Improvement of terahertz field effect transistor detectors by substrate thinning and radiation losses reduction

Dominique Coquillat; Jacek Marczewski; Pawel Kopyt; Nina Dyakonova; Benoit Giffard; Wojciech Knap

doi:10.1364/OE.24.000272

1. Introduction

Emission and detection of terahertz (THz) radiation by use of field effect transistors (FETs) was predicted in the middle nineties [1,2 ] and then experimentally proved [3]. Since then it has become evident that FETs can become valuable candidates for cheap and fairly sensitive THz detectors working at room temperature. It should be pointed out that effective THz detection by FETs occurs at frequencies many times higher than their standard cut-off (f_t or f_max) frequencies [4,5 ].

One of the most important factors deciding about responsivity of a THz detector based on FET is the effective coupling of the FET channel with an incident wave. That is usually achieved with antennas delivering the alternate voltage to the terminals of the transistors. Efficiency of the detector is limited by several parasitic elements like gate-source capacitance or channel resistance that may be significantly reduced by use of sub-micron sized transistors. However the detection concept is quite tolerant and even low frequency nanometer size n-type FETs may offer responsivity desired for simple imaging systems operating at room temperature [6,7 ]. One of the biggest problems in the effective coupling of the FET channel with an incident wave comes from the fact that part of incoming energy of the radiation penetrates into the substrate. This part of the THz radiation may be lost and/or may be re-directed to other detectors (cross-talk effects).

The classic waveguide theory [8] predicts effective propagation of electromagnetic (EM) waves in form of the so-called dielectric slab waveguide modes supported in planar dielectric structures of geometry similar to typical substrates used in the microelectronics industry. The substrate with metalized back-plane (or mounted on a metalized package) becomes a dielectric waveguide. The modes propagating in such a waveguide do not feed the detector active device, but propagate in the substrate. They may become one of the loss mechanisms responsible for diminished responsivity of any detecting circuit [9]. In all realistic cases, where the substrate is of finite dimensions, such waves will create also multiple reflections from the sides of the substrate (dice sides). This effect leads to volumetric dissipation of the energy as well as to excitation of resonances at frequencies, which in general, are independent of the antenna dimensions.

One of the solutions of the problem is thinning the detector substrate. One may expect that in sufficiently thin substrate the effects of THz radiation propagation and losses will be diminished. Of course the choice of the right thickness depends on the substrate dielectric constant and the radiation wavelength. The effect of the influence of the substrate thickness has been already mentioned in the earlier work (see [10]). Here we present a systematical experimental and theoretical study of the influence of substrate thickness on the responsivity of Si-MOSFET-based THz detectors. We generalize also our results for other semiconductor substrates and whole sub-THz range.

In this paper Si-MOSFET-based THz detectors were fabricated, thinned by grinding, and measured using sub-THz radiation sources operating in the bandwidth 265–375 GHz. The responsivity measurements were carried out as a function of the gate voltage and frequency $f = 2 π ω$ for four different thicknesses and the loading effect that influence the measurement of the responsivity was taken into account. A careful analysis of the dielectric waveguide modes propagating in the substrate of different thickness and affecting the performance of the antenna is presented. The measurement results are compared with predictions validating theoretical model. Finally simple quantitative rules of losses minimization by choosing a proper substrate thickness of FET THz detectors are derived for common materials (Si, GaAs, InP, GaN) used in semiconductor technologies.

2. Experimental methods

To study the effects related to energy lost in the substrate beneath the antenna, four identical chips were thinned to tens of microns by grinding. The chips were designed and fabricated entirely in an industrial 130 nm CMOS technology on bulk silicon substrate with a resistivity of ρ = 10 Ωcm. Each test chip contained different detectors designed for 300 GHz or 650 GHz bands by varying the FET dimensions, and the antenna geometry. Here we presented systematical studies of the 300 GHz band.

