## 4 SRAM Start-Up Behavior  
This section describes and shows the experimental PUF start-up data obtained. As explained in previous sections, cells can be powered down and started up again, as a result, they will end up at '0' or '1' logic values. This behavior depends on slight cell imbalances caused by random parameter variations originated during the manufacturing process. \begin{table}
\begin{tabular}{c c} \hline \hline
**Cell-Related Parameter** & **Value** \\ \hline Supply Voltage & 1.20 V \\ Static Noise Margin (SNM) & 448 mV \\ Read Static Noise Margin (RSNM) & 173 mV \\ Write Static Noise Margin (WSNM) & 450 mV \\ Word-line voltage Margin (WLVM) & 408 mV \\ Single-cell current consumption & 0.104 nA \\ Single-cell write energy & 4.65 fj \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cell-related parameters of interest. Preliminary experimental results showed that, as expected, each cell started up at logic '0' or logic '1' showing a spatial random pattern different in the SRAM block of different chips. It was expected because of the random nature of the start-up bias of each cell. This spatial distinctive random pattern will be further analyzed later in this section, and it is the basis for generating a unique fingerprint for each chip. After these preliminary results, the experimental start-up probability of each cell was measured. To obtain this, the shut-down and power-up process was repeated 1000 times under nominal conditions. We define the start-up at logic '1' probability (SUP\({}_{1}\)) of a cell as the ratio of times that it starts up at 1 (\(N_{1}\)) with respect to the total number of start-ups, \(N\). \[\text{SUP}_{1}=\frac{N_{1}}{N} \tag{1}\]  
In a similar way, the start-up at logic '0' probability (SUP\({}_{0}\)) can be calculated as the ratio of times that it starts up at 0 (\(N_{0}\)) with respect to \(N\). It follows that SUP\({}_{1}\) + SUP\({}_{0}\) = 1. \[\text{SUP}_{0}=\frac{N_{0}}{N}=1-\text{SUP}_{1} \tag{2}\]  
In this paper, the SUP\({}_{1}\) parameter will be primarily used. Once the probability of each cell to start up at logic '1' was measured, it was possible to represent in a histogram the relative frequency of cells as a function on SUP\({}_{1}\). These results are shown in Figure 3a. Figure 3a shows that most cells have a preferred logic value to start up. These cells are located at both ends in the horizontal axis of the graph. Note the abrupt change in relative frequency of occurrence around 0.09 and 0.91 SUP\({}_{1}\) values. Probabilities very close to 1 mean that the cell is very likely to start up at logic '1', whereas probabilities very close to 0 values mean that the cell is not likely to start up at logic '1', and thus very likely to start up at logic '0'. Figure 3: (**a**) Histogram of the relative frequency of cell as a function of the SUP\({}_{1}\) (start-up at logic ‘1’ probability) obtained from experimental data. Three different regions (A0, B, and A1) can be established. (**b**) Representation of the SUP\({}_{1}\) for each different cell in the cell matrix (256 rows \(\times\) 64 columns) as a function of its location. The matrix is split in two parts for visualization purposes only. By contrast, only a few cells show medium probability and, thus, have an undefined start-up value. These cells are located in the middle (and flat) part of the histogram in Figure 3a. This allows classifying cells into two different categories: (i) cells with a high probability of starting up at a known value (cells located in both extremes of Figure 3a, in regions A0 and A1). These cells are the most reliable from a PUF application and are a 92% of the total number of cells; and (ii) cells without a clear tendency to start up to a known value (cells located in the middle of Figure 3a, in region B). These cells are unreliable from a PUF point of view and are 8% of the total. Figure 3b shows the spatial distribution of the \(\mathrm{SUP_{1}}\) value of each cell over the entire SRAM floor plan (256 rows \(\times\) 64 columns).