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Outline of the physics, mathematics, and recent experiments taking place regarding diodes producing power from natural ambient thermal noise that exists in all matter. In terms of the mathematics, diodes must rectify such thermal noise according to conventional small signal diode modeling physics. Thermal noise is a natural ambient thermal energy that exists in all matter, which is sustained by Solar energy. Theoretically, each diode could produce over 20nW of continues power. Creating a diode array chip consisting of hundreds of billions of microscopic diodes would be inexpensive if mass produced. Extensive recent measurements conducted in rural desert areas have shown that the SMS7630, a zero bias diode, contained within sufficient shielding are producing a DC voltage ranging from nano volts to over one micro volt per diode. If present research is correct, then diodes produce "Free-Energy."

According to preliminary predictions, each heavy doped n-InSb Palladium Schottky diode with a plate area of 30nm x 30nm would produce between 11.4mV per diode-- see Physics of Semiconductors for the math. The calculated resistance per diode is 4.5M ohms. Given a spacing of 40nm per diode, the predicted power is 18K (18000) Watts/m^2. Such a diode chip requires a lot of diodes, but modern semiconductor fabrication methods deposit the entire layer of material at once; i.e., each diode is *not* made at a time. Such a chip could be affordable given mass production. Compare such a chip to standard solar panels that produce 50 Watts per square meter, which comes to ~ 17 Watts per square meter when consider the average power for the entire 24 hour day in a sunny location such as Southern California.

Still Unknown by Conventional Science

Often someone will ask, if diodes produce a DC voltage then why hasn't it been detected by now. The three main reasons are,

1. According to the mathematics, the DC voltage produced by nearly all diodes is in the pico to nano volt region-- far too difficult to detect over noise.

2. A simple diode, say a 1N914A, connected to a voltage meter produces a measurable DC voltage, sometimes in the millivolts, due to the rectification of RF noise such as radio stations and WiFi routers. For this reason, an Electrical Engineer detecting a DC voltage from a diode would immediately dismiss it as such.

3. Producing measurable DC voltages requires a diode array consisting of dozens of ultra high frequency diodes connected in-series-- over 100 diodes in series is recommended. Such a diode array consisting of common diodes would have incredibly high impedance at so-called thermal equilibrium, thus would be extremely difficult to detect the DC voltage. A typical diode may be 30 Mohms per diode at thermal equilibrium. At 156 diodes in-series, the resistance would be 30.0Mohms * 156 = 4.68Gohms. To bring the impedance down to 50Mohms would require 156 in-series and 94 in-parallel, for a total of nearly 15 thousand diodes-- an expensive project. According to present mathematics, diode arrays should be made of a certain type of diode commonly referred to as a Zero Bias Diode (ZBD). A ZBD has low resistance at thermal equilibrium, typically 1Kohm to 10Kohms per diode; e.g., the SMS7630.

Replication

The following outlines how to replicate this research, a diode array that produces a continuous DC voltage and the electrometer to detect such DC voltage. There is a type of diode that the semiconductor industry refers to as a Zero Bias Diode (ZBD). A ZBD is a heavy doped diode, typically a Schottky diode such as the SMS7630 made by Skyworks Inc. According to the datasheet, the total capacitance for each SMS7630 diode is 0.3pF. According to Diode NATE, version 0.3, if each SMS7630 diode has 0.3pF, the diode would produce 0.5uV DC. Note, Diode NATE v0.3 has not been thoroughly tested for bugs. Furthermore, future versions of Diode NATE will take advantage of further details, thus improving the accuracy.

The researcher should place each diode in-series, not in parallel. Diode physics is very clear that the kTC noise across the junction is nearly cut in half for every four diodes in parallel. Each SMS7630 diode is soldered on top of each other to minimize the size of the entire diode array.

Minimizing the diode array size reduces the amount of external RF noise/signals the diode array will pick up. My diode array wall consisting, which consists of 156 SMS7630 diodes (78 diode chips-- two diodes per chip) in-series is less than 1" x 1". Such a diode array is so small that very little shielding is required, even within a large industrial city such as Los Angeles, CA. Due to the compact size of such diode arrays, it is now possible to conduct the research is urban areas.

