The analog noise produced by semiconductor junctions is thought to be the fundamentally unpredictable sum of astronomical numbers of independent quantum actions. The unpredictability part of this makes noise attractive for cryptography. Alas, real noise often exhibits measurable and predictable correlations which contradict the simple model.

Ordinary semiconductor junctions are not intended for noise
production.
If anything, most electronic devices are designed for *minimum*
noise, not maximum.
As a result, the noise produced by these devices is rarely under
manufacturing control.
Noise amounts vary widely, even between devices of exactly the same
type.

The measured values are the readings observed on an ancient analog RMS voltmeter based on dBm(600). The observed reading is the signal after 61.0dB of amplification, with a filter-enforced bandwidth of 21,355Hz. A measurement is made at each of 6 different device currrents, and with the junction voltage also recorded.

**RMS.**
Root-Mean-Squared.
For a sampled signal, the square root of the sum of the squares of
each sample.
For a sampled voltage signal, an RMS value is proportional to power,
and noise is measured as power.

**dB.**
Decibel.
A measure of power ratios.
10 times the base-10 logarithm of the ratio of two power values.
Equivalently, for a fixed common resistance value, 20 times the
base-10 logarithm of the ratio of two voltage values.

**dBm(600).**
A common if older reference base for power: 1 milliwatt (1mW) into
600 ohms.

Since P=E*E/R, E=SQRT(PR).The 0dBm voltage across 600 ohms is SQRT(0.001*600)= SQRT(0.6)= 0.775 volts or 775mv (millivolts).

An interesting and useful fact is that 20dB represents a factor of 10 in voltage. So -60dBm =775uv (microvolts) and -120dBm =775nv (nanovolts). The signal levels we are dealing with here are in the very low microvolt range, or lower.

**Preamps.**
The tiny noise signal is amplified by 61.0dB.
Thus, a signal read as -53.5dBm actually represents a -114.5dBm
input.
-114.5dBm is a voltage ratio of 10**(114.5/20) = 10**5.725 or 530,884
below the base of 0.775v, or about 1.46uV.

**Noise Density.**
The amount of energy expected in a bandwidth of 1Hz.
At the most general level, we model white noise as flat distribution
of energy across frequency.
The more bandwidth we have, the more energy we expect.
Noise energy should accumulate as the square root of bandwidth.
Here our bandwidth is 21,355Hz, a factor of 146 above 1Hz, so a
reading of 1.46uV is a noise density of about 10nV/SQRT(Hz).
So for measuring -114.5dBm, we want our noise preamp to have an
input noise of 2.5nV/SQRT(Hz) or less.

Each device was measured at 6 different currents, NONE and from 1uA to 10mA. At each current, the dBm(600) output signal was read and recorded, along with the DC junction voltage. Due to preamplification, the absolute signal level is 61.0dB lower than the recorded value.

400mW and +/-10 percent voltage tolerance, except suffix A for +/-5 percent.

NONE 1uA 10uA 100uA 1mA 10mA1N749-53.2 -53.5 -53.2 -55.2 -60.3 -63.0 (4.3V @ 20mA) ----- 1.31V 1.70V 2.20V 2.84V 3.62V1N751A-53.1 -53.3 -50.6 -42.5 -43.3 -50.2 (5.1V @ 20mA) ----- 2.26V 3.81V 4.45V 4.63V 4.70V1N753-53.0 -53.4 -49.2 -37.4 -37.2 -47.9 (6.2V @ 20mA) ----- 2.22V 5.07V 5.73V 5.82V 5.86V

1.0W and +/-10 percent voltage tolerance, except suffix A for +/-5 percent.

