I know this topic was inactive for some time (albeit PHA topic as whole is all the time hot).
I had an urge to reply to some comments like this:
I had never noticed this before. Too bad, getting Cameca to change this firmware behavior will require a lifetime of effort. I wonder what their reasoning was/is?
and this:
That makes perfect sense, I had forgotten about this. Increasing the gain does of course broaden the peaks (gain = multiplication), but I'd still rather have control over it myself.
How else can I show students the noise peak? 
Thankfully Cameca is not JEOL and legitimately removes the noise with hardware. More over with newer hardware the noise is removed adaptivelly - which is an improvement. That is the huge feature -- not a drawback, compared to JEOL, which leaves the background noise to PHA.
The technical reason:
Everything in PHA graph (and everything not, which is out from the right side of PHA scale (more than 5V or 5.5V)) introduce dead-time, as for background noise level pulse to be recognized as a pulse and give some digital amplitude value (so that it would be plotted on PHA graph, or that PHA filtering would work in real-time during acquisition) the electronics for deterministic set time is blocked from other incoming pulses. Not filtering out the noise from signal, and passing the raw noisy signal into PHA would produce floating (depending from electronic noise, which depends from many variables) large dead-time even at very faint X-ray intensities.
Filtering with hardware (zener diode, offset on pulsehold-trigger (actually I think a comparator) chip or DC shifting values with voltage-divider) makes electron background noise to make no impact on dead time.
Actually one can see the electronic noise if background noise deteriorates (increases in amplitude) for some reasons. I had learned this recently in the hard way as had noticed such noise started to show up in PHA at higher gain (much higher than normally set by auto) on one of spectrometer. The noise generated if passed to PHA was creating order of magnitude more counts than real X-ray counts thus very largely impacting the dead time. After comparing signals with oscilloscope I found that signal from that spectrometer is much more noisier, while ground (0V) had the same characteristics on all spectrometers (dominated with noise originating from crappy old Phillips 70A VME +5V PSU, but it does not matter as it is later filtered out with differential OPAMP). After opening spectrometer electronics cover (where preamplifier is mounted) I had noticed that one of HV bypass (3kV, 2nF) capacitors is cracked

). Nonetheless, if using "normal/auto" PHA conditions, that higher noise is completely hardware-cut-out and does not influence the measurements at all anyhow. In case of JEOL - any hardware component degeneration would dynamically increase the noise and dynamically change the dead-time of counter. So Cameca way is clever engineered and superior compared to lazy approach on Jeol probes.
BTW: to see the Argon esc peak better (for educational use i.e.; Normally it is poor idea overpush the bias, and lower bias than auto is always better idea) the Bias can be increased a bit temporary, which increase the peak/bkgd ratio in proportional counter, and separates the Ar esc peak from noise.