Tunable terahertz emission from Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ mesa devices

We have measured coherent terahertz emission spectra from Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ mesa devices as a function of temperature and mesa bias voltage. The emission frequency is found to be tunable by up to 12% by varying the temperature and bias voltage. We attribute the appearance of tunability to asymmetric boundaries at the top and bottom and the nonrectangular cross section of the mesas. This interpretation is consistent with numerical simulations of the dynamics of intrinsic Josephson junctions in the mesa. Easily tunable emission frequency may have important implications for the design of terahertz devices based on stacked intrinsic Josephson junctions.

Figure 1

(a) Diagram of the device structure on a Bi-2212 crystal (after Ref. 2). Applying the correct bias current excites the transverse fundamental cavity mode on the width $w$. Terahertz radiation is emitted from the long side-faces, with the highest intensity occurring roughly 45° to the crystal surface (Ref. 6). (b) Arrangement of the measurement apparatus. Radiation emerges from the chip in two beams roughly 90° relative to each other. One of these is used for detecting the overall emission intensity (bolometer A), whereas the other is measured by the spectrometer, which employs bolometer B as its detector.

Figure 2

(a) I-V characteristics (filled circles, red) and terahertz-radiation power (open circles, orange) for an 80 × 300-μm mesa. The hysteretic behavior of underdoped IJJs, the backbending due to self-heating at high-bias currents (which can be weakly detected by the bolometer), and the progressive retrapping of the entire stack as the current is swept back down are seen. Terahertz emission is observed near mesa voltages of ∼0.7, 0.45, and 0.33 V. The two low-voltage emission features result from subsets of junctions in the stack. (b) Detail of the main emission peak at 20 K (lighter, or blue, lines) and 30 K (darker, or red, lines), showing excess current (and power) drawn by the mesa when the terahertz resonance is excited. The shift to lower voltage of the retrapping and of the emission feature with increasing temperature is seen.

Figure 3

FTIR emission spectra taken at a range of mesa bias voltages at (a) 20 K and (b) 30 K. With increasing temperature, the emission band shifts to lower frequencies. The envelope of the emission peaks tracks well the voltage dependence of the total emission power, as shown in Fig. 2b. The arrows mark the average frequencies used in Fig. 4.

Figure 4

Temperature dependence of the measured emission frequencies (red squares) and of the calculated emission frequencies of the $m$ $=$ 0 and $m$ $=$ 1 modes using the penetration depth data from Ref. 16. The error bars are determined by the width of the emission range shown in Fig. 3. The inset shows schematics of the $c$-axis dependence of the cavity mode.

Figure 5

Illustration of three possible scenarios in stacks with a distribution of junction areas as characterized by the parameter α. The left column of plots shows I-V characteristics, and the right column shows the distribution of the average voltage drops for all junctions in the stack at the current values that are marked in the I-V curves by boxes. The parameters used in these simulations are $N$ $=$ 50, $l$ $=$ 50, $L_1$ $=$ 12.5, and $\tilde{T}$ $=$ 0.

Figure 6

The current dependences of (a) the resonance-mode amplitude and (b) the excess current obtained by simulations of a stack with parameters $N$ $=$ 100, α $=$ 0.8, $l$ $=$ 100, and $\tilde{T}$ $=$ 0.02 on decreasing bias current. The nonmonotonous voltage dependence of the mode amplitude agrees well with the measured voltage dependences shown in Figs. 2b and 3. Plots on the right show the distribution of the average junction voltage $V_n$ for two bias currents. The outline of the shaded (colored) areas represents the trapezoidal cross section of the mesa. The voltage values are also visualized by shade (color) coding, revealing a band of synchronized junctions moving up the stack with decreasing bias current.