ptical cross-talk is a critical characteristic of Silicon
Photomultipliers (SiPMs) and represents a significant source of the
excess noise factor, exerting a substantial influence on detector
performance. During the avalanche process of SiPMs, photons
generated can give rise to both internal cross-talk within the same
SiPM and external cross-talk when photons escape from one SiPM and
trigger avalanches in others. In scenarios where SiPMs are arranged
in a compact configuration and positioned facing each other, the
external cross-talk could even dominate the cross-talk
phenomenon. This paper investigates two distinct methods for
measuring external cross-talk: the counting method, which involves
operating SiPMs face-to-face and measuring their coincident signals,
and the reflection method, which employs a highly reflective film
attached to the surface of the SiPMs. External cross-talk
measurements have been conducted on several types of SiPMs,
including Vacuum Ultra-Violet (VUV) sensitive SiPMs that Fondazione
Bruno Kessler (FBK) and Hamamatsu Photonics Inc (HPK) produced for
nEXO as well as visible-sensitive SiPMs provided by FBK, HPK and
SensL Technologies Ltd (SenSL) for JUNO-TAO. The results reveal a
significant presence of external cross-talk in all tested SiPMs,
with HPK's SiPMs exhibiting a dominant external cross-talk component
due to the implementation of optical trenches that effectively
suppress internal cross-talk. Furthermore, we found that the number
of fired SPADs resulting from internal cross-talk can be described
by combining Geometric and Borel models for all tested SiPMs, while
the external cross-talk can be predicted using a pure Borel
model. These distinct probability distributions lead to different
excess noise factors, thereby impacting the detector performance in
varying ways.