Thin-Film Transistors (a-Si, LTPS, IGZO, Organic)

1. Theory

• Definition: A thin-film transistor (TFT) is a field-effect transistor whose channel is a thin semiconductor film deposited on an insulating substrate such as glass or plastic.
• Scope: Hydrogenated amorphous silicon (a-Si:H), low-temperature polysilicon (LTPS), amorphous oxide semiconductors such as IGZO, and organic semiconductors.
• Accumulation-mode device: The gate accumulates majority carriers in the undoped channel film, rather than inverting a doped substrate.
• Trap-dominated behaviour: The square-law form applies above threshold, but mobility, threshold and swing are set by traps in the disordered channel.
• a-Si:H: Directional $s{p}^3$ bonds and bond-angle disorder create broad tail states, giving mobility near $1\mathrm{c}{\mathrm{m}}^2/V\mathrm{s}$.
• IGZO: The conduction band comes from overlapping spherical metal s-orbitals, so mobility stays around $10\mathrm{c}{\mathrm{m}}^2/V\mathrm{s}$ even when amorphous, with very low off-current.
• LTPS: Laser-crystallized grains give high mobility (about 50 to over $100\mathrm{c}{\mathrm{m}}^2/V\mathrm{s}$), limited by charged grain-boundary barriers.
• Organic: Carriers hop between weakly coupled molecules, so mobility is thermally activated.

2. Working Principle

• Gate-voltage-dependent mobility: Most induced carriers fill traps at low gate voltage, so the effective mobility rises with overdrive.
• Multiple trapping and release: Carriers repeatedly drop into and escape from localized states, giving thermally activated transport.
• Subthreshold swing: Interface and bulk trap density set the swing, usually well above 60 mV/dec.
• Bias-stress instability: Long gate bias traps charge and shifts $V_{TH}$ over time, a key reliability issue for display pixels.
• Pixel hold time: Low off-current (especially IGZO) lets a storage capacitor hold its voltage longer, allowing low refresh rates.
• Contact resistance: Source/drain contacts can dominate in short-channel and organic TFTs.

3. Applications

• LCD backplanes (a-Si): Pixel switches in large LCD TVs and monitors.
• Smartphone OLED backplanes (LTPS): High-mobility pixel and driver circuits, often combined with IGZO as LTPO for variable refresh rates.
• Large OLED TVs, tablets and laptops (IGZO): High-resolution, low-power panels.
• Flat-panel X-ray detectors (a-Si): Large-area medical and industrial imaging arrays.
• Flexible and printed electronics (organic): E-paper, flexible sensors and RFID tags (emerging).

