Any physical system has two types of noise, thermal noise (important at high temperature, relatively low frequency), and quantum noise (uncertainty principle, important at low temperature, very high frequency).

This means even if we make perfect resistors and perfect transistors in fabrication, we will still have to deal with these noises.

For the frequencies of interest to electrical engineering, we are mostly interested in thermal noise. The so called transistor shot noise is actually a result of thermal noise as well at a microscopic level.

Johnson first measured open circuit noise voltage of resistor in 1926, and
found it to be independent of material,
frequency, and only dependent on R and T.
Its physical origin is *random walk*
of electrons, or velocity fluctuation
first studied by Einstein in 1906 and
then formulated by Langevin.

Shortly after, Nyquist explained the 4kTR noise observed by Johnson using a transmission line cavity and second law of thermodynamics, without involving its microscopic origin. However, it relies on the assumption of thermal dynamic equilibrium, that is, no applied voltage and current.

Experimentally the same 4kTR noise was observed at non-equilibrium, or when DC or AC currents are flowing. It was puzzling for a long time until relatively recently.

It took several decades for us to quantitatively connect the microscopic voltage noise 4kTR with the microscopic velocity fluctuation studied by Einstein.

The major noise sources in a bipolar transistor are the base resistance
*thermal* noise, or Johnson noise, the base current *shot* noise and the
collector current *shot* noise. The base resistance thermal noise is
typically described by a noise voltage with a spectral density of
, and the shot noise is described by a spectral density of
, with being the DC base current or collector
current. These descriptions are based on *macroscopic* views. The
standard derivation of the magic shot noise assumes a
Poisson stream of an elementary charge . These charges need to
overcome a potential barrier, and thus flow in a completely uncorrelated
manner. In a bipolar transistor, the base current shot noise
results from the flow of base *majority* holes across the
EB junction potential barrier. The reason that appears in
the base shot noise is that the amount of hole current overcoming the EB
barrier is determined by the *minority* hole current in the emitter,
. Similarly, the collector current shot noise results from
the flow of emitter *majority* electrons over the EB junction potential
barrier, and has a spectral density of .

Surprisingly, however, both the resistor noise and the
shot noise can be attributed to the same physical origin at
the *microscopic* level, the Brownian motion of electrons and holes,
also referred to as *diffusion* noise as the same mechanism is
responsible for diffusion. The thermal motion of carriers gives rise to
fluctuations of carrier velocities, and hence fluctuations of current
densities. The density of such current density fluctuation is
according to microscopic treatment of carrier motion .

The current density fluctuation at each location propagates towards
device terminals, giving rise to device terminal voltage or current
noise. The problem of noise analysis is now equivalent to solving the
transfer functions of noise propagation at each location and summing
over the whole device space. These transfer functions can be solved
analytically for ideal transistor operation with simplified boundary
conditions, or numerically for arbitrary device structures, and the
later process is referred to as *microscopic noise simulation*.

Various mathematical methods have been developed,
all based on the
impedance field method developed by Schockley and his colleagues , and
its various generalizations. A very satisfying early application is the
successful derivation of the Johnson noise, a macroscopic
model result, from the
microscopic *noise source density*.
The impedance field approach is
equivalent to the Green
function based approaches,
which can be rigorously derived from the
general master equation.
Efficient numerical algorithms have been
developed, which enabled the recent implementation of noise analysis in
commercial device simulators, e.g. DESSIS from ISE and Taurus from TMA.

We research measurement, understanding, microscopic level simulation and macroscopic level compact modeling of noise in transistors and circuits, from low-frequency noise to high frequency noise as well as phase noise.

For high frequency noise that is of particular interest for low-noise RF and microwave amplifier design, we take a unified approach of modeling the macroscopic level terminal current and voltage noise as results of microscopic level Brownian motion and related carrier transport or propagation.

For these new noise models to be useful to IC designers, we develop techniques of implementing our new compact models in non-linear circuit simulators and propotype such implementation techniques with low-noise amplifier designs.