1. Zener diodes biased in reverse (at Zener voltage like 6 to...32 V) do generate a good noise level but due to a high junction capacitance, the bandwidth extends to several MHz only.
2. A common P/N junction can generate noise in avalanche mode. I have used many RF and microwave noise generators "for free". Take a RF SMD transistor, any type, and connect its e-b diode through a ~1 kOhm resistor to a DC power supply. A typical reverse breakdown occurs at 6 to 8 V (I used a 9V battery for the power source)_ and use a variable resistor to adjust 5 to 10 mA current. I connected such e-b diode in an half-wave dipole, to make C-band and Ku-band "noise radiators". At 5...10 mA the noise bandwidth was quite flat, over 9 to 12 GHz, and the measured ENR was ~30 dB. Compared to expensive ($80) noise diodes, this is good solution.
3. If you need a higher ENR, a RF or a microwave amplifier can be added. Such "amplified" noise sources are offered e.g. by NoiseCom and other companies. I tested also a 3x3 matrix of my "noise dipoles", to achieve the >5x noise intensity on-axis, no amplifiers needed.
If you are interested, google Polivka : Microwave noise fields about my experiments.