1. Theory

Definition: Charge pumping applies repetitive pulses to a MOSFET gate, with source and drain at a fixed bias, and measures the DC body current produced by recombination of electrons and holes through interface traps (TU Wien; Keithley).
Proportionality: Each pulse cycle fills and empties the traps once, so the current is proportional to frequency, area and trap density (TU Wien; Keithley 2508).
Energy window: Only traps in an energy window around midgap, set by the pulse edges, temperature and capture cross sections, contribute (Entner; Lai et al.).
Advantage: The method works on small transistors and on gate oxides below 2 $nm$ , where C-V methods fail (Keithley 2508).

2. Working Principle

Accumulation to inversion: The pulse drives the surface from accumulation to inversion and back, so traps capture electrons in inversion and holes in accumulation (Entner; Lai et al.).
Body current: The recombined charge appears as a DC current in the body SMU, in the picoamp to nanoamp range (Keithley).
Sweeps: The base level or amplitude is swept to map the plateau and local threshold and flat-band voltages (Keithley 2508).
Leakage correction: Gate leakage is removed by subtracting a low-frequency measurement (Keithley 2508).

3. Applications

Interface quality: Mean trap density of process splits and gate stacks (Keithley).
Hot-carrier and NBTI damage: Trap generation under stress, including its location along the channel (TU Wien; Keithley 2508).
Thin and high-k gate stacks: Trap characterization below 2 $nm$ and of traps beyond the interfacial layer (Keithley 2508).

