An empirical study of dynamic properties of an individual carbon nanotube electron source system

In this paper we present an empirical study of some dynamic properties of an individual carbon nanotube (CNT) field emission electron source system. We propose a circuit model that represents the CNT cathode to anode diode as a capacitor in parallel with a voltage-controlled variable resistor. The transient response of the CNT electron source system to the falling edge of a voltage step input was evaluated. For input voltages below the threshold voltage for field emission, the nanotube loop is effectively open and the circuit response is consistent with a discharging capacitor. On the other hand, for input voltages above field emission threshold, the nanotube loop conducts and now the capacitor discharges to a certain extent through the nanotube loop as well. Field emission current versus voltage data also shows that the resistance across the CNT cathode to anode diode varies as a function of applied voltage. Below turn-on voltage, the diode behaves as an open circuit (4 TΩ at the ammeter noise floor). Above turn-on voltage, resistance falls exponentially, as expected from the Fowler–Nordheim equation for cold field emission current. Experimental current–voltage data is presented for a simple emitter array consisting of two CNTs with equal lengths. Despite the similarity in their lengths the turn-on voltages of the nanotubes varied significantly, viz. 26 V versus 109 V. This large difference in the turn-on voltages can be attributed to tip imperfections. For advanced array applications such as high-throughput parallel e-beam lithography, in which precise dose control is necessary, the diode circuit model will be useful for controlling individually addressed nanotubes to account for dissimilar field emission properties. The model may also be applied to optimize the design of a SEM incorporating a single CNT electron source.