, Rep. Prog. Phys.
**64**, 1533 (2001)ADSCrossRefGoogle Scholar - 27.A. Kosterev, F. Tittel, IEEE. J. Quant. Electron.
**38**, 582 (2002)ADSCrossRefGoogle Scholar - 28.D. Weidmann, F. Tittel, T. Aellen, M. Beck, D. Hostetter, J. Faist, S. Blaser, Appl. Phys. B
**79**, 907 (2004)ADSCrossRefGoogle Scholar - 29.C. Charlton, B. Temelkuran, G. Dellemann, B. Mizaikoff, Appl. Phys. Lett.
**86**, 194102 (2005)ADSCrossRefGoogle Scholar - 30.A. Kosterev, G. Wysocki, Y. Bakhirkin, S. So, R. Lewicki, M. Fraser, F. Tittel, R. Curl, Appl. Phys. B
**90**, 165 (2008)ADSCrossRefGoogle Scholar - 31.V. Spagnolo, A. Kosterev, L. Dong, R. Lewicki, F. Tittel, Appl. Phys. B
**100**, 125 (2010)ADSCrossRefGoogle Scholar - 32.A. Lee, B. Williams, S. Kumar, Q. Hu, J. Reno, IEEE Photon. Technol. Lett.
**18**, 1415 (2006)ADSCrossRefGoogle Scholar - 33.S. Kim, F. Hatami, J. Harris, A. Kurian, J. Ford, D. King, G. Scalari, M. Giovannini, N. Hoyler, J. Faist, G. Harris, Appl. Phys. Lett.
**88**, 153903 (2006)ADSCrossRefGoogle Scholar - 34.B. Behnken, G. Karunasiri, D. Chamberlin, P. Robrish, J. Faist, Opt. Lett.
**33**, 440 (2008)ADSCrossRefGoogle Scholar - 35.R. Martini, C. Gmachl, J. Falciglia, F. Curti, C. Bethea, F. Capasso, E.A. Whittaker, R. Paiella, A. Tredicucci, A. Hutchinson, D.L. Sivco, A.Y. Cho, Electron. Lett.
**37**, 191 (2001)CrossRefGoogle Scholar - 36.R. Martini, C. Bethea, F. Capasso, C. Gmachl, R. Paiella, E.A. Whittaker, H.Y. Huang, D.L. Sivco, J.N. Baillargeon, A.Y. Cho, Electron. Lett.
**38**, 181 (2002)CrossRefGoogle Scholar - 37.C. Juang, K.J. Kuhn, R.B. Darling, Phys. Rev. B
**41**, 12047 (1990)ADSCrossRefGoogle Scholar - 38.S. Datta, Superlattice Microstruct.
**28**, 253 (2000)ADSCrossRefGoogle Scholar - 39.R. Lake, G. Klimeck, R.C. Bowen, D. Jovanovic, J. Appl. Phys.
**81**, 7845 (1997)ADSCrossRefGoogle Scholar - 40.A.Y. Song, R. Bhat, P. Bouzi, C.-E. Zah, C.F. Gmachl, Phys. Rev. B
**94**, 165307 (2016)ADSCrossRefGoogle Scholar - 41.S.-C. Lee, A. Wacker, Phys. Rev. B
**66**, 245314 (2002)ADSCrossRefGoogle Scholar - 42.G. Klimeck, R. Lake, R.C. Bowen, W.R. Frensley, T.S. Moise, Appl. Phys. Lett.
**67**, 2539 (1995)ADSCrossRefGoogle Scholar - 43.A. Wacker, M. Lindskog, D.O. Winge, IEEE J. Sel. Top. Quantum Electron.
**9**, 1200611 (2013)Google Scholar - 44.W.R. Frensley,
*Heterostructures and Quantum Devices*(Academic, San Diego, 1994), p. 284Google Scholar - 45.S. Hershfield, J.H. Davies, J.W. Wilkins, Phys. Rev. B
**46**, 7046 (1992)ADSCrossRefGoogle Scholar - 46.Y. Meir, N.S. Wingreen, Phys. Rev. Lett.
**68**, 2512 (1992)ADSCrossRefGoogle Scholar - 47.J.M. Ortega, W.C. Rheinboldt,
*Iterative Solution of Nonlinear Equations in Several Variables*(SIAM, Classics in Applied Mathematics, 2000), p. 183Google Scholar