Insulator capacitance

To understand the electrical behaviour of the LAPS-based measurement, the LAPS set-up can be represented by an electrical equivalent circuit (see Fig. 5.2). Vbias represents the voltage source to apply the dc voltage to the LAPS structure. Re is a simple presentation of the reference electrode and the electrolyte resistance followed by a interface capacitance Cinterface (this complex capacitance can be further simulated by different proposed models as they are described, e.g., in Refs. [2,21,22]). In series to the interface capacitance, the insulator capacitance Cj will summarise the capacitances of all insulating layers of the LAPS device. The electrical current due to the photogeneration of electron-hole pairs can be modelled as current source Ip in parallel to the... 

Fig. 1.9. Variation of the potential drop at the insulator-semiconductor interface as a function of gate voltage for two values of the insulator capacitance.

The variation of the interface potential as a function of gate voltage is shown in Fig. 1.9. The value of the gate voltage is calculated for two values of the insulator capacitance, 10 and 100 nF cm-2. In most practical cases the actual value lies between these numbers, so it can be stated that Vs can be neglected in Eq. (11). 

Fig. 1.10. Calculated ratio of the charge in the first u total charge in the conducting channel as a function of gaTe voltage multiplied by insulator capacitance. The ratio is calculated for two-layer and ten-layer thin films.

The drain current Id is proportional to the charge-carrier mobility the transistor dimensions, where W and L are the channel width and length respectively, the applied voltage, where Vgs and VT are the gate-source and threshold voltage, and the insulator capacitance Cj (Eq. 1). Thus, the impact of the dielectric material on transistor performance is given by the dielectric capacitance which results from a geometrical quotient of area A and distance d (distance is the film thickness of the dielectric layer) and a material factor where s0 and er are the dielectric constant in a vacuum and of the material, respectively (Eq. 2). As consequences of these correla-... 

C insulator capacitance per unit area L channel length Vq gate voltage Vf threshold voltage Vj) drain voltage... 

Table 6.3. Device performance, structure, and test parameter table for IEEE 1620 compliance, adapted from [114], Fig. 4. At least two of the specific gate insulator capacitance, relative dielectric constant, and gate dielectric thickness are required. Reprinted with permission from IEEE Standard 1620-2004, IEEE Standard for Test Methods for the Characterization of Organic Transistors and Materials, Copyright 2004 by IEEE.

Figure 8.12a and b shows the frequency dispersion in the C-V characteristics of MOS capacitor structure after series resistance correction. The frequency dispersion at accumulation is mainly due to the presence of interface traps at the semiconductor insulator contact region. The capacitance of such a layer acts in series with the insulator capacitance causing frequency dispersion. However, negligible frequency dispersion is observed in the inversion region. 

The complete ac equivalent circuit of an EIS is complex, as it involves components such as the bulk resistance and space-charge capacitance of the semiconductor, the capacitance of the gate insulator, the interface impedance at the insulator-electrolyte interface, the double-layer capacitance, the resistance of the bulk electrolyte solution and the impedance of the reference electrode [58-60]. However, considering usual values of insulator thickness ( 30-100 nm), the ionic strength of the electrolyte solution (>10 -10 M) and low frequencies (<1000 Hz), the equivalent circuit of an EIS structure can be simplified as a series connection of insulator capacitance and space-charge capacitance for the semiconductor, which is similar to the MIS capacitor [58-60]. Therefore, the capacitance of the EIS structure may be expressed in terms of the electrolyte solution/ insulator interface potential (cp) as ... 

Figure 4.3.4. A plot of (CJCf - 1 for n-type Si/SOj EIS, where C, is the insulator capacitance derived from high-frequency data and C is the total capacitance of the system. The oxide thickness is 94 nm and pH = 2.5. The values of the doping density Nd and the flat-band potential Ep calculated from the linear portion of the curve are 2.2 x 10 /m and -0.06 V, respectively (Diot et al. [1985]).

The insulator capacitance can be determined as described above. Thus, at any given reference potential the surface conductance Gp can be determined as a function of frequency. An example for typical results (Diot et al. [1985]) of a Si-SiOa-elec-trolyte EIS is shown in Figure 4.3.6. Alternatively, Gp (0 can be calculated as the reference potential is swept and then converted to the representation in Figure 4.3.6. 

As a measure for the achievable working frequency one can use the cut-off frequency /t = m/(2 rCGs) as the frequency at which the current gain becomes unity. The maximum value is determined by the transconductance = dlo/dVos vj,5 of the transistor, and the gate-source capacitance Cqs, which is larger than the insulator capacitance due to parasitic capacitances, i.e., Cqs > One obtains... 

Electrical characterisation of the MIS device is restricted to measurement of the conq )lex impedance the equivalent circuit is shown in figure 23, and can be considered as a series circuit of the insulator (capacitance Q) and the semiconductor (capacitance Cs and conductance Gs). Where Gs is low, we have... 

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