# Security Implications for Ultra-Low Power Configurable SoC FPAA Embedded Systems
## 5 FPAAs for Unique Functions
MOSFET channel current (I) in saturation is a function of source (\(V_{s}\)), drain (\(V_{d}\)), and gate (\(V_{g}\)) voltages. \(\kappa\) and \(\sigma\) are the gate and drain to surface potential coupling, respectively. \(I_{th}\) is the current at threshold, \(V_{T0}\) is the threshold voltage, and U\({}_{T}\) is kT/q or the thermal voltage (25.8 mV). \(V_{T0}\) is typically a combination of a constant term due to charge and barrier differences and an nFET or pFET proportional to U\({}_{T}\). \(\kappa\) and \(\sigma\) are weak functions of temperature (e.g \(<\)200 ppm/C), and \(I_{th}\) is a weak power law between 0 and 1/2 of temperature. where \(V_{1}\) is directly a function of \(V_{fg2}\) and nearly insensitive with temperature. \(\kappa_{p}\) and \(\kappa_{n}\) and \(\sigma_{n}\) and \(\sigma_{p}\) have little change with temperature. The output is dependent on difference of threshold voltages, subtracting the temperature component, and leaving the constant mismatch terms. Even though the charge loss on a single FG device is very small, 1-100 \(\upmu\)V for 10 years, the effective charge loss on a differential FG device is significantly less, 1 \(\upmu\)V for 10 years (e.g., [46]). FG charge directly account for threshold voltage differences. The temperature in sensitive behavior is verified by similar circuits presented elsewhere [45]. Therefore we get a typical of common-source circuit topology where the gain and logical threshold is independent of temperature. The circuit SNR estimates the very low resulting bit-error rate when sensing the resulting output code. The logical threshold noise, effectively, the input referred noise on \(V_{fg1}\), is proportional to the kT/C noise calculation at \(V_{out}\). The load capacitance would be between 100 fF and 1 pF (typical) for FPAA routing, resulting in 100-200 \(\upmu\)V total RMS noise for the smallest capacitance load. The useful FG voltage variation is roughly U\({}_{T}\) for this application, resulting in greater than 40 dB SNR for this comparison. The resulting Bit Error Rate (BER) for this SNR level would be negligible (<10\({}^{-15}\)). Figure 7 shows measured output from the selected unique function circuit stimulated by a 16-bit random code followed by 16 0 values. The input modulates the shift register data values. A longer input signal is possible. The output code can be a part of the streaming output, adding additional security. Figure 8 shows measurement of this FPAA unique function circuit. The circuit operation is illustrated using a 16 bit demonstration output code with all FG currents programmed identically. The particular bias current used is chosen by the original design, and can be any subthreshold bias current level. Figure 9 shows the measurement of this particular FPAA unique function circuit programmed slight variation current variation. Once the chip is programmed, one cannot tell externally. Figure 7: Selected PUF response for an input code. (**a**) Input 32 bit code = 1011010100110000. The input code modulates the data input into the shift register; (**b**) Another response for input 32 bit code = 011010000000000. Figure 8: Circuit measurement of our unique function circuit, showing the scanned output current measurement, voltage measured output using FG pFET scanning element, and the voltage measured using an OTA element to threshold this output voltage. All of the elements were programmed to the same current (15 nA). The threshold can be chosen, programmed in the FG pFET setting the nFET current mirror. The variation of the code is due to indirect threshold voltage mismatch, mismatch typically removed in programming the FPAA device. The shift register is scanning all the values by having a 1 for the first clock cycle, and 0 for the following 15 clock cycles. Measurement sample rate was 500 Hz. Figure 5:0 Measurement of our unique function circuit with slightly different programmed currents at each FG device.