In this Maxim appnote the avalanche noise of a zener diode is amplified by two cascaded LNAs (Low-Noise Amplifiers):
You can guess what my question is: why use low-noise amplifiers if you want noise in the first place? Don't ordinary opamps produce white noise?
Most noise in opamps, like thermal noise and Schottky noise ("shot" noise) is white, i.e. has a flat spectrum, but for instance flicker noise (aka 1/f noise) isn't. The MAX2650 will have lower noise overall, both white and colored.
But even if the overall noise is close to white there may be other reasons not to choose an opamp, and they are not always technical.
Application notes by manufacturers are not just to offer the customer a service. They're also/mainly a promotion vehicle, to place the manufacturer's products in the spotlights. Maybe the marketing guys at Maxim thought that the MAX2650 didn't get enough attention.
This TI document tells you more about noise in opamps.
There's no guarantee that there is a totally good answer. It's a "design idea" and it appears it may have been based on a magazine circuit idea. The reasoning of the designer is not guaranteed to be holy writ
The object is to use a noise source that as much as possible provides truly random noise. He notes that
An op amp will not have avalanche noise as a dominant noise source.
His figure 2 (copied below) further makes the point.
Arguably the best result is given with all power off, but the amplitude is 46 dB+ lower than the final result, and the source is ill defined (at best).
The op-amp only curve is as flat overall as the final result (but with opposite slope) but has far more variation at selected points and some very major excursions (5 or so spikes of 15 dB+, many more of 5 dB+ and a large degree of general variability. Hardly an indication of a genuine white noise source.
The final curve is much closer to flat overall, apart from a generally falling magnitude with frequency which could be easily compensated for. Notably there are a number of minor peaks (2 to 5 dB range) at a number of frequencies which correspond exactly to major peaks in the op amp only response. This indicates that they are attributes of the basic system and not of the zener source and that it is the noise output shortcomings of the basic amplifier that are limiting the overall performance - a good indicator that low noise devices are justified.
That said, the pronounced spike at about 1.3 divisions from 1 MHz, giving about a 20 dB spike in the op-amp only plot and a 10 dB spike in the final plot suggests an external noise source of some magnitude. Frequency is about 1.3/4 = 0.325 of the way fro 1 to 10 MHz on a log scale ~~~= 2.1 MHZ. This may be an IF frequency in the testgear (1.6 MHz ?). Similarly the high magnitude narrow range spikes in the 20 Mhz - 80 MHz op-amp only range suggest measuring system or op-amp spurious responses.
Interestingly, the sudden change in the op-amp only response in the 80 - 100 MHz range with few noise spikes and wide general variability is not reflected to anywhere the same extent in the final output.
Overall it seems that the op-amp noise is a major factor in the non ideality of the final result. If the observed "errors" in the op amp response were subtracted from the final result a far superior noise source would be produced. As this is true with low noise op amps it seems likely that higher noise devices would have produced an even worse result.
they could have used any op amp to do the job. The diode's genereated noise is so high entering the first op amp (~40dB above thermal noise) that the "signal" (here, the desired noise)-to-noise ratio is already firmly established, and no op amp choice is going to change or color it.