Supporting Information

Transcription

1 upporting Information Graphene-baed Thermopile for Thermal Imaging Application Allen L. Hu, Patrick K. Herring,3, Naaniel M. Gabor 4, ungjae Ha, Yong Cheol hin 5, Yi ong, Matew Chin 6, Madan Dubey 6, Anana P. Chandrakaan, Jing Kong, Pablo Jarillo-Herrero*, Tomá Palacio* Department of Electrical Engineering and Computer cience, Maachuett Intitute of Technology, Cambridge, Maachuett 39, UA Department of Phyic, Maachuett Intitute of Technology, Cambridge, Maachuett 39, UA 3 Department of Phyic, Harvard Univerity, Cambridge, Maachuett 38, UA 4 Department of Phyic and Atronomy, Univerity of California, iveride, iveride, California 95, UA 5 Department of Material cience and Engineering, Maachuett Intitute of Technology, Cambridge, Maachuett 39, UA 6 Army eearch Laboratory, 8 Powder Mill oad, Adelphi, Maryland 783, UA

2 .) Device Fabrication The tarting ubtrate wa a 4 p++ bare i wafer wi a ingle ide polih. A dielectric tack coniting of nm io / 5 nm in / nm io wa depoited uing a T-PECVD depoition tool at 3 C. The total train of e depoited film wa kept below MPa. Gate electrode were en patterned by a tandard liftoff proce uing PMMA expoed at 5 kev wi an Elionix 5 ytem and nm Ti/ nm Pt were evaporated uing a Temecal Ebeam-Evaporator wi fat pump at e-6 mtorr. eleae via were patterned uing a photoreit hardmak (OCG-85) and a CF4 plama (Plamaquet). The entire tructure wa en recoated wi anoer layer of PE-CVD io 8 nm ick and e ame etch a before wa performed to etch open e releae via to e underlying acrificial ilicon. CVD Graphene wa grown by LP-CVD on Cu foil and tranferred uing a wet, tranfer proce involving FeCl 3. Ohmic metal ( nm Ti/ 3 nm Au) were en evaporated and patterned uing PMMA and a lift-off proce a decribed earlier. Mea iolation of e graphene wa accomplihed uing A4 PMMA a a in hard etch mak for reactive oxygen etching done uing a Plamaerm (5V) for 5. A layer of A4 PMMA i pun on top and en expoed by an Elionix 5 to open up e etch releae hole. Finally, e chip i expoed to XeF for cycle for 3 uing a E Tech E- XM at a preure of ~45 mtorr. The mall etch hole in e center erve (hown in Figure (b)) to aid in e in releae tep, while e larger etch hole along e periphery erve to minimize any paraitic ermal tranport. Figure (c) how an optical picture of e fully upended membrane at normal incidence. While e upended membrane at normal incidence how a pecific color due to optical interference, e membrane itelf i in enough to be optically tranparent when viewed at a glancing angle. The individual ermopile junction can be wired eier externally or rough liography to form a multi-junction ermopile..) Device Characterization The device were teted under vacuum, at room temperature in a Jani cryotat wi anti-reflection coated Zne window. To characterize ee device, e reitance () of a two junction ermopile wa meaured a a function of V G and V G (Figure (a)) uing an AC bia of V M-M 5 µv at frequency of 35 Hz. For e two junction meaurement, M of one junction i connected to M of an adjacent junction externally rough a breakout box, while e correponding gate for each portion of e device were connected to e ame voltage ource. Due to e PMMA paivation layer, we find a light p-type doping for e graphene wi a maximum reitance (Charge Neutrality Point) occurring at gate voltage (V G and V G ) of + and + V repectively, yielding a field effect mobility (µ) of ~86 cm V - -. The device were ubequently characterized optically utilizing a confocal CO (λ.6 µm) canning ytem (ee Infrared Optical etup). The CO laer pot ize i approximately 5- µm in diameter. The temperature enitive region i located at e junction between e two gate contact (V G and V G ) and e two ohmic contact (V M and V M ) are ued to read out e photo-ermal voltage (V PH ) from e infrared detector. The open-circuit photovoltage (V PH ) repone from our detector wa meaured wi a laer input of (P 8 µw, f mod Hz), while meauring V PH a a function of V G and V G (Figure (b)) rough a lock in amplifier (tanford eearch ytem). We moved on to characterize bo e voltage reponivity ( V ) and e ermal time contant (τ) of our device, by fixing e laer pot at e mot enitive portion of e device (near e corner

