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Applied Physics B

, 124:129 | Cite as

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

  • Kanuo Chen
  • Fu-Chen Hsiao
  • Brittany Joy
  • John M. Dallesasse
Article
  • 77 Downloads
Part of the following topical collections:
  1. Mid-infrared and THz Laser Sources and Applications

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.

The proposed device, which utilizes the alignment of quantum states to achieve the goal of controlling the radiative recombination rate, provides an extra channel for imparting an optical signal onto a LET or TL. It, therefore, serves as a potential device for optical communication applications as an innovative light-emitting source. Furthermore, by reducing the number of cascade periods in the superlattice region, it may be a strong candidate for next-generation sources for higher speed optical modulation. In this letter, the design and theoretical modeling of the QCLET is discussed first, followed by details regarding the fabrication of a GaAs-based QCLET. In the fourth section, the quantum modulation of the QCLET is characterized and analyzed.
Fig. 1

Visualizing illustration of the QCLET, showing the electronic and hole band diagram, optical output and the carrier dynamics

Fig. 2

Schematic illustration of the QCLET, showing electron and hole flow, as well as areas of both electron–hole recombination and unipolar intersubband transitions

2 Design of the QCLET

For a GaAs-based QCLET the device starts from an n-type-doped GaAs substrate and AlGaAs bottom cladding layer with 90\(\%\) Al concentration to improve optical confinement. The collector is n-type GaAs. The quantum cascade region grown on top of the GaAs collector has 28 stages of intrinsic GaAs/Al\(_{0.45}\)Ga\(_{0.55}\)As quantum wells and barriers. The p-type-doped GaAs base and n-type-doped In\(_{0.49}\)Ga\(_{0.51}\)P emitter form the emitter–base heterojunction. On top of the emitter is the top cladding layer of Al\(_{0.9}\)Ga\(_{0.1}\)As followed by a heavily n-type-doped GaAs–InGaAs emitter cap for electrical contact purposes. The epitaxial layer structure doping and thickness values are shown in Table 1. A self-consistent Schrödinger–Poisson equation solver is developed to model the carrier transport and electronic steady states in the device under non-equilibrium conditions. The non-equilibrium Green’s function (NEGF) theory has become one of the most powerful simulation techniques for modeling quantum charge transport in an open system [37, 38]. The theory can easily incorporate quantum effects such as interface roughness and impurity and electron–phonon scattering processes [39, 40]. It treats quantum effects which are beyond the capability of conventional semi-classical models with a full quantum mechanical description. For device modeling applications, it has been applied to the analysis of many electronic as well as optoelectronic devices, such as tunnel diodes [41] and conventional QCL devices [40, 42]. A brief overview of the NEGF theory used in QCLET simulation is presented. The NEGF formulas present in this article are mainly adopted from [41]. The Hamiltonian in the simulation contains three parts: \(H_0=H^\mathrm{L}_0+H^\mathrm{D}_0+H^\mathrm{R}_0\) which represents the Hamiltonian of the left reservoir, the device, and the right reservoir, respectively. The tight-binding basis \(\langle \mathbf r |\mathbf k ,n \rangle = e^{i\mathbf k \cdot \mathbf r }\phi _n(z)/\sqrt{A}\), where \(\mathbf k\) is the wave vector perpendicular to growth direction, 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]:
$$\begin{aligned} \Sigma _{1,1}^\mathrm{{RB}} = g_{0,0}^\mathrm{{R}} |t_{0,1}|^2 \end{aligned}$$
(1)
$$\begin{aligned} \Sigma _{N,N}^\mathrm{{RB}} = g_{N+1,N+1}^\mathrm{{R}} |t_{N,N+1}|^2, \end{aligned}$$
(2)
where \(g^\mathrm{R}\) represents the self-energy of the reservoir when it is unconnected to the device (i.e., \(t_{0,1}=t_{N,N+1} = 0\)). The self-energies in Eqs. 1 and 2 are zero for sites \(\{i,j\} \ne \{1,1\}\) or \(\{n,n\}\). The equation of motion for the retarded Green’s function, \(G^\mathrm{R}\) in the device, hence can be written in matrix form: \((E-H_0^\mathrm{D}-\Sigma ^\mathrm{{RB}})G^\mathrm{R}=1\). A simple three-site device is taken as an example to explicitly illustrate the retarded Green’s defined above:
