Subsections

• 6.4.2.1 Studying the Angular Dependence of DNA in Relation to the Surface on the Device Characteristics
• 6.4.2.2 Studying different Models for DNA Sensing with Low Concentrated Buffers in SGFETs

6.4.2 DNA Hybridization Sensors

6.4.2.1 Studying the Angular Dependence of DNA in Relation to the Surface on the Device Characteristics

Fig. 6.6a and Fig. 6.6b sketch a DNAFET with a functionalized surface, exhibiting single DNA strands containing 12 phosphate groups. Every phosphate group possesses one elementary charge ($-1e$). Thus, the unbound single stranded DNA is charged with $-12\,e$ elementary charges (Fig. 6.6), while the hybridized DNA strand features $-24\,e$ elementary charges.

Here, the Poisson-Boltzmann model with homogenized interface conditions (see Section 6.2.3) has been applied. It allows to introduce the angular dependence of the molecule orientation in relation to the surface by its mean dipole moment. Starting with a data set from a protein data bank [2], one can calculate the overall charge and the dipole moment for a single DNA strand. Since, only the dipole moment perpendicular to the surface enters in (6.4), one hast to calculate the perpendicular dipole moment for different inclination angles of the DNA. The charge and dipole moment of the single (unbound) and the double (bound/hybridized) DNA strand can be related to average charge densities and dipole moments by introducing an average distance between the macromolecules.

Figure 6.6: a.)The unbound single-stranded DNA at the surface of the dielectric.
b.)Single-stranded DNA on the oxide surface. Two iso-surfaces for plus and minus $0.2 \frac{k_{B}T}{q \AA{}^{2}}$ are shown.

a.)	b.)

Simulations were carried out for two average distances $\lambda$ ( $10\,$nm and $15\,$nm). For each mean distance the potential profiles and output characteristics at different states were simulated. The states were: the unprepared surface, where no DNA is attached, the prepared but unbound state, where single-stranded DNA is attached to the surface, and the bound state, when the single-stranded DNA has been hybridized to double-stranded DNA. Additionally, calculations for $0^{\circ }$ (dipole moment perpendicular to the surface) and $90^{\circ }$ (dipole moment parallel to the surface) were carried out. $100\%$ binding efficency was assumed. $SiO_{2}$was chosen as dielectric. The potential at the reference electrode was setto $0.4\,\mathrm{V}$, setting the nMOS to moderate inversion as proposed by [160].

Figure 6.7: a.) Potential profile in the whole device for double-stranded DNA perpendicular to surface.
b.) Potential profile at the interface (from left to right: semiconductor, oxide, solute).

a.)	b.)

Figure 6.8: a.) Output characteristics before hybridization for a mean distance $\lambda =10nm$ and $\lambda =15nm$ without dipole moment.
b.) Output characteristics after hybridization for a mean distance $\lambda =10nm$ and $\lambda =15nm$ without dipole moment.

a.)	b.)

Figure 6.9: a.) Output characteristics after hybridization for a mean distance $\lambda =15nm$: without dipole moment, with $0^{\circ }$, and $90^{\circ }$.
b.) Potential profile from semiconductor to oxide (left to right).

a.)	b.)

Fig. 6.7a illustrates the potential profile in the BioFET including the solute. Fig. 6.7b shows the potential profile for a cut throughout the middle of the device orthogonal to the interface of the dielectric, for the unprepared state and the bound state. As can be seen, when the negatively charged DNA is attached to the interface, the potential in the channel changes. This upward shift is related to a threshold voltage decrease, and in conjunction with this, an increase in the channel resistance. Fig. 6.8a shows the influence of the DNA surface concentration on the output curves for single-stranded DNA (unbound state), while Fig. 6.8b depicts the relation of the DNA surface concentration to the output curves for double-stranded DNA (bound state). Comparing these two figures shows that for higher concentrations (smaller $\lambda$) the change in the output curves increases. The unbound state (single-stranded DNA) exhibits $-12\,e$ elementary charges, while the bound state (double-stranded DNA) possesses twice the charge, equal to $-24\,e$ elementary charges. Therefore, the bound state of double-stranded DNA features a larger negative surface charge, which results in a reduced current. This reduction is more pronounced for higher DNA concentration as demonstrated in Fig. 6.8a and Fig. 6.8b.

