Differential conductance energy

Fig. 1.21. Tunneling spectroscopy in classic tunneling junctions, (a) If both electrodes are metallic, the HV curve is linear, (b) If one electrode has an energy gap, an edge occurs in the HV curve, (c) If both electrodes have energy gaps, two edges occur. A "negative differential conductance" exists. (After Giaever and Megerle, 1961).

Fig. 35. Temperature dependence of the differential conductance d//dV versus bias voltage V of a resonant tunneling diode with a (Ga,Mn)As emitter. No magnetic held is applied (Ohno et al. 1998). (b) Calculated resonant tunneling spectra as a function of the exchange energy NqP (Akiba et al. 2000b).

Now, let us consider the current-volt age curve of the differential conductance (Fig. 7). First of all, Coulomb staircase is reproduced, which is more pronounced, than for metallic islands, because the density of states is limited by the available single-particle states and the current is saturated. Besides, small additional steps due to discrete energy levels appear. This characteristic... 

V. The molecular vibrator is represented by a harmonic oscillator located in the vacuum gap. When the electron energy eV is smaller than the vibrator eigenenergy, the final state of an inelastic transition would be a sample filled state (a) the inelastic channel is closed. Hence electrons tunnel without interaction with the oscillator. When eV reaches the mode energy hoj, empty final states at the sample s Fermi energy become accessible the inelastic channel is open. The opening of the inelastic channel causes (c) a sharp increase AG in the tunneling differential conductance d//dV or (d) peaks in the second derivative d2//dV 2. The activation of the inelastic channel takes place indistinguishably of the bias polarity. 

Here o is electrical conductivity, u is thermopower, k is thermal conductivity, t is energy of carrier, p is chemical potential, e is bare charge of electron, and f (e) is Fermi-Dirac distribution function. In deriving eq.(2) we treat the lattice thermal conductivity as a constant. Following we consider the n-type semiconductors, then the change of differential conductivity can be given by ... 

As shown in the photoelectron spectra (see Fig. 4.2), the hydrogen induced state exhibits a binding energy of about 4 eV and is therefore nearly unaccessible to STM investigations. It is nevertheless possible to resolve the spatial distribution of hydrogen since the suppression of the Gd surface state leads to a drastic reduction of the differential conductance at low bias voltages. 

As the temperature is increased from T = 29 K up to 293 K both peaks obviously shift towards the Fermi level, i.e. zero bias. This observation is in strong disagreement with a pure spin mixing behavior as proposed on the basis of PE experiments performed by Li et al. [121]. However, increasing the temperature above 293 K does not lead to a further shift of both peaks. Unfortunately, the binding energy of the occupied surface state could not be determined above T — 360 K. This is caused by the background of the differential conductance... 

This is the simplest, qualitative extension of Eq. (49) when ignoring the variation of the transmission T with energy. With semiconductors and higher gap voltages the normalized differential conductance Psampie( ) oc dlldU)/ I/U) is used [208]. Such Psampie( ) curves reproduce pronounced features of the real... 

A differential conductance measurement of the double-island device at Uquid He temperatures is shown in Figure 5.49a. In this case, due to Coulomb blockade the conductance is suppressed in the region of Vds = 0. The Coulomb charging energy was calculated from the size of the diamonds, and had a value 20 meV, which was in good agreement with that obtained from the simulation of the conductivity expected for such a described device. The basic model for this simulation and the conductance plot are shown in Figure 5.49b and c. 

Figure 8.7. Left density of states at a metal-superconductor contact the shaded regions represent occupied states, with the Fermi level in the middle of the superconducting gap. When a voltage bias V is applied to the metal side the metal density of states is shifted in energy by e V (dashed line). Right differential conductance d//dV as a function of the bias voltage eV at T = 0 (solid line) in this case the measured curve should follow exactly the features of the superconductor density of states AtT > 0 (dashed line) the measured...

To illustrate how the superconducting gap is observed experimentally we consider a contact between a superconductor and a metal. At equilibrium the Fermi level on both sides must be the same, leading to the situation shown in Fig. 8.7. Typically, the superconducting gap is small enough to allow us to approximate the density of states in the metal as a constant over a range of energies at least equal to 21A around the Fermi level. With this approximation, the situation at hand is equivalent to a metal-semiconductor contact, which was discussed in detail in chapter 5. We can therefore apply the results of that discussion directly to the metal-superconductor contact the measured differential conductance at T = 0 will be given by Eq. (5.25),... 

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