3 periphery of e central upended in aborber between e underlying plit capacitive gate) and varying e optical modulation frequency (f mod ) wi an optical chopper wheel (Figure (c)). The optical tranmiion of e in membrane wa meaured by Fourier Tranform Infrared pectrocopy (FTI). The τ in at λ.6µm i only 5-5%.; however, e in provide a much broader aborption pectra an io 3,4. 3.) Extraction of Thermal Time Contant We can model e time dependent change in temperature by e following differential equation. C d T dt + G T εφ e iωt (Eq. 3.) Where C i e ermal capacitance, G i e ermal conductivity, ε i e emiivity, and Φ i e optical power auming a inuoidal time dependence (ω), and ΔT i e change in temperature. The olution to Eq. 3. i written in Eq. 3.. ω εφ εφ εφ T( ) (Eq. 3.) C + ω C + ω τ G + ω G Therefore e meaured reponivity can be expreed in Eq ( ω) V T ( ω) Φ Φ εk ( ω ) + ω τ (Eq. 3.3) + ω τ which i e expreion ued to fit e Data in Figure (c). 4.) Infrared Optical etup Detail of e infrared confocal laer canning ytem and electrical characterization can be found in 5. For our infrared imaging and blackbody ermal detection, we utilized e ame Jani cryotat a ued in our previou work, except we altered e beam pa to include a calibrated blackbody ource from Omega wi a diameter output wi temperature tabilization. The blackbody ource wa placed behind an optical chopper at e focal point of e optical relay ytem coniting of two off axi parabolic (OAP) Al mirror (Thorlab) wi a focal leng (f L ) of 5.8 mm and an OAP diameter (d OAP ) of 5.4 mm, which direct and focu e infrared light rough cyrotat window onto e device. eflective optic were choen to avoid chromatic aberration due to e broadband nature of e ource. The off axi parabolic mirror were held in place wi a erie of cage optic and e focal point were placed orogonal to each oer to furer enure at no tray infrared light wa tranmitted to e detector, which

4 wa placed inide e Jani cryotat wi a Zne (A coated IP Optic) window. A hown in Figure 3(a), an incoherent calibrated blackbody ource (Omega) wa placed at e focal point of OAP, while e graphene ermopile wa placed at e focal point of OAP. A ingle junction device wa ued for i et of imaging experiment. Bo OAP mirror have equivalent f-number (F#) uch at ere i no optical magnification in our relay optic. For imaging experiment, we utilized two motor controller x-y tranlation tage (Thorlab) to can an image 5 mm x 5 mm in ize cut out of.8 tainle teel laer cut from tencil Unlimited. The aperture wa placed at e focal point of e firt off axi parabolic mirror and e blackbody ource wa placed behind. The tage were controlled rough Labview and e tep ize wa et to.5 mm and an integration time of 3 econd per data point. Unlike previou laer canning meaurement, where our ermal ource i a localized laer pot; in our optical relay, we are illuminating our entire device wi only an effective blackbody emitter of equivalent ize a our detector (~ µm x ~ µm). For imaging wi e hand, a human hand wa placed behind e optical chopper and en held ere for and en removed leaving no ermal object wiin e focal point of e off axi parabolic mirror. The meaured noie floor for our ytem (V noie_floor ) of our electrical etup i. µv and i plotted in Figure 3(b). 5.) Improvement of Thermal Iolation due to upenion The hape factor given a upported membrane on an emi-infinite medium i equal to ( ) κ d laer i, where d laer i e diameter of e laer beam (5 µm), and κ i i e ermal conductivity of e ilicon (49 Wm - K - ). Auming a upended device operating in vacuum, e predominate ermal lo mechanim i till rough conduction from e ermal iolation leg, which each have a ermal reitance of ( ) κ, where α i at in in e apect ratio (W/L /4) of e leg, t in i e ickne of e ilicon nitride membrane (.7 µm) and κ in i e ermal conductivity of in ( Wm - K - ). The ratio of ermal reitance between e two cae i u /, which yield a ratio of ermal reitance of approximately 57. In addition, we can compute an etimated reponivity baed on reaonable aumption regarding e material parameter and non-idealitie of e optical ytem. V N j T P ( ) N ( ) α N ( ) α N t κ j j (Eq. 5.) in _ tot l L W Where N j i e number of junction in erie,, are e eebeck Coefficient of each ide of e graphene ermocouple, P in_tot i e total input power on e device, i e ermal reitance of e device, α i e