NONE 1uA 10uA 100uA 1mA 10mA1N4728A-54.0 -54.0 -54.4 -57.4 -61.9 -64.4 (3.3V @ 76mA) ----- 0.70V 0.91V 1.24V 1.68V 2.28V1N4730A-51.0 -45.0 -39.3 -40.3 -48.8 -57.4 (3.9V @ 64mA) ----- 0.93V 1.25V 1.68V 2.21V 2.90V1N4732-54.6 -54.8 -53.6 -53.5 -55.7 -58.5 (4.7V @ 53mA) ----- 1.85V 2.54V 3.19V 3.85V 4.35V1N4733-53.7 -54.0 -52.0 -43.7 -44.4 -53.9 (5.1V @ 49mA) ----- 2.16V 3.59V 4.35V 4.63V 4.68V1N4734A-53.7 -53.2 -52.0 -46.5 -47.5 -53.5 (5.6V @ 45mA) ----- 2.20V 3.78V 4.57V 5.01V 5.14V1N4735#1-53.3 -53.4 -51.3 -35.6 -35.8 -43.7 (6.2V @ 41mA) ----- 2.11V 4.54V 5.32V 5.39V 5.42V1N4735#2-53.2 -53.4 -49.2 -26.4 -35.2 -42.2 ----- 2.19V 5.23V 5.66V 5.68V 5.72V1N4735#3-53.2 -53.3 -13.3 -17.7 -39.4 -50.0 ----- 2.25V 5.66V 5.66V 5.68V 5.74V1N4736-53.3 -54.4 -9.0! -14.0 -41.7 -48.8 (6.8V @ 37mA) ----- 2.23V 5.95V 5.95V 5.96V 6.02V1N4738-55.7 -55.6 -50.X -35.6 -28.4 -36.5 (8.2V @ 31mA) ----- 2.18V 5.30V 7.38V 7.65V 7.73V1N4739#1-53.2 -53.2 -53.6 +6.4! -30.3 -34.6 (9.1V @ 28mA) ----- 2.21v 6.33V 8.25V 8.18V 8.26V1N4739#2-53.3 -53.4 -53.6 +6.8! -24.5 -17.6 ----- 2.45V 6.31V 8.12V 8.07V 8.15V

400mW and limited +/-10 percent voltage tolerance, except suffix A for full +/-10 percent and B for +/-5 percent.

NONE 1uA 10uA 100uA 1mA 10mA1N5221B-54.1 -53.8 -54.6 -57.7 -62.0 -64.0 (2.4V @ 20mA) ----- 0.64V 0.83V 1.13V 1.54V 2.09V1N5225-53.7 -53.7 -54.0 -56.7 -61.5 -63.8 (3.0V @ 20mA) ----- 0.79V 1.04V 1.41V 1.91V 2.56V1N5228B-53.5 -53.x -52.x -54.x -59.x -63.x (3.9V @ 20mA) ----- 1.09V 1.45V 1.95V 2.59V 3.40V1N5229B-53.2 -53.5 -53.6 -55.0 -60.0 -63.0 (4.3V @ 20mA) ----- 1.39V 1.81V 2.33V 3.00V 3.77V1N5230B-53.3 -53.3 -53.8 -54.0 -57.8 -59.2 (4.7V @ 20mA) ----- 1.69V 2.27V 2.92V 3.68V 4.32V1N5235B-53.4 -53.6 -47.8 -20.5 -30.2 -38.4 (6.8V @ 20mA) ----- 2.10V 5.72V 6.36V 6.38V 6.44V1N5236B-53.4 -53.5 -48.X -23.X -20.2 -32.3 (7.5V @ 20mA) ----- 2.04V 5.44V 6.47V 6.52V 6.59V1N5238B-53.2 -53.4 -53.5 -4.7! -15.7 -16.1 (8.7V @ 20mA) ----- 2.16V 6.31V 8.01V 8.03V 8.11V

NONE 1uA 10uA 100uA 1mA 10mABZT52C2V4-53.5 -53.6 -54.0 -57.0 -61.4 -64.0 (2.4V @ 5mA) ----- 0.79V 1.03V 1.38V 1.85V 2.48VBZT52C2V4-54.0 -53.5 -54.0 -57.0 -61.5 -64.1 ----- 0.79V 1.03V 1.38V 1.85V 2.47VBZX84C2V7-53.7 -53.7 -54.0 -56.7 -61.4 -64.0 (2.7V @ 5mA) ----- 0.87V 1.14V 1.52V 2.02V 2.68VBZV90-C2V4-54.1 -54.0 -54.4 -57.2 -62.0 -64.2 (2.4V @ 5mA) ----- 0.83V 1.06V 1.39V 1.83V 2.42V

NONE 1uA 10uA 100uA 1mA 10mA1N4625-53.2 -53.3 -51.9 -46.2 -47.3 -53.8 (5.1V @ 250uA, low noise) ----- 2.17V 3.82V 4.60V 5.03V 5.16VBZX8V2-54.2 -53.3 -53.2 0.0! -20.2 -30.2 ----- 2.18V 6.30V 7.45V 7.48V 7.54V

NONE 1uA 10uA 100uA 1mA 10mAMPS2222A-53.2 -53.2 -49.3 -21.0 -30.0 -39.7 (6.0V min @ 10uA) ----- 2.28V 6.39V 6.59V 6.61V 6.66VJAN2222-53.2 -53.3 -35.8 -16.5 -23.8 -37.4 (5.0V min @ 10uA) ----- 2.16V 6.46V 6.52V 6.54V 6.60V2N3904-53.2 -53.3 -53.5 +0.6! -06.0 -20.0 (6.0V min @ 10uA) ----- 2.29V 6.53V 7.13V 7.18V 7.27V2N3906-53.2 -53.3 -53.5 -13.5 -24.3 -37.6 (5.0V min @ 10uA) ----- 2.03V 6.51V 7.66V 7.69V 7.76V2N4401-53.2 -53.3 -53.6 -7.4! -20.0 -31.0 (6.0V min @ 100uA) ----- 2.18V 6.46V 7.01V 7.03V 7.07VFN4402-53.2 -53.3 -53.6 -13.3 -22.0 -32.0 (5.0V min @ 100uA?) ----- 2.17V 6.44V 7.50V 7.51V 7.55V