Charge-Pumping Relations

Name	Formula	Related Formulae	Variables/Constants
Charge-pumping current and trap density	$N_{i t} = \frac{I _{C P}}{q f A}$	$D_{i t} = \frac{I _{C P}}{q f A Δ E}$	$N_{i t} : in t er f a ce t r a p d e n s i t y p er a r e a$ $I_{C P} : c ha r g e - p u m p in g (b o d y) c u r r e n t$ $q : e l e m e n t a r y c ha r g e$ $f : p u l se f r e q u e n cy$ $A : c hann e l a r e a$ $D_{i t} : t r a p d e n s i t y p er a r e a p er e V$ $Δ E : e n er g y w in d o w b e tw ee n t h e in v er s i o n an d a cc u m u l a t i o n F er mi l e v e l s; K e i t h l ey 2508 an d K e i t h l ey c ha r g e - p u m p in g n o t e : t h ese e q u a t i o n s, I_{C P} u s u a l l y in t h e nan o am p or p i co am p r an g e, p r e am pl i f i er b e l o w 1 nA, f r e q u e n cy in t h e k i l o h er t z t o m e g ah er t z r an g e; T U W i e n : B r ug l er an d J es p er s (1969) f o u n d t h e c u r r e n t p r o p or t i o na l t o g a t e a r e a an d f r e q u e n cy an d d u e t o r eco mbina t i o n a t in t er f a ce t r a p s$ $(co m p u t e d : 2 \times 1 0^{- 11} A a t 1 MHz o n a 10 b y 0.5 μ m n - M O S F E T g i v es N_{i t} = 2.5 \times 1 0^{9} c m^{- 2})$
Energy window (Groeseneken)	$Δ E = 2 k_{B} T ln [\frac{1}{v _{t h} n _{i} σ _{n} σ _{p} \frac{∣ V _{F B} - V _{T} ∣}{∣ Δ V _{A} ∣} t _{r} t _{f}}]$	$I_{C P} = q f A \overline{D_{i t}} Δ E$	$k_{B} : B o l t z mann co n s t an t$ $T : t e m p er a t u r e$ $v_{t h} : t h er ma l v e l oc i t y$ $n_{i} : in t r in s i c d e n s i t y$ $σ_{n}, σ_{p} : c a pt u r e cr oss sec t i o n s$ $V_{F B}, V_{T} : f l a t - ban d an d t h r es h o l d v o l t a g es$ $Δ V_{A} : p u l se am pl i t u d e$ $t_{r}, t_{f} : r i se an d f a l l t im es, \overline{D_{i t}} : m e an t r a p d e n s i t y in t h e w in d o w; f or m a s in E n t n er, E q s . 4.1 t o 4.5, w h ose e mi ss i o n t im es a r e ∣ V_{F B} - V_{T} ∣ t_{f} / ∣ Δ V_{A} ∣ an d ∣ V_{F B} - V_{T} ∣ t_{r} / ∣ Δ V_{A} ∣ an d w h ose I_{C P} co n t ain s t h e s q u a r e r oo t o f t h e i r p r o d u c t; L ai e t a l . : e mi ss i o n - t im e e x p r ess i o n s f r o m G r oese n e k e n e t a l . (1984); T U W i e n : G r oese n e k e n e t a l . es t ab l i s h e d t h e m e t h o d o n M O S F E T s$ $(a ss u m e d : v_{t h} = 1 \times 1 0^{7} cm/s, n_{i} = 1 \times 1 0^{10} c m^{- 3}, σ = 1 \times 1 0^{- 16} c m^{2}, t_{r} = t_{f} = 100 ns, ∣ V_{F B} - V_{T} ∣ = 1 V, Δ V_{A} = 2 V; co m p u t e d : Δ E = 0.75 eV a t 300 K, an d 2.5 \times 1 0^{9} c m^{- 2} b eco m es 3.3 \times 1 0^{9} c m^{- 2} e V^{- 1})$
Pulse conditions	$V_{ba se} < V_{F B} and V_{ba se} + Δ V_{A} > V_{T}$	$I_{C P} = I_{C P, ma x} (plateau of the base-level sweep)$	$V_{ba se} : p u l se ba se l e v e l; co n d i t i o n f or f u l l p u m p in g, t h e s u r f a ce s w in g in g f r o m a cc u m u l a t i o n t o in v er s i o n (E n t n er : s w ee p in g f r o m a cc u m u l a t i o n t o co m pl e t e in v er s i o n g i v es t h e l a r g es t c u r r e n t; L ai e t a l . : ba se l e v e l v a r i e d t o d r i v e t h e s u r f a ce f r o m a cc u m u l a t i o n t o in v er s i o n); K e i t h l ey 2508 : ba se s w ee p w i t h f i x e d am pl i t u d e an d w i d t h g i v es D_{i t} a g ain s t ban d b e n d in g, am pl i t u d e s w ee p a t f i x e d ba se an d f r e q u e n cy g i v es s imi l a r in f or ma t i o n, e x am pl es w i t h 1.2 V am pl i t u d e o v er - 2 t o 2 V ba se; K e i t h l ey c ha r g e - p u m p in g n o t e : ba se s w ee p o v er ab o u t - 3.0 t o - 0.5 V, am pl i t u d e s w ee p o v er ab o u t 1 t o 9 V$ $(co m p u t e d : w i t h V_{F B} = - 0.9 V an d V_{T} = 0.4 V, a 1.2 V p u l se c ann o t s p an b o t h, so t h e pl a t e a u i s n e v er f u l l y r e a c h e d)$

