Deep-Level States

Deep-level states play an important role in solid-state devices through their behavior as recombination centers. For example, deep-level states are tmdesirable when they facilitate electronic transitions that reduce the efficiency of photovoltaic cells. In other cases, the added reaction pathways for electrons result in desired effects. Electroluminescent panels, for example, rely on electronic transitions that result in emission of photons. The energy level of the states caused by introduction of dopants determines the color of the emitted light. Interfacial states are believed to play a key role in electroluminescence, and commercieil development of this technology will hinge on understanding the relationship between fabrication techniques and tile formation of deep-level states. Deep-level states also influence the performance of solid-state varistors. 

The impact of deep-level states can be significant, even in concentrations that are very low by normal chemical standards. Several states can be associated with a chemical species, and such states may also appear as a result of vacancies or other crystalline defects. Traditional chemical means of detection, therefore, do not pro- 

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Figure 12.1 Schematic representation for the quantum mechanical energy band structure of a semiconductor a) intrinsic semiconductor without dopants or deep-level states b) semiconductor showing energy levels for electron donors and electron acceptors Eai and c) semiconductor with deep-level states of energy f as presented in Section 12.1.3.

Figure 12.4 Schematic representation of electronic transitions, including Shockley-Read-Hall processes for a deep-level state.

The influence of deep-level states or traps on the statistics of electron-hole recombination was first described by Shockley and Read and Hall. Deep-level states, as their name implies, lie close to the middle of the energy bandgap of the semiconductor. Due to the large energy separation from the valence-band and conduction-band edges, deep-level states are not fully ionized at room temperature. In contrast, shallow-level states are those considered to be fully iordzed at room temperature due to thermal excitation. 

The interaction between a deep-level state and electrons and holes can be described by processes 1 to 4 represented in Figvire 12.4. Process 1 involves the emission of a valence-band electron to the deep-level state after receiving energy (Et — Ep). This can also be thought of as hole emission from the deep-level state to the valence band since an electron vacant deep-level state has been filled by a valence-band electron, thus leaving a hole in the valence band. 

Process 3 involves a trapped electron being emitted to the conduction band after receiving an amoimt of energy equal to (Ec — E() from optical or thermal excitation. Process 4 involves a conduction-band electron that comes in the vicinity of a deep-level state and is "trapped" by it. In order for this electron to be trapped, it must lose an amount of energy equal to (Ec — Ef) by radiative (photon) or non-radiative (phonon) processes. 

Process 5 represents excitation of a valence-band electron to the conduction band, thus producing an electron and a hole. The reverse process 6 can be considered to be recombination of an electron and hole. Processes 5 and 6 do not require presence of deep-level states. 

A schematic representation of the band bending at an interface is presented in Figure 12.5. The probability of occupancy of a state is equal to 1/2 at the Fermi energy. The band bending shown in Figure 12.5 causes the deep-level state to make the transition from being fully occupied far from the interface to being fully vacant at the interface. 

Similar circuits have been used to account for both homogeneous and interfacial electronic states. The circuit shown in Figure 12.8 cannot be used to distinguish between surface and bulk deep-level states. It is possible to distinguish the two types of states by means of the Mott-Schottky plots described in Sections 12.3.2 and 18.3. 

Figure 16.9 Electrical circuit analogue developed to account for the influence of two Shockley-Read-Hall electronic transitions through deep-level states. See the discussion of Figure 12.8.

Graphical techniques based on application of an Arrhenius relationship are illustrated here for an -GaAs single crystal diode with a Ti Schottky contact and a Au, Ge, Ni Schottky contact at the eutectic composition. This material has been well characterized in the literature and, in particular, has a well-known EL2 deep-level state that lies 0.83 to 0.85 eV below the conduction band edge. Experimental details are provided by Jansen et... 

An example of the use of Mott-Schottky plots is presented in Figure 18.8. The capacitance was measured at a frequency of 1 MHz applied across the semiconductor sample described in Figure 18.4 as a function of reverse bias with a DLTS spectrometer. Deep-level states are not expected to influence the signal at such a high frequency thus, the slope can be interpreted in terms of the doping level. 

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