Abstract
A thorough treatment of Schottky (metal–semiconductor) diodes, MIS (metal–insulator–semiconductor) diodes and (bipolar) pn-diodes is given, focussing on suitable materials, the formation of space charge layers and the forward and reverse current–voltage characteristics. Applications of such devices based on their rectifying properties are discussed.
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Notes
- 1.
The simplest device is a resistor made from a homogeneous piece of semiconductor, used, e.g., as a part of an integrated circuit or as a photoresistor as discussed in Sect. 22.2.
- 2.
This distinction is not only made for diodes but also many other semiconductor devices such as transistors, see Chap. 24.
- 3.
This situation is similar to the heterostructure interface (Sect. 12.3.4), with the metal, however, having a very short screening length.
- 4.
We denote the energy barrier height with \(F_{\mathrm {B}}=-e\phi _{\mathrm {B}}\).
- 5.
The functional integration method is limited to bijective potentials \(\phi (x)\), i.e. strictly monotonously falling or rising potentials [1422] and thus covers monotonously varying doping density within the depletion layer.
- 6.
The term \(\epsilon _{\mathrm {s}}^3\) is technically \(\epsilon _{\mathrm {s}} \epsilon _{\mathrm {d}}^2\) where \(\epsilon _{\mathrm {d}}\) is the image-force dielectric constant. \(\epsilon _{\mathrm {d}}\) is equal to \(\epsilon _{\mathrm {s}}\) if the transit time of an electron from the metal to the maximum of the potential energy is sufficiently long to build up the dielectric polarization of the semiconductor [1406].
- 7.
Probing the capacitance as a function of the ac frequency is called admittance spectroscopy .
- 8.
This is valid as long as \(\varphi (x)\) is strictly monotonous.
- 9.
Obviously \(n=1\) for the ideal characteristic (21.48). Otherwise \(n \ge 1\).
- 10.
This phenomenon is similar to the red-shift of luminescence lines (Stokes shift) due to thermalization in the presence of disorder , see Sect. 12.4.
- 11.
Reconstructions are accompanied by redistributions of the valence charge with respect to the undisturbed bulk (Sect. 11.4). The subsequent extra interface dipoles alter the barrier heights of reconstructed interfaces [1455].
- 12.
Also a Schottky diode has an Ohmic back contact.
- 13.
This poling is a forward bias of the respective Schottky diode since the positive pole is at the p-type semiconductor.
- 14.
We note that in order to reach the situations shown in Fig. 21.30 from the zero bias case of Fig. 21.29, a current must have flowed since charge carriers are redistributed. Figure 21.30 depicts the stationary equilibrium after transient voltage switch-on effects have subsided. The time, however, that is needed in order to reach such stationary equilibrium from zero bias (thermal equilibrium) may be very long (e.g. days, cf. Sect. 22.3.8).
- 15.
\(\varPsi _{\mathrm {s}}\) represents the voltage drop across the semiconductor that will be discussed in more detail in Sect. 21.3.3. In this sense, \(\varPsi _{\mathrm {s}}\) for the MIS diode is related to \(V_{\mathrm {bi}}-V\) for the Schottky contact.
- 16.
We note that we discuss the space-charge region now only with regard to \(\varPsi _{\mathrm {s}}\), the voltage drop across the semiconductor, and the dependence of \(\varPsi _{\mathrm {s}}\) on the bias of the diode will be discussed in the next section.
- 17.
For \(N_{\mathrm {A}}/n_{\mathrm {i}}=10^4\), \(10^6\) and \(10^8\), we find \(\gamma =2.33\), 2.25 and 2.20, respectively.
- 18.
Typically, a dc bias voltage V is set and the capacitance is sampled with a small ac voltage of amplitude \(\varDelta V\), with \(\delta V \ll V\).
- 19.
The choices of dopant and the growth conditions, in particular the temperature, need to be made such that no interdiffusion of the dopants takes place.
- 20.
An abrupt decrease of the majority carrier density at the border of the space-charge region corresponds to zero temperature.
- 21.
We remind the reader that \(\mu _{\mathrm {n}}\) was defined as a negative number.
- 22.
- 23.
That in military applications could make the mixer detectable by the enemy.
- 24.
Pseudomorphic high electron mobility transistors, cf. Sect. 24.5.8.
- 25.
We note that for the 1N4396 silicon tunneling diode [1517] the phonon structure of germanium was found in [1516].
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Grundmann, M. (2016). Diodes. In: The Physics of Semiconductors. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-23880-7_21
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DOI: https://doi.org/10.1007/978-3-319-23880-7_21
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