NONE 1uA 10uA 100uA 1mA 10mAICL8069-54.1 -54.2 -51.5 -23.3 -25.7 -26.5 (1.23V, 50uA..5mA) ----- 0.58V 0.78V 1.19V 1.22V 1.23VTL431C-54.8 -54.0 -56.2 -57.4 -33.7 -33.6 (2.495V, 1mA..100mA) ----- 1.01V 1.15V 1.63V 2.37V 2.37VLM336-54.0 -53.2 -52.0 -47.2 -34.4 -34.5 (2.49V, 400uA..10mA) ----- 1.00V 1.14V 1.21V 2.36V 2.36V

NONE 1uA 10uA 100uA 1mA 10mASR2220M4-62.6 -63.2 -55.5 -18.5 -15.X -5.5 (5.5V, 20mW max) ----- 1.75V 3.94V 6.11V 7.00V 7.63V

NONE 1uA 10uA 100uA 1mA 10mA1N4148-55.0 -55.0 -58.9 -63.6 -65.0 -65.0 (200mA, 75 PIV) ----- 0.39V 0.47V 0.56V 0.66V 0.78VBYW56-58.7 -56.0 -60.7 -63.8 -64.8 -64.7 (2A, 1k PIV) ----- 0.39V 0.45V 0.52V 0.62V 0.71V

NONE 1uA 10uA 100uA 1mA 10mAold red-53.5 -54.1 -58.9 -64.1 -65.5 -65.6 ----- 1.32V 1.42V 1.51V 1.60V 1.76Vsml clr red-53.3 -54.2 -59.4 -64.1 -65.4 -65.6 ----- 1.34V 1.44V 1.53V 1.64V 1.79Vtiny red-53.4 -54.4 -59.7 -64.2 -65.3 -64.2 ----- 1.34V 1.42V 1.51V 1.65V 1.76Vpink red-54.9 -54.3 -59.5 -64.2 -65.5 -64.7 ----- 1.35V 1.44V 1.52V 1.61V 1.80V

**Rubber References.**
Semiconductor junctions simply do not have a single breakdown or
forward voltage.
Instead they have a wide range of voltages, depending upon the
amount of current flowing through them.
The physical mechanism for this may be a plethora of distinct
microsites, each of a different voltage and limited to a tiny
amount of current.

**Variation with Current.**
As a gross generalization, "good" devices may reduce the amount of
noise they generate by about 3dB for every 10x increase in current.
In reality, each device is unique and behaves differently, sometimes
wildly differently.
Some devices are particularly bursty, with heavy 1/f noise peeking
through despite strong filtering.

**Oscillation.**
The vast increases in signal from particular devices at particular
current ranges are what one might expect from oscillation.
Presumably that would be due to the diode taking on a negative
dynamic resistance and exciting incidental resonance structures
inside the measurement box.
In cryptographic use we need to be very concerned about oscillations,
which of course repeat predictably while masquerading as
unpredictable diode noise.

**Best Device Types.**
I lean toward noise sources that operate at low voltages, but the
list is short.
The 2.4V and 2.7V zeners typically have very low noise output.
The IC voltage references produce much more noise:
The ICL8069 should work at 50uA.
The TL431C and LM336 produce less noise and need more current.
When higher voltages are available, a low-voltage Metal Oxide
Varistor (MOV) can produce a lot of noise at 100uA.
The usual strategy of using a bipolar transistor B-E junction also
requires higher voltages.
Consistent device characteristics may be the real advantage of the
IC references.

**Time Correlation.**
If we describe noise as a range of frequencies, the sine wave energy
at each must impose some degree of amplitude correlation between time
samples.
Moreover, low frequency signals must intrude on more nearby samples
than high frequency signals.
Both effects can be reduced significantly by taking the difference
between adjacent samples and using that as noise data.

**Autocorrelation.**
Previous work has exposed apparently unknown and complex
autocorrelation structure in noise (see:
Experimental Characterization of Recorded Noise).
The existence of autocorrelation structure directly contradicts the
idea that noise must be completely unpredictable because of its
quantum origin.
Unfortunately, deep analysis is now required.
In practice, it may be necessary to actually skip some number of
noise samples until autocorrelations become acceptably small.