Corrections and Frequency Effects

Name	Formula	Related Formulae	Variables/Constants
Gate-leakage correction	$I_{m} = I_{C P} + I_{l e ak, p e ak} D + I_{l e ak, ba se} (1 - D)$	$I_{C P} (f) \approx I_{m} (f) - I_{m} (f_{l o w})$	$I_{m} : m e a s u r e d b o d y c u r r e n t$ $I_{l e ak, p e ak}, I_{l e ak, ba se} : g a t e l e ak a g e a t t h e p u l se t o p an d ba se$ $D : d u t y cy c l e$ $f_{l o w} : r e f er e n ce f r e q u e n cy; K e i t h l ey 2508 : t hi s e q u a t i o n, l e ak a g e in d e p e n d e n t o f f r e q u e n cy w hi l e I_{C P} f a l l s w i t h f r e q u e n cy, s u b t r a c t i o n o f t h e 300 Hz m e a s u r e m e n t, n e g a t i v e u n cor r ec t e d N_{i t} n e a r - 4 \times 1 0^{10} c m^{- 2}, q u a s i - s t a t i c C - V im p r a c t i c a l b e l o w 3 t o 4 nm an d hi g h - f r e q u e n cy C - V b e l o w 2 nm w hi l e c ha r g e p u m p in g w or k s b e l o w 2 nm w i t h t hi s cor r ec t i o n$ $(co m p u t e d : a t 300 Hz t h e p u m p e d c u r r e n t i s 1/3333 o f i t s 1 MHz v a l u e, so t h e l o w - f r e q u e n cy r e a d in g i s esse n t ia l l y l e ak a g e)$
Frequency dependence	$\frac{I _{C P}}{q f A} = N_{i t} (f), N_{i t} (f_{1}) \geq N_{i t} (f_{2}) (f_{1} < f_{2})$	$\frac{d N _{i t}}{d l n f} (traps responding between two frequencies)$	$N_{i t} (f) : a pp a r e n t t r a p d e n s i t y a t f r e q u e n cy f; K e i t h l ey 2508 : t h e ma x im u m N_{i t} a t l o w er f r e q u e n cy i s a l w a y s l a r g er b ec a u se t r a p s r es p o n d in g t o f a s t p u l ses a l so r es p o n d t o s l o w o n es, d i s t r ib u t i o n m e a s u r e d f r o m 1 kHz t o 1 MHz, d i f f er e n t ia l N_{i t} p e ak in g n e a r 2.5 \times 1 0^{10} c m^{- 2}, cor r ec t e d N_{i t} u p t o ab o u t 1.1 \times 1 0^{11} c m^{- 2}; H an e t a l . (N I S T) : c ha r g e p u m p in g in c l u d es s l o w s t a t es (b or d er t r a p s) t ha t ma y n o t b e d e t ec t e d a t r e l a t i v e l y hi g h f r e q u e n cy$ $(co m p u t e d : i f t h e e d g es sc a l e w i t h t h e p er i o d, t h r ee d ec a d es o f f r e q u e n cy w i d e n t h e w in d o w b y 2 k_{B} T ln 1 0^{3} = 0.36 eV a t 300 K, e a c h e mi ss i o n l e v e l m o v in g b y 0.18 eV)$
Stress monitoring	$Q_{inj} = \int I_{l e ak} d t$	$Δ N_{i t} = N_{i t} (t) - N_{i t} (0)$	$Q_{inj} : inj ec t e d c ha r g e d u r in g s t r ess$ $Δ N_{i t} : g e n er a t e d in t er f a ce t r a p s; K e i t h l ey 2508 : inj ec t e d c ha r g e f r o m in t e g r a t e d l e ak a g e c u r r e n t; T U W i e n : c ha r g e p u m p in g u se d f or t r a p g e n er a t i o n u n d er h o t - c a r r i er s t r ess$ $(a ss u m e d : 1 nA f or 1000 s; co m p u t e d : Q_{inj} = 1 μ C)$

