Semiconductors forward bias

The simplest and most widely used model to explain the response of organic photovoltaic devices under illumination is a metal-insulaior-metal (MIM) tunnel diode [55] with asymmetrical work-function metal electrodes (see Fig. 15-10). In forward bias, holes from the high work-function metal and electrons from the low work-function metal are injected into the organic semiconductor thin film. Because of the asymmetry of the work-functions for the two different metals, forward bias currents are orders of magnitude larger than reverse bias currents at low voltages. The expansion of the current transport model described above to a carrier generation term was not taken into account until now. 

Figure 27. Minority charge carrier profiles near the semiconductor/electrolyte junction. calculated for a silicon interface at two different electrode potentials. Uf- -0.25 V and Uf= 5.0 V10 ((//= forward bias = t/ - Ufl>).

FIGURE 3.47 The structure of a p-n junction allows an electric current to flow in only one direction, (a) Reverse bias the negative electrode is attached to the p-type semiconductor and current does not flow, (b) Forward bias the electrodes are reversed to allow charge carriers to be regenerated. 

The photovoltage is esentially determined by the ratio of the photo- and saturation current. Since io oomrs as a pre-exponential factor in Eq. 1 it determines also the dark current. Actually this is the main reason that it limits the photovoltage via Eq. 2, The value of io depends on the mechanism of charge transfer at the interface under forward bias and is normally different for a pn-junction and a metal-semiconductor contact. In the first case electrons are injected into the p-region and holes into the n-region. These minority carriers recombine somewhere in the bulk as illustrated in Fig. 1 c. In such a minority carrier device the forward current is essentially determined... 

Fig. 3a—c. Charge transfer processes at semiconductor-electrolyte interface a) and b) under forward bias. 

The Aviram-Ratner D-ct-A molecule is analogous to a pn junction rectifier the electron-rich donor region D would be similar to the electron-rich semiconducting n region, while the electron-poor A region would be similar to a semiconductor s p region [79]. However, note that under forward bias the preferred direction of Aviram-Ratner electron flow is from A to D, while in a pn junction rectifier the preferred direction is from n to p. 

The speed of response of the photodiode depends on the diffusion of carriers, the capacitance of the depletion layer, and the thickness of the depletion layer. The forward bias itself increases the width of the depletion layer thus reducing the capacitance. Nevertheless, some design compromises are always required between quantum efficiency and speed of response. The quantum efficiency of a photodiode is determined largely by the absorption coefficient of the absorbing semiconductor layer. Ideally all absorption should occur in the depletion region. This can be achieved by increasing the thickness of the depletion layer, but then the response time increases accordingly. 

As shown in Fig. 3.13(b) and 3.13(c) when ratio n/nsfl is less than or greater than 1 the system is in non-equilibrium resulting in a net current, with the electron transfer kinetics at the semiconductor-electrolyte interface largely determined by changes in the electron surface concentration and the application of a bias potential. Under reverse bias voltage, Vei > 0 and ns,o > ns as illustrated in Fig. 3.13(b), anodic current will flow across the interface enabling oxidized species to convert to reduced species (reduction process). Similarly, under forward bias, Ve2 < 0 and ns > ns,o as illustrated in Fig. 3.13(c), a net cathodic current will flow. 

Fig. 3.13 Semiconductor-electrolyte interface (a) at equilibrium, (b) under reverse bias (c) under forward bias. Arrows denote direction of current flow [reduction reaction ox + e red], (d) Electron transfer mediated through surface states.

The sample, a reverse-biased p-n or metal-semiconductor junction, is placed in a capacitance bridge and the quiescent capacitance signal nulled out. The diode is then repetitively pulsed, either to lower reverse bias or into forward bias, and the transient due to the emission of trapped carriers is analyzed. As discussed in the preceding section, for a single deep state with JVT Nd the transient is exponential with an initial amplitude that gives the trap concentration, and a time constant, its emission rate. The capacitance signal is processed by a rate window whose output peaks when the time constant of the input transient matches a preset value. The temperature of the sample is then scanned (usually from 77 to 450°K) and the output of the rate window plotted as a function of the temperature. This produces a trap spectrum that peaks when the emission rate of carriers equals the value determined by the window and is zero otherwise. If there are several traps present, the transient will be a sum of exponentials, each having a time... 

