In a perfect crystal of, say, Ge or Si, all the atoms are at their lattice sites and do not have ability to trap additional charge carriers. If impurities are introduced in a perfect crystal, they get ability to trap charge carriers. It may be noted that self interstitial and vacancies are also defects and can trap charge carriers. In real crystalline structure grown for use in devices, contain a variety of defects and sometimes form defect clusters. These clusters are normally composed of vacancy-dopant or interstitial-dopant clusters. These extended clusters can trap a considerable fraction of electrons or holes present in the active volume of a device.
It is thought that these types of extended defect clusters are present in N-type Ge and prevent the feasibility of high speed electronic devices. Depending upon crystal and dopant, preset defect clusters can trap electrons or holes depending on the coulomb potential around defect, impurities or a defect cluster. Electron-hole plasmas are found in electronic devices crystals exposed to optical excitations etc. Defect clusters are exposed to electron and hole currents due to which they are charged. Defect charging in semiconductors is quite complex. After charging processes end, charged defects start discharging naturally. Charging/discharging of defect clusters in semiconductor devices are important and affect performance of devices. Charging and discharging of defects can be used for characterization of charge carrier traps in micro and nanoelectronic devices. Behaviour of deep level traps, which forms the basis for DLTS technique, is described by a schematic in
Suppose an electron-hole plasma is generated in an electronic device with electron density as ne and hole density nh For simplicity, we assume here extended defect clusters capable of trapping a considerable number of electrons. We consider a case of net electron trapping or negatively charged defects in a semiconductor device. The model situation resembles the typical case of ion implanted Ge:Sb. For the simplicity, we assume that at the time of generation of electron-hole plasma, ne – nh. In implanted Ge:Sb, highly stable vacancy-antimony-Ge clusters (
) are present which are thought to be electron traps in this n-type Ge. These extended defect clusters get charged like dust particles and grains in electron-ion plasma. Let the density of defect cluster or dust grain in e-h plasma, generated in the above mentioned device, is nd.
We further assume here that densities of electrons and holes are below the limit at which inter particle distance becomes lower than de Broglie wavelength of any specific specie which assures that that the case e-h plasma being discussed here is of classical nature. If we take charge of electron as –e, hole as +e and defect or dust grain s – Zd·e, the well-known condition of charge neutrality can be written as below:
Using simple algebra,
For any practical device, defect grain density is much lower than densities of electrons and holes, so the number
which is the case of isolated dust or defect grains [8-11]. It may also be noted that in present devices defect grains can be only up to a few nanometer size. Maximum charge on defect depends upon defect structure and its size. A isolated defect or dust grain in e-h plasma attains a floating potential 
which is determined by electron repulsion and hole collection in case of net negative charging of defects. The electron current responsible for depositing electrons on the defect is given by,
where me and Te are electron effective mass and temperature, and 
is the radius of the equivalent sphere of defect grain. The hole current compensating electron charging of a defect is given by,
where mh and Th are hole effective mass and temperature. For further details of equations (3), (4), please see Refs. [8-12]. The charging equation of a negatively charged grain can be written as below, [8-10].
Case of hole or positive charging of defects can be described using a simple analogy and comparison between electrons and holes.
Electron traps are centers in a semiconductor capable of trapping electrons with a certain binding energy. Traps cause power dissipation and reduce conductivity of the device. When electrons and holes are present in the form of a plasma in an electronic device, dust or defect grains are exposed to both electron (Te) and hole (Th) currents. These currents simultaneously charge and discharge defect grains. When e-h plasma is first generated (t = 0) in an electronic device, a charging transient is produced after which charging and discharging perturbation continues until the device operation ends (end of e-h pair generation). After this, a discharging transient is produced in which electrons are released due to thermal agitation and thermally generated holes. UV light can also produce discharging through photoelectron emission.
is given by [
is the equilibrium capacitance value at reverse voltage, 
is the lowering of 
at t = 0 and ep is the hole emission coefficient. The above equation will be valid for electron traps with ep replaced with en (the electron emission coefficient) and 
is the rise of 
at t = 0. DLTS spectrum is generated by applying a sine-function correlation with period P to 
as,
. For exponential transients, the period P, the emission coefficient ep and Tmax for which 
shows a maximum, are related as [
corresponding to a particular hole trap.
during dust or trap discharge after the application of the filling pulse. So, dust mode frequency transient 
for the same hole trap as in Equation (4), an analogue to capacitance transient
, can be defined as,
and 
are, respectively, equilibrium dust mode frequency and full magnitude of the frequency transient at t = 0. In the same way as in Equation (5), dust mode frequency DLTS or DMF-DLTS signal, 
, can be generated by applying the correlation sine-function as in Equation (5),
signal, each corresponding to a particular dust specie. This spectrum of peaks will be similar to a DLTS spectrum (
and change 
are measured, further details of experimental and analysis aspects of implementation of this new DLTS can be seen by a selected studies available in the common literature [13-19].