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[2025A00601G_HotElectronEngineering_SI.pdf](https://mdr.nims.go.jp/filesets/40666ca2-0f18-461b-aa99-cf5f7402834d/download)

## Creator

Pushkar Dasika, Patrick Hays, Suchithra Puliyassery, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Seth Ariel Tongay, Kausik Majumdar

## Rights

This document is the Accepted Manuscript version of a Published Article that appeared in final form in ACS Nano, copyright © 2025 American Chemical Society. To access the final published article, see https://doi.org/10.1021/acsnano.4c14983.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Hot Electron Engineering in Layered Heterojunctions for Efficient Infrared Detection](https://mdr.nims.go.jp/datasets/2c3ef0e5-9403-4d19-811e-50adf4ed69f1)

## Fulltext

Supplementary Information for:Hot electron engineering in layeredheterojunction for efficient infrared detectionPushkar Dasika1, Patrick Hays2, Suchithra Puliyassery1, Kenji Watanabe3,Takashi Taniguchi4, Seth Ariel Tongay2 and Kausik Majumdar1∗1Department of Electrical Communication Engineering,Indian Institute of Science, Bangalore 560012, India2Materials Science and Engineering, School for Engineering of Matter,Transport and Energy,Arizona State University, Tempe, Arizona 85287, USA3Research Center for Electronic and Optical Materials,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-044, Japan4Research Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-044, JapanCorresponding author∗E-mail: kausikm@iisc.ac.in1S1. SEM and AFM data of devices D2 and D310 μm 10 μmD3D2(a) (b)WSe2AuWS2MoS2GraphiteFig. S1: SEM image of device (a) D2 and (b) D3.(b)(d)(a)7 nm11 nm8.5 nm(c)D2WS2WSe2MoS2213Fig. S2: (a) AFM image of Device D2. Thickness profile along line marked (b) 1, (c) 2 and(d) 3 in (a). These profiles correspond to WS2 , WSe2 and MoS2 layers, respectively.2(b)6 nm 15 nm(c)D312WS2MoS2(a)Fig. S3: (a) AFM image of Device D3. Thickness profile along line marked (b) 1 and (c) 2in (a). These profiles correspond to MoS2 and WS2 layers, respectively.Table 1: Summary of thicknesses of various layers in D2Layer ThicknessMoS2 8.5 nmWSe2 11 nmWS2 7 nmTable 2: Summary of thicknesses of various layers in D3Layer ThicknessMoS2 6 nmWS2 15 nm3S2. Electrical characteristics of Device D1 under darkconditions(a) (b)VD = 0.05:1:3.05 VVG = -2:1:5 VFig. S4: (a) Transfer characteristics and (b) Output characteristics of device D1.4S3. Hot-electron photocurrent modelThe structure used in the physical model for the device is shown in the figure below. Theemitter, barrier and collector layers are considered thin, separated by a physical distance t.This distance is typically the van der Waal gap between the materials.EmitterBarrierCollectorh-BNGate (VG)tins tFig. S5: Device structure considered for simulationSince the layers are assumed thin, they are equipotential with the electrostatic potentialof the three layers denoted by ϕE, ϕB and ϕC . The system of equations that govern thesystem are:ϵϕE − VGtins+ ϵϕE − ϕBt= e(NDE − nE)ϵϕB − ϕEt+ ϵϕB − ϕCt= e(NDB − nB)ϵϕC − ϕBt= e(NDC − nC)where NDi and ni represent the fixed doping concentration and electron concentrationinside the ith layer (i : E,B,C). e is the absolute charge of an electron, and ϵ is the effectivedielectric constant (assumed to be uniform in the device). The carrier concentration is5related to the electrostatic potential of the layer by:n(ϕ, T, EF ) =gsgvm∗kBTπh̄2 log(1 + exp(e(EF −D + ϕ)kBT))where gs and gv are spin and valley degeneracies, respectively. EF is the Fermi level, m∗is the effective mass, and kB is the Boltzmann constant. Under dark conditions, we takeEF = 0. D is the position of the conduction band with respect to Fermi level EF = 0 atϕ = 0. This parameter represents the doping of the layer.Under illumination, we assume the temperature of the electrons to be Te > T in bothcollector and emitter layers. Unlike an inter-band photo-excitation, the number of carriersin the conduction band will remain constant. Also, since the carrier concentration doesnot change, we do not expect the electrostatic potentials to change either. Using theseconstraints, we can calculate the new quasi-Fermi level, EFe using the relation:n(ϕ, T, EF = 0) = n(ϕ, Te, EFe)The new quasi-Fermi level and the higher temperature define the distribution of electronsin the conduction band under illumination.Once the distribution is obtained, the number of carriers in the emitter layer with energyhigher than the conduction band edge of the barrier layer is calculated [nE(TEe )]. Similarly,the number of carriers in the collector layer with energy greater than the barrier layerconduction band edge is calculated [nC(TCe )]. The photocurrent, then, is proportional tothe difference between the two.Iph ∝ nE(TEe )− nC(TCe )6S4. Response of structure D2 to various wavelengthsD2 exhibits a similar wavelength response to various radiation of the SWIR spectrum as D3.Normalized PhotocurrentFig. S6: Response of D2 to infrared radiation from 1.1 µm to 1.8 µm.7S5. Characterization of additional D3 deviceThe results of the characterization of device D3 from another fabrication run are shown inthe figure below. The device shows qualitatively similar behaviour as the device presentedin the main text. The device shows a peak responsivity of 12.5 mA/W.(a) (b)(c)Fig. S7: (a) Dependence of photocurrent on collector bias. (b) Responsivity as a function ofinput power. (c) SNR for various collector biases as a function of input power.8S6. MoS2 thickness dependent photoresponse of D31 nm 6 nm 50 nm120 nm1010109108107Photcurrent [A]Fig. S8: Comparison of photoresponse of four D3 devices with varying thicknesses of MoS2 -monolayer, 6 nm, 50 nm, and 120 nm. The device with 6 nm thick MoS2 showed significantlyhigh photoresponse compared to the other three devices.9S7. Frequency response of D3 for excitation with 633nm radiationWith 633 nm radiation, we can detect signals up to 100 kHz with the same device.(a)(b)Fig. S9: (a) Frequency response to excitation with 633 nm radiation. (b) Time response ofD3 from excitation of 633 nm radiation from 1 kHz to 100 kHz.10S8. Performance benchmarkingDeviceWavelength[nm]Responsivity[AW−1]Response time[s]Circuit (PCB)integrationMoS2-WS2 [18](Interband)400-800 1.8× 10−7 16 NoMoS2-WS2 [19](Interband)450 2.3 - NoMoS2-WS2 [20](Interband)405 298 - NoGraphene [25](Interband)1550 6.1× 10−3 6.25× 10−11 NoGraphene-Si [37](Plasmonic hot electron)1550 0.37 - NoGraphene-Si [38](Hot electron)1550 9.9× 10−3 - NoMoS2-Au [40](Hot electron)1550 17× 10−3 1.5× 10−4 -PtSe2 [22](Interband)200-2000 0.5 1× 10−5 NoTe [23](Interband)1550 13 1× 10−3 NoGraphene [50](Gr-hBN tunnel barrier)8600 8.6× 10−4 - NoThis work(Hot electron)633-180042× 10−3(@ 1550 nm)150× 10−3(@ 633 nm)4× 10−4(@ 1550 nm)1× 10−4(@ 633 nm)Yes11