Interferometrically enhanced sub-terahertz picosecond imaging utilizing a miniature collapsing-field-domain source

The currently dominant terahertz time-domain spectroscopy and imaging technique is based on laser-driven pulse systems,^1–4 the practical use of which is limited by their large size, high cost, and high power consumption. The option of miniaturizing the CW solid-state sources^5–7 by means of SiGe CMOS or III-V hetero-bipolar transistor (HBT)/HEMT integrated circuits^8,9 compatible with on-chip antennas¹⁰ suffers from complexity and low (sub-mW) power. Higher power, in the sub-terahertz range, can be obtained at the expense of further complication, costs, and size by using multipliers and amplifiers,^11,12 or in the THz range using quantum cascade lasers,¹³ which require cryogenic temperatures.

Current trends in high-resolution THz imaging rely on both detector and emitter arrays^7,14 offering real-time operation but requiring simple, miniature and energy-efficient solid-state sources. The simplest ever microwave oscillator based on the Gunn effect has an inherent limitation of about 80 GHz on its fundamental mode of operation with traditionally used GaAs. Use of hot electron injection,¹⁵ advanced semiconductor materials, and planar technology¹⁶ pushed the fundamental-mode frequency to 200–300 GHz, making the performance of the Gunn oscillators in the sub-THz band comparable to that of sub-millimetre IC, although their efficiency and output power remained low.

A recently discovered physical phenomenon termed the collapsing field domain (CFD)¹⁷ provides an original approach to the problem. First found in high-voltage (∼100–500 V) GaAs bipolar junction transistors (BJTs) during their superfast^18,19 (picosecond) avalanche switching, these domains were proved in other experiments.¹⁷ Later, the same domains interpreted the old puzzle of superfast switching and lock-on in a bulk GaAs optically triggered switch.²⁰ Despite the fact that the GaAs structures of the high-voltage avalanche transistors mentioned above, optically triggered switches²⁰ and the low-voltage sub-micron THz emitters suggested here differ drastically from each other, the properties of the CFDs in all these structures are the same. The collapsing domains are physically caused by negative differential mobility (NDM) in extreme electric fields (above the ionization threshold),²¹ and the most detailed experimental and numerical investigation into their properties was undertaken using both hydrodynamic²² and drift-diffusion^17–19,23 approaches for high-voltage bipolar transistors. This study inspired the idea of realizing CFD in a miniature, low-voltage source in which a nano-scale domain circulating in a sub-micron active layer would produce pulsed sub-THz emission.

We present here a description of the original source and its operation principle which has allowed sub-picosecond time-domain imaging (TDI) resolution to be achieved and a method to be developed, termed here interferometrically enhanced time-domain imaging (IE-TDI). This method provides an order of magnitude improvement in time-of-flight imaging contrast.

The basic architecture of our sub-THz source, having a BJT structure with a submicron n₀ collector layer, is shown in Fig. 1(a). It was grown using vapour-phase (MOVPE, Aixtron 200/4) or molecular beam (MBE, Riber 49) epitaxy on semi-insulating substrates and processed using state-of-the-art technology similar to that of HBT fabrication. Both subcollector (∼1 μm in thickness) and emitter (∼50 nm in thickness and ∼8 μm² in area) are doped with a donor (Si) density of ∼(4–6)×10¹⁸ cm⁻³ while a p-base of ∼70 nm in thickness is doped by carbon to 3 × 10¹⁹ cm⁻³ aiming at low base-emitter resistance. Direct on-chip connections of the emitter and collector ohmic contacts to the antenna flares ensured as low parasitic inductance as a few pH, while the “external circuit” also realized on the chip provided total loop inductance below ∼1 nH. It is important for our device to have a specific contact resistivity to the emitter as low as ∼10⁻⁷Ω × cm², since the current density in the switching channels reaches ∼10⁷ A/cm². In our processes, the contact resistivity for heavily doped InGaAs layers ranged from 2 × 10⁻⁷ to 6 × 10⁻⁷Ω × cm², while for GaAs heavily doped with tellurium, the resistivity did not typically exceed 0.6 × 10⁻⁷Ω × cm².