General Thin-Film Transistor Relations

Name	Formula	Related Formulae	Variables/Constants
Drain current (above threshold)	$I_D={\mu }_{FE}{C}_i\frac{Z}{L}\left[\left(V_{GS}-V_{TH}\right)V_{DS}-\frac{V_{DS}^2}{2}\right]$ $I_{D,sat}={\mu }_{sat}{C}_i\frac{Z}{2L}{\left(V_{GS}-V_{TH}\right)}^2$	$V_{DS,sat}=V_{GS}-V_{TH}$	$I_D:draincurrentinthelinearregion$ $I_{D,sat}:saturationdraincurrent$ $\begin{array}{r}{\mu }_{FE},{\mu }_{sat}:field-effect\\ mobilitiesextractedinthelinearand\\ saturationregions\end{array}$ $C_i:gateinsulatorcapacitanceperunitarea$ $Z,L:channelwidthandlength$ $V_{TH}:thresholdvoltage$
Field-effect mobility extraction	${\mu }_{FE}=\frac{L}{Z{C}_i{V}_{DS}}{g}_m,g_m=\frac{\partial I_D}{\partial V_{GS}}$	${\mu }_{sat}=\frac{2L}{Z{C}_i}{\left(\frac{\partial \sqrt{I_D}}{\partial V_{GS}}\right)}^2$	$\begin{array}{r}{g}_m:transconductanceinthelinear\\ region(small{V}_{DS})\end{array}$ $\begin{array}{r}{\mu }_{FE}:field-effectmobility,lower\\ thanthebandmobilitybecausetrapped\\ chargedoesnotconduct\end{array}$ $\begin{array}{r}{\mu }_{sat}:saturationmobilityfromthe\\ slopeofthesquarerootofthe\\ saturationcurrent\end{array}$
Subthreshold swing and interface trap density	$S=\frac{\partial V_{GS}}{\partial {\log }_{10}{I}_D}$	$N_{ss}^{max}=\left(\frac{qS}{k_{B}T\ln 10}-1\right)\frac{C_i}{q}$	$S:subthresholdswing$ $\begin{array}{r}{N}_{ss}^{max}:maximumtrapdensityatthe\\ channel/insulatorinterfaceperunitarea\\ andenergy,assumingthatthebulktrap\\ contributionisnegligible\end{array}$ $C_i:gateinsulatorcapacitanceperunitarea$ $k_B:Boltzmannconstant$
Gate-voltage dependent mobility	${\mu }_{eff}={\mu }_0{\left(\frac{V_{GS}-V_{TH}}{V_{AA}}\right)}^{\gamma }$	$I_D={\mu }_0{C}_i\frac{Z}{L}\frac{V_{DS}}{V_{AA}^{\gamma }}{\left(V_{GS}-V_{TH}\right)}^{\gamma +1}(V_{DS}\ll V_{GS}-V_{TH})$	$\begin{array}{r}{\mu }_{eff}:effectivemobility,definedby\\ I_D={\mu }_{eff}{C}_i(Z/L)(V_{GS}-V_{TH})V_{DS}.\\ Thedifferentialfield-effectmobility\\ from{g}_{m}is(\gamma +1){\mu }_{eff}\end{array}$ ${\mu }_0:mobilityat{V}_{GS}-V_{TH}=V_{AA}$ $V_{AA}:reference(characteristic)voltage$ $\begin{array}{r}\gamma :empiricalexponentdescribingthe\\ increaseofmobilityastrapsfill,zero\\ foranidealcrystallinechannel\end{array}$
Contact resistance (transfer length method)	$R_{tot}=\frac{R_{sh}L}{Z}+2R_c$	$R_c=\frac{\sqrt{{\rho }_c{R}_{sh}}}{Z}\coth \left(\frac{L_c}{L_T}\right),L_T=\sqrt{\frac{{\rho }_c}{R_{sh}}}$	$\begin{array}{r}{R}_{tot}:totalchannelpluscontact\\ resistanceatfixedgateoverdrive\end{array}$ $R_{sh}:channelsheetresistance$ $R_c:resistanceofonecontact$ ${\rho }_c:specificcontactresistivity$ $L_c,L_T:contactlengthandtransferlength$
Bias-stress threshold shift	$\Delta V_{TH}(t)=\Delta V_0\left\{1-\exp \left[-{\left(\frac{t}{\tau }\right)}^{\beta }\right]\right\}$	$\tau ={\tau }_0\exp \left(\frac{E_{\tau }}{k_{B}T}\right)$	$\Delta V_{TH}:thresholdshiftafterstresstimet$ $\begin{array}{r}\Delta V_0:saturationvalueoftheshift\\ (limitedbythestressvoltage)\end{array}$ $\tau :characteristictrappingtime$ $\begin{array}{r}\beta :stretchingexponentbetween0and\\ 1,setbythedistributionoftrapping\\ times\end{array}$ $E_{\tau }:activationenergyofthetrappingprocess$ $\begin{array}{r}\text{(Libsch}\text{and}\text{Kanicki,}\text{Appl.}\text{Phys.}\text{Lett.}\\ \text{62,}\text{1286}\text{(1993))}\end{array}$ $k_B:Boltzmannconstant$
Pixel hold time	$t_{hold}=\frac{C_{st}\Delta V_{max}}{I_{off}}$		$\begin{array}{r}{t}_{hold}:timeforwhichtheTFTholds\\ thepixelvoltagewithintheallowed\\ drop\end{array}$ $C_{st}:storagecapacitanceofthepixel$ $\begin{array}{r}\Delta V_{max}:maximumtolerateddropin\\ thestoredvoltage\end{array}$ $I_{off}:off-stateleakagecurrentoftheTFT$

