Semiconductor Device Physics for TFTs

Abstract

Two device physics topics are discussed in this chapter, namely, surface band bending and surface charges in the metal–insulator–semiconductor, MIS, structure, and electron-hole pair recombination/generation processes. The treatment of the MIS structure covers the relationship between the voltage on the metal gate, the induced surface charge in the semiconductor and the resulting surface potential. This is treated analytically, using single crystal equations, and the relationships are fundamental to the understanding of IGFET operation. Equally, the concepts are widely employed in analysing TFT behaviour. The electron-hole pair generation process underlies the leakage current behaviour of many semiconductor devices, and can be applied to the analysis of TFT off-state behaviour. The recombination process determines steady state carrier concentrations under injection conditions, such as optical illumination. Finally, there is a brief discussion of carrier flow in semiconductor devices, including the equations used in numerical simulation packages.

Appendix: Summary of Key Equations

A number of the simplified equations from the text, which can be used in basic analytical calculations, are reproduced below. The equation numbers are retained for quick reference back to the original derivations.

1.1 Semiconductor Surface Band Bending

Relationships between surface potential, V_s, space charge density, Q_s, gate voltage, V_G, and threshold voltage, V_T.

• (a) Depletion and Inversion Space Charge Density

  $$ Q_{s} \cong - \sqrt {2q\varepsilon_{0} \varepsilon_{s} } \left[ {n_{i} \frac{kT}{q}exp\frac{{q(V_{s} - V_{F} )}}{kT} + N_{a} V_{s} } \right]^{0.5} $$

  (2.12)

• (b) Depletion Space Charge Density

  $$ Q_{s} \cong - \sqrt {2q\varepsilon_{0} \varepsilon_{s} N_{a} V_{s} } $$

  (2.13)

• (c) Gate Voltage, Surface Potential and Space Charge Density

  $$ {\text{V}}_{\text{G}} = {\text{ V}}_{\text{s}} - {\text{ Q}}_{\text{s}} /{\text{C}}_{\text{i}} $$

  (2.22)

• (d) Gate Threshold Voltage

  $$ V_{T} = V_{FB} + \frac{{\sqrt {2q\varepsilon_{0} \varepsilon_{s} N_{a} 2V_{F} } }}{{C_{i} }} + 2V_{F} $$

  (2.28)

  and, from Eq. 2.5, V_F = (kT/q)ln(N_a/n_i)

• (e) Depletion Layer Thickness at Inversion

  $$ x_{d\hbox{max} } = \sqrt {\frac{{2\varepsilon_{0} \varepsilon_{s} 2V_{F} }}{{qN_{a} }}} $$

  (2.18)

• (f) Flat-Band Voltage

  $$ {\text{V}}_{\text{FB}} = \Upphi_{\text{MS}} - {\text{ Q}}_{\text{ieff}} /{\text{C}}_{\text{i}} - {\text{ Q}}_{\text{ss}} /{\text{C}}_{\text{i}} $$

1.2 Carrier Recombination and Generation

Relationships between trap density, N_T, and capture cross section, σ, and the carrier generation/recombination rates.

• (a) General Recombination and Generation Rate Expression

  $$ R_{GR} = \frac{{\sigma v_{th} N_{T} [n_{i}^{2} - np]}}{{n + p + 2n_{i} cosh(E_{T} - E_{i} )kT}} $$

  (2.63)

• (b) Generation Leakage Current

  $$ \, J_{R} \equiv qn_{i} W/\tau_{g} $$

  (2.70)

• (c) Generation Lifetime, τ_g

  $$ \tau_{\text{g}} = { 1}/(0. 5 {\text{N}}_{\text{T}} \sigma {\text{v}}_{\text{th}} ) $$

  (2.71a)

• (d) Carrier Recombination Rate, and Recombination Lifetime, τ_R

  $$ R_{R} = - \sigma_{p} v_{th} N_{T} \Updelta p \equiv \Updelta p/\tau_{R} $$

  (2.81)

• (e) Recombination Lifetime (Low Injection Level)

  $$ \tau_{R} = 1/\sigma_{p} v_{th} N_{T} $$

  (2.82)

• (f) Recombination Lifetime (High Injection Level)

  $$ \tau_{R} = 1/\sigma_{p} v_{th} N_{T} + 1/\sigma_{n} v_{th} N_{T} $$

  (2.89)