Abstract
We demonstrate a room-temperature sub-terahertz photoconductive detector based on graphite nanosheet （GN） using electromagnetic induced well （EIW） effect produced in the metal-GN-metal structure. The detector achieves high performance of room-temperature THz detection. It shows a responsivity of over 20 kV/W at 0.035 THz and 11 kV/W at 0.1673 THz， as well as NEP of about 1.25 pW/H
Graphene has several advantages compared with other material
THz technology has attracted great attention in recent years， because of its wide application in many fields， such as medicine， biology， weather forecast， and environmental protection. Different detection mechanisms have been propose
Fig. 1 The schematic diagram of the metal-GN-metal structure
图1 金属-石墨-金属结构器件的示意图
The graphite nanosheets were peeled off from bulk graphite crystal by the way of micro-mechanical exfoliation using scotch type. After that， the nanosheets were transferred onto a high resistance Si substrate （>10000）. The nanosheets could be identified by the optical microscope and the thickness of the flakes could be measured by atomic force microscope （AFM） as shown in
Fig. 2 AFM images of two opposite interfaces between graphite nanosheet and Si substrate， the two-step heights between graphene nanosheets and high resistance Si are calculated by the difference of the maximum peak height and minimum peak height， the two-step heights are 148 nm （left picture） and 144 nm （right picture） respectively
图2 石墨纳米材料与高阻硅衬底两侧界面的AFM图，石墨纳米材料与高电阻 Si 之间的两个台阶高度通过最大峰高和最小峰高的差值计算，两个台阶高度分别为 148 nm（左图） 和 144 nm（右图）
Ti （）， and Au （） electrodes were evaporated on the top of the GN. The evaporation mask was fabricated using standard UV lithography. Metal-GN-metal structure was used to form an electromagnetic induced well （EIW） in graphite nanosheets. Both the top and the two side walls of the GN were covered in order to prevent the leakage of electromagnetic waves from the two sides and achieve a large optical gain. The width of the metal antenna was 0.5 mm and the total length of the metal antenna was 4 mm. The active receiving area of the device was 1142 and the thickness was 146 on average. The gap length （11） was close to the distance designed.
The Terahertz test system is established for sub-THz detection， as shown in
Fig. 3 The schematic diagram of Terahertz test system
图3 太赫兹测试系统示意图
Fig. 4 （a） The I-V curve of the detector， （b-c） the responsivity of the detector at the source frequency of 0.02-0.04 THz and 0.165-0.173 THz with the bias voltage of 0.1V， respectively， （d） the noise spectrum at the frequency from 250 Hz to 100 kHz with the bias voltage from 0.1 V to 0.01 V
图4 （a）器件的IV特性曲线，（b-c）器件在偏置电压为0.1V时工作在源频率分别为0.02~0.04 THz与0.165~0.173 THz下的响应率光谱曲线，（d）器件在不同偏置电压下的250 Hz到100 kHz噪声频谱图
It is important to confirm the effective receiving area for estimating the performance of the detector. In all kinds of THz detector based on graphene， different methods of calculating the effective receiving area have been used. In plasma-wave-assisted mechanism in Field effect transistors （FETs）， photoinduced voltage is derived from the amplitude of radiation induced modulation of the source to gate voltage， which is originating from the metal antenna， so the antenna effect must be considere
Here we measure the resistance change of the GN， which depends on the change in carrier mobility or carrier concentration. In the latter discussion， we exclude the bolometric effect of this detector， so the resistance change comes from variation of carrier concentration. It is caused by the electrons trapped in the GN by the EIW. Thus， we consider the effective receiving area should be the GN material area between the electrodes. In order to further prove this point， two points have been stated： （1） we have made the semiconductor devices with different sizes. It is found that the voltage response is proportional to the material area and is independent on the antenna area （not shown here）. （2） we have considered the portion of metal on the mesa， because the electrons wrapped in the GN come from the metals. This small part of metal contributes to the increase in the conductance of the detector and is small enough to be ignored during calculating the effective receiving area. Of course， the metal antenna is supposed to be considered because of its contribution to the increasing of power density which is shown as gain factor （）. Therefore， we calculate the responsivity according to
| . | （1） |
In formula （1）， originates from the Fourier transform of the square-wave modulated signal detected as rms value with a lock-in amplifie
As shown in
NEP is a key parameter to evaluate the performance of the detectors in consideration of noise characteristic， as the noise of the detector should be suppressed. The noise signal of our detector was recorded by a spectrum analyzer （MODEL SR 770）. The modulation frequency was set to cover from 250 Hz to 100 kHz， and the bandwidth was 250 Hz. Firstly， we measured the short noise （） when the circuit was shorted， and then connected the detector into the circuit for measuring the total noise （）， finally we calculated the detector noise（） by using a simple mean square root formul
| . | （2） |
NEP is calculated by
| . | （3） |
In this formula，is the responsivity of the detector mentioned above. Different noise spectra of the detector were measured by varying the operating voltage （0.01 V， 0.02 V， 0.05 V， and 0.1 V）. As shown in
The time constant represents the speed of a detector responding to an incident electromagnetic wave. The value of time constant is defined as the time from the moment the incident light irradiated onto the surface of the detector to the moment that the signal reaches 63 percent of the maximum rise（fall）.