Of prime importance for device operation is avalanche switching, which implies avalanche injection into the n₀ layer (≤0.7 μm in thickness) of the impact-generated holes that in turn cause electron injection from the emitter across the p–base. Biased initially to the voltage close to the base-collector breakdown (≤23 V), avalanching is triggered by the current pulse applied to the base. The high base doping at a relatively low donor concentration in the emitter (in the absence of hetero-barrier for the holes) determines very low common emitter current gain β ∼0.1. This is not acceptable for an amplifier, but suffices for triggering of the avalanche switching.

The low-ohmic load and very low β prevent the collector voltage reduction due to base current amplification that would happen in “linear” hetero-bipolar transistor (HBT) amplifiers. (HBT with low-ohmic load might be applicable as well, but with various complications. In particular, a static high-field domain in hetero-emitter competing with moving CFDs may appear, and thus the development of a HBT-based avalanche sub-THz source is an open question). The electron injection modifies the collector field domain in such a way that the peak in the electric field arises at the n₀-n⁺collector interface, exceeding the ionization threshold. The resulting double injection of the electrons and holes creates electron-hole plasma in the n₀ layer. Then, CFD forms at the base-collector interface and starts moving towards the n⁺ subcollector provided the current density exceeds ∼1 MA/cm². [Note the three domains of ∼0.4–0.6 MV/cm in amplitude and ∼100–50 nm in width simulated in this work and shown in Fig. 1(a)]. The reasonable agreement between the measured and simulated waveforms [see Fig. 1(b)] confirms the parameters of the CFDs, the current, and carrier densities in the switching channels and the lattice temperature, etc., that were obtained in the simulations.

The studies of the 3-D peculiarities of avalanche switching in high-voltage BJTs^18,19,23 performed so far show a filamentary switching character, with one or more switching channels of a diameter comparable to the thickness of the n₀ collector layer. In our case, this means one or more channels of area ∼1 μm² [see magenta cylinders in Fig. 1(a)]. Despite the extreme current density in the channel and the electric field amplitudes, there is no danger for the device, as a CFD circulates for only a limited time (∼100 ps) and the lattice overheating after a single avalanche switching is only ∼30 K.

Unlike the large number of CFDs coexisting in the n₀ layer of a high-voltage transistor, the single CFD circulates in the submicron n₀ collector of this our device as in a Gunn diode: nucleating near the anode (base) and annihilating at the cathode (n⁺ subcollector). The travel time of CFD across the n₀ layer (<10ps) determines the period of sub-THz emission, while the wavetrain length is determined by the current pulse duration (discharge time of capacitor C). Sub-THz current oscillations pass across the on-chip antenna and cause emission of the wavetrain [coloured blue in Fig. 1(a)], with a central oscillation frequency f₀ determined by the domain transit time.

Initial measurements of the resulting THz emission have been made using a large elliptical mirror. The chip was placed at one focus of the mirror while the receivers (zero bias Schottky detectors of Virginia Diodes equipped with horn antennas) were mounted near the other focus. The waveforms of the detected pulses were recorded using a LeCroy WaveMaster 830Zi-A oscilloscope. Examples of waveforms obtained for the pulsed sources of the first and second emitter generations are given in Fig. 1(c), and their spectra, evaluated using a set of resonant metal-mesh THz bandpass filters, are shown in Fig. 1(d). To measure the output power of the source, the Schottky detectors were replaced with a Golay cell. Alternatively, for the transmission imaging mode, the source was glued onto hyper-hemispherical silicon lens and the THz pulse was further collimated using a polytetrafluoroethylene (PTFE) lens of focal length 10 mm.

Figure 2 illustrates the advantage of using for the transmission TDI a second-generation source with single-shot jitter reduced from the ∼10 ps (typical of the first generation) to ∼1 ps and a somewhat increased central frequency of the wavetrain. The much better shape stability and lower jitter of the pulse emitted by the second-generation source [I_E(2), L_E(2) curves in Fig. 1(b)] may be attributed to the realization of single channel operation. We assume that the much higher jitter in the first-generation source was caused by the multichannel character of the switching^18,23 when several conducting channels, each having its own sub-THz oscillations figure, mutually shunt the oscillations generated in the other channels, thus obstructing their penetration to the antenna. The randomness of the switching instants for the different channels unavoidably increases this jitter and causes variations in the front edge shapes of individual pulses. A number of technological and circuitry measures implemented for suppressing multichannel operation in the second-generation source require detailed discussions and will be presented elsewhere.

