The homework is composed of discussions of the capacitor - voltage relationship (C-V characteristics) in MOS capacitors. Transistors are also part of the homework. The capacitor-voltage analysis is a technique that is widely used to determine wide range parameters of MOS capacitors. These parameters involve flat-band voltage, threshold voltage, substrate doping concentration and the thickness of the gate oxides.
The MOS capacitance is characterized by its capacitance, Cox. It has two capacitors that are connected in series at the depletion layer. These two capacitors are depletion layer and oxide capacitors that is, Cdep and ...view middle of the document...
The capacitor is as a result of the area of the metal gate. The MOS capacitor capacitance is dependent on the DC voltage (Montoro, 2007, pg. 312).
The MOS capacitor with a p-type polysilicon gate is depended on the applied voltage at the gate. Unlike the metal gate, the polysilicon MOS capacitor has three operation regimes. Two voltages, VT and VFB separates the three operation regimes. See figure 1 for more description. The three regimes are accumulation, depletion and inversion. In the case of the accumulation regime, the same type carriers accumulate at the surface of the body. With depletion operation regime, the surface is occupied by the depletion layer only. In other words, the surface becomes devoid of carries.
In the third operation regime, there is an aggregate of all the opposite type carriers at the surface and, therefore, inverting the conductivity type. The flat band voltage VFB is responsible for separating the depletion regime from the accumulation regime. The threshold voltage VT demarcates the inversion regime from the depletion regime.
Cmax = Cox
CHF Cmin = Cmos(VT)
Figure 1: MOS capacitance; graph of capacitance against Gate voltage
The threshold voltage of a p-type poly-silicon gate MOS capacitance has a negative value unlike that of a metal gate. Considering a positive flat-band voltage that is lesser than the gate voltage. Negative charges are induced on the semiconductor. Take note that for a metal gate positive charges are induced. Electrons being the only negative charges they accumulate at the surface of the semiconductor. The electron accumulation process is referred to as surface accumulation (Nicollian, 2006, pg. 89).
The flat band voltage is the voltage that appears on the surface when there are no charges at the surface. At this instance and across the oxide there appears no electric field. CMOS, accumulation = Cmax = Cox = ε ox tox as the capacitance when the slope of the graph is linear at the accumulation operation regime (Montoro, 2007, pg. 67).
tox = 10 nm,
ox = 3.9 and
T = 300K
K = 1.38 * 10-23
To find the slope before the stress choose two points along the before stress curve
P1 = (0, 10-12) and P2 = (0.5, 10-8)
Slope = ΔyΔx = ΔIΔV
Slope = 10-8 - 10-120.5-0 = 1.9998 *10-8
Therefore, the slope before the stress = 1.9998 *10-8
Slope after the stress can be calculated using the same formula as that before the stress (Kapoor, 2013, pg. 37)
P1 = (0.3, 10-12) and P2 = (0.5, 10-10)
Slope = ΔyΔx = ΔIΔV
Slope = 10-10 - 10-120.5-0.3 = 4.95 * 10-10
Cox = ε ox tox = 3.9 10 = 0.93
Cox = 0.93
∆Dit = Cox2.3kT(1slope before - 1slope after)
∆Dit = 0.932.3* 1.38 * 10-23 * 300(11.9998 *10-8 - 14.95 * 10-10)
∆Dit = 1.92 * 1029 cm-2eV-1