The diode array should be placed inside a magnetic metal shield, such as steel, and a non-magnetic shield, such as Aluminum-- the larger the better. I use a Hammond Aluminum shild -->

The Hammond Aluminum shield is then placed inside a large microwave oven rotated such that the door is facing up. The microwave oven offers magnetic shielding as well.

A capacitor should be placed across the *entire* diode array, in parallel. See the diode photo above. The capacitor will help stabilize the diodes performance since it appears diodes at thermal equilibrium are highly sensitive to changes in DC current. Also, the capacitor will help short-out external RF noise across the diode array. A 4.7uF Mylar capacitor works fine.

To measure the DC voltage output from a diode array, one should use an electrometer. Presently I using the INA116P electrometer op-amp. The INA116P is recommended over the INA116PA since it has a lower maximum bias current. Recently I purchased a few LMP7721MA electrometer op-amps, which are better than the INA116P, at least on paper-- less noise, less temperature drift, less Ib(max) bias current, operates on less DC voltage. Although the INA116P is an instrumentation op-amp circuit. So, if you use the LMP7721MA, then you should buy at least two so as to make an instrumentation op-amp circuit. Such electrometer op-amps produce insignificant bias current, typically 3fA (0.003pA or 3e-15 amps). To achieve minimum bias current the electrometer op-amp should be suspended in the air by the wires that are soldered to it. The wires that are solder to the electrometer op-amp hold the electrometer op-amp in the air. This is a common method to maintain minimum bias current.

The electrometer op-amp output goes to a voltage-to-current converter op-amp (I'm using an LT1055, a FET op-amp) circuit to drive an LED. I use a common 100mW red LED, but a infrared LED may be a better choice for more op-amps. The LED shines through a small hole in first (innermost) shield. On the other side of the hole is a fiber optic cable, which goes through a hole in the microwave oven, and connects to another chassis (chassis #2) through a small hole. On the other side of chassis #2 is a photodiode that picks up the light from the optic cable. I use the same type of 100mW red LED as a photodiode. The photodiode is connected to an appropriate op-amp circuit. I use an NTE857M, a FET op-amp. Here is circuit diagram of the second circuit:

The electrometer circuit should be inside the chassis with the diode array and the diode arrays capacitor (the 4.7uF Mylar capacitor). I use a small mechanical DPST switch placed between the diode array output and the electrometer input. The switch, when toggled, reverses the diode array relative to the electrometer input. This method allows the electrometer to detect the diode array DC voltage regardless of the op-amp output temperature drift. Another option, perhaps better, is to replace the small mechanical DPST switch with a small latching relay switch. A few recommendations are ASX21003, TXS2-L-3V, D3043. The first two latching relays require just 35mW to toggle. The toggle time is typically 3 ms. The latching relay requires no power after being toggled.

Important: Once the diode array (at least 100 diodes in-series) is soldered, and the 4.7uF Mylar capacitor has been soldered across the entire diode array, and an appropriate load (~ 5400 ohms per diode; e.g., 850K ohms for a 156 in-series diode array) is soldered across the diode array output, it is highly recommended that the diode array is placed inside the shields, undisturbed, connected to the electrometer (make sure the electrometer is turned off during this period) for at least three weeks.

Mathematics of Modeling Diodes

Diodes Semiconductor physics is well established and is used to model real diodes, not just ideal diodes. Low signal diode modeling equations are used for signals far below the thermal voltage, which is 25mV at 295K (22C, 71F). Such low signal diode equations have been used for micro and nano volt signals. The thermal voltage equation is

Vt = kb * T / q

where kb is the Boltzmann constant (1.3806503E-23 J/K), T is temperature in Kelvin, and q is the elementary charge (1.602176487E-19 C).

According to low signal diode modeling, the DC voltage produce by a diode ,due to the rectification of AC signals, is relative to the square of the AC voltage. This is known as the Diode Square Law, which is used for Diode Square Law detectors. It is know in conventional physics that if the weak AC signal placed on a diode is decreased by half of the AC voltage ,then the DC voltage produced by the diode due to rectification will decrease by roughly one fourth. The Diode Square Law is appreciably linear for signals below the thermal voltage (~ 25mV at room temperature), and becomes increasingly linear at weaker signals. For example, if the AC signal is 1mV rms, and the produced DC voltage is 10uV DC (due to rectification), and lets say the AC signal suddenly drops to 1uV rms, then the DC voltage will drop to roughly [ 10uV DC * (1uV rms / 1mV rms)2 ] = 10pV DC.

