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"""
Calculate electron drift speed and relate it to transistor switching (tick) rate for a modern GPU.
Assume: We want to simulate 900 quintillion (9e20) transistor switches per second (B200 scale).
"""
# Physical constants
ELEM_CHARGE = 1.602e-19 # Coulombs
ELECTRON_MASS = 9.109e-31 # kg
VACUUM_PERMITTIVITY = 8.854e-12 # F/m
SILICON_MOBILITY = 0.14 # m^2/(V·s) (typical for electrons in Si at room temp)
# Example parameters (can be tuned for realism)
VOLTAGE = 0.7 # V (typical for advanced nodes)
CHANNEL_LENGTH = 5e-9 # 5 nm process
ELECTRIC_FIELD = VOLTAGE / CHANNEL_LENGTH # V/m
SPEED_OF_LIGHT_VACUUM = 3e8 # m/s
SILICON_REFRACTIVE_INDEX = 3.5
speed_of_light_silicon = SPEED_OF_LIGHT_VACUUM / SILICON_REFRACTIVE_INDEX
# Calculate drift velocity (v = μE)
drift_velocity = speed_of_light_silicon # m/s
# Calculate time for electron to cross channel (t = L / v)
transit_time = CHANNEL_LENGTH / drift_velocity # seconds
# Calculate max theoretical switching frequency (f = 1 / t)
max_switch_freq = 1 / transit_time # Hz
# For 900 quintillion switches/sec, but with 600 billion transistors
TARGET_SWITCHES_PER_SEC = 9e20
TRANSISTORS_ON_CHIP = 6e11 # 600 billion
transistors_needed = TARGET_SWITCHES_PER_SEC / max_switch_freq
required_switch_freq_per_transistor = TARGET_SWITCHES_PER_SEC / TRANSISTORS_ON_CHIP
# Speed of light in silicon (approx 2/3 c)
# --- NAND Flash Floating Gate Transistor Model ---
class FloatingGateTransistor:
def __init__(self, channel_length, drift_velocity):
self.channel_length = channel_length
self.drift_velocity = drift_velocity
self.trapped_electrons = 0 # Number of electrons trapped
self.state = 0 # 0 or 1, representing data
def program(self, electrons):
self.trapped_electrons += electrons
self.state = 1 if self.trapped_electrons > 0 else 0
prog_time = self.channel_length / self.drift_velocity
return prog_time
def erase(self):
self.trapped_electrons = 0
self.state = 0
erase_time = self.channel_length / self.drift_velocity
return erase_time
def read(self):
return self.state
if __name__ == "__main__":
print(f"Electron drift velocity: {drift_velocity:.2e} m/s")
print(f"Channel transit time: {transit_time:.2e} s")
print(f"Max transistor switching frequency: {max_switch_freq:.2e} Hz")
print(f"To achieve {TARGET_SWITCHES_PER_SEC:.1e} switches/sec:")
print(f"- You'd need {transistors_needed:.2e} transistors switching at max speed in parallel.")
print(f"- For a chip with 600B transistors, each must switch at {required_switch_freq_per_transistor:.2e} Hz.")
print(f"- Electron drift speed: {drift_velocity:.2e} m/s vs. speed of light in silicon: {speed_of_light_silicon:.2e} m/s")
print(f"- Electron drift is ~{(drift_velocity/speed_of_light_silicon)*100:.2f}% the speed of light in silicon (photon speed).")
# NAND Flash Floating Gate Transistor Demo
print("\n--- NAND Flash Floating Gate Transistor Demo ---")
fgt = FloatingGateTransistor(CHANNEL_LENGTH, drift_velocity)
electrons_to_trap = 1000
# Real-time trapping analysis (simulated)
print("\nSimulating electron trapping in real time:")
electrons_per_step = 100
total_steps = electrons_to_trap // electrons_per_step
for step in range(1, total_steps + 1):
prog_time = fgt.program(electrons_per_step)
print(f"Step {step}: Trapped electrons = {fgt.trapped_electrons}, State = {fgt.read()}, Time for this step = {prog_time:.2e} s")
# Final state after all electrons trapped
print(f"Final: Trapped electrons = {fgt.trapped_electrons}, State = {fgt.read()}")
erase_time = fgt.erase()
print(f"Erasing: State = {fgt.read()}, Time = {erase_time:.2e} s")
print(f"(Operation speed is limited by electron drift velocity: {drift_velocity:.2e} m/s)")
print("Higher drift velocity = faster programming/erasing; lower drift velocity = slower data ops.")
# --- SR, D, JK, T Flip-Flop Physics/Timing Summary ---
print("\n--- Flip-Flop Types and Switching Physics ---")
print("SR Flip-Flop: Set-Reset, basic memory, built from NAND/NOR gates.")
print("D Flip-Flop: Data/Delay, synchronizes input to clock, used in registers.")
print("JK Flip-Flop: Universal, toggles or sets/resets based on inputs.")
print("T Flip-Flop: Toggle, divides clock, used in counters.")
print("All flip-flops are built from logic gates, so their switching speed is limited by the gate delay (set by electron drift and channel length).\n")
# Example: Calculate flip-flop switching time (assuming 4 gate delays per flip-flop)
GATE_DELAY = transit_time # seconds, from above
FF_GATE_COUNT = 4 # typical for basic flip-flop
flip_flop_delay = FF_GATE_COUNT * GATE_DELAY
flip_flop_max_freq = 1 / flip_flop_delay
print(f"Estimated flip-flop delay: {flip_flop_delay:.2e} s (for {FF_GATE_COUNT} gates)")
print(f"Max flip-flop switching frequency: {flip_flop_max_freq:.2e} Hz")
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