Supporting Information Vertical charge transfer and lateral transport in graphene/germanium heterostructures Alireza Kazemi 1, 4, Sam Vaziri 2, Jorge Daniel Aguirre Morales 3, Sébastien Frégonèse 3, Francesca Cavallo 4, Marziyeh Zamiri 5, Noel Dawson 4, Kateryna Artyushkova,6, Ying Bing Jiang 7, Steven J. R Brueck 4, and Sanjay Krishna 1,4* 1 Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, United States. 2 Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA. 3 Université Bordeaux 1, CNRS, UMR 5218, 33405 Talence, France. 4 Center for High Technology Materials, University of New Mexico, Albuquerque, NM, United States. University of Wisconsin-Madison, Madison, WS, United States. 6 Department of Chemical and Nuclear Engineering, University of New Mexico Albuquerque, NM, United States. 7 Center for Micro- Engineered Materials, University of New Mexico, Albuquerque, NM, United States. * Corresponding author email address: krishna.53@osu.edu 1
Figure S1 AFM images and the corresponding height profiles evaluated from statistical analysis of the AFM images, and histograms of (a-b) SiO2/p + Si, (d-e) GOI, and (g-h) Ge NM/SiO2/p + Si substrates before the graphene transfer. (c,f, i) The histogram of the height measurements along with the RMS roughness of the AFM profiles. Number of events was corrected for a linear off set. 2
Figure S2 (a) Optical micrograph of scanned area for Raman analysis. (b) Raman spectra of Gr/SiO2 and Gr/Ge obtained from different spots. (c) The 2D band intensity of the Gr/SiO2 and Gr/Ge. (d) Close-view 2D band intensity of the Gr/SiO2 and Gr/Ge. (e) The G band intensity of the Gr/SiO2 and Gr/Ge. (f) Close-view G band intensity of the Gr/ SiO2 and Gr/ Ge. 3
Figure S3 Transfer characteristics of field effect devices processed on Gr, Gr/Ge, and Ge. Source drain current (Id) versus gate voltage (Vg) recorded at different source-drain voltages and Id versus source-drain voltage (Vds) obtained at room temperature for (a, b) Gr/SiO2/p + Si or (Gr-FET) (c, d) Gr/Ge/SiO2/p + Si or (Gr/Ge-FET) (e, f) Ge/SiO2/p+Si or (Ge-FET). 4
Figure S4 (a) Optical micrograph of the TLM structure patterned on Gr/SiO2/p + Si (b) The closeview image of the TLM structure on Gr/SiO2/p + Si (c) Optical micrograph of the TLM structure patterned on Gr/Ge/SiO2/p + Si. (d) The close-view image of the TLM structure on Gr/Ge/SiO2/p + Si. 5
Figure S5 Measured TLM current and total resistance versus TLM contact distance (a, b) Gr/SiO2 (c, d) Gr/Ge 6
Solving Kirchhoff s law in the equivalent circuit for Metal Insulator Germanium Graphene (MiGeG): Applying the Kirchhoff s law to the equivalent circuit in Figure 7a, the following relationship between gate voltage, channel potential and potential variation due to Vds is established C inv C (Eq. S1) inv VCH x VCH x VCH CTOP 1 CTOP 1 VGS V x e NF 0 CGE CGE where CTOP is the equivalent top gate capacitance of the oxide and germanium stack given by C TOP 1 1 1 C C OX GE 3 e and COX is the oxide capacitance. is defined as v f 2. The charge in the Ge composed of two terms induced by insulating and inversion layers. The zeroes of this second degree polynomial can be calculated and give the channel potential solution V CH x C C 4C V V x e N 2 2 Eq Eq Eq GS F (Eq. S2) Comparing Eq. S2 to the previous model Ref [66], the COX capacitance is replaced by C Eq 1 1 1 C C OX GE C 1 C inv GE. 7
Modeling Ge-FETs in TCAD: In order to extract the Cinv parameter, the Ge-FET structure has been measured and modeled using a commercial TCAD simulator. The calibration procedure has considered the different steps such as Schottky barrier for source and drain contact, adjustment of the Germanium doping and mobility in the inversion layer. The Figure S5 presents the comparison of the measurement and simulation of the transfer characteristics of the Ge-FET. Figure S6 Drain current versus gate voltage at Vds=1 mv for the Ge-FET, measurement (symbols) and TCAD simulation (solid line). 8
Calculation of charge densities in Ge: From the TCAD simulation results, the charge in the inversion layer can be extracted as described in the Figure S6. As expected, a linear approximation of the charge is sufficient to evaluate the charge in the Germanium layer (Cinv=135 µf/m²). Figure S7. Integration of the carrier density (electron and hole) in the Germanium region of the Germanium FET. 9
Extracted electron and hole mobilities, dopings and puddle densities in Gr- and Gr/Ge- FETS: We have considered a finite DOS close to the Dirac point due to disorder from quasilocalized defects. E0 is the energy limit of the disorder beyond which the electron DOS starts to dominate over the disorder DOS (N.M.R. Peres et al. "The transport properties of graphene: An introduction", Reviews of Modern Physics ). Table S1. *The n puddle is a residual carrier density induced by the spatial inhomogeinity within the graphene layer. Instead of the traditional "V" nature of the DOS, we incorporated in the model a DOS curve as shown here below 10
Calculation of charge densities in Gr and Gr/Ge channels: I d (ma) V 1.5x10-3 ds = 1 mv Simulation: Gr Simulation: Gr/Ge 1.0x10-3 5.0x10-4 5x10-4 4x10-4 3x10-4 2x10-4 I d (ma) 0.0 V 1x10-4 Dirac = 10.05 V V Dirac = 60.65 V -100-50 0 50 100 V g (V) Figure S8. Simulated IV characteristics of the Gr-FET and Gr/Ge-FET. V CH = V GS V FB Q CH C OX = V GS V FB At Dirac point V CH = 0 V GS V FB = qn F C eq q ( q2 π(ħv f )² V CH V CH + N F ) C eq = Q C eq Calculating the difference of charge at the Dirac point between the Gr-FET and Gr/Ge-FET, VFB vanishes. Q = Q GrGe Dirac Q Gr Dirac = C eqgrge V GS,DiracGrGe C eqgr V GS,DiracGr Q GrGe Dirac = C eqgrge V GS,Dirac q GrGe Dirac = ε 0 ε r EOT V GS,DiracGrGe GrGe q = 8.85 10 12 3.9 10.05 309 10 9 1.602 10 19 q GrGe Dirac = 7.00 10 11 cm 2 Q Gr Dirac = C eqgr V GS,DiracGr q Gr Dirac = ε 0 ε r EOT V GS,DiracGr Gr q = 8.85 10 12 3.9 60.65 285 10 9 1.602 10 19 q Gr Dirac = 4.58 10 12 cm 2 11
Charge Transfer is computed to be in the order of: q Gr Dirac q GrGe Dirac = 3.88 10 12 cm 2 12