An outline of diode modeling mathematics is found at Diode modelling

Mathematics of Modeling Thermal Noise

The noise voltage produced by electrical resistance is

Vn = Sqrt(kb * T * R * B)

where kb is the Boltzmann constant (1.3806503E-23 J/K), T is temperature in Kelvin, R is resistance in ohms, and B is bandwidth in Hz. All electrical resistance has parallel capacitance, and therefore in order to correctly model Thermal noise one must consider the parallel capacitance, which is known as kTC noise. The kTC noise voltage equation is

Vn = Sqrt(kb * T / C)

where C is the parallel capacitance across the electrical resistance in farads. The kTC equation provides the noise voltage across the diodes junction. Knowing the kTC noise is insufficient to know the DC voltage produced by the diode. Due to the Diode Square Law, we must know the noise distribution. As far as I am aware the noise distribution for kTC noise is Gaussian. Gaussian distribution mathematics is found at

Gaussian distribution

Physics of Semiconductors

Depletion Width

When metal comes in contact with a semiconductor, a Schottky barriers is created. This forms a depletion region. Nearly 100% of the diodes resistance is caused by the depletion region. The effective depletion depth for a Schottky barrier is

W = sqrt(|Vbi| * 2 * eS / (q * N))

where Vbi is the built-in voltage in the Schottky contact, eS is the permittivity of the semiconductor (1.05e-10 F/m for Silicon) in F/m, q is elementary charge (1.602176462E-19 C) in Coulombs, N is the semiconductor dopant density in dopant atoms per m3.

Built-in Voltage

The build-in voltage, Vbi, is calculated as,

Vbi = F - Eea + Vt * ln(Ns / ni) - Eg / 2

where F is the work function of the metal, in electron volts. See the work function table. The function "ln" is the natural loge. Eea is the Electron affinity (see table below), in eV. Vt is the Thermal voltage (see the section above title, "Mathematics of Modeling Diodes"). Vt is 26mV at 300K. Ns is the semiconductor dopant density, in dopants/m3. ni is the Intrinsic carrier density (see table below), in dopants/m3. Eg is the bandgap in electron volts.

See the table at Dirty Details

Junction Capacitance, Cjo

The diodes effective depletion plate capacitance is

Cjo = eS * A / W

where A is the plate area.

Resistance, Ro

Before calculating the diodes zero bias resistance, Ro, we need to know the average velocity with which the electrons at the interface approach the barrier. This velocity is know as the Richardson velocity, and is calculated as,

Vr = sqrt(k * T / (2 * π * m))

where k is the Boltzmann constant, T is the temperature in Kelvin, m is the electron mass. We can use 9.11E-31 m/s for m, which comes to 27e+3 m/s at 300 Kelvin.

Now we can calculate the current density. Ignoring the tunneling current, the current density is calculated as,

Jn = q * Vr * Nc * exp(- B / Vt) * [exp(V / Vt) - 1]

where Nc is the dopant density, B is the barrier height, Vt is the thermal voltage (equation provided above), and V is the applied voltage.

Bandgap

Eg(300K) = Eg(0K) - α * T2 / (T + β)

Example, the bandgap of silicon at 0K is 1.166. Therefore, Eg(300K) = 1.166 - 0.473e-3 * 3002 / (300 + 636) = 1.12 eV

See the table at Dirty Details

Intrinsic Carrier Density

ni(300K) = sqrt(Nc * Nv) * exp(-Eg / (2 * k * T))

where Nc is the effective density of states in the conduction band in /m3, Nv is the effective density of states in the valence band in /m3, Eg is the bandgap in electron volts, k is the Boltzmann constant, T is the temperature in Kelvin.

Effective densities of states

Nc = 2 (2 * π * me * k * T)3/2 / h2

where me is the effective conduction electron mass, k is the Boltzmann constant, T is the temperature in Kelvin, and h is the plank constant.

The same equation applies to Nv, where me would be the effective valence electron mass.