Fig. 6.9 illustrates the influence of the DNA orientation on the output curves of the DNAFET. It demonstrates that the orientation perpendicular to the surface ($0^{\circ }$) possesses the highest resistance in comparison to the other curves. Also the DNA orientation parallel to the surface shows an increased resistance in comparison to the curve without dipole moment. This is caused by the inhomogeniously distributed charge along the DNA strand and linked to this the non-vanishing dipole moment. For the orientation perpendicular ($0^{\circ }$) to the surface the threshold voltage shift is the most negative one, while for the orientation parallel to the surface ( $90^{\circ }$) it is almost absent as compared to the case without dipole moment.

Over several years there was a discussion, wether the orientation of the molecules attached to the surface affects sensing [229,230,231,232,233]. Indeed biomolecules exhibit an inhomogeneous charge distribution and therefore possess a dipole moment. The orientation of the biomolecule must obey the energy minimization principle and, therefore, there is an orientation that is preferred over others.

In the works [229,230,231,232,233] the change of orientation has been resolved, optical techniques to detect DNA were applied. Although extra study is needed, one should mention that for optical detection techniques it is more important to choose the linking molecule in a way that the reaction is not impeded by steric effects (receptors blocking each other) or the binding sites are obstructed or even destroyed by the crosslinker. However, in the case of DNAFETs, a field-effect as working principle is exploited. Thus it is decisive to provide a linker which is as short as possible, so that the molecule is closer to the surface. In order to increase the signal to noise ratio, the linker should have as little charge as possible.

6.4.2.2 Studying different Models for DNA Sensing with Low Concentrated Buffers in SGFETs

The experimental data of a suspend gate field-effect transistor (SGFET) have been investigated via three different modeling approaches. A SGFET is basically a standard MOSFET except it possesses an elevated gate with a hollow below it. The resulting bare gate-oxide layer is biofunctionalized with single stranded DNA, which is able to hybridize with a complementary strand in a subsequent process step. As already mentioned, caused by the intrinsic charge of the phosphate groups (minus one elementary charge per group) of the DNA, big shifts in the transfer characteristics are generated. This way, label-free, time-resolved, and in-situ detection of DNA is possible.

At first, I will take a short review on the experiment carried out by Harnois et al. [234] to build the basis for a better understanding of the behavior of the system. In their work $60$ oligo-deoxynucleotides (ODN), also known as single stranded DNA, were attached onto a glutaraldehyd coated nitride layer. Subsequently, one test run with mismatched ODNs and one test run with matching ODNs were performed. The test samples with the mismatching DNA sequences display no relevant change in the output curves, while for the matching single stranded DNA a big shift in the threshold voltage is observed. The outcome of their experimental series features two interesting properties. Firstly, they exhibit a threshold voltage shift of about $800\,\rm {mV}$ between the probe curve and the target transfer curve and, secondly, the probe transfer curve is situated in the center between the target and the reference curve. A typical threshold voltage shift lies within a range from several mV to $100\,\rm {mV}$ [235], determined by the featured buffer concentration. Therefore, the $800\rm {mV}$ shift is quite big and additionally the Poisson-Boltzmann regime shows commonly a big shift between the reference and the probe/target ( $\sim100\,\rm {mV}$), but a much smaller shift between probe and target curves ( $10-20\,\rm {mV}$) [149]^6.4.

In order to reproduce the device behavior, the Poisson-Boltzman model in combination with a space charge representing the charged DNA ($60$ base pairs probe and $120$ base pairs target), the Poisson-Boltzman model with a sheet charge describing the DNA, and the Debye-Hückel model with a corresponding space charge were investigated, trying to match the device tranfer curves.