Artefacts and Setup

Name	Formula	Related Formulae	Variables/Constants
Geometric component	$t_{r}, t_{f} \geq t_{min} (L)$	$I_{C P, m e a s} = I_{C P} + I_{g eo}$	$I_{g eo} : b o d y c u r r e n t n o t d u e t o in t er f a ce t r a p s$ $t_{min} : s h or t es t e d g e t im e f r ee o f i t$ $L : c hann e l l e n g t h; L ai e t a l . : g eo m e t r i c co m p o n e n t es p ec ia l l y in l o n g - c hann e l d e v i ces w i t h s h or t r i se an d f a l l t im es, n e g l i g ib l e f or e d g es ab o v e 150 ns a t 20 μ m an d 300 ns a t 50 μ m, 200 ns l o w er l imi t f or d e v i ces b e l o w ab o u t 20 μ m$ $(co m p u t e d : f r o m L ai e t a l ., t_{min} d o u b l es f r o m 150 t o 300 ns f or a 2.5 - f o l d l o n g er c hann e l)$
Measurement setup	$gate: pulser; source, drain: V_{r} or ground; body: SMU measuring I_{C P}$	$I_{C P} sign opposite to the junction leakage$	$V_{r} : r e v er se bia s o n so u r ce an d d r ain; K e i t h l ey c ha r g e - p u m p in g n o t e : S M U o n t h e b u l k, seco n d S M U a ppl y in g V_{r} or se t t o co mm o n, p u l ser L O t i e d t o S M U L O c l ose t o t h e d e v i ce, d e v i ce in a m e t a l e n c l os u r e o n S M U L O; K e i t h l ey 2508 : so u r ce, d r ain an d b o d y g r o u n d e d in t h e ba s i c se t u p w i t h b o d y c u r r e n t m e a s u r e d, s w i t c h ma t r i x o pt i o na l; T U W i e n : c u r r e n t o pp os i t e t o t h e j u n c t i o n l e ak a g e$ $(co m p u t e d : a 1 pA p r e am pl i f i er r eso l u t i o n o n a 2 \times 1 0^{- 11} A s i g na l i s 5 p er ce n t)$

Important Questions

Ques: What does charge pumping measure, and why on transistors?

The density of traps at the gate-oxide interface, measured on a real transistor. Pulsing the gate between accumulation and inversion, with source and drain grounded, makes each trap capture an electron and then a hole once per cycle, giving a DC body current proportional to gate area and frequency, as Brugler and Jespers found in 1969 (TU Wien). Keithley gives $N_{i t} = I_{C P} / (q f A)$ ; its 10 by 0.5 $μ m$ n-MOSFET example shows about $2 \times 1 0^{- 11}$ $A$ at 1 $MHz$ , which is $2.5 \times 1 0^{9}$ $c m^{- 2}$ (computed). Because no large capacitor is needed, small devices can be measured, and with leakage correction the method works below 2 $nm$ of oxide, where quasi-static C-V is impractical below 3 to 4 $nm$ and high-frequency C-V below 2 $nm$ . Reference: S. Starkov, PhD thesis chapter ‘The Charge-Pumping Technique’, TU Wien Institute for Microelectronics (introduction only) (fetch-tool summary); Keithley, ‘Charge Pumping’ application note 2508 for thin-gate-oxide MOSFETs with the 4200-SCS (fetch-tool summary).

Ques: Which trap energies does charge pumping sample?

Those in a window around midgap, whose width depends on the pulse edges. During the rise and fall, traps far from the band edges cannot emit their carriers before the surface passes them, so they recombine; traps near the band edges emit back to the bands and do not contribute. The window is $Δ E = 2 k_{B} T ln [1/ (v_{t h} n_{i} σ_{n} σ_{p} (∣ V_{F B} - V_{T} ∣ / ∣ Δ V_{A} ∣) t_{r} t_{f})]$ (in the form given by Entner, whose emission times scale as $∣ V_{F B} - V_{T} ∣ t_{f} / ∣ Δ V_{A} ∣$ ; Lai et al. trace it to Groeseneken et al.). With 100 $ns$ edges, cross sections of $1 \times 1 0^{- 16}$ $c m^{2}$ and a 2 $V$ pulse spanning 1 $V$ between flat band and threshold, it is about 0.75 $eV$ at 300 $K$ (computed), so $2.5 \times 1 0^{9}$ $c m^{- 2}$ means a mean density of $3.3 \times 1 0^{9}$ $c m^{- 2} e V^{- 1}$ (computed). Keithley uses $D_{i t} = I_{C P} / (q f A Δ E)$ . Reference: R. Entner, PhD thesis, TU Wien, section 4.1 ‘Charge Pumping Method’: Eqs. 4.1 to 4.5 (emission levels, emission times scaled by |V_fb - V_th|/|dV_A| times t_f and t_r, I_CP with the square root of their product), pulse from accumulation to complete inversion gives the largest current (fetch-tool summary, equation fragments); P. T. Lai et al., IEEE Trans. Electron Devices 45(4), 1998: Groeseneken et al. 1984 as source of emission-time expressions, base level varied from accumulation to inversion, geometric component in long channels with short edges, negligible above 150 ns (20 um) and 300 ns (50 um), 200 ns lower limit below about 20 um, hot-carrier Dit near the drain (fetch-tool summary); Keithley, ‘Performing Charge Pumping Measurements with the 4200-SCS’, application note (fetch-tool summary).