See the table at Dirty Details

Example

Lets find Cjo for a heavy doped n-InSb Palladium Schottky diode at 300K where the plate area is 30nm x 30nm, and the dopant density is 5e+24 per m3. The calculated barrier height would be 0.21eV. The bandgap for Silicon is 1.12 eV with an electron affinity of 4.05 eV, and an intrinsic carrier density of 9.65e+15 per m3. The work function for Palladium is 4.80 eV.

First we need find the built-in voltage. The Thermal voltage at 300K is 26mV. The built-in voltage is therefore,

Vbi = 4.80 - 4.59 + 25.9mV * ln(5e+24 / 2e+22) - 0.17 / 2 = 0.2677 volts.

Next we need to calculate the depletion width. The permittivity for p-Silicon is 1.05e-10 F/m. The depletion width is,

W = sqrt(0.2677 * 2 * 1.05e-10 / (q * 5e+24)) = 8.4nm

Therefore, the junction capacitance is,

Cjo = 1.05e-10 * 30nm * 30nm / 8.38nm = 11aF.

With an effective depletion width of 8.4nm, the diode capacitance is 11aF. Solving the DC voltage produced by the above diode is solvable only by means of numerical analysis. By using the kTC noise equation, along with Gaussian distribution equations (see "Mathematics of Modeling Thermal Noise" above), diode modeling equations (see "Mathematics of Modeling Diodes" above), and the above diode parameters, we can predict the DC voltage. A computer program I wrote, Diode NATE, uses all of such mathematics in a numerical analysis to predict the DC voltage a diode will produce. Using a common emission coefficient of 1.05, according to Diode NATE, the aforementioned diode would produce 14mV DC per diode.

Using the Ro equation (see above), and applying a relatively low voltage of 1uV, the current density is,

Jn = q * 27e+3 * 5e+24 * exp(- 0.21 / Vt) * [exp(1e-6 / Vt) - 1] = 248 A/m2

Note, the barrier height and Vt must be accurate to obtain an accurate answer. Try using 25.8520269e-3 for Vt.

The current is,

248 * (30nm * 30nm) = 0.223 pA

Therefore, the our diodes zero bias resistance is,

V / I = 1e-6 / 0.223e-12 = 4.5M ohms.

Photos

See Photos

NATE (Natural Ambient Thermal Energy)

I refer to NATE (Natural Ambient Thermal Energy) as the total internal energy contained in matter at room temperature-- Reference: Internal energy. All matter contains vast amounts thermal energy. Such thermal energy is sustained by our Sun.

2LoT (2nd Law of Thermodynamics)

2LoT (2nd Law of Thermodynamics) is interpreted as meaning there is no usable energy in a closed system in equilibrium. Fortunately for humanity it is impossible for any system to be in perfect equilibrium, as such a system would require infinite insulation in a real world. At room temperatures atoms and subatomic particles are always in random motion, as one atom may be at standstill while its neighbor may be traveling at 5000 m/s. In the year 2006 I spent considerable time analyzing natural ambient temperature fluctuations on a macro scale by means of two thermistors and an appropriate amplifier. Each thermistors was ~ 1mm in length. Regardless of how well the system was insulated there were always thermal fluctuations. A simpler method of analyzing macro scale thermal energy is by means of a magnifying glass with at least 10X power. By sprinkling a light fine powder such as fine powdered cumin (a common herb used for cooking) on the surface of water one can see Brownian motion. You will need some patience using a 10X hand held magnifying glass since the degree of motion is a Gaussian distribution. With an inexpensive $40 child's microscope you will instantly see Brownian motion. Such motion is governed by macro scale mechanics. On a nanoscopic scale NATE is a violent world where particles are in rapid random motion. Regardless of sample duration, temperature in any closed system will vary over time. One interesting universal effect is 1/f noise (also referred to as flicker noise or Pink noise, see Occurrences) where the 1/f noise (in this case temperature fluctuations) is relative to the reciprocal of frequency. It appears the Universe will not allow anything to be 100% consistent, as 1/f noise alone prevents consistent measurements regardless of sample duration. The Universe has not reached equilibrium, but then such a question becomes meaningless when asked at what point in time would the Universe be at 100.0...0% perfect equilibrium. Beyond the fact that there is no such thing as equilibrium in the real world, the laws of thermodynamics is an imperfect theory at the microscopic scale. Quote from the conventional science community at WikiPedia, "Thermodynamics is a theory of macroscopic systems at equilibrium and therefore the second law applies only to macroscopic systems with well-defined temperatures. On scales of a few atoms, the second law does not apply; for example, in a system of two molecules, it is possible for the slower-moving ("cold") molecule to transfer energy to the faster-moving ("hot") molecule. Such tiny systems are outside the domain of classical thermodynamics, but they can be investigated in quantum thermodynamics by using statistical mechanics. For any isolated system with a mass of more than a few picograms, the second law is true to within a few parts in a million-- Reference: Landau, L.D.; Lifshitz, E.M. (1996). Statistical Physics Part 1. Butterworth Heinemann. ISBN 0-7506-3372-7."