The detector consisted of a nMOSFET as rectifying device with a source-drain distance of L = 300 nm, a gate length of L_g = 300 nm and a gate width of W = 2 μm. The bow tie antenna radius was 120 μm for an angle of 120°, for detection of 300 GHz radiation (inset of Fig. 1(a) ) and the pixel pitch is 420 μm. The broad band bow-tie antenna realized in the metal interconnect layers was connected to the source and the gate terminals. The role of the antenna was to couple the incident THz radiation to the detecting FET, leading to an ac voltage U_a sin(ωt) between source and gate. More details of the structure can be found in Ref. 7. We studied the four different chips with reduced substrate thickness d from 125 μm, 90 µm, 70 µm down to 55 μm (see Table 1 ). After grinding the thinned chips were glued using non-conducting epoxy to gold plated ceramic chip carriers. The dc source-to-drain current dependence on the gate voltage (transfer characteristics $I_{d s} (V_{g})$ ) of the devices were measured in absence of the THz radiation for small source-to-drain voltage, in the range 1 to 5 mV. This voltage is comparable with the voltage induced by the THz radiation during the detection experiments. The transfer characteristics are shown in Fig. 1(a).

Fig. 1 (a) Right scale (thin black curve): dc transfer characteristics for 5 mV of source-to-drain voltage. Left scale: Comparison of directly measured responsivity $R_{m e a s}$ as a function of the gate voltage (thick black curve) and calculated responsivity from transfer characteristics using Eq. (1). The calculated responsivities $R_{Z L = \infty} and R_{Z L}$ were determined for open circuit ( $Z_{l} = \infty$ , blue open triangles) and taking into account the loading effect ( $Z_{l}$ calculated using 10 MW for the input resistance and 120 pF for the capacitance, blue dashed curve), respectively. For the fitting parameter, we have used A = 28.1 V²/W. The inset shows a photo of the transistor integrated with antenna. (b) Responsivity $R_{m e a s}$ as a function of the frequency of the incident radiation, for a gate voltage close to the threshold voltage (around + 110 mV) for transistors with different substrate thicknesses. Inset: the black circles mark the measurement points corresponding to the maximum of the responsitivity of the unloaded detector $R_{Z L = \infty}$ at peak frequency as a function of the substrate thickness ( $V_{g}$ around + 110 mV).

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Table 1. Responsivity of the thinned detectors

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Optical characterization of the devices was performed in the frequency range 265-375 GHz using a broadband electrically tunable solid state source with maximum output power of the order of 1 mW. The detector was illuminated from the antenna side (upside). The off-axis parabolic mirrors were used to focus the incident radiation to $d_{s p o t} =$ 4.0 mm diameter spot. The system enabled also precise adjustment of detector position in the focal plane and on the spot using a computer-controlled nano-positioning stage. The radiation intensity was modulated by a mechanical chopper at 619 Hz. The total beam power $P_{t}$ incident in the detector plane was measured with a Thomas-Keating power meter. The total electromagnetic THz power $P_{a}$ impinging on the detector may be calculated by taking into account the physical detector area $S_{a}$ defined as the pixel pitch area (0.176 mm²) [7] and the beam spot area given by $S_{t} = d_{s p o t}^{2} / 4$ ; $P_{a}$ can then be calculated as $P_{a} = P_{t} (S_{a} / S_{t})$ . We obtained $P_{a}$ = 14 μW in the whole frequency range . To evaluate the detector performance we have measured the photoinduced source-drain dc voltage ΔU_meas at the drain contact, while keeping V_sd = 0 and the source contact grounded, with a lock-in amplifier connected to a low-noise voltage preamplifier having an input impedance of 10 MΩ. The typical value of the capacitance of the read-out circuit together with cables connecting the transistor to the preamplifier was of the order of 120 pF. For each chip, in agreement with antenna calculations, the maximum of the signal was observed for the electric-field polarization of the incoming radiation parallel to the antenna axis. All measurements were done at room temperature.

For response measurements as a function of the gate voltage, the measured responsivity $R_{m e a s}$ of the detector is defined as the ratio between the photoresponse ΔU_meas and the radiation power $P_{a}$ impinging on the active area of the device, and is illustrated as thick curve in Fig. 1(a).

