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Effect of oscillator strength and intermediate resonance on the performance of resonant phonon-based terahertz quantum cascade lasers
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Image of FIG. 1.
FIG. 1.

A schematic diagram of the four relevant states in a three-well resonant phonon-based THz QCL. Ωij are the tunnel coupling strengths. The injection (Ω12) and the extraction (Ω34) coupling channels are shown in green, while undesired parasitic leakage channels such as the wrong injection (Ω13) and wrong extraction (Ω24) are shown in red. The detuning energies between states are noted Δij = E i-E j. The double side dashed arrow represents the indirect coupling between states 1 and 4 via the couplings 1 ↔ 2 ↔ 4 and 1 ↔ 3 ↔ 4, which cause a small anticrossing AX14 when states 1 and 4 are close to alignment. Explanations for the Ωup and Ωdown “couplings” are given in Sec. IV B .

Image of FIG. 2.
FIG. 2.

Product of population inversion and oscillator strength (Δρ × f 23) versus temperature for the seven designs presented in Table I . The curves were obtained from Eqs. (1) and (2) , the radiative transition, E23, was set to 15 meV, the hot electron temperature was set 90 K higher than the lattice temperature, and a 10 ps temperature independent lifetime component was assumed. The right scale translates the product Δρ × f 23 into a coarse estimation of peak gain by assuming a 3D carrier concentration of 7 × 1015 cm−3 and a gain spectrum bandwidth of ∼ 1.5 THz.

Image of FIG. 3.
FIG. 3.

Pulsed L-J curves of the f-series devices at different temperatures. (a)–(e) f26, f30, f35, f41, and f47, respectively. (f) Normalized light vs. current density at 10 K for the five f-series devices with similar dimensions of ∼144 um wide waveguide and ∼1 mm long cavity length.

Image of FIG. 4.
FIG. 4.

Lasing spectra of the f-series structures (f26-f47) tested with Au double-metal ridge waveguides at 10 K and temperatures close to their respective T max.

Image of FIG. 5.
FIG. 5.

(a) Threshold current density (J th) vs. heat sink temperature for the f-series devices with Au-Au waveguides and different oscillator strengths. (b) Relative dynamic range vs. temperature for the same set of devices.

Image of FIG. 6.
FIG. 6.

Theoretical and experimental T max vs. oscillator strength in SDM optimized QCL structures. The continuous lines are T max values theoretically predicted using simplified density matrix formalism under different cavity losses (20, 25, 29, 30, 35 cm−1). The open star symbols represent experimental T max for f-series devices with Au-Au waveguides and the solid star symbols represent experimental T max for f-series devices with Cu-Cu waveguides and the top n-GaAs contact layer removed.

Image of FIG. 7.
FIG. 7.

Conduction band diagram of the f35 QCL active region at an electric field of 8.8 kV/cm, at which the injection level (1) aligns with extraction level (4), resulting in a ∼0.75 meV anticrossing energy (AX14) between the hybridized states. This intermediate resonance between levels 1 and 4 creates a parasitic leakage channel, which can be dominant when the lasing oscillator strength is very low.

Image of FIG. 8.
FIG. 8.

(a) SDM simulated leakage current due to the intermediate resonance (J 14) vs. the calculated 1-4 anticrossing (AX14). Several structures including the f-series devices and those published in Refs. 8, 10, 35, 36, 48, and 49 were simulated using the SDM approach. Results show that J 14 increases superlinearly with AX14. (b) Comparison between experimental data and SDM simulation results of J 14. The experimental data were obtained by looking at the 2nd derivative of V-J curves to find the pre-threshold shoulder that corresponds to the intermediate resonance. All experimental data were scaled in such a way that the active-region sheet doping concentration of different devices is normalized to 3 × 1010 cm−2. The figure shows that the SDM model over-estimates J 14.

Image of FIG. 9.
FIG. 9.

Voltage vs. current density curves, measured in pulsed mode with a current source at 4.2 K, with non-lasing devices from wafers V775 (f47), V814 (f41), V774 (f35), and V812 (f30) processed as metal-metal mesas with PdGe contacts. The theoretical anticrossing voltages V AX for the four structures are within the patterned horizontal band. The last three devices show very high differential resistance after the anticrossing voltage (V AX), whereas V775 shows the smoothest electrical characteristics. The V-J curve of a V774 Fabry-Pérot laser with the same contact is also displayed. The inset highlights the voltage recession (marked by a vertical down arrow) at the V774 lasing threshold.

Image of FIG. 10.
FIG. 10.

V-J curves of f-series lasing devices at 9-10 K where the current plateau before threshold is emphasized.

Image of FIG. 11.
FIG. 11.

Illustrations of a hypothesis based on the formation of high-field domains across the 10 μm thick active region, which may explain the voltage recession at laser threshold. (a) Devices with higher oscillator strengths. (b) Devices with lower oscillator strengths. Note that the operating bias point transition from the laser-off state to the laser-on state.

Image of FIG. 12.
FIG. 12.

J-V curves of f-series devices at different temperatures. The voltage recession after the threshold changes with temperature and disappears at higher temperatures.

Image of FIG. 13.
FIG. 13.

(a) DC I-V curve of a small mesa device with PdGe Ohmic contacts made from wafer V812 (f30 device) at 4.2 K. The bottom plot (b) shows the differential resistance dV/dI. The position of the dashed vertical line corresponds to the maximum second derivative, i.e., the anticrossing bias.

Image of FIG. 14.
FIG. 14.

L-J curves of a V812 QCL device (f30) with a Cu-Cu waveguide at different temperatures. The maximum lasing temperature of this device is 199.3 K, which is just slightly lower than T max = 199.5 K from a QCL device made from V775 (f47) wafer reported in Ref. 23 . Nevertheless, the threshold current of this device is significantly lower (−31%), J th = 0.675 kA/cm2 (f30 device) vs. 0.975 kA/cm2 (f47 device) at 8 K. The inset shows the lasing spectra of the f30 device with a Cu-Cu waveguide at 9 K and 190 K. The single peak lasing frequency at 190 K of this Cu-Cu QCL device is close to that of the f30 device with a Au-Au waveguide. However, at low temperatures, the lasing spectrum of the Cu-Cu device spans over a much wider range than that of the Au-Au device.


Generic image for table
Table I.

Simulation parameters and results of seven designs that were optimized using a SDM formalism approach. The experimental results are summarized in the last four rows; with a subscript “exp Au” the numbers are relative to Au-Au double metal ridge waveguides, ∼1 mm long and ∼143-144 μm wide, and with a subscript “exp Cu” to Cu-Cu waveguides fabricated at MIT.”


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Effect of oscillator strength and intermediate resonance on the performance of resonant phonon-based terahertz quantum cascade lasers