Spice Simulations

Spice simulations predict that diodes should rectify thermal energy. Spice was first created by the University of California-Berkeley in the early 1980s. Over the decades physicists and engineers around the world have improved Spice. Modern Spice mathematical equations are a reflection of modern quantum physics. The creator of LTspice, Mike Engelhardt, acknowledges that Spice predicts diodes will rectify Thermal noise.

Standard Gaussian Thermal Noise Equation

Standard Gaussian thermal noise equation used in modern nonlinear physics violates the laws of thermodynamics. Reference: (large pdf file: 9MB) Thermodynamically valid noise models for nonlinear devices. Mathematics offers no interpretation, but is merely a tool. People interpret mathematics, and therein often lies the problem.

Mathematical Approximations

Mathematical approximations governs semiconductor physics; e.g., flicker noise-- Reference: Noise Sources in Bulk CMOS by Kent H. Lundberg, 2002. A few quotes from Kent H. Lundberg, "No entirely satisfactory physical explanation has been developed, and in fact, available evidence seems to suggest that the origins of flicker noise in different devices may be quite different-- reference M. J. Buckingham, "Noise in Electronic Devices and Systems", Ellis Horwood Limited, Chichester, England, 1983." and another quote from Kent H. Lundberg, "Two competing models have appeared in the literature to explain flicker noise: the McWhorter number fluctuation theory and the Hooge mobility fluctuation theory." Considering every occurrence in semiconductor diodes from the micro to macro scale, hand written equations are not 100% accurate. The quantum physics of semiconductors is based on mathematical approximations.

Software News

Diode NATE

Diode NATE is a free Microsoft Windows numerical analysis application that I wrote to predict the DC voltage that a diode will produce. The user enters the junction capacitance, and the Emission coefficient, presses Start, and within a few seconds Diode NATE displays the predicted DC voltage. The mathematics evolves conventional small signal diode modeling, kTC noise, gaussian distribution in a numerical analysis.

Trapdoor

Trapdoor is a Microsoft Windows numerical analysis application that I wrote to simulate a trapdoor between two chambers. It's presently unavailable until I complete the GUI suitable for viewing. The trapdoor is made of bonded atoms, and is aligned such that the trapdoor, when undisturbed, aligns slightly in the left chamber. Both chambers contain gaseous atoms. The simulation shows more atoms migrating to the left chamber. There are two chambers, left and right, both are separated with a dividing wall. In the middle of the dividing wall is the trapdoor, which tends to allow atoms in the right chamber enter the left chamber, while preventing the opposite. The trapdoor, being made of atoms, can flex, but such atoms are bonded. During the simulation, every so often an energetic atom in the left chamber will cause the trapdoor to flip to the other side such that the trapdoor will begin rectifying in the opposite direction. The natural thermal energy of atoms and blackbody radiation quickly cause the trapdoor to flip back to the left chamber. Regardless, over time more atoms end up in the left chamber on average. On average there's more pressure in the left chamber.

LTspice

LTspice is a free Microsoft Windows application written by Mike Englehardt. It's perhaps the most accurate spice simulation available. According Mike Englehardt, Spice predicts that diodes rectify Johnson noise. Download LTspice.

Diode Battery

In 2007 I predicted the possibility of mixing the proper chemicals (e.g., semiconductors, conductors, insulators) followed by a heating process while contained within an electric field (thousands of volts) could form natural microscopic and nanoscopic diodes with a net junction orientation aligned in one direction. The heated material within the electric field would cause a percentage of such natural diode junctions to form in one orientation. This would form what I call a Diode Battery. Countless microscopic diodes would rectify NATE (natural ambient thermal energy).

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