For responsivity measurements as a function of the frequency of the radiation, the detector was biased at a gate voltage close to the threshold voltage (around + 110 mV) for the different substrate thicknesses Fig. 1(b). The peak responsivity at cir. 280 GHz shows a more than 10-fold increase of the responsivity of the 55-µm thick chip as compared with the thickest variant. When the substrates modes are reduced using a thinned substrate, better responsivities are achieved as indicated by the curves in Fig. 1(b). Thanks to using this thinning process, measured responsivities as high as 600 V/W around 285 GHz have been achieved. The antenna response was strongly polarization sensitive, showing a 93% responsivity reduction in the polarization in direction perpendicular to the antenna axis.

Due to the contribution of the loading effect — related to the impedance of the read-out circuit— the measured responsivity $R_{m e a s}$ in the sub-threshold region is weaker than the unloaded detector responsivity $R_{Z L = \infty}$ . We have used an approach developed in Ref. 11 that allows calculating the expected THz responsivity using static dc transfer characteristics completed by the loading effects. One can simulate the open circuit photoresponse $Δ U$ with the following expression:

Δ U = (\frac{U_{a}^{2}}{4}) \frac{d}{d V_{g}} \ln [I_{d s} (V_{g})] \frac{1}{1 + R_{d s} / Z_{L}},

where U_a is the amplitude of the ac gate-to-source voltage induced by the incident THz radiation (it reflects the antenna coupling efficiency and the power of the THz source). The impedance

Z_{L}

can be written as

1 / Z_{L} = (1 / R_{I N}) + i ω C

where

R_{I N}

is the input impedance of the preamplifier and

C

is the capacitance of the cables between the transistor and the preamplifier and

ω

the modulation frequency of the incident THz radiation. Equation (1) is useful to extract the open circuit responsivity

R_{Z L = \infty} = Δ U / P_{a}

and suppress the loading effect. For the different substrate thicknesses, the fitting parameter

A = U_{a}^{2} / 4

is determined over a whole range of

V_{g}

and the open circuit detector responsivity

R_{Z L = \infty}

was de-embedded from the measured responsivity

R_{m e a s}

.

Such an analysis is illustrated in Fig. 1(a) for the 55-µm chip. The registered responsivity curve $R_{m e a s} = U_{m e a s} / P_{a}$ to the 285-GHz radiation (frequency giving the maximum of signal) is presented as thick black curve on the left scale. From the calculated responsivity using Eq. (1) when the loading effects are neglected i.e. for Z_L = ∞ (blue dots), and the calculated signal taking into account loading effects (solid blue curve), we have determined the fitting parameter value $A$ = $U_{a}^{2} / 4$ = 28.1 and used this value to calculate the responsivity $R_{Z L = \infty}$ of the unloaded detector. Table 1 shows the main results obtained for the four detectors such maximum measured responsivity, the fitting parameter $A$ , and finally the responsivity $R_{Z L = \infty}$ of the unloaded detector reflecting the energy lost in the substrate. $R_{Z L = \infty}$ is also reported in the inset of Fig. 1(b) in form of black circles.

3. Theory and discussion

The phenomenon of a loss mechanisms due to the propagation of EM waves in the substrate [8], which is responsible for diminished responsivity, can be effectively analyzed using a simplified 1-dimensional model [9]. To this end, one assumes that the substrate is represented by a dielectric slab extending towards infinity in the directions of the OZ and OY axes, and with finite thickness d (in the direction of the OX axis). In such a geometry, the waveguide modes are typically denominated as the TM modes (transverse components of the H field and longitudinal component of the E field in the substrate: H_x, H_z and E_y) or the TE modes (transverse components of the E field and longitudinal component of the H field in the substrate: E_x, E_z and H_y). Each mode has its cut-off frequency, below which it cannot exist, and which is defined with the formula [8]:

f_{n}^{T M, T E} = \frac{n c}{4 d \sqrt{ε_{r} - 1}};

where n = 0, 2, ... or 1, 3, … is the mode number for the TM or TE modes, respectively, while c is the speed of light in vacuum. Following the solution procedure detailed in [8], one obtains the distribution of the electromagnetic (EM) field components, which reveals that the TE or TM wave propagates with propagation constant β_z (magnitude of the wave vector) not only in the substrate but also in the air above it. What also becomes clear upon solving the problem, is that the portion of the wave’s energy propagating in the substrate strongly depends on the frequency, the dielectric thickness d, as well as the electric permittivity ε_r of the substrate. This effect is illustrated in Figs. 2(a) and 2(b) , where the frequency dependence of β_z for the TM and the TE modes, respectively, is shown for a silicon (Si) slab (ε_r = 11.7) for several values of d. For comparison, the propagation constant for a plane wave propagating in air (straight line marked “Air”) and in Si (“Si”) is also shown.

