I-V analysis

The cornerstone of device analysis is the simple, yet very powerful current-voltage (I- V) measurement. I-V analysis of a simple Schottky diode, can provide the breakdown voltage (VB) and the leakage current (IL) when reverse biased. The forward voltage drop

(VF), ideality factor(n), Schottky Barrier Height (SBH)

¡

Φ0

B,n

¢

and specific on-resistance (Ron,sp) can all be found under forward biased conditions.

4.3.1.1 Low Power I-V analysis

The majority of the I-V measurements described within this document were performed on a simple probe station and the low power Agilent Technologies B1500A Semiconductor Device Analyser. The probe station was setup for either lateral or vertical device mea- surements with four Karl-Suss probes providing two pairs of force and sense, a setup that removes probe resistances. A conducting back plate allows connections to be made to the back of a device.

To perform a simple voltage ’sweep’, the analyser provides a known voltage across the device and measures the current being passed through it. The voltage is incremented in predetermined steps, for example, from -10 to 10 V at 20 mV steps is a very typical 1001 step sweep. The amount of current allowed to pass through the device is limited by the power rating of each Source Measuring Unit (SMU) used. The high power SMU is able to reach 20 V at 1 A or 200 V at 50 mA.

4.3 Electrical Characterisation Techniques

An example of a simple J-V plot for a heterojunction Schottky diode is presented in Fig. 4.4 to demonstrate the extraction techniques. The same data has been plotted twice, in logarithmic form, and in linear form. The logarithmic shows the very small leakage current in the reverse direction, as well as the turn on characteristics up until the point at approximately 1 V, where the current begins to become limited by the specific on-resistance. This can be seen in the linear plot where Ohms law allows for the simple extraction of the resistance.

Figure 4.4: A typical current-voltage trace for a heterojunction Schottky diode with the parameter extraction techniques indicated.

Considering the logarithmic plot, the linear turn-on characteristic displayed from ap- proximately 0.3 to 0.8 V can be used to extract Φ0

B,n and the ideality factor. The linear

region is dictated by the thermionic emission equation, rearranged here from Equation 3.12,

J =Js

¡

4.3 Electrical Characterisation Techniques

and where the saturation current, Js, is defined as,

Js=A∗∗T2e−βΦ

0

B,n. (4.2)

Js can be determined graphically from the logarithmic plot of Fig. 4.4 by extrapolating

the linear region of the plot to V = 0. This enables the extraction of Φ0

B,n from Eq. 4.2,

given that the other values are all known constants. The ideality factor can be found by rearranging Eq. 4.1 to,

ln (J) =βV /n+ ln (Js) (4.3)

which is in fact the equation for the straight line in the logarithmic plot of Fig. 4.4. There- fore the gradient of this line is equal to β/n, which then easily leads to the determination of n due toβ being a constant.

The extraction of Φ0

B,n and the ideality factor requires a reasonably high resolution I-V

sweep, so that there are sufficient data points available within the linear turn-on region. The linear fit to this data is then carried out in Microcal Origin, a piece of software designed specifically for graphing and data-analysis. It is worth pointing out that the values of Φ0

B,n and ideality factor quoted herein are estimates, and the software gives an

uncertainty value as to the accuracy of these figures. All the data used in Chapter 6 was found to be within 0.25% accuracy - for example the maximum error of Φ0

B,n was

±0.0026 eV, though this was more typically lower than±0.0015 eV. For this reason, these values are quoted in this thesis to three decimal places with a good degree of accuracy.

4.3.1.2 I-V measurements at varying temperature

The SBH found via a single I-V measurement is a very useful first indicator; however, in reality the SBH of an interface is a complex parameter that is dependent on temperature,

4.3 Electrical Characterisation Techniques

whilst the quality of the interface and the build up of imperfections can lead to local SBH fluctuations. Considering the SBH against temperature is a useful way to find out more information about the parameter, and indeed the nature of the interface.

In order to extract this information, a Tenney environmental chamber is used to step the ambient temperature up in 25o_{C intervals from -50}o_{C to 175}o_{C (225-450 K). To}

contact to the diodes from outside the chamber, the individual diodes are wire bonded to a PCB board, from which, heat proof wires are passed out of the chamber to the Agilent Technologies B1500A Semiconductor Device Analyser. The temperature was controlled and monitored in the chamber by a Watlow Series 942 temperature controller and verified using a Fluke 52 II Thermometer, the ends of which were placed on the PCB board.

-4 -2 0 2 4 1E-5 1E-3 0.1 10 1000 C u r r e n t D e n s i t y [ A / c m 2 ] Voltage [V] -75C -50C -25C 0C 25C 50C 75C 100C 125C 150C 175C Arrows denote increasing T emperature

Figure 4.5: Current-voltage curves taken at ambient chamber temperatures from -75◦_C

to 175◦_C

Figure 4.5 shows a temperature dependent I-V plot of a Schottky, heterojunction diode. The temperature is seen to have a direct effect on the plot due to the reliance on tem-

4.3 Electrical Characterisation Techniques

perature of most of a device’s key parameters. Carrier mobility drops away significantly with rising temperature because increased lattice vibrations mean that there are more scattering events. This causes the rise in resistance observed above 1 volt. Furthermore, as temperature rises, thermionic emission current will increase, and the built-in poten- tial decreases causing respectively, the variations in reverse leakage current and turn-on voltage.

Using the techniques described previously, the SBH, ideality factor and the saturation current may be extracted from each of the individual I-V plots of Figure 4.5. Though not immediately obvious, the SBH and the ideality factor both rely on temperature to a similar degree. Therefore, plotting the values against each other for a given temperature reveals a straight line. One technique suggested by Schmitsdorf et al [69] uses the extrapolation of this linearity to find an “ideal” barrier height, denoted Φη=1, at η= 1.0.

The saturation current was defined in Equation 4.2, and this may be rearranged in order to quantify the SBH independent of temperature.

ln µ JS T2 ¶ =−qφRich k 1 T + ln (A ∗∗_{). (4.4)}

Hence, plotting ln (J/T2_{) against the inverse temperature will reveal a SBH value (φ}

Rich)

on its slope and the natural log of the Richardson constant (A∗∗_{) at its Y-intercept. φ}

Rich

represents an average value of all those extracted from the I-V-T plots. This technique is known as a Richardson plot.

The techniques used to find Φη=1 and φRich will be used in Section 7.2, where we will

4.3 Electrical Characterisation Techniques

4.3.1.3 High Power I-V analysis

The Agilent Technologies B1500A Semiconductor Device Analyser, is perfect for low volt- age, high resolution testing. However, in analysing our devices we need to consider higher voltages for breakdown and leakage tests. An ideal diode would have a very high break- down voltage, up to which no reverse current would flow. In practice, the breakdown voltage can reach hundreds of volts, but there will always be at least some minute leak- age. To facilitate the higher voltages required, breakdown tests are carried out using a Tektronix 571B Curve Tracer, a facility that can be run under high current (30 V/100 A) or high voltage (3000 V/10 mA) modes. Whilst the resolution is not as high as the Agi- lent, simple I-V plots can be acquired showing the point at which the reverse current has suddenly surged, indicating breakdown.