$$\begin{aligned} \left[ \begin{array}{c} G^\mathrm{R} \end{array} \right] = \begin{bmatrix} E-\varepsilon _{k,1}-\Sigma _{1,1}^\mathrm{{RB}}&t_{1,2}&0 \\ t_{2,1}&E-\varepsilon _{k,2}&t_{2,3} \\ 0&t_{3,2}&E-\varepsilon _{k,1}-\Sigma _{3,3}^{RB} \end{bmatrix}^{-1}. \end{aligned}$$
(3)
In the QCLET simulation the self-energies of the semi-infinite region (reservoir), \(g^\mathrm{R}\), are obtained simply by applying an iteration loop with the assumption that adding or subtracting one layer from a semi-infinite region does not change the properties of the boundary. In the actual implementation, the corresponding spectral function is usually introduced, \(a=-2\text {Im}g^\mathrm{{R}}\), for the sake of numerical efficiency. In our simulation, ballistic transport is assumed for the sake of simplicity and the recursive Green’s function algorithm [46] is applied for calculating the inverse of the matrix in Eq. 3. Once the retarded Green’s function is obtained, the carrier density can be calculated using
$$\begin{aligned} N_i= & {} \frac{1}{A\Delta }\sum _\mathbf{k }\int \frac{{\rm d}E}{2\pi }n_{i}(\mathbf k ,E), \end{aligned}$$
(4)
where \(n_i=f_{\rm {L(R)}}\text {Im}G_{i,i}^\mathrm{{R}}\) for the contact region and \(n_i=f_{\rm {L}}a_{0,0}|t_{0,1}G_{i,1}^\mathrm{R}|^2+f_{R}a_{N+1,N+1}|t_{N,N+1}G_{i,N}^\mathrm{R}|^2\) for the device region, \(f_{\rm{L(R)}}\) is the Fermi–Dirac distribution of the left(right) contact which incorporates the bias applied to the device while \(\Delta\) is the site spacing.
Now the goal turns to incorporating the carrier density obtained in Eq. 4 into the Poisson equation to from a self-consistent iteration loop. In the simulation of QCLET the device is assumed to connect to charge reservoirs at room temperature (300 K). The quantum cascade region is considered to be a multi-quantum well structure along the growth direction and homogeneous in the plane normal to the growth direction. Therefore, the NEGF method is mainly applied in the growth direction while electron behavior in the lateral direction is treated as a plane wave that can be expressed in closed form. The spatial variation along the z-direction, which is the growth direction in the QCLET simulation, is given as follows:
$$\begin{aligned} \frac{\mathrm{d}}{\mathrm{d}z}\epsilon (z)\frac{\mathrm{d}}{\mathrm{d}z}\phi (z)+q[N_\mathrm{D}^{+}(z)-N_\mathrm{A}^{+}(z)+p(z)-n(z)]=0, \end{aligned}$$
(5)
where \(N_\mathrm{D}^{+}\) is the ionized donor density, \(N_\mathrm{A}^{+}\) is the ionized acceptor density, 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.
The structure of iteration loop of NEGF–Poisson self-consistent solver is described here. First of all, the carrier density calculated from Eq. 4 in the device region together with the one in reservoirs serves as input of Poisson’s equation in Eq. 5. Poisson’s equation then provides a new value for the potential throughout the device, \(-q\phi _j, j=1,\ldots ,N\). This updated potential is then added onto the diagonal elements of the Hamiltonian and start up the new iteration loop by calculating the updated Green’s function until it achieves a certain convergence condition. In the simulation of QCLET, the convergence condition is assigned to be demanding that the potential difference between the adjacent loop is smaller than 0.1 meV, which means the deviation error of the band diagram from the self-consistent result is less than 0.1 meV. From the self-consistent calculation, the charge distribution and the energy band diagram with applied external voltage is obtained by following the procedure described above. The Newton–Raphson iteration method is implemented in the self-consistent calculation loop to enhance convergence [47]. The modeled energy band diagram of the QCLET is shown in Fig. 3.
Table 1

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\(^{-3}\)

 
Fig. 3

Conduction band diagram of the GaAs-based QCLET modeled by a self-consistently Schrödinger–Poisson solver