Due to the significant improvement in the spatial resolution and quality of the image [compare (a) and (b) in Fig. 2], more challenging applications can now be addressed. Sub-picosecond precision is needed, e.g., for differentiating healthy and malignant areas in freshly excised tissue slices, and this may open the way to intra-operative real-time histology in cancer surgery (as a replacement for the laboratory-demonstrated optoelectronic THz TDI approach,^24,25 which suffers from the large setup size, high costs, etc.). In our transmission experiments with fresh samples of breast tissue, the time delay corresponding to a slice thickness of 200 μm was around 1 ps, with the jitter reduced to ∼0.1–0.3 ps by averaging 100 measurements. Such accuracy is not sufficient for reliable cancer detection, while any further increase in slice thickness would reduce the transmitted signal. To solve this dilemma, we suggest interferometric enhancement (IE) for a significant improvement in TDI contrast. This IE-TDI method utilizes the reflection mode and the intrinsic properties of the wavetrains emitted by our source.

We used an original reflection-mode setup permitting only a ∼30% reduction in the amplitude of the emitted pulse instead of the 75% reduction optimistically expected in the traditional scheme employing a THz beamsplitter. A hollow dielectric waveguide with an internal diameter of 20 mm (termed a beamguide²⁶) was excited at the centre by an emitter chip glued onto a Si lens, and the resulting wavefront was focused on the tissue slice using a PTFE lens (25.4 mm in diameter, focal length 25 mm). The reflected wave spreading back in the beamguide crossed the excitation point and was collected by a horn into the waveguide of the Schottky detector. The system resolution was ∼3.5 mm.

The tissue slice was placed on a quartz substrate backed with a metal mirror, and the contrast between the cancerous and healthy tissues was then evaluated from the variations in the time delay of the reflected signal during 2-D scanning of the sample. The waves reflected from the metal mirror and the quartz surface [Fig. 3(a)] interfere constructively [Fig. 3(b)] or destructively [Fig. 3(c)], causing shifts in the leading edge of the resultant pulse [Fig. 3(d)]. The time delay in the envelope of the reflected sub-THz pulse was calculated by the spectral method. The results of the numerical calculations and corresponding experimental points are given in Fig. 3(e) for two substrate materials, quartz and polyethylene terephthalate (PETP). The shape of wavetrain used is shown [FWHM ∼40ps, spectral width Δf ≈ ±20 GHz, see the green inset in Fig. 3(e)].

The IE-TDI principle consists of maximization of the increment in the experimentally measurable pulse delay caused by variations in the effective substrate thickness (thickness × refractive index). Selection of the operating point near the slope centres of the solid lines in Fig. 3(e) by proper selection of the substrate thickness under the layer of interest yields an order of magnitude gain with respect to the dashed lines representing the conventional round-trip propagation delay in the dielectric layer (i.e., ignoring reflections from the dielectric interfaces).

The fractions of the orange curve highlighted in blue and red in Fig. 3(e) were used for the experimental studies of healthy and malignant tissues by IE-TDI in comparison with conventional amplitude and time-delay images (Fig. 4).

The poorest cancer/image correlation was observed in the amplitude image [Fig. 4(c)], while the time-delay image [Fig. 4(d)] is considerably better, despite the fact that the time-delay contrast of ∼1 ps does not seem to be quite sufficient. Significant improvements were achieved using IE-TDI even for thinner tissue samples of 100 μm, providing a direct contrast of +5 ps for a 1.2 mm quartz submount and a reverse contrast of –13 ps for 1.0 mm (see images (e) and (f) in Fig. 4).

More complicated differentiation between fibrous and malignant tissue requires recording TDI delay differences of ∼0.2 ps, which are hardly measurable by conventional transmission, while IE-TDI can resolve this challenging task. The proposed method is therefore well suited for intra-operative detection of malignant tissues and corresponds to the current medical trend for point-of-care diagnostics.

In summary, the miniature sub-THz source suggested here is well suited for high-resolution imaging arrays, and its combination with the IE-TDI method approaches the time-domain contrast obtainable at present only with bulky and costly optoelectronic systems.

This work was supported by the Academy of Finland and TEKES (Grant Nos. 255359 and 310152), and the strategic TEKES MIWIM project. The authors are grateful for engineering support from MNTC at the University of Oulu.

Permission for use of the breast cancer tissue samples (Reg. No. 59-2009) was obtained from the Institutional Ethical Board of Oulu University Hospital, Finland.