Ques: What do base-level and amplitude sweeps show?

Where the pumping turns on and how traps are spread along the channel. In a base-level sweep, the amplitude and width are fixed and the base is stepped; this drives the surface from accumulation to inversion (Keithley 2508; Lai et al.). The current plateaus only while the pulse spans both the flat-band and threshold voltages, so the edges of the curve mark local values of both (my reading); Lai et al. cite such measurements for locating hot-carrier damage near the drain. A 1.2 $V$ pulse, as in Keithley’s examples, cannot reach a full plateau if the threshold and flat-band voltages differ by more than 1.2 $V$ (computed). Amplitude sweeps at fixed base, over about 1 to 9 $V$ in Keithley’s example, give similar information. Reference: Keithley, ‘Charge Pumping’ application note 2508 for thin-gate-oxide MOSFETs with the 4200-SCS (fetch-tool summary); P. T. Lai et al., IEEE Trans. Electron Devices 45(4), 1998: Groeseneken et al. 1984 as source of emission-time expressions, base level varied from accumulation to inversion, geometric component in long channels with short edges, negligible above 150 ns (20 um) and 300 ns (50 um), 200 ns lower limit below about 20 um, hot-carrier Dit near the drain (fetch-tool summary); Keithley, ‘Performing Charge Pumping Measurements with the 4200-SCS’, application note (fetch-tool summary).

Ques: How is gate leakage separated from the charge-pumping current?

By using the fact that leakage does not depend on frequency. In thin oxides, tunnelling current during the pulse top and base adds to the body current: $I_{m} = I_{C P} + I_{l e ak, p e ak} D + I_{l e ak, ba se} (1 - D)$ , with D the duty cycle (Keithley 2508). The pumped current scales with frequency, while the averaged leakage does not, so Keithley subtracts a measurement at 300 $Hz$ , where the pumped current is 1/3333 of its 1 $MHz$ value (computed). Without correction its example shows negative apparent trap densities near - $4 \times 1 0^{10}$ $c m^{- 2}$ ; after correction, values up to about $1.1 \times 1 0^{11}$ $c m^{- 2}$ . The method assumes gate capacitance is small enough to ignore transient currents. This correction is what extends charge pumping below 2 $nm$ of oxide. Reference: Keithley, ‘Charge Pumping’ application note 2508 for thin-gate-oxide MOSFETs with the 4200-SCS (fetch-tool summary).

Ques: Why does the trap density depend on frequency?

Because slower traps take part only at low frequencies. Keithley’s 2508 note states that the maximum trap density at lower frequency is always larger, because traps responding to fast pulses also respond to slow ones; its distribution from 1 $kHz$ to 1 $MHz$ shows a differential density peaking near $2.5 \times 1 0^{10}$ $c m^{- 2}$ . Two effects are responsible: when the edges scale with the period, slower edges widen the energy window, by about 0.36 $eV$ over three decades at 300 $K$ (computed), and slow traps inside the oxide, called border traps, take part; Han et al. (NIST) note that such slow states may not be detected by relatively high-frequency charge pumping. Keithley notes that charge beyond the silicon interfacial layer can be sensed in high-k stacks. Comparing frequencies therefore separates interface traps from oxide traps, but the mean density should always be quoted with its frequency. Reference: Keithley, ‘Charge Pumping’ application note 2508 for thin-gate-oxide MOSFETs with the 4200-SCS (fetch-tool summary); J.-P. Han et al. (NIST), IEEE Electron Device Lett. 25(3), 2004: charge pumping includes slow states (border traps) that may not be detected by relatively high-frequency CP (fetch-tool summary).