Band engineering is another important factor in the design of the QCLET as it determines the electron-quantized state energies and wave functions in the quantum cascade region. With the self-consistent Schrödinger–Poisson solver, the electron bound states are calculated and the quantum cascade region design is optimized [41]. In Fig. 4, the conduction band of one and a half stages of the quantum cascade region with electron bound states is shown under the desired biasing condition. The quantum well is GaAs and the barrier is Al\(_{0.45}\)Ga\(_{0.55}\)As. The layer sequence of one stage in nanometers starting from the injection barrier is \(\mathbf 2.8 /3.4/\mathbf 1.7 /3.0/\mathbf 1.8 /2.8/\mathbf 2.0 /3.0\) \(/\mathbf 2.6 /3.0/\mathbf 4.6 /1.9/\mathbf 1.1 /5.4/\mathbf 1.1 /4.8\). The layers in bold are the AlGaAs barriers. The energy difference between the upper and lower lasing level is 113.3 meV to accommodate the availability of the testing equipment. In the QCLET, the same stage is repeated 28 times.
Fig. 4

The design of the quantum cascade lasing active region based on the self-consistent Schrödinger–Poisson solver and electron-quantized states in one and a half stages

3 Fabrication of a GaAs-based QCLET

The epitaxial layer structure of the GaAs-based QCLET designed and discussed above is grown via molecular beam epitaxy (MBE) by a commercial supplier of epitaxial material. The fabrication of the device starts with defining the emitter mesa. The emitter mesa is formed by wet chemical etching of the AlGaAs top cladding layer with 1:8:80 H\(_2\)SO\(_4\):H\(_2\)O\(_2\):H\(_2\)O etchant followed by wet chemical etching of the InGaP emitter layer with HCl. A thin conformal layer of silicon nitride is deposited by plasma-enhanced chemical vapor deposition (PECVD). The silicon nitride layer is patterned with CF\(_4\) reactive ion etching to expose the emitter and the base semiconductor layers. The emitter and the base metal contacts are formed via e-beam evaporation. Because of the high doping concentration in the emitter cap layer and the base cap layer both metal contacts are Ti/Pt/Au. With lapping and chemical–mechanical polishing of the substrate (which is \(\approx\)500 \(\upmu\)m thick) the chip is thinned down to a thickness of \(\approx\)150 \(\upmu\)m. The backside AuGe/Ni/Au contact for the collector terminal is deposited via e-beam evaporation and alloyed to form an Ohmic contact. The processed chip is then cleaved and die-bonded onto a copper heatsink for measurement. In Fig. 5, the cross section of a GaAs-based QCLET at the emitter mesa edge is shown.
Fig. 5

Cross-sectional view of a GaAs-based QCLET at the emitter mesa edge

4 Quantum modulation of the QCLET

4.1 Transistor electrical performance

The QCLET is usually biased using a common-base configuration so that the voltage drop across the quantum cascade region can be controlled directly using the base–collector junction voltage \(V_\mathrm{{CB}}\). The electrical characteristics of a bipolar junction transistor are defined by its family of curves, which shows the collector current for swept base–collector junction voltage under a stepped emitter current injection or emitter–base bias voltage steps. In Fig. 6a, the family of curves of a GaAs-based QCLET under common-base operation is shown. The device is driven by an Agilent E3631A DC power supply. For a fixed emitter injection level, as the base–collector junction is increasingly reverse biased, the collector current first increases dramatically then stays relatively stable. As the emitter injection level increases the collector current at a specific \(V_\mathrm{{CB}}\) also increases. From Fig. 6, one can observe that the transistor turns into the forward active mode around \(V_\mathrm{{CB}}=7\) V. The variation of the base and collector currents (i.e., \(\delta I{b}\) and \(\delta I{c}\)) around \(V_\mathrm{{CB}}=7\) V under \(V_\mathrm{{BE}}=1.9\) V are, hence, used to calculated the collector current gain. The calculated collector current gain \(\beta =\frac{\delta I{c}}{\delta I{b}}\) for the QCLET in Fig. 6a is 11.5. Compared with conventional heterojunction bipolar transistor where the linear region is fairly short, it takes higher \(V_\mathrm{{CB}}\) in a QCLET to move into forward active range. This is due to the voltage required to establish the cascade path for electron in the relatively long quantum cascade region in the base–collector junction.
Fig. 6

a Collector current, b base current and the overlap of the upper and lower lasing level wave functions of the QCLET to emit photons from intersubband transitions and c radiative base recombination vs. the base–collector junction voltage under different emitter injection levels. The inset in c shows the spectrum of the base recombination light output when \(V_\mathrm{{BE}}\)=2.5V and \(V_{\rm {CB}}=2.0\)  V