Amorphous Silicon and Amorphous Oxide Semiconductors

Name	Formula	Related Formulae	Variables/Constants
Subgap density of states	$g(E)=g_{tail}\exp \left(\frac{E-E_C}{k_B{T}_t}\right)+g_{deep}\exp \left(\frac{E-E_C}{k_B{T}_d}\right)$		$\begin{array}{r}g(E):densityoflocalizedstatesbelow\\ theconductionbandedge\end{array}$ $\begin{array}{r}{g}_{tail},g_{deep}:densityprefactorsof\\ thetailanddeepstates\end{array}$ $\begin{array}{r}{k}_B{T}_t,k_B{T}_d:characteristicenergiesof\\ thetailanddeepstatedistributions\end{array}$ $E_C:conductionbandedge$ $k_B:Boltzmannconstant$
Multiple trapping and release	${\mu }_{eff}={\mu }_0\frac{n_{free}}{n_{free}+n_{trap}}$	${\mu }_{eff}\approx {\mu }_0\frac{N_C}{N_t}\exp \left(-\frac{E_C-E_t}{k_{B}T}\right)(\text{single trap level})$	$\begin{array}{r}{\mu }_0:free-carrier(band)mobilityin\\ theextendedstates\end{array}$ $\begin{array}{r}{n}_{free},n_{trap}:densitiesoffreeand\\ trappedelectrons\end{array}$ $\begin{array}{r}{N}_C:effectivedensityofstatesofthe\\ conductionband\end{array}$ $\begin{array}{r}{N}_t,E_t:densityandenergyofatrap\\ levelbelow{E}_C\end{array}$ $k_B:Boltzmannconstant$
Activated mobility and the Meyer-Neldel rule	$\mu (T)={\mu }_{00}\exp \left(\frac{E_a}{E_{MN}}\right)\exp \left(-\frac{E_a}{k_{B}T}\right)$		$E_a:activationenergyofthemobility$ $\begin{array}{r}{E}_{MN}:Meyer-Neldelenergy,whichmakes\\ thecurvesfordifferent{E}_{a}crossat\\ onetemperature\end{array}$ ${\mu }_{00}:mobilityprefactor$ $k_B:Boltzmannconstant$

Low-Temperature Polysilicon (LTPS)

Name	Formula	Related Formulae	Variables/Constants
Grain boundary potential barrier (Seto)	$E_B=\frac{q^2{N}_t^2}{8{\epsilon }_{si}N}(L_{g}N>N_t)$ $E_B=\frac{q^2{L}_g^{2}N}{8{\epsilon }_{si}}(L_{g}N<N_t)$	${\mu }_{eff}={\mu }_0\exp \left(-\frac{E_B}{k_{B}T}\right),{\mu }_0=\frac{q{L}_g}{\sqrt{2\pi m^{\ast }{k}_{B}T}}$	$\begin{array}{r}{E}_B:potentialbarrierheightatagrain\\ boundary.Thefirstformholdsfora\\ partiallydepletedgrain(trappedcharge\\ N_{t}smallerthanthedopantcharge\\ N{L}_g),thesecondforafullydepleted\\ grain\end{array}$ $\begin{array}{r}{N}_t:densityoftrappedstatesperunit\\ areaattheboundary\end{array}$ $N:dopingconcentration$ $L_g:grainsize$ $m^{\ast }:effectivemass$ ${\mu }_0:intragrainthermionicprefactor$ $k_B:Boltzmannconstant$

Organic Thin-Film Transistors

Name	Formula	Related Formulae	Variables/Constants
Hopping transport in organic semiconductors	$\mu (T)={\mu }_0\exp \left[-{\left(\frac{T_0}{T}\right)}^2\right]$		${\mu }_0:mobilityprefactorathightemperature$ $\begin{array}{r}{T}_0:characteristictemperatureofthe\\ Gaussiandisorderinthedensityof\\ states,T_0=2\sigma /(3k_B)foraGaussian\\ withwidth\sigma \end{array}$ $\begin{array}{r}\text{(the}\text{Gaussian}\text{disorder}\text{model}\text{of}\\ \text{Bassler,}\text{valid}\text{for}\text{hopping}\text{at}\text{low}\\ \text{carrier}\text{density)}\end{array}$ $k_B:Boltzmannconstant$

Important Questions

Ques: Why does the extracted mobility depend on gate voltage in an amorphous or disordered TFT, and what does $\gamma$ mean?