| . | （4） |
When ， . is the time constant. Here， we record the waveform at a modulation frequency of 1 kHz by an oscilloscope and the waveform is shown in
Fig. 5 （a） The waveform of the detector and time constant derivation from the waveform at 0.035 THz with the modulation frequency of 1 kHz， （b） the frequency dependent responses of the detector with different bias voltage （0.01 V， 0.02 V， 0.05 V and 0.1 V） at the source frequency of 0.035 THz， （c-d） the responsivity of the detector under different bias voltages at the source frequency of 0.035 THz and 0.1673 THz with the modulation frequency of 1 kHz， respectively
图5 （a）器件工作在太赫兹源0.035 THz，调制频率1 kHz时的响应波形与时间常数，（b）器件工作在太赫兹源0.035THz时不同偏置电压（0.01 V， 0.02 V， 0.05 V and 0.1 V）下的响应率随调制频率变化曲线，（c-d）器件分别工作在太赫兹源0.035 THz和0.1673 THz，调制频率为1kHz下的响应率随偏置电压的变化曲线
Bolometric effect is an important effect in graphite and graphene， so it is necessary to confirm if the voltage response is dominated by the bolometric effect. First， hot electron effect plays an important role in graphene and graphite. The strong e–e interactions will lead to ultrafast heating of the electron. Thus， an effective temperature of electron remains higher than that of the lattice for femtosecond timescale. The electron-phonon scattering occurs for a slower time of several picoseconds. The hot electron concept described in the above is justified if the inequality relation below is satisfied with a conductor of size
| ， | （5） |
here， is the diffusion length of electrons for electron-electron equilibration， where is the electron-electron scattering time and is the diffusion constant with the average speed of electrons and the momentum relaxation time. is the diffusion length of electrons for electron-phonon equilibration， where is the electron-phonon energy relaxation time. The half of the inequality relation，， requires that a low rate of electron-phonon scattering， which leads to a nonequilibrium state between electrons and the lattice， yielding the effective electron temperature higher than that of the lattice. A life-time estimate of electron-phonon scattering in graphite is 7 ps for THz pulse
Next， we made an estimation for the temperature rise in order to eliminate the bolometric effect in our detector. We neglected the thermal conductivity of the graphene material， and assumed that the photon energy was completely converted into thermal energy and the detector was in a thermally insulated state for estimating the temperature rise of the material. Thus，
| ， | （6） |
where is the mass of the material， is the specific heat capacity of graphite （710 ）， is the response time of the detector， and is the power from the sub-THz source. Considering that the energy of the THz source can be coupled to the active element by the metal electrodes， the effective power can be enlarged because of field enhancement. The field enhancement is simulated to be close to 1 because the permittivity values of graphite and metal are close to each other. If the device is dominated by the bolometric effect， the voltage signal is estimated to be V， which is two orders smaller than the measured value in magnitude. The large difference indicates that bolometric effect does not play an important role in this detection.
The responsivity of the device is linear with the bias voltage， which is consistent with the expected results of the EIW theory. The increasing of the bias voltage means a larger internal bias field， thus the EIW generated in the GN will wrap more electron from metal electrode， which explains the linear behavior of responsivity with bias voltage. According to the formula of EIW， the responsivity of this device is supposed to be 60.5 kV/W
In summary， a room-temperature sub-THz detector with high responsivity has been fabricated based on a simple metal-GN-metal structure. We have used graphite nanosheets to increase the optical absorption of the material. The EIW mechanism has been used to explain the THz detection based on the metal-GN-metal detector， while the contribution of bolometric effect has been excluded. Since the NEP performance declines slightly from 0.035 THz to 0.17 THz， it is expected that its detection performance for higher THz frequencies can be further improved by using ultrashort channel length of GN mesa， or by increasing the coupling effect between the electrodes and the GN material.
