Organic Charge Trap Transistor Memory (Polymer Electret and Nanoparticle)

1. Theory

Definition: An organic charge-trap transistor memory is an organic thin-film transistor (e.g. pentacene channel) with a charge-storage layer in its gate stack, giving two stable threshold voltages.
Storage forms: A floating gate of metal nanoparticles (e.g. Au), a polymer electret (e.g. polystyrene or PVA) that traps charge, or a layer of charge-trapping molecules.
Placement: It sits in the non-volatile folder because the state is stored as trapped charge, like its inorganic counterparts.
Threshold shift: Stored charge shifts $V_{T}$ by $- Q_{t} / C_{c t r l}$ .
Nanoparticle charging energy: Each nanoparticle can hold only a few electrons because of its charging energy $q^{2} /2 C_{N P}$ .
Organic transport: Carriers move by multiple trapping and release in localized states, giving mobility of roughly $0.1$ to a few $c m^{2} /V s$ .

2. Working Principle

Program and erase: Gate pulses move charge between the organic channel and the storage layer, shifting the threshold up or down.
Read: The drain current is measured at a gate voltage between the two thresholds.
Memory window: Set by the storage-site density and the applied voltage; a thinner blocking layer lowers voltage but hurts retention.
High voltages: Many devices need tens of volts, reduced by thin or high-k dielectrics.
On/off ratio: At most about $1 0^{M W / S}$ (exact when both states are read below threshold), so interface traps that worsen the swing reduce it.
Photo-programming: Some organic phototransistor memories can be written with light under gate bias.

3. Applications

Current status: Research devices; not yet in commercial products.
Flexible and printed electronics (target): Non-volatile memory for flexible sensors, RFID tags and wearable circuits built on plastic substrates.

