Overview
This experiment requires an accurate measure of the current versus voltage curve for a tunneling diode. In particular, the derivatives of the I-V characteristic reveal the energy of emitted phonons, due to the dramatic increase in conductivity when the applied voltage equals the energy of the phonon.
To measure the I-V characteristic as well as the derivatives, a programmable, a DC voltage is varied across the entire operating range of the diode, which is added to a constant amplitude AC signal. The diode is attached to a current pre-amp which converts the input current to a voltage, allowing measurement with a DC voltmeter. To measure the derivatives, the fluctuations in current due to the superimposed AC signal are measured with a lock-in amplifier. Furthermore, the second derivative is proportional to the voltage of the second harmonic frequency of the reference which can be measured by the lock-in amplifier.
Circuit Details
The circuit shown above is a summing, negating amplifier which adds the DC voltage and reference voltage with separate gains. A programmable HP E3631A was used for the DC voltage source, with a 0 to 6.1 volt full operating range. This defined a suitable gain ( G = 97 / 9.4k) for the DC signal, so the output voltage varied across the diode's operating range (0-60mV). The diode is placed in forward bias, accommodating a negative output from the op-amp. The AC signal is the reference signal of the lock-in amplifier, set to 1kHz and 50mV amplitude. An AC gain is employed to reduce the amplitude to around 1mV, which is the smallest signal for which accurate measurements could be made.
The entire circuit enclosed in an aluminum box to shield against noise. The box contains 5 BNC connectors for DC input, AC input, +15V, -15V, and Vout (as specified in the diagram above). The diode was placed in a separate aluminum box for the room temperature data. It was dipped in a glass lined dewer for the liquid nitrogen data. For the liquid helium run, a hollow, 5/16" diameter by 1.4m, stainless steel tube was used to dip the diode into a storage container. The tube was stuffed with cotton at four places to avoid oscillations in the liquid level.
Measurements
The voltage across the diode (Vd) is measured with a Philips PM2525 multimeter in DC mode at the output of the op-amp. A Stanford Research SR570 current pre-amp is connected in series with the diode, and it's input is assumed to be ground even though the pre-amp specifications estimate an input impedance of 1ohm. While this assumption introduces errors in the current measurement, it is a non-trivial task to correct since one cannot add a resistor in series with the diode while preserving the constant amplitude of the AC signal. The current pre-amp's output is measured with a DC voltmeter and scaled according to the sensitivity setting of the pre-amp (given in A/V) to give the current passing through the diode.