References
Bonaccorso F， Sun Z， Hasan T， et al. Graphene photonics and optoelectronics ［J］. Nature Photonics， 2010， 4 （9）， 611-622. 10.1038/nphoton.2010.186 [Baidu Scholar]
Ferrari A C， Bonaccorso F， Fal'ko V， et al. Science and technology roadmap for graphene， related two-dimensional crystals， and hybrid systems ［J］. Nanoscale， 2015， 7 （11）， 4598-4810. 10.1039/c4nr01600a [Baidu Scholar]
Suzuki D， Okamoto T， Li J， et al. Terahertz and infrared response assisted by heat localization in nanoporous graphene ［J］. Carbon， 2021， 173， 403-409. 10.1016/j.carbon.2020.10.059 [Baidu Scholar]
Dawlaty J M， Shivaraman S， Chandrashekhar M， et al. Measurement of ultrafast carrier dynamics in epitaxial graphene ［J］. Applied Physics Letters， 2008， 92 （4）， 042116. 10.1063/1.2837539 [Baidu Scholar]
Brida D， Tomadin A， Manzoni C， et al. Ultrafast collinear scattering and carrier multiplication in graphene ［J］. Nat Commun， 2013， 4， 1987. 10.1038/ncomms2987 [Baidu Scholar]
Xia F N， Mueller T， Lin Y M， et al. Ultrafast graphene photodetector ［J］. Nat. Nanotechnol，. 2009， 4 （12）， 839-843. 10.1038/nnano.2009.292 [Baidu Scholar]
Mueller T， Xia F N A， Avouris P. Graphene photodetectors for high-speed optical communications ［J］. Nature Photonics， 2010， 4 （5）， 297-301. 10.1038/nphoton.2010.40 [Baidu Scholar]
Liu M， Yin X B， Ulin-Avila E， et al. A graphene-based broadband optical modulator ［J］. Nature， 2011， 474 （7349）， 64-67. 10.1038/nature10067 [Baidu Scholar]
Li H， Yan M， Wan W， et al. Graphene-Coupled Terahertz Semiconductor Lasers for Enhanced Passive Frequency Comb Operation ［J］. Adv Sci （Weinh） ， 2019， 6， （20）， 1900460. 10.1002/advs.201900460 [Baidu Scholar]
Grigorenko A N， Polini M， Novoselov K S. Graphene plasmonics ［J］. Nature Photonics， 2012， 6 （11）， 749-758. 10.1038/nphoton.2012.262 [Baidu Scholar]
Sun Z P， Hasan T， Torrisi F， et al. Graphene Mode-Locked Ultrafast Laser ［J］. Acs Nano， 2010， 4 （2）， 803-810. 10.1021/nn901703e [Baidu Scholar]
Gan X T， Shiue R J， Gao Y D， et al. Chip-integrated ultrafast graphene photodetector with high responsivity ［J］. Nature Photonics， 2013， 7 （11）， 883-887. 10.1038/nphoton.2013.253 [Baidu Scholar]
Pospischil A， Humer M， Furchi M M， et al. CMOS-compatible graphene photodetector covering all optical communication bands ［J］. Nature Photonics， 2013， 7 （11）， 892-896. 10.1038/nphoton.2013.240 [Baidu Scholar]
Principi A， Vignale G， Carrega M， et al. Impact of disorder on Dirac plasmon losses ［J］. Physical Review， B 2013， 88 （12）， 1405. 10.1103/physrevb.88.121405 [Baidu Scholar]
Ryzhii V， Ryzhii M. Graphene bilayer field-effect phototransistor for terahertz and infrared detection ［J］. Physical Review B， 2009， 79 （24）， 5311. 10.1103/physrevb.79.245311 [Baidu Scholar]
Dyakonov M， Shur M. Detection， mixing， and frequency multiplication of terahertz radiation by two-dimensional electronic fluid ［J］. IEEE Trans. Electron Devices， 1996， 43 （3）， 380-387. 10.1109/16.485650 [Baidu Scholar]
Tomadin A， Polini M. Theory of the plasma-wave photoresponse of a gated graphene sheet ［J］. Physical Review B， 2013， 88 （20）， 5426. 10.1103/physrevb.88.205426 [Baidu Scholar]
Basko D. Applied physics. A photothermoelectric effect in graphene ［J］. Science， 2011， 334 （6056）， 610-611. 10.1126/science.1214560 [Baidu Scholar]
Cai X， Sushkov A B， Suess R J， et al. Sensitive room-temperature terahertz detection via the photothermoelectric effect in graphene ［J］. Nat Nanotechnol， 2014， 9 （10）， 814-819. 10.1038/nnano.2014.182 [Baidu Scholar]
Zhai Y， Xiang Y， Yuan W， et al. Fabrication of Graphene Nanomesh FET Terahertz Detector ［J］. Micromachines （Basel） ， 2021， 12 （6）， 641. 10.3390/mi12060641 [Baidu Scholar]