In a disordered channel most induced carriers fall into localized states below the band edge. The mobile fraction $n_{free}/(n_{free}+n_{trap})$ is small at low gate voltage and rises as the Fermi level approaches the band edge and the traps fill, so the effective mobility rises with gate overdrive. The empirical exponent $\gamma$ in ${\mu }_{eff}={\mu }_0[(V_{GS}-V_{TH})/V_{AA}{]}^{\gamma }$ measures how strongly trapping depends on the Fermi level; it is zero for an ideal single-crystal channel and larger for broad tail-state distributions (a larger characteristic tail temperature). For this reason a single mobility number is meaningful only when quoted with a gate voltage and temperature. Reference: M. Shur and M. Hack, “Physics of amorphous silicon based alloy field-effect transistors,” J. Appl. Phys. 55, 3831 (1984).

Ques: Why do oxide semiconductors such as IGZO have much higher mobility than amorphous silicon?

The conduction band minimum of IGZO is formed by overlapping spherical metal $s$ orbitals, whose overlap is not strongly affected by bond-angle disorder, so electrons move with a band-like mobility of roughly $10\mathrm{c}{\mathrm{m}}^2/V\mathrm{s}$ even in an amorphous film. In amorphous silicon the conduction path uses directional $s{p}^3$ orbitals, and bond-angle disorder produces broad tail states that trap carriers, so ${\mu }_{FE}$ stays near $1\mathrm{c}{\mathrm{m}}^2/V\mathrm{s}$. The wide bandgap of IGZO also gives extremely low off currents, so the hold time $C_{st}\Delta V_{max}/I_{off}$ of a pixel can be long, which is useful for low-power displays. Reference: T. Kamiya, K. Nomura, and H. Hosono, “Present status of amorphous In-Ga-Zn-O thin-film transistors,” Sci. Technol. Adv. Mater. 11, 044305 (2010).

Ques: What limits mobility in low-temperature polysilicon?

Low-temperature polysilicon is made of crystalline grains separated by grain boundaries that carry trapped charge. The trapped charge depletes the grain edges and produces a barrier $E_B=q^2{N}_t^2/(8{\epsilon }_{si}N)$ when the grain is only partly depleted ($L_{g}N>N_t$), or $E_B=q^2{L}_g^{2}N/(8{\epsilon }_{si})$ when it is fully depleted ($L_{g}N<N_t$), so the effective mobility is thermally activated and falls with the trap density. Grain boundary traps also create leakage and variability, which is why grain size, grain orientation and hydrogen passivation are the main process variables. Reference: J.Y.W. Seto, “The electrical properties of polycrystalline silicon films,” J. Appl. Phys. 46, 5247 (1975).

Ques: Why is charge transport in organic semiconductors thermally activated?

Organic films are made of weakly coupled molecules, so carriers localize on single molecules and move by hopping between sites whose energies are spread out by disorder. In the Gaussian disorder model, hops to higher-energy sites need thermal activation, which gives $\mu \propto \exp [-(T_0/T{)}^2]$ with $T_0=2\sigma /(3k_B)$, so mobility rises with temperature, opposite to the band-like behaviour of crystalline silicon. Highly ordered films with small $\sigma$ show weaker temperature dependence. Reference: H. Bassler, “Charge transport in disordered organic photoconductors,” Phys. Status Solidi B 175, 15 (1993).

Related pages in this vault: Thin-Film Transistors (a-Si, LTPS, IGZO, Organic) (degradation), Organic Light Emitting Diode (OLED), Carbon Nanotube and Two-Dimensional Material FETs, Long Channel MOSFET, Sensor Field Effect Transistors (ISFET, ChemFET, BioFET, EGOFET), Graphene Field Effect Transistor, Organic Charge Trap Transistor Memory (Polymer Electret and Nanoparticle), Schottky Barrier and Dynamic Threshold_MOSFET, Organic and Molecular Resistive Memory, Plasma and Radical Oxidation Tool, Laser Annealing System.