Measurement I2: Can instabilities be reduced with a stabilized filament resistance ?

In measurement I2 it was tested if a feedback loop acting on resistance changes can stabilize the evaporation rate. In an ideal case a feedback loop would stabilize the crucible temperature. But as no direct reading of the crucible temperature exists during the oven operation, the filament resistance serves as an alternative way to measure the temperature inside of the oven.

If during a change of temperature inside of the oven the crucible and the filament change their temperature at the same time, the resistance also changes. So when the feedback loop acts on a resistance change, it indirectly reacts on a temperature change inside of the oven.

During the previously presented measurements the heating power was leveled by a feedback loop that changes the current in the filament with the aim to achieve a certain heating power, as presented in section 4.1.1. This control loop was modified to instead level the filament resistance. After the change, the loop changed the current of the oven power supply until a desired resistance value, within a tolerance of 30 mΩ, was reached.

5.3. Unstable evaporation rates

During measurement I2 the oven was operated by manually changing the resistance setpoint, until a desired evaporation rate was measured. When the evaporation rate dropped during the measurement, the setpoint was manually raised, which increased the heating current until the evaporation rate recovered. The measurement was done in a similar setup to the measurement I1, with chemically clean lead and the reduced heat reflective tantalum foil inside the oven.

Results

Figure 5.24 shows the resulting evaporation rate during measurement I2.

0 100 200 300 400 500

0 2 4 6

0 10 20

t [h]

R[mgh−1 ] P[W]

Evaporation rate,R Oven power,P

Figure 5.24.:Evaporation rate and power of measurement I2, where the filament current is auto-matically adjusted to keep the filament resistance at a desired value. The oven was operated by manually changing the resistance setpoint.

At the beginning of the measurement the evaporation rate stayed almost constant at a value of 3 mg h⁻¹for more then 100 h. Then it dropped below 2 mg h⁻¹in less than 1 h.

As the evaporation rate stayed at that value it was decided to raise the resistance setpoint which led to a higher filament current and a higher power in the oven. This happened several times and in the second half the evaporation rate underwent more fluctuations than in the beginning.

Figure 5.25 shows the evaporation rate over the time of the complete measurement together with the value given by equation 5.3. Even though the resistance was controlled by the feedback loop it underwent sudden drops, that the feedback loop reacted on by raising the heating current.

It is evident that the first significant evaporation rate drops correlate with negative

0 100 200 300 400 500 0

2 4 6

0 0.2 0.4 0.6 0.8 1

t [h]

R[mgh−1] |r0 neg,norm|[a.u.]

Evaporation rate,R res. derivation,|r_neg,norm⁰ |

Figure 5.25.:Evaporation rate of the oven together with drops of the resistance during measurement I2.

changes of the oven resistance. As the feedback loop acted on these changes the filament resistance was brought back to an allowed value by raising the current in the filament and thereby the power. Figure 5.26 shows this reaction for the first drop of the evaporation rate.

The resistance suddenly decreased and when its value dropped below the allowed dif-ference of 30 mΩto the setpoint, the feedback loop reacted and raised the current in the filament. With the higher current the power increased by approximately 0.2 W. This higher power also needed to be maintained to keep the filament resistance close to the setpoint value after the drop. The evaporation rate however stayed below 2 mg h⁻¹after the drop, even when the resistance was brought back into the allowed range by the feedback loop.

Figure 5.27 depicts the resistance setpoint with its tolerance as a colored region, together with the measured resistance and the evaporation rate during a selected time window.

Only a manual increase of the resistance setpoint for the feedback loop, resulting in a significantly higher heating power, could restore an evaporation rate similar to the one before the drop.

Discussion

This behaviour again demonstrates that parts of the evaporation rate instabilities come from temperature instabilities of the oven itself. A feedback loop reacted in a desired way, changing the oven power at the right time and into the right direction when the evaporation rate dropped.

But while the loop reacted on the evaporation rate instabilities, only stabilizing the

5.3. Unstable evaporation rates

2.115 2.12 2.125

2 3

9.1 9.2

130 132 134 136 138 140

2.07 2.08 2.09

r[Ω]

R[mgh−1 ] P[W]

t [h]

I[A]

Fil. res.,r Ev. rate,R

Power,P Current,I

Figure 5.26.:Filament resistance, oven current and oven power together with the evaporation rate in the time frame of the first evaporation rate drop.

2.12 2.14 2.16 2.18

130 132 134 136 138 140 142 144 146 148 150 152 154 156 2

3

r[Ω]

t [h] R[mgh−1 ]

Fil. res.,r Ev. rate,R

Figure 5.27.:Resistance setpoint together with the measured resistance and the evaporation rate during a time window where the evaporation rate dropped. Only by manually choos-ing a new setpoint the evaporation rate could be restored.

resistance was not sufficient to keep the evaporation rate stable. This can be interpreted as such that the process in the oven, that changes the thermal distribution within it, affects the crucible stronger than the filament temperature and thereby its resistance.

It is not understood why this measurement showed more resistance changes than the measurement before (5.22 compared to 5.25). It is possible that structural changes of the oven, like aging of the heat reflective foil, or difference in the tightness of the screws holding the oven cover caused this behaviour.