Name	Formula	Related Formulae	Variables/Constants
Organic thin-film transistor current	$I_{D} = \frac{W}{L} μ C_{i} [(V_{G} - V_{T}) V_{D} - \frac{V _{D}^{2}}{2}]$	$I_{D, s a t} = \frac{W}{2 L} μ C_{i} (V_{G} - V_{T})^{2}$	$I_{D} : d r ain c u r r e n t o f an or g ani c t hin - f i l m t r an s i s t or in t h e l in e a r r e g im e (g r a d u a l c hann e l a pp r o x ima t i o n)$ $W, L : c hann e l w i d t h an d l e n g t h$ $μ : f i e l d - e f f ec t m o bi l i t y o f t h e or g ani c se mi co n d u c t or (w hi c h d e p e n d s o n t h e g a t e v o l t a g e in man y or g ani c f i l m s)$ $C_{i} : g a t e d i e l ec t r i c c a p a c i t an ce p er u ni t a r e a$ $V_{G}, V_{D}, V_{T} : g a t e, d r ain an d t h r es h o l d v o l t a g e$ $I_{D, s a t} : s a t u r a t i o n c u r r e n t f or V_{D} ab o v e V_{G} - V_{T}$
Threshold shift from the stored charge	$Δ V_{T} = - \frac{Q _{t}}{C _{c t r l}}$	$\frac{1}{C _{c t r l}} = \frac{t _{b}}{ε _{0} ε _{b}}$ $M W = V_{T, E R A S E D} - V_{T, P R O G}$	$Δ V_{T} : s hi f t o f t h e t h r es h o l d v o l t a g e c a u se d b y a s i g n e d s t or e d c ha r g e p er u ni t a r e a Q_{t} (p os i t i v e s t or e d c ha r g e g i v es a n e g a t i v e s hi f t)$ $Q_{t} : s t or e d c ha r g e p er u ni t a r e a, w i t h i t s s i g n$ $C_{c t r l} : c a p a c i t an ce p er u ni t a r e a b e tw ee n t h e g a t e an d t h e t r a pp in g l a y er (t h e b l oc k in g d i e l ec t r i c)$ $t_{b}, ε_{b} : t hi c k n ess an d r e l a t i v e p er mi tt i v i t y o f t h e b l oc k in g d i e l ec t r i c$ $M W : m e m or y w in d o w, t h e d i f f er e n ce b e tw ee n t h e t h r es h o l d v o l t a g es o f t h e er a se d an d t h e p r o g r amm e d s t a t e$ $(t h e s am e c ha r g e - s h ee t r u l e a s o n t h e F l o a t in g G a t e F l a s h an d C ha r g e T r a p F l a s h p a g es)$ $(s i g n b y c a r r i er : t r a pp e d e l ec t r o n s (Q_{t} < 0) s hi f t V_{T} p os i t i v e an d t r a pp e d h o l es (Q_{t} > 0) n e g a t i v e, f or p - c hann e l an d n - c hann e l d e v i ces a l ik e; in a p - c hann e l p e n t a ce n e d e v i ce V_{T} i s n e g a t i v e, so e l ec t r o n t r a pp in g mak es i t l ess n e g a t i v e)$
Nanoparticle storage: charging energy and threshold shift	$E_{C} = \frac{q ^{2}}{2 C _{N P}}$ $C_{N P} = 4 π ε_{0} ε_{m} r_{N P}$	$Δ V_{T} = - \frac{q n _{N P} N _{e}}{C _{c t r l}}$	$E_{C} : e n er g y t o a dd o n e e l ec t r o n t o a m e t a l nan o p a r t i c l e (c ha r g in g e n er g y, a s o n t h e N an ocr y s t a l M e m or y p a g e)$ $C_{N P} : se l f - c a p a c i t an ce o f t h e nan o p a r t i c l e in a m e d i u m (a s p h er e in a u ni f or m d i e l ec t r i c; a n e a r b y g a t e or c hann e l a dd s ima g e - c ha r g e c a p a c i t an ce, so t hi s C_{N P} i s a l o w er b o u n d an d E_{C} an u pp er b o u n d)$ $ε_{m} : r e l a t i v e p er mi tt i v i t y o f t h e s u r r o u n d in g p o l y m er$ $r_{N P} : r a d i u s o f t h e nan o p a r t i c l e$ $Δ V_{T} : t h r es h o l d s hi f t w h e n e a c h nan o p a r t i c l e h o l d s N_{e} e l ec t r o n s$ $n_{N P} : a r e a l d e n s i t y o f t h e nan o p a r t i c l es$ $N_{e} : a v er a g e n u mb er o f s t or e d e l ec t r o n s p er nan o p a r t i c l e$ $C_{c t r l} : c a p a c i t an ce p er u ni t a r e a b e tw ee n t h e g a t e an d t h e nan o p a r t i c l e l a y er$
Subthreshold slope and read on/off ratio	$S = ln 10 \frac{k _{B} T}{q} (1 + \frac{q ^{2} D _{i t}}{C _{i}})$	$\frac{I _{r e a d, E R A S E D}}{I _{r e a d, P R O G}} \approx 1 0^{M W / S}$	$S : s u b t h r es h o l d s w in g o f t h e t r an s i s t or (t h e g a t e v o l t a g e f or o n e d ec a d e o f c u r r e n t)$ $k_{B}, T, q : B o l t z mann co n s t an t, t e m p er a t u r e an d e l e m e n t a r y c ha r g e$ $D_{i t} : d e n s i t y o f in t er f a ce t r a p s p er u ni t a r e a an d e n er g y$ $C_{i} : g a t e d i e l ec t r i c c a p a c i t an ce p er u ni t a r e a$ $M W : m e m or y w in d o w$ $I_{r e a d, E R A S E D}, I_{r e a d, P R O G} : c u r r e n t s o f t h e tw o s t a t es a t a r e a d g a t e v o l t a g e b e tw ee n t h e tw o t h r es h o l d s (t h e r a t i o i s e x a c t o n l y w h e n b o t h s t a t es a r e r e a d in t h e i r s u b t h r es h o l d r e g i o n w i t h t h e s am e co n s t an t S; i f t h e l o w er - t h r es h o l d s t a t e i s ab o v e t h r es h o l d a t t h e r e a d v o l t a g e, t h e r a t i o i s s ma l l er, so 1 0^{M W / S} i s an u pp er b o u n d)$
Multiple trapping and release	$μ_{e f f} = μ_{0} θ$	$θ \approx [1 + \frac{N _{t}}{N _{c}} exp (\frac{E _{t}}{k _{B} T})]^{- 1}$	$μ_{e f f} : e f f ec t i v e m o bi l i t y o f t h e or g ani c se mi co n d u c t or l imi t e d b y t r a pp in g$ $μ_{0} : m o bi l i t y o f t h e f r ee c a r r i er s in t h e t r an s p or t ban d$ $θ : f r a c t i o n o f t h e t im e t ha t a c a r r i er s p e n d s in t h e t r an s p or t ban d$ $N_{t} : d e n s i t y o f t h e t r a p s a t a s in g l e e n er g y E_{t} b e l o w t h e t r an s p or t ban d$ $N_{c} : e f f ec t i v e d e n s i t y o f s t a t es o f t h e t r an s p or t ban d$ $E_{t} : t r a p d e pt h$ $k_{B}, T : B o l t z mann co n s t an t an d t e m p er a t u r e$