5 optical aborption at a pecific waveleng, κ i e ermal conductivity, and e dimenion of e device (L,W,t). Auming from our previou paper a eebeck coefficient of +/-5µV/K for and repectively, and at e ermal reitance i dominated by e conduction rough e iolation leg (N l 8) of e device (compoed of nm io /5nm in/nm io ) each wi an apect ratio of L/W 4. The weighted average of e ermal conductivity of io and in (io κ io.4 W/(mK), in κ in W/(mK)) yield 7.5 W/(mK). Here α at µm from Fig (c) inet i 5% and N j i e number of junction being meaured in Fig. (c). Thi yield an etimated V of 9.5 V/W which agree well wi value in Fig. auming our propoed ermal detection mechanim. 6.) Figure of Merit for Thermopile (D* and NETD) Eq. 6. how e expreion for Detectivity (D*), auming a ermo-electric detection mechanim 6. D * ermopile V a b f V N ε + ω τ Na b 4k B T e ρ h (Eq. 6.) Where, i e ermal reitance of e device, N i e number of junction, a and b are e dimenion of e infrared aborbing region of e ermopile, e i e electrical reitance of a branch of e ermopile, and ε i e emiivity of e device (aumed to be ~ auming an ideal infrared aborbing ubtrate non idealitie are taken into account later in NETD rough optical tranmiion of e ubtrate τ (λ)). Thermopile are often very low noie detector ince ey are only limited by Johnon noie ( V 4k N B T e ) -- unlike oer type of detector, uch a bolometer, which contain /f noie due to active biaing. To compare only e material pecific propertie of D*, we make two aumption: () low frequency operation (ω << /τ ) and () i dominated by e ermally iolated upport membrane (i.e. e ickne of e ermoelectric material i much maller an e ickne of e ilicon nitride membrane (t TE << t in ), which i e cae for many depoited in film. Under ee condition, e only material dependent component are e eebeck coefficient () and e bulk reitivity (ρ h ). In addition to D*, anoer ueful figure of merit which depend not only on e material but alo e entire imaging ytem i e noie equivalent temperature difference (NETD), which meaure e mallet detectable change in temperature of a blackbody ource (Eq. 6.).

6 Vnoie _ floor NETD( T ) dvph ( T ) dt T πf L A a b a b f D * λ ( λ) τ ( λ) dλ W ( λ, T ) T (Eq. 6.) Where A i e ize of e len, f L i e focal ditance of e len, τ i e tranmiion coefficient of e optic and detector, V noie_floor i e electronic noie floor, T i e current temperature of e blackbody ource, W λ i e pectral radiant emittance of a blackbody ource, and f i e bandwid of e detector. 7.) Calculation of D* graphene. To begin, e ignal repone from our graphene baed ermo-pile follow from Mott relationhip (Eq. 7.), where we have expreed e eebeck coefficient () in term of heet carrier concentration (n ) of e graphene. 3 k q T h ( n ) d dn ( n ) dn π B h (Eq. 7.) de E f Where, h i e heet reitance of graphene, k B i e boltzmann contant, T i temperature, q i unit of charge, and E i energy. Utilizing a quare root charge model to take into account charge puddle (n ) near e Dirac point, we can expre e heet reitance in Eq. 7. h q µ n + n (Eq. 7.) Where, μ i e carrier mobility wiin graphene. Therefore, combining equation (7.) and (7.), we can derive an explicit relationhip for e eebeck coefficient in term of n. π kbt n 3 q hv π n f 3 / ( n + ) (Eq. 7.3) Where v f i e Fermi velocity (~ 6 m/). The eebeck coefficient i a tunable value; however, we can expre e maximum and minimum eebeck coefficient from Eq. 7.3, which occur at n MAX ± 3n. Auming e graphene i biaed at n MAX, en we can expre e maximum value in Eq. 7.4, which interetingly doe not explicitly depend on carrier mobility, but raer charge-puddle denity (n ). MAX 3/ 4 π kbt 3 ± 3 q hv π 4 n (Eq. 7.4) f

7 While i analyi aume a maximal repone independent of carrier mobility, e relative figure of merit for any detector i in fact e ignal to noie, which i often expreed a detectivity (D*). Therefore to expre D*, we look at e reponivity (), noie (V N ), dimenion of detector (a, b ) and bandwid of ytem (Δf). D * ermopile a b f V N ε + ω τ Na b 4k B T e ρ h (Eq. 7.5) Combining equation 7. and 7.3, and auming n >> n reult in Equation 7.5. If we look at only e material dependent factor we arrive at e following expreion (Eq. 7.6) h π 3 k BT q qµ hv f π, n >> n (Eq. 7.6) (Eq. 7.7). Combining equation 7.5 and 7.6, we arrive at e full expreion for e D* of a graphene ermopile D * ermopile π 3 k BT q qµ ab hv κ in t f π in N layer 8Nk B T L W (Eq. 7.7) Where v f i e Fermi velocity, κ in i e ermal conductivity of in, N layer i e number of graphene heet, N i e number of junction, L i e leng of e ermal iolation leg, and W i e wid of e ermal iolation leg, µ i e carrier mobility, and we aume two electrical branche of graphene for a ingle ermocouple junction. While Eq. 7.7 appear to tend toward infinity a e area increae, i expreion i only valid when electrical noie i e dominant noie ource, which doe not hold true for extremely large device. Furermore, while achieving larger D* at a conequence of area, alo place large contraint on e peed of e device a e larger ermal ma will alo make e device prohibitively low for certain imaging application. We alo aume at for a ingle junction (N), ere i only a ingle contribution toward e repone, but twice e reitance due to e traveral between e hot and cold region. 8.) Calculation of NETD of graphene auming % optical aborption. To calculate e effect of NETD auming % optical aborption, we firt aumed tranmiion rough e atmophere and e Zne window auming a tandard blackbody emiion. Where τ ATM i e atmopheric tranmiion from HITAN auming an optical pa leng of.5 feet for our relay ytem, τ Zne i e optical tranmiion rough a Zne window wi antireflection coating (Thorlab), τ in i e optical tranmiion of e ilicon Nitride (Figure (c)). Therefore e improvement factor i calculated in Eq. 8..