Figure 8. Schematic representations of p-n junctions and corresponding energy band diagrams under various conditions (a) uniformly doped p-type and n-type semiconductors before junction is formed, (b) thermal equilibrium, (c) forward bias, and (d) reverse bias. Abbreviations are defined as follows Ec, electron energy at conduction band minimum E, , electron energy at valence band minimum IF, forward current Vf, forward voltage Vr, reverse voltage ...

Figure 24 Schottky barrier contact with an insulating interfacial layer. In the semiconductor and the insulator, the valence and conduction levels are shown as solid lines at zero bias (barrier heights Vty and < >) and as dashed lines at forward bias (barrier heights VD and ct>ps).

Figure 6 Schottky junction between a metal and an n-type semiconductor (a) before contact (b) after contact, without bias (c) forward bias (d) reverse bias.

The depletion layer profile contains information about the density of states distribution and the built-in potential. The depletion layer width reduces to zero at a forward bias equal to and increases in reverse bias. The voltage dependence of the jimction capacitance is a common method of measuring W V). Eq. (9.9) applies to a semiconductor with a discrete donor level, and 1 is obtained from the intercept of a plot of 1/C versus voltage. The 1/C plot is not linear for a-Si H because of the continuous distribution of gap states-an example is shown in Fig. 4.16. The alternative expression, Eq. (9.10), is also not an accurate fit, but nevertheless the data can be extrapolated reasonably well to give the built-in potential. The main limitation of the capacitance measurement is that the bulk of the sample must be conducting, so that the measurement is difficult for undoped a-Si H. 

Three important elements of inorganic semiconductor device structures are shown in Figure 3. A Schottky contact between a metal and a semiconductor, to inject or collect electrons (or holes) in a semiconductor, is shown in Figure 3a. In this diagram, the Schottky contact is in forward bias, Vj it is easier for electrons to flow from the semiconductor into the metal than vice versa because of the smaller energy barrier that must be surmounted when electrons move in the semiconductor-to-metal direction. In... 

Fermi level pinning the ability of surface states to buffer the Fermi level of the semiconductor from changes in the electrochemical potential of the contacting phase Forward bias the sign of the applied potential that results in an exponential increase in the current passing through a semiconductor junction... 

Figure 6 An energy diagram of the charge-transfer process at an n-type semiconductor/metal interface when an external potential (F) is applied across the semiconductor electrode. The applied potential changes the electric potential difference between the semiconductor surface and the bulk region. This perturbs the concentration of electrons at the surface of the semiconductor (ns), and a net current flows through the semiconductor/metal interface. The forward reaction represents the transfer of electrons from the semiconductor to the metal and the reverse reaction represents the injection of electrons into the semiconductor from the metal. The width of the arrows indicates schematically the relative magnitude of the current, (a) The reverse bias condition for an n-type semiconductor (V > 0). The forward reaction rate is reduced relative to its equilibrium value, while the reverse reaction rate remains constant. A net positive current exists at the electrode surface, (b) The forward bias condition (V < 0), the forward reaction rate increases compared to its equilibrium value, while the reverse reaction rate remains unaffected. A net negative current exists at the electrode surface...

The p-n junction involves the contact of a p-type and an n-type semiconductor, (a) The charge carriers of the p-type region are holes ( ). In the n-type region the charge carriers are electrons (Q). (b) No current flows (reverse bias), (c) Current readily flows (forward bias). Note that each electron that crosses the boundary leaves a hole behind. Thus the electrons and the holes move in opposite directions. 

Figure 12. Three situations for an n-type semiconductor-electrolyte interface at equlibrium (a), under reverse bias (b) and under forward bias (c). The size of the arrows denotes the magnitudes of the current in the two (i.e., anodic and cathodic) directions.

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