4.2 Radiative base recombination measurement

The radiative base recombination is measured under common-base configuration so that the control of the base–collector voltage and quantum state alignment over the intensity of the optical output from base recombination can be characterized. The transistor family of curves is measured with an Agilent E3631A DC Power Supply. This is a triple output DC power supply. The emitter–base junction is forward biased by the third output, which sources and measures up to 6 V and 5 A. The base–collector junction is reverse biased by the first output, which sources and measures up to \(-25\) V and 1 A. The base terminal is grounded. The device, after being mounted onto a copper heat sink is placed on a probe station. A silicon-based photodetector is placed directly on top of the device to measure the optical output. The radiative base recombination emits from the top of the device. The spectrum is collected through an optical fiber with a ball lens at the tip to maximize light collection and analyzed with an Hewlett-Packard 70951B Optical Spectrum Analyzer. The optical power is collected and measured using a Newport 818-SL silicon photodetector. In Fig. 6b, c, the base current and the base recombination optical power under different emitter–base bias levels are shown as a function of the base–collector junction voltage. In Fig. 6b, the wave function overlap between the upper and lower lasing levels, which roughly characterizes the electron tunneling rate through the cascade route, is presented with various \(V_\mathrm{{CB}}\) as well to illustrate the carrier dynamics under various reversed bias conditions. When the emitter injection level is constant, as the base–collector junction voltage is put under larger reverse bias, the base current first decreases and then stays stable. As the emitter injection level increases the base current increases. The base current provides carriers for both radiative and non-radiative recombination, as well as for a small amount of hole injection across the heterobarrier into the emitter. For the radiative output, the optical spectra from the base can be found in the inset of Fig. 6c. The optical output power follows the trend of the base current. As the base–collector junction is more strongly reverse biased, the optical output from the base decreases as the field across the quantum cascade region approaches the quantum cascade lasing design value, allowing electrons to more easily transit through the base–collector junction. Under higher emitter injection levels (increasing \(V_\mathrm{{BE}}\)) the optical output is higher. When the emitter–base junction is highly biased, the base current increases slightly with increasing \(V_\mathrm{{CB}}\) with no corresponding increase in optical output power. This is likely due to the enhanced injection of holes from the base into the emitter. Under the same injection level, the base recombination stays relatively flat as more power is injected into the device under higher \(V_\mathrm{{BE}}\). This is partly due to the extrinsic base resistance. The base metal contact is Ti/Pt/Au which is a common choice for p-type GaAs. However, this contact does not guarantee the lowest contact resistance. Therefore, at high emitter injection level and high base–collector biasing point the radiative base recombination is partly limited by the extrinsic base resistance. Also when the emitter injection level is higher, the device enters the forward active mode at a higher \(V_\mathrm{{CB}}\). This is because the moderate doping concentration in the base and the thickness of the base layer create a voltage drop inside the base itself. With higher emitting injection level the higher base current requires more voltage drop across the base, thus pushing the turning point of forward active region to a higher \(V_\mathrm{{CB}}\). The heat from the high-power injection causes an increase in junction temperature giving holes in the base more energy to overcome the emitter–base heterobarrier. This enhances the probability of holes to be injected from the base into the emitter, decreasing emitter injection efficiency and slightly reducing radiative base recombination. This is validated by the observation of red emission from the InGaP emitter at higher injection levels as holes injected into the InGaP recombine (data not shown). The light output from the base is stable under high emitter–base injection level and high base–collector biasing condition. The emission wavelength of the optical output is measured with a Hewlett-Packard 70951B Optical Spectrum Analyzer. The base is bulk GaAs so the emission wavelength is 880nm as is shown in the inset of Fig. 6c.
Fig. 7

Electron-quantized states in one and a half stages of the quantum cascade region under different base–collector biasing conditions. The wave function of the quantum states is positioned on the energy eigen value. The red arrow shows the intersubband transition. The red number shows the transition energy.

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).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignChampaignUSA

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