P(VDF/TrFE) Capacitor

The first structure to study was the simplest to make, a simple capacitor structure.

Circular electrodes of diameter 200 µm were deposited using a shadow mask onto the P(VDF/TrFE) and no etching was performed. With this structure it was only possi-ble to estimate the change of the electron sheet concentration in the 2DEG with C-V measurements.

C-V curves

C-V curves were performed to ensure that there was retention of the DC gate voltage applied, indicating ferroelectric characteristics and depletion of electrons in the 2DEG.

When ferroelectric switching is observed the C-V curve is in the counterclockwise direc-tion, however if the mechanism behind the switching is due to charge injecdirec-tion, clockwise C-V curves should be observed. Henceforth this is a very simple technique used in order to determine the role of the ferroelectric layer on the 2DEG located in the AlGaN.

140 CHAPTER 7. FERROELECTRIC GATE OPERATION

The total capacitance of the structure can be estimated by using the following equation 7.1 and calculating the total capacitance for two capacitors in series. Where one layer is AlGaN and the other is P(VDF/TrFE), table 7.6 has been used to better visualise this.

The final value of the capacitance per area is independent on the area of the capacitor studied, C/A=4.17x10^{−4 F}/m².

C = _oA

d (7.1)

Table 7.4: Summary of parameters to calculate the capacitance/area of the 250 nm P(VDF/TrFE)/20 nm AlGaN structure

o 8.85x10^{−12 C2}/Nm²

_Al0.3Ga0.7N 10.2

P(VDF/TrFE)(70:30) 13 dAl0.3Ga0.7N 20 nm dP(VDF/TrFE)(70:30) 250 nm

Area_Capacitor 2x10⁻⁸m² CAl0.3Ga0.7N 8.85x10⁻¹¹F CP(VDF/TrFE)(70:30) 9.20x10⁻¹²F CTotalCapacitor 8.34x10⁻¹²F

C/A 417^µF/m²

(a) (b)

Figure 7.13: C-V curve of a spin casted 250 nmP(VDF/TrFE) with a 100 nm Cr top electrode. Per-formed with 0.05 V_AC and 0.5 s application of the DC voltage a) at 10 kHz for a DC bias from 0 V to −15 V, and b) at 1 MHz for a DC voltage from 0 V to −40 V.

Top electrodes of 100 nm Cr, with circular shape, diameter 200 µm, were deposited by sputtering and a bottom electrode of indium was used. No structure was etched into the P(VDF/TrFE) or the AlGaN. These experiments were preliminary in helping us understand that the P(VDF/TrFE) did exhibit ferroelectric properties and it was possible to measure this ferroelectricity when it was deposited onto AlGaN.

C-V measurements were done at a frequency range of 1 kHz to 1 MHz, all of which had curves that showed hysteretic behavior. Shown in figure 7.13 are two extremes, in figure

7.4. P(VDF/TRFE) GATE 141

Table 7.5: Summary of the ferroelectric memory window, ∆V1 and ∆V2, observed in the capaci-tance/area vs voltage curves of the 250 nm P(VDF/TrFE)/20 nm AlGaN structure

∆V₁ ∆V₂ Frequency V_DC T_DC V_AC

7.13a is the measurement done at 1 kHz to −15 V and in figure 7.13b is the measurement done at 1 MHz to −40 V. Table 7.5, summarises a larger series of C-V measurements performed on the same sample and allows to observe the change of the memory window,

∆V₁ and ∆V₂, with the measurement parameters. ∆V₁ is the measured as the FWHM of the first CV curve done, that is for the first cycle from 0 V to −V_DC and ∆V₂ is measured as the FWHM for the second curve done after the first cycling without any delay. It is expected that for the first cycle it should take a larger negative DC bias for depleting the 2DEG than for the second curve. Ideally, the 2DEG should stay depleted until a positive DC bias is applied, but a reduction in its memory window is also a sign of retention of the depletion state. From here it can be noted that the memory window is biggest when using a large DC bias, a DC bias applied for a long time, small AC frequency and small AC modulation voltage.

The retention of this structure is not expected to be long term due to the fact that the second consecutive hysteresis loop has a finite memory window of ∆V2 where the capacitance after the first loop returns to the original value. Since no positive bias was applied, it should be expected that the 2DEG should remain in the depleted state but this is not the case. The C-V curve that exhibited the best retention was performed at 10 kHz with −40 V and had memory windows of ∆V₁=9.05 V and ∆V₂=1.5 V.

Sheet Concentration from C-V curves

Using the estimation for the electron sheet concentration introduced in section 2.1.2, equation 7.2, it was possible to estimate the change of the sheet concentration due to the poling voltage for the C-V curves presented above in section 7.4.1. This method is for the approximation that the AlGaN layer is an ideal dielectric with a huge Schottky barrier between it and the ferroelectric layer. Mechanisms such as charge injection, and charge trapping are ignored in this approximation

n_s= C_gV_gt

Aq (7.2)

To determine the most accurate sheet concentration one can only consider the measure-ments at low AC frequency. The variation of sheet concentration with AC frequency is

142 CHAPTER 7. FERROELECTRIC GATE OPERATION

Table 7.6: Summary of parameters to calculate the depleted electron sheet concentration of the 2DEG in the P(VDF/TrFE)/AlGaN structure from C-V curves.

Frequency DC field DC bias n_s [kHz] [kV/cm] [V] [electrons/cm²]

visible in table 7.6 where the sheet concentration decreases with increasing AC frequency.

It is therefore decided to be most reliable to only determine the sheet concentration for C-V curves done with an AC frequency of 10 kHz. This is due to the fact that the capac-itance or dielectric constant of a material is frequency dependent. Also these calculations were compared with transport measurements done when poling the ferroelectric and de-pleting the 2DEG. It was determined from those transport measurements that it was not possible to deplete the sheet concentration to as low as 2x1012 electrons/cm², especially keeping in mind that the electron sheet concentration should not variate more than 5%

in an AlGaN heterostructure. The calculation for the electron sheet concentration using the C-V curve should rather be used to demonstrate the effect of depletion and not for precise electron sheet concentration calculations.