Photomultiplier Dark Current, Gain & Lifetime Measurements

Photomultiplier Characteristics

What is dark current?

The dark current is a small amount of current flowing in the photomultiplier even when it is not illuminated. This current should be minimized for accurate measurements. The region between 800 V and 1300 V is often ideal for operating the photomultiplier.

The primary source of dark current is the thermionic emission rate from the photocathode and dynodes. Other sources include:

• Leakage current
• Incandescent lighting phenomena
• Field emission
• Current from residual gas ionization
• Radioactive contamination within the device materials

What is the photomultiplier gain?

The gain (G) of a photomultiplier is the ratio between the number of electrons at the output and the number of photons incident on the photocathode. It can be expressed experimentally as:

G = K • V^an

Where V is the applied voltage, and K, a, and n are constants determined experimentally by measuring the amplified output intensity versus the applied voltage.

Understanding Experimental Results and Graphs

Small differences between theoretical calculations and experimental values may arise primarily from the accuracy of measurements at the photomultiplier output. At low potential differences between the photocathode and the anode, the measured signal can be obscured by the dark current (i.e., current due to thermionic noise).

Results obtained for a constant brightness level are often plotted (e.g., Fig a), clearly showing the dependence of the gain on the applied voltage to the photomultiplier.

A separate plot (e.g., Fig b) typically shows the dark current. Its shape also depends on the potential. Even at the highest applied voltages, the dark current behavior can relate to the gain expression. When virtually no photons are incident on the photocathode, the gain equation effectively decomposes into a sum of terms corresponding to each dynode stage, each showing a potential dependence on the applied voltage.

Up-Conversion (IR to UV Energy Conversion)

How is the average lifetime measured?

The lifetime of an energy level is defined as the time it takes for the population of this level to decrease by a factor of e (Euler's number, approximately 2.718).

The decay can often be modeled by the equation:

V(t) = A • e^{(-t / τ)}

Where V(t) is the signal intensity at time t, A is the initial intensity, and τ is the lifetime.

To measure the lifetime (often referred to as half-life in experimental contexts, though technically distinct), the following procedure can be used:

1. Excite a laser-doped glass sample using a laser.
2. Use a lens and collimator to focus the laser beam into a chopper (with controlled frequency) to modulate the excitation, allowing for both excitation and de-excitation cycles of the sample.
3. Place a lens after the chopper to focus the modulated beam onto the sample, transferring energy to electrons and promoting them to an excited state.
4. The sample will then emit light, with characteristics dependent on the concentrations of the lanthanides it contains.
5. Position a monochromator to select a specific emission wavelength (e.g., 830 nm). Adjust the entrance and exit slits of the monochromator.
6. Place a photomultiplier after the exit slit of the monochromator to detect the selected emission.
7. Collect the signal using an oscilloscope.
8. Send the data to a computer for graphical analysis using software like Origin.
9. Determine the lifetime by fitting the decay curve to an exponential function.

Photoluminescence and Harmonics

What are harmonics and how can they be avoided?

Monochromators are typically black inside to absorb stray light. Any unwanted light entering the instrument should not reach the diffraction grating or should be rapidly attenuated by the inner walls. If not suppressed, this stray light could pass through the exit slit, leading to false signals in the measurement.

Another critical consideration when making measurements at a specific wavelength (λ) is the potential presence of harmonics. These are wavelengths that satisfy the diffraction grating equation for different diffraction orders (m) at the same angle:

d (sin(α) + sin(β)) = mλ

This means that light at wavelengths λ/2 (second harmonic, m=2), λ/3 (third harmonic, m=3), etc., can exit the monochromator along with the desired wavelength λ (fundamental, m=1).

For example, if the monochromator is set to output 900 nm, the signal might also contain second-harmonic radiation at 450 nm (which is weaker but must be considered) and third-harmonic radiation at 300 nm (which is typically even weaker). Higher-order harmonics (λ/4, λ/5, etc.) usually have negligible intensity.

To eliminate these unwanted harmonics, an appropriate optical filter (e.g., a long-pass filter that transmits wavelengths longer than a certain cutoff) is placed in the beam path (often before or after the monochromator) to selectively pass the desired wavelength while blocking the shorter-wavelength harmonics.