Liu C， Wang L， Chen X， et al. Room-temperature photoconduction assisted by hot-carriers in graphene for sub-terahertz detection ［J］. Carbon， 2018， 130， 233-240. 10.1016/j.carbon.2018.01.020 [Baidu Scholar]
Huang Z， Tong J， Huang J， et al. Room-temperature photoconductivity far below the semiconductor bandgap ［J］. Adv Mater， 2014， 26 （38）， 6294-6598. 10.1002/adma.201402352 [Baidu Scholar]
Huang Z， Zhou W， Tong J， et al. Extreme Sensitivity of Room-Temperature Photoelectric Effect for Terahertz Detection ［J］. Adv Mater， 2016， 28 （1）， 112-117. 10.1002/adma.201503350 [Baidu Scholar]
Sakowicz M， Lifshits M B， Klimenko O A， et al. Terahertz responsivity of field effect transistors versus their static channel conductivity and loading effects ［J］. Journal of Applied Physics， 2011， 110 （5）， 054512. 10.1063/1.3632058 [Baidu Scholar]
Knap W， Dyakonov M， Coquillat D， et al. Field Effect Transistors for Terahertz Detection： Physics and First Imaging Applications ［J］. Journal of Infrared， Millimeter， and Terahertz Waves， 2009， 30： 1319–1337. 10.1109/icimw.2010.5612702 [Baidu Scholar]
Tauk R， Teppe F， Boubanga S， et al. Plasma wave detection of terahertz radiation by silicon field effects transistors： Responsivity and noise equivalent power ［J］. Applied Physics Letters， 2006， 89 （25）， 253511. 10.1063/1.2410215 [Baidu Scholar]
Vicarelli L， Vitiello M S， Coquillat D， et al. Graphene field-effect transistors as room-temperature terahertz detectors ［J］. Nat Mater， 2012， 11 （10）， 865-871. 10.1038/nmat3417 [Baidu Scholar]
Castilla S， Terres B， Autore M， et al. Fast and Sensitive Terahertz Detection Using an Antenna-Integrated Graphene pn Junction ［J］. Nano Lett， 2019， 19 （5）， 2765-2773. 10.1021/acs.nanolett.8b04171 [Baidu Scholar]
Wu C， Zhou W， Yao N， et al. Silicon-based high sensitivity of room-temperature microwave and sub-terahertz detector ［J］. Applied Physics Express. 2019， 12 （5）， 052013. 10.7567/1882-0786/ab14fc [Baidu Scholar]
Weng Q， Komiyama S， Yang L， et al. Imaging of nonlocal hot-electron energy dissipation via shot noise ［J］. Science， 2018， 360 （6390）， 775-778. 10.1126/science.aam9991 [Baidu Scholar]
Kampfrath T， Perfetti L， Schapper F， et al. Strongly coupled optical phonons in the ultrafast dynamics of the electronic energy and current relaxation in graphite ［J］. Phys Rev Lett， 2005， 95 （18）， 187403. 10.1103/physrevlett.95.187403 [Baidu Scholar]
Alzahrani A Z， Srivastava G P. Gradual changes in electronic properties from graphene to graphite： first-principles calculations ［J］. J Phys Condens Matter， 2009， 21 （49）， 495503. 10.1088/0953-8984/21/49/495503 [Baidu Scholar]
Stange A， Sohrt C， Yang L X， et al. Hot electron cooling in graphite： Supercollision versus hot phonon decay ［J］. Physical Review B， 2015， 92 （18）， 184303. 10.1103/physrevb.92.184303 [Baidu Scholar]
Asgari M， Riccardi E， Balci O， et al. Chip-Scalable， Room-Temperature， Zero-Bias， Graphene-Based Terahertz Detectors with Nanosecond Response Time ［J］. ACS Nano， 2021， 15 （11）， 17966–17976. 10.1021/acsnano.1c06432 [Baidu Scholar]
Zak A， Andersson M A， Bauer M， et al. Antenna-integrated 0.6 THz FET direct detectors based on CVD graphene ［J］. Nano Lett， 2014， 14 （10）， 5834-5838. 10.1021/nl5027309 [Baidu Scholar]
Viti L， Cadore A R， Yang X， et al. Thermoelectric graphene photodetectors with sub-nanosecond response times at terahertz frequencies ［J］. Nanophotonics， 2020， 10 （1）， 89-98. 10.1515/nanoph-2020-0255 [Baidu Scholar]
Suzuki D， Okamoto T， Li J， et al. Terahertz and infrared response assisted by heat localization in nanoporous graphene ［J］. Carbon， 2021， 173， 403-409. 10.1016/j.carbon.2020.10.059 [Baidu Scholar]