## 2 Device Structure and Fabrication  
Here, the static and dynamic performance of two types of devices (A and B) are studied in detail. Figure 1a,b shows conceptual cross-sectional views of the demonstrated devices A and B, respectively, with their top-illuminated structure. Note that these figures are not drawn in scale. From top to bottom, the structure of both devices are composed of a p\({}^{+}\)-In\({}_{0.53}\)Ga\({}_{0.47}\)As contact layer, p\({}^{+}\)-In\({}_{0.52}\)Al\({}_{0.48}\)As window layer, graded/intrinsic In\({}_{0.53}\)Ga\({}_{0.47}\)As absorbing layer, two p-type In\({}_{0.52}\)Al\({}_{0.48}\)As charge layers, and N\({}^{+}\) In\({}_{0.52}\)Al\({}_{0.48}\)As/InP contact layers. For more detail about the epi-layer structure and the working principles of the demonstrated APDs (Device A), the interested reader can refer to our previous work [11]. Two In\({}_{0.52}\)Al\({}_{x}\)Ga\({}_{0.48-x}\)As graded bandgap layers are inserted at the interfaces between the absorber/window and absorber/multiplication layers. The thickness of each epi-layer is specified in detail in this figure.  
The electric field distribution within the device was simulated using the Silvaco Technology Computer Aided Design (TCAD) tools (Semtech; 200 Flynn Road, Camarillo, CA 93012. Product: GN1085). Figure 2a shows the calculated electric fields for Device B along the vertical direction at the punch-through (V\({}_{\rm pt}\)) and breakdown voltage (V\({}_{\rm br}\)). To obtain a stepped electric field profile for fabricated ADPs, the thick multiplication (M-) layer is divided into two partitions (148 nm divided into 60, 88 nm for Device A and 500 nm divided into 200 and 300 nm for Device B) with an additional charge control layer [12]. APDs with dual M-layer are introduce stepped electric field profile, where the electrons will be energized by the first M-layer (from the top). However, the strength of the electric field is insufficient to trigger significant impact ionization, they transit to the second M-layer to initiate successive impact ionization. This design provides better localization of impact ionization than can be achieved in a uniformly thick M-layer, therefore it can reduce the delay time induced by the avalanche process in the APD.  
Figure 1: Conceptual cross-sectional views of the demonstrated (**a**) Device A and (**b**) Device B. The radius of the active mesa is 12.5 and 120 \(\upmu\)m, as specified in the figures.  
Moreover, the stepped E-field may also reduce excess noise (k-factor) for the APD. Due to cascade avalanche process, a smaller avalanche delay time and an ultra-high GBP, compared to those of the traditional APD design can be expected. Similar working principles are realized for the impact-ionization-engineered (I\({}_{2}\)E) APD structures [13; 14], where the impact ionization process in the materials is localized with the narrowest bandgap in the M-layer, forming a hetero-junction with several different bandgap materials. In contrast to the I\({}_{2}\)E structure, our M-layer acts as a homo-junction, but with several charge layers and different doping densities to localize the avalanche process in the region which has the highest E-field. As can be seen in Figure 1a,b, the same triple mesa structure is adopted for both devices A and B, confining the E-field within the first mesa (active region) diameter of 25 \(\upmu\)m and 240 \(\upmu\)m, respectively. The first mesa is etched through the upper charge layer (field-control) and p-type window layer and stops at the 60 nm In\({}_{0.52}\)Al\({}_{0.48}\)As buffer layer and 2 \(\upmu\)m thick In\({}_{0.53}\)Ga\({}_{0.47}\)As absorption layer in devices A and B, respectively. For detailed E-field distributions for our device structure please refer to our previous work [12]. Figure 2b,c shows top-views of the fabricated devices with 25 \(\upmu\)m and 240 \(\upmu\)m mesa active diameters and corresponding optical windows of 12 \(\upmu\)m and 200 \(\upmu\)m for devices A and B.