Ques: What is the geometric component, and how is it avoided?

It is extra body current not due to interface traps. Lai et al. find that it appears especially in long-channel devices driven by pulses with short rise and fall times, and that it is negligible when the edges exceed 150 $ns$ for a 20 $μ m$ device and 300 $ns$ for a 50 $μ m$ device; they suggest 200 $ns$ as a lower limit for devices shorter than about 20 $μ m$ . The required edge time doubles for a 2.5-fold longer channel (computed). A likely mechanism is inversion charge in the middle of a long channel that cannot drift back to the junctions during a fast edge and recombines in the substrate (my reading). It is avoided with short channels, slower edges and a check of the current against edge time. Modern submicron devices, like Keithley’s 0.5 $μ m$ example, are usually free of it (my reading). Reference: P. T. Lai et al., IEEE Trans. Electron Devices 45(4), 1998: Groeseneken et al. 1984 as source of emission-time expressions, base level varied from accumulation to inversion, geometric component in long channels with short edges, negligible above 150 ns (20 um) and 300 ns (50 um), 200 ns lower limit below about 20 um, hot-carrier Dit near the drain (fetch-tool summary).

Ques: How is a charge-pumping measurement set up?

With a pulse generator on the gate and an SMU measuring the body. Keithley’s charge-pumping note connects SMU1 to the bulk to measure the current, SMU2 to the tied source and drain to apply a reverse bias or set to common, and the pulser to the gate, with the pulser LO connected to the SMU LO as close to the device as possible. Currents are usually in the picoamp to nanoamp range, so a preamplifier is needed below 1 $nA$ and the device should be in a metal enclosure on SMU LO. A 1 $pA$ resolution on a 20 $pA$ signal is a 5 per cent uncertainty (computed). The current flows opposite to the junction leakage (TU Wien), which helps identify it. Stress-measure sequences track injected charge as $\int I d t$ (Keithley 2508). Reference: Keithley, ‘Performing Charge Pumping Measurements with the 4200-SCS’, application note (fetch-tool summary); S. Starkov, PhD thesis chapter ‘The Charge-Pumping Technique’, TU Wien Institute for Microelectronics (introduction only) (fetch-tool summary); Keithley, ‘Charge Pumping’ application note 2508 for thin-gate-oxide MOSFETs with the 4200-SCS (fetch-tool summary).

References

S. Starkov, “The Charge-Pumping Technique,” chapter 4 of PhD thesis, Institute for Microelectronics, TU Wien. Available: https://www.iue.tuwien.ac.at/phd/starkov/node39.html
Keithley Instruments, “Charge Pumping” application note 2508 (thin-gate-oxide MOSFET charge pumping with the 4200-SCS). Available: https://docs.ampnuts.ru/eevblog.docs/Keithley/Appnotes/2508%20ChargePumping.pdf
R. Entner, Modeling and Simulation of Negative Bias Temperature Instability, PhD thesis, Institute for Microelectronics, TU Wien, section 4.1 “Charge Pumping Method.” Available: https://www.iue.tuwien.ac.at/phd/entner/node17.html
P. T. Lai, J. P. Xu, C. K. Poek and Y. C. Cheng, “Analysis on accuracy of charge-pumping measurement with gate sawtooth pulses,” IEEE Trans. Electron Devices, vol. 45, no. 4, pp. 947-952, 1998. Available: https://repository.hku.hk/bitstream/10722/42765/1/33982.pdf
J.-P. Han, E. M. Vogel, E. P. Gusev, C. D’Emic, C. A. Richter, D. W. Heh and J. S. Suehle, “Asymmetric energy distribution of interface traps in n- and p-MOSFETs with HfO2 gate dielectric on ultrathin SiON buffer layer,” IEEE Electron Device Lett., vol. 25, no. 3, 2004. Available: https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=31451
Keithley Instruments, “Performing Charge Pumping Measurements with the Model 4200-SCS,” application note. Available: https://xdevs.com/doc/Keithley/Appnotes/ChargePumping_AppNote.pdf

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