Important Questions

Ques: How is an organic transistor memory built, and where is the charge stored?

It is an organic thin-film transistor in which a layer in the gate stack holds charge, so the threshold voltage has two values. Three forms are used: a floating gate of metal nanoparticles (for example Au) embedded in the gate dielectric or in a polymer; a polymer electret (such as polystyrene or PVA) between the gate and the channel, which traps charge at its interfaces and in its bulk; and a layer of charge-trapping molecules or a charge-transfer layer. A gate pulse transfers charge from the semiconductor into the storage layer (or removes it), the stored charge shifts the threshold by $Δ V_{T} = - Q_{t} / C_{c t r l}$ , and the state is read as the drain current at a gate voltage between the two thresholds. Reference: K.-J. Baeg et al., “Organic non-volatile memory based on pentacene field-effect transistors using a polymeric gate electret,” Adv. Mater. 18, 3179 (2006); T. Sekitani et al., “Organic nonvolatile memory transistors for flexible sensor arrays,” Science 326, 1516 (2009).

Ques: Why is the memory window of an organic transistor memory limited, and how can it be increased?

The window is the threshold shift from the stored charge, $Q_{t} / C_{c t r l}$ , and the stored charge is limited by the density of storage sites and the voltage that can be applied. A thinner blocking layer raises $C_{c t r l}$ and lowers the voltage for a given charge, but also lowers the retention, since the charge can leak back. A larger charge density needs more nanoparticles per area (the nanoparticle row), a higher number of electrons per nanoparticle (limited by the charging energy $E_{C}$ ) or a thicker electret. The programming voltage in many organic memories is tens of volts, which is high for flexible circuits, and it is lowered by a high-permittivity or thin dielectric. Reference: T. Sekitani et al., Science 326, 1516 (2009); K.-J. Baeg et al., Adv. Mater. 18, 3179 (2006).

Ques: What limits the read current and the on/off ratio?

The organic semiconductor has a mobility of the order of 0.1 to a few cm $^{2}$ /Vs, which is low because the carriers are trapped and released in the localized states (the multiple trapping and release row), so the drain current is low for a given geometry. The on/off ratio of the two states is set by the memory window and the subthreshold swing, $1 0^{M W / S}$ , so a large swing from the interface traps (the $D_{i t}$ term) reduces it. Increasing the dielectric capacitance lowers $S$ and the operating voltage. Reference: G. Horowitz, “Organic field-effect transistors,” Adv. Mater. 10, 365 (1998); G. Horowitz and P. Delannoy, “An analytical model for organic-based thin-film transistors,” J. Appl. Phys. 70, 469 (1991).

Ques: Can the memory be written with light?

Photo-programming is used in organic phototransistor memories: light of a suitable wavelength creates excitons in the semiconductor or in the storage layer, the carriers of one sign are injected into the storage layer under a gate bias, and the threshold shifts. The state is erased by a gate pulse or by light of another wavelength. The mechanism combines the charge transfer between layers (the stored charge row) with the optical absorption, which is outside the scope of the device-level rows of this page. Reference: a general description, without a single source; K.-J. Baeg et al., Adv. Mater. 18, 3179 (2006), for the gate-electret structure only.

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