Fig. 2 Frequency dependence of the propagation constant for EM modes supported in grounded dielectric waveguide made of Si of thickness d calculated analytically and numerically shown for the TM₀ mode (a) and for the TE₁ mode (b).

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At low frequencies (but higher than the cut-off frequency) or for thin slabs the waves propagate with the propagation constant close to that for air. For higher frequencies, β_z approaches values typical for propagation in homogeneous Si. The threshold frequency at which dominating portion of the wave’s energy propagates in the substrate depends on its thickness – for thick dielectric slabs this effect occurs at much lower frequencies than in case of thin layers. Using the analytic expressions for spatial distribution of EM field components one can calculate the power propagating in air and in the substrate for each mode through spatial integration of the averaged Poynting vector.

P_{A i r} = \frac{1}{2} \int_{x = d}^{\infty} Re (E \times H *) d x,

P_{S u b s t r a t e} = \frac{1}{2} \int_{x = 0}^{d} Re (E \times H *) d x,

where P_Air is the power contained in the EM field above the substrate (i.e. in the air), while P_Substrate is the power of the EM field in the substrate. As a result of the integration one obtains

P_{A i r}^{T M} = \frac{1}{2} \frac{B^{2} p^{2} β_{z} ω ε_{0} e^{-2pd}}{2 p} and P_{A i r}^{T E} = \frac{1}{2} \frac{B^{2} p^{2} β_{z} ω μ_{0} e^{-2pd}}{2 p},

\begin{array}{l} P_{S u b s t r a t e}^{T M} = \frac{1}{2} \frac{A^{2} h^{2} β_{z} ω ε_{0} ε_{r}}{4 h} (2 h d + \sin (2 h d)), and \\ P_{S u b s t r a t e}^{T E} = \frac{1}{2} \frac{A^{2} h^{2} β_{z} ω μ_{0}}{4 h} (2 h d - \sin (2 h d)), \end{array}

where h and p are real solutions of the so-called characteristic equation in the substrate and in the air, respectively, A and B are amplitudes of the wave coupled through boundary conditions at the interface between the substrate and the air (continuity of the tangential EM fields at x = d), ω is the angular frequency of the wave, while

ε_{0}

and

μ_{0}

are the electric permittivity and magnetic permeability of vacuum.

Based on Eq. (4) , a ratio R of the substrate-contained power to the total power can be calculated for each mode at a particular frequency, substrate thickness and its permittivity as

R = \frac{P_{S u b s t r a t e}}{P_{S u b s t r a t e} + P_{A i r}} .

The EM analysis of the sample including a bow-tie antenna integrated with an active device and fabricated on a substrate requires a numerical full-wave approach. To this end, a 3-dimensional (3D) model of the structure was created and solved using the finite difference time domain (FDTD) algorithm implemented in the QuickWave 3D environment [12, 13 ]. The same algorithm (1-dimensional model) was used also to verify results obtained analytically, which were presented in Fig. 2(a) and 2(b).

The 3D model consisted of a grounded infinite slab of lossless silicon with thickness d, with a planar bow-tie antenna described previously [inset of Fig. 1(a)] and printed on the top surface. The planar antenna printed on a dielectric slab launches not only the plane wave propagating away from the structure, but also the substrate waves. This effect can be analyzed by numerically calculating the portion of the power propagating away from the antenna while being confined to the substrate only. The results of EM power that can be received by the active device (portion of the power not lost in the substrate) obtained at the frequency f = 300 GHz are shown in Fig. 3 . The more power propagates in the substrate, the lower becomes efficiency of the radiator at emitting (or receiving) the plane wave into the air.

