## Materials and Methods
### Preparation of TbPO\({}_{4}\cdot\)H\({}_{2}\)O@silica-NH\({}_{2}\) Nanomaterials  
Terbium orthophosphate monohydrate (TbPO\({}_{4}\cdot\)H\({}_{2}\)O): Tb(NO\({}_{3}\))\({}_{3}\cdot\)5H\({}_{2}\)O (Sigma, 99.9 %) was added to NH\({}_{4}\)H\({}_{2}\)PO\({}_{4}\) solution (Merck) in the presence of polyethylene glycol 2000 (PEG-2000) and stirred for 3-12 h. The pH of the obtained solution was adjusted in the range of 4-12 by adding 10% NaOH solution before incubating at 200 \({}^{\circ}\)C for 24 h. The product (TbPO\({}_{4}\cdot\)H\({}_{2}\)O) was centrifuged at 5900 rpm and washed with ddH\({}_{2}\)O before drying at 60 \({}^{\circ}\)C for 5-10 h. The nanomaterial was then coated with silica through a hydrolysis reaction with tetra ethyl orthosilicate (TEOS) (Aldrich, 99.99%). Briefly, TbPO\({}_{4}\cdot\)H\({}_{2}\)O was added to a mixture solution containing TEOS, ethanol, acetic acid, and water and stirred for 15 min (TbPO\({}_{4}\)/TEOS molar ratio of 1:0.2). The solution was then centrifuged and washed three times with 33% ethanol solution. Glycerol solution (0.5 mL) was added to a hydrous mixture of ethanol containing TbPO\({}_{4}\cdot\)H\({}_{2}\)O coated silica (TbPO\({}_{4}\cdot\)H\({}_{2}\)O@silica) and stirred for 30 min. 3-aminopropyl trimethoxy silane (APTMS) was dispersed in ethanol before being mixed with TbPO\({}_{4}\cdot\)H\({}_{2}\)O@silica solution (TbPO\({}_{4}\cdot\)H\({}_{2}\)O@silica/APTMS molar ratio of 1:0.2) and stirred for 15 min to functionalize the surface with -NH\({}_{2}\). The TbPO\({}_{4}\cdot\)H\({}_{2}\)O@silica-NH\({}_{2}\) (TM) materials were washed two times with ethanol, two times with ddH\({}_{2}\)O, and finally dispersed in phosphate buffer saline (PBS) (1X, pH 7).  
Conjugation of TbPO\({}_{4}\):H\({}_{2}\)O@silica-NH\({}_{2}\) Nanomaterials with CD133 Monoclonal Antibody and PD-L1 Monoclonal Antibody (mAb)  
The TbPO\({}_{4}\):H\({}_{2}\)O@silica-NH\({}_{2}\) nanomaterial in sodium phosphate solution was gently vortexed before adding 0.5% glutaraldehyde solution in a ratio of 1:0.5 (_v/v_) and mixed for 1 h at room temperature (RT) to disperse completely. The mixture was centrifuged and washed three times with PBS solution to remove glutaraldehyde. Then, 40 \(\upmu\)g of CD133 antibodies (Thermo Fisher, Invitrogen, Carlsbad, CA, USA) was added into the 400 \(\upmu\)L glutaraldehyde pre-activated TbPO\({}_{4}\):H\({}_{2}\)O@silica-NH\({}_{2}\) and incubated at 37 \({}^{\circ}\)C for 30 min. After incubation, the suspension was centrifuged at 6000 rpm for 5 min at 4 \({}^{\circ}\)C; the supernatant was retained to determine the amount of unconjugated antibodies in the combined efficiency study. The TbPO\({}_{4}\):H\({}_{2}\)O@silica-NH\({}_{2}\)-mAb'CD133 residue after rinsing with PBS three times was continuously conjugated with mAb'PD-L1 by adding 40 \(\upmu\)g of this PD-L1 mAb at 37 \({}^{\circ}\)C for a further 30 min. After a centrifuge step at 6000 rpm for 5 min at 4 \({}^{\circ}\)C, the supernatant solution was retained to determine the conjugation efficiency. The PBS washing residue of TbPO\({}_{4}\):H\({}_{2}\)O@silica-NH\({}_{2}\)-mAb'CD133-mAb'PD-L1 (**TMC**) nanocomplex was reconstituted in PBS and stored at 4 \({}^{\circ}\)C before being used for further experiments.  
Conjugation efficiency was measured through the indirect determination of unbound IgG in the supernatant after combining mAb with nanomaterials using a NANOPHOTOMETER P300 system (IMPLEN.INC., USA). The conjugated efficiency was calculated using the following fomula:  
\[\text{CE}\%\ =\ 100\%\ -\ \frac{\text{amount IgG in supernatant solution}}{\text{amount total input IgG}}\ \times\ 100. \tag{1}\]