Fig. 6.10a,b,c illustrate the transfer characteristics for the unprepared SGFET (reference), the prepared but unbound (probe), and after the DNA has bound to functionalized surface (target), respectively. The curves of the experiment are indicated by discrete grey dots. As shown by Fig. 6.10a and Fig. 6.10b, even for the very low salt concentration of $0.6\: \rm {mmol}$, the shift between the reference curve and the probe/target is bigger than between the probe and target curves.

This behavior abides with the observations by [149] and is assigned to the nonlinear screening of the used models. Studying Fig. 6.11 and Fig. 6.12 reveals that doubling the charge at the interface does not cause twice the potential shift. There is also a bigger shift for the sheet charge model due to the description of the DNA charge as sheet with infinitely small height observeable. This is the result of lesser screening compared to the space charge model which spreads the same amount of charge over $20\,\rm {nm}$.

However, it is impossible to fit the experimental data by only decreasing the salt concentration. On the other hand the Debye-Hückel model shows acceptable agreement for the same parameter set as for the Poisson-Boltzmann models (Fig. 6.10). For the Debye-Hückel model, doubling the charge is reflected in twice the potential shift (Fig. 6.13), due to the linear screening behavior of the model (6.6).

Understanding the failure of the Poisson-Boltzmann model and the success of the Debye-Hückel model demands a second look at the models and checking the validity constraints of their formulation. One can get a feeling for the problem by assuming a single $60$ bases DNA strand contained in a box of $10 \cdot 10 \cdot 20\,\rm {nm^{3}}$ at one mmol sodium-chloride bulk concentration. In this volume there will be only one sodium/chlorine ion on average. Therefore, strong nonlinear screening is extremely unlikely in such cases. The Poisson-Boltzmann model is a continuum model, which describes the salt concentration as a continuous quantity. This is the reason why it overestimates the screening and, therefore, it is not valid for small salt concentrations.

The Debye-Hückel model is derived by expanding the exponential terms into a Taylor series and neglecting all terms higher than second order [226]. Taking the laws of series expansion into account, $\frac{q \psi}{k_{\text{B}} T} \ll 1$, thus the potential has to be small compared to the thermal energy. Furthermore, treating the ions as infinite small point charges leads to a big mean distance between the ions in the solution and, in conjunction with this, to a low bulk salt concentration. However, even though only one of the constraints is fullfilled, the Debye-Hückel model is able to fit the data. One possible explanation is that in this case the extended Poisson-Boltzman model and the Debye-Hückel model coincide as shown in Section 6.3 (Fig. 6.5) and thus the screening is controlled by the average closest possible approach.

Figure 6.10: a.)Transfer characteristics of a SGFET for Poisson-Boltzmann model and DNA charge modeled via space charge density.
b.)Transfer characteristics of a SGFET for Poisson-Boltzmann model and DNA charge modeled via sheet charge density.
c.)Transfer characteristics of a SGFET for Debye-Hückel model and DNA charge modeled via space charge density.

a.)	b.)	c.)

Figure 6.11: Potential for the Poisson-Boltzmann model with space charge, starting from the semiconductor (left) and ending in the analyte (right). It can be seen that doubling the charge does not lead to twice the potential shift due to nonlinear screening.

Figure 6.12: Potential for the Poisson-Boltzmann model with sheet charge, starting from the semiconductor (left) and ending in the analyte (right). Here the shift is a bit increased but far away from the values from the measurement. However, also here doubling the charge does not lead to twice the potential shift due to nonlinear screening.

Figure 6.13: Potential for the Debye-Hückel model with space charge, starting from the semiconductor (left) and ending in the analyte (right). It can be seen that doubling the charge leads to twice the potential shift due to the weaker linear screening.

Footnotes

...Shinwari2006^6.4

Due to the strong non linear screening in the Poisson-Boltzmann regime doubling the charge does not lead to twice the potential shift.