Fig. 3 Portion of the power contained in air obtained by numerical integration of the Poynting vector over an surface located above the bow-tie antenna- thus only the waves that propagates along the vector normal to the chip top surface is accounted for. The circles mark the measurement points corresponding to the maximum of $R_{Z L = \infty}$ normalized by arbitrary value of 1150 V/W.

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A comparison of the curves of Fig. 3 obtained numerically for the bow-tie antenna and those derived analytically for consecutive substrate modes reveals that the planar structure is quite effective at launching the waveguide modes into the substrate. For low values of d the portion of the power emitted into the dielectric by the bow-tie follows exactly the predictions for the TM₀ mode as defined with Eq. (5). The two curves visibly diverge starting from d greater than 76.6 μm, which, according to Eq. (2), is the threshold thickness at which the TE₁ mode can exist (at f = 300 GHz). At that point the total power launched into the dielectric by the bow-tie splits, because a part of it couples to the TM₀ mode, and the other part couples to the TE₁ mode. While for the TM₀ mode a slab of d = 76.6 μm is relatively thick resulting in significant portion of the mode’s power propagating in the substrate, for the TE₁ mode it is electrically thin meaning that nearly all of the power that couples into that mode propagates in air. Thus, the total power in the substrate is reduced, which explains the slower rise of the bow-tie curve in the area. A similar effect occurs for d larger than 153 μm, which is the threshold thickness for the TM₂ mode. Now, the power launched by the bow-tie couples to as many as three substrate modes, with the TM₂ mode initially propagating mostly in air. The behavior of this mode (its R ratio) results in a significant reduction of total power observed in the substrate for the bow-tie antenna and for relatively wide range of d reaching up to the threshold thickness of the next mode – TE₃ – where the cycle repeats.

The maximum of responsivity $R_{Z L = \infty}$ of the unloaded detectors shown in Tab. 1 and presented as a function of the substrate thickness in the inset of Fig. 1(b), can be compared with calculated portion of the power contained in air. In order to be compared with the theoretical curve, the maximum of detection of the unloaded detectors was normalized by arbitrary value of 1150 V/W for the four devices. It is obvious that the theoretical curve follows very closely the experimental results for the four devices. It seems that the theory of the substrate modes explains quite well the results obtained numerically for an infinite 3D radiating structure. It was also demonstrated that the results of the numerical analysis of such problems agree well with the expectations based on analytical solutions of simplified problems and that the analytical approach helps to find an interpretation of the numerical results. We have then validated the 3D FDTD model of the infinite slab of silicon with a bow-tie antenna printed on the top surface that gives known portion of the power contained in air as a function of the substrate thickness. The predictions of the model can then be used to calculate, in the whole 100 −700 GHz frequency range, the thickness that produces the arbitrarily chosen threshold value of 30% of the power contained in the substrate to the total power. Obviously the smaller the threshold value, the less power propagates in the substrate, the better from the point of view of the responsivity. The results obtained with the 3D model are shown in Fig. 4 (black open circles). The kink in the characteristics occurs at a point where the TE₁ mode is excited, which lowers the inclination of the curve. Anyway, this is clear that for antennas operating at 600 GHz or higher frequencies, the substrate must be really thin: ∼40 µm at 600 GHz.

Fig. 4 Thickness of the Si substrate as a function of the frequency for a threshold value of 30% of the power lost in the substrate, calculated using the 3D FDTD model of the infinite slab and a bow-tie on it (black open dots) and with purely analytical calculations limited to the TM₀ mode (solid black curve). The curves delimit the region over which more than 30% of the power is lost in the Si substrate. Similar analytical calculations in the case of GaAs or InP substrates (red dashed curve) and GaN substrate (blue dashed-dotted curve). Inset: Substrate thickness for a threshold values of 10% and 30% for most common materials (Si, GaAs or InP, GaN) used in technologies employed for transistor-based THz detectors.

