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Supplementary Information Fig S1 a top-down SEM image of PS template. b. cross-sectional SEM of PS template (with diameter of 440 nm). Fig. S2 The cross-sectional SEM of the dense Ge film(a) and 3DOM Ge film (b). In order to show the thickness of the films, the cross-sectional SEM images of the Ge and 3DOM Ge films are added in Fig. S2. The thickness is about 1μm for dense Ge film and 2μm for 3DOM Ge, respectively. The mass of the electrodes is about 0.7mg. The electrodes are disks with diameter of 14mm, and the mass load is about 0.455 mg/cm 2.

Fig. S3 Grazing incident XRD of Ge film on Cu substrate by ionic liquid electrodeposition XRD analysis of the films was done by grazing incidence XRD (GIXRD) model using monochromatic Cu Ka radiation with a D8 Bruker diffractometer. X-ray scan is with an increment of 0.01 o with time per step and the incident angle is 0.5 o. Fig. S3 shows the XRD pattern of Ge film on Cu substrate. The diffraction peaks are corresponding to (111), (220) and (331) planes of the diamond structure of Ge (JCPDS number 04-0545). A broad 2θ peak at ~20-30 o is attributed to the amorphous germanium. Ge(220) shows characteristic of nanocrsytalline germanium. And Ge (331) plane is overlapping with Cu (220), and shows a broad peak. Fig. S4 Nyquist plots of the only Ge electrode and 3DOM Ge electrode (all of them are coated with carbon to enhance the conductivity).

Fig. S5 Raman spectra of 3DOM Ge after 50 cycling. Fig. S6 Discharge-charge curves of only Ge electrode between 0 and 2V under a current density of 0.2C.

Table S1 Comparison of cycling performance with previous reports on Ge-based electrodes. Cycling performance Ref. Year Structure Fabrication method rate cycle reversible capacity(mah/g) 2013 3DOM Ionic liquid electrodepsition 0.2 50 844 1 2012 Ge@C/RGO 940 Capped with oleylamine 0.031C 50 Ge@C 490 2 2008 n-c/ge Solid-state pyrolysis 0.093C 50 From 1190 to 923 3 2013 Ge-NP slurry cast 40:20:40 =Ge NP : 1C in binder :Super-P EC:DMC 10-200 from 1083 to 552 4 2011 Ge NW Solid-liquid solution 963 to 0.5C 100 method 400 5 2008 Ge NW VLS growth 0.05C 20 1141 6 2013 Ge NW/ Graphite LPCVD NF (Ge/G-30) 0.1C 30 remain 800 7 2013 Ge NW Sn Catalyzed Ge NWs 0.4C 50 Sn/Ge 1000 8 2013 Graphene / Ge NW VLS GeNW Graphene CVD 4C 200 1059 9 2011 Ge Nanotube Kirkendall effect 40C 400 >1000 As-deposited Ge 200-240nm thick 0.14C 25 325 10 2012 Ge nano structured film Ion beam modified 0.14C 25 From 1352 to 1260 11 2004 Nanocrystline PVD 236 μg 50 1400 to 840 filme 0.25C PVD(60-250nm) 0.042 Amorphous film 60 1700 μg 12 2010 Ge film Electron beam -40%SWCN evaporation 0.046C 10 825 to 700 13 2007 NP-Ge in Carbon Na naphthalide matrix reduction 0.2C 30 729 14 2010 Mesoporous Ge GeO+Mg etching 0.93C 20 950 to 789 15 2013 Ge-based 3D electrode rf-sputtering 1C 50 1272 16 2013 Ge-CNT-Cu foam GeO 2 reduction 0.93C 100 800 17 2013 Ge/graphene thermal evaporation 0.625C 5 about 880 3DOM Ge dense 18 2012 1027 wall CVD 0.2C 100 3DOM Ge porous 1155 wall

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