8 Γ τ W( λ, T) τ W( λ, T) τ ATM ATM ( λ) τ Zne( λ) dλ ( λ) τ ( λ) τ ( λ) Zne in dλ (Eq. 8.) The effect of tranmiion i hown in Figure (a). The olid line how e effect of tranmiion due to e atmophere and Zne window on an ideal blackbody ource. The dotted line how e effect of e optical aborption due to e in membrane. Figure (b) how e integral of e pectral radiant emittance which i e total power emitted by e blackbody ource. The ratio between ee value i computed by Eq. 8.. Figure. Calculation of Improvement Factor Auming % Optical Aborption (a) pectral adiant Emittance a a function of waveleng for an ideal blackbody ource (olid line) for variou blackbody temperature (T) after tranmiion rough.5 feet of atmophere and Zne A coated window. Dotted line repreent total amount of optical light aborbed rough e ilicon nitride membrane. (b) The computed optical power of an ideal blackbody ource (blue) veru e collected power in our device (red). The ratio of ee two i e computed improvement factor a a function of blackbody temperature (T). 9.) Comparion of Graphene to ilicon Thermopile To highlight e advantage of graphene a a ermopile material, we examine in e following ection a direct comparion wi tandard ilicon baed ermopile. The eebeck coefficient for ilicon a expreed in ogalki, et al..6 k B e log ρ ρ (9.)

9 Where ρ 5 µω-m. Variou value of can be achieved rough proper doping control of ilicon reitivity. Given 9., we can expre e detectivity of a ilicon baed device in term of reitivity. D * Wt ρ L t ρ ρ ρ t log (9.) ρ Where, W,L,t are e wid, leng and ickne of e ilicon in film. From 9., a larger ickne can increae D* auming at e t << t in to enure at e ermal conduction rough e ermoelectric film can be neglected. Therefore, to provide a point of comparion, we examine D* normalized to any geometric term, which reult in a figure of merit proportional to /ρ /. Therefore, if we maximize 9., we find at e maximum value occur when ρ ρ e 37 µω-m, yielding a figure of merit (/ρ / ) of 74 µv K - (µ Ω -/ m -/ ). In e cae of graphene, due to it linear band tructure, e maximum achievable eebeck coefficient in Graphene i lited in Equation 7.4. MAX 3/ 4 π kbt 3 ± 3 q hv π 4 n (9.3) f Thi maximum value occur at a carrier concentration (n ) where n 3 n. Therefore auming a quare-root charge model a dicued earlier, e reitivity i actually h qµ n tg ρ qµ n + n qµ n (9.4) Auming t G.345 nm, o given recent advance wi hbn to minimize n and maximize µ, we can aume an achievable n x /cm and µ, cm V - -. Therefore we can obtain a minimum reitivity of.78 µω-m, and a correponding max 3 µv/k. Thi give u a figure of merit (/ρ / ) of 75 µv K - (µ Ω -/ m -/ ), which how e potential performance achievable wi graphene over conventional ilicon for application where device ickne i a contraint. eference. Li, X. et al. Large-area ynei of high-quality and uniform graphene film on copper foil. cience 34, 3 4 (9).. Kim,. M. et al. The effect of copper pre-cleaning on graphene ynei. Nanotechnology 4, 3656 (3).

10 3. Fei, Z. et al. Infrared Nanocopy of Dirac Plamon at e Graphene io Interface. Nano Lett., (). 4. Palik, E. D. Handbook of Optical Contant of olid, Volume I, II, and III: ubject Index and Contributor Index. (Elevier cience & Tech, 985). 5. Herring, P. K. et al. Photorepone of an Electrically Tunable Ambipolar Graphene Infrared Thermocouple. Nano Lett. 4, 9 97 (4). 6. ogalki, A. Infrared Detector. (CC Pre, ).