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The 3D FDTD model of the infinite slab and a bow-tie on it can be compared with purely analytical calculations limited to the TM₀ mode, only. The results obtained with the analytical approach [Eq. (5)] were calculated also for a ratio of the substrate-contained power to the total power R = 30%. The curves obtained for the infinite slab of silicon from the two models are pretty much the same, which is interesting given the simplicity of the analytical model. Again, this suggests that the bow-tie is very efficient at excitating the TM₀ mode in the substrate. Hence, by looking at the behaviour of this mode we can predict the behaviour of more complex structures.

In Fig. 4 we compare results for Si, GaAs or InP and GaN technology FET based THz detectors. One can see only slight differences related to differences in dielectric constants. The limit curves obtained for 30% radiation losses due to substrate thickness are relatively close to each other. It is interesting to note that as shown in the inset of Fig. 4, to decrease losses by factor of 3 (30% to 10% losses in the substrate) it is enough to make substrate thinner by only roughly ~10 µm. Such a result can also be used in the case of the new detectors based on InP double heterojunction bipolar transistors [14].

The effect of radiation losses related to the modes propagated in the substrate is a general phenomenon that takes place for all types of metal antennas deposited on semiconductor substrates. We have checked that changing the antenna shape may slightly change the frequency at which the modes start to propagate in the substrate or modify the coupling between individual modes and the load of the antenna. The general conclusions of this work predicting the thickness of substrate for which the energy losses are higher than certain critical value (e.g. 30%) at certain given frequency stay practically unchanged. Our results allow not only to explain the observed effects on Si-MOSFETs and validate the theoretical model but also predict behavior for THz detectors made using also other semiconductors (GaN, GaAs) and operating in whole sub-THz range. The information that can be clearly taken from this work by all THz detector designers and physicists is the indication of the proper choice of substrate thickness depending on material and on the operating frequency range of the detectors.

4. Conclusion

In conclusion, we carried out a detailed investigation of single Si-MOSFET detectors integrated with bow-tie antenna and with substrate of varying thickness (in the range 55 −125 µm). The measurements reveal a strong dependence of the responsivity on Si substrate thickness. Placing the antenna on thick dielectric substrate diminish strongly the responsivity of the structure. A 3D approach to analyze the responsivity has been presented and used to estimate the influence of the substrate modes that affect the performance of the antenna. This approach can provide curves of radiation efficiency of the antenna as a function of the substrate thickness that well match results of measurements. In the range of 300 GHz, the thickness of the substrate must be kept lower than 50 µm. When the substrate modes were suppressed by thinning the substrate, unloaded detector responsivities as high as 600 V/W around 280 GHz have been achieved. The predictions of the 3D model were used to calculate the thickness that gives the threshold value of 30% of the power contained in the substrate, in the whole 100 −700 GHz frequency range, Finally, simple quantitative rules of losses minimization by choosing a proper substrate thickness for most common materials (Si, GaAs or InP, GaN) used in technologies employed to manufacture transistor-based THz detectors are presented.

Acknowledgments

The authors would like to thank F. Schuster for his help in the fabrication of the Si MOSFET detectors. This work was partly supported by the ANR P2N NADIA “Integrated NAno-Detectors for terahertz Applications” (ANR-13-NANO-0008), the IMPAD imaging project from the french defense procurement and technology agency DGA, the MPNS COST Action “MP1204 TERA-MIR Radiation: Materials, Generation, Detection and Applications” and the PHC Polonium “Investigation of FET Transistors as THz detectors and its development in imaging applications”. This work was partially supported by the National Centre for Research and Development in Poland (grant no. PBS1/A9/11/2012), the Laboratoire International Associé “TERAMIR”, and the project HARMONIA. The electromagnetic modelling presented in this work was supported by the Polish National Science Centre with grant no UMO-2012/05/B/ST7/02112.

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d (µm) ^a	$R_{m e a s}$ (V/W) ^b	$A$ (V²/W) ^c	$R_{Z L = \infty}$ (V/W) ^d
125	62.6	2.57	77
90	457	18.4	560
70	568	23.4	700
55	696	28.1	870

Improvement of terahertz field effect transistor detectors by substrate thinning and radiation losses reduction

Abstract

1. Introduction

2. Experimental methods

3. Theory and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (4)

Tables (1)

Equations (7)

Optics Express