Junctionless Transistor

1. Theory

Definition: A junctionless transistor is a multi-gate (planar double-gate or nanowire) MOSFET whose source, channel and drain all have the same doping type and concentration, so there is no PN junction along the current path.
Gated resistor: It is essentially a heavily doped resistor whose conducting cross-section the gate can squeeze down to zero.
Depletion turn-off: The body is thin enough that the gate can deplete it completely; the threshold is the gate voltage at which full depletion occurs.
Flat-band on-state: At flat band the whole body is neutral and conducts as a plain resistor.
Doping-set threshold: $V_{T H}$ depends directly on $N_{D}$ and body thickness (or radius), not mainly on the work function as in inversion-mode devices.
No abrupt junctions needed: It avoids the ultra-sharp source/drain doping gradients that are hard to make at short gate lengths.

2. Working Principle

Off state: Below $V_{T H}$ the body is fully depleted and only a subthreshold current flows.
Partial depletion: Between $V_{T H}$ and $V_{F B}$ , a neutral conducting layer in the middle of the body widens as the gate voltage rises.
On state: At or above flat band the full body conducts, with current proportional to $q μ_{n} N_{D} t_{s i}$ .
Bulk conduction: Current flows through the body volume rather than an interface layer, so surface-roughness scattering and interface traps matter less.
Impurity-limited mobility: The heavy doping lowers mobility through ionized-impurity scattering.
High variability: Small changes in body thickness or doping shift $V_{T H}$ strongly; uniformity is the main manufacturing challenge.

3. Applications

Current status: Mainly a research device, not yet used in mainstream CMOS production.
Monolithic 3D integration (research): Junction-free processing avoids high-temperature dopant activation, suiting stacked device layers.
Thin-film and sensing transistors: Many oxide TFTs and nanowire sensors operate on the same depletion-mode, junction-free principle.

Name	Formula	Related Formulae	Variables/Constants
Threshold voltage (planar double-gate body)	$V_{T H} = V_{F B} - \frac{q N _{D} t _{s i}}{2 C _{o x}} - \frac{q N _{D} t _{s i}^{2}}{8 ε _{s i}}$	$V_{F B} = Φ_{m s} = Φ_{M} - (χ_{s i} + \frac{k _{B} T}{q} ln \frac{N _{C}}{N _{D}})$	$V_{T H} : g a t e v o l t a g e a t w hi c h t h e b o d y b eco m es f u l l y d e pl e t e d an d t h e c hann e l t u r n s o f f$ $V_{F B} : f l a t - ban d v o l t a g e (t h e g a t e v o l t a g e a t w hi c h t h e w h o l e b o d y i s n e u t r a l)$ $N_{D} : u ni f or m d o n or d o p in g o f t h e so u r ce, c hann e l an d d r ain$ $t_{s i} : s i l i co n b o d y t hi c k n ess$ $C_{o x} : g a t e o x i d e c a p a c i t an ce p er u ni t a r e a$ $ε_{s i} : s i l i co n p er mi tt i v i t y$ $Φ_{M}, χ_{s i} : g a t e w or k f u n c t i o n an d s i l i co n e l ec t r o n a f f ini t y, b o t h in v o l t s$ $N_{C} : e f f ec t i v e d e n s i t y o f s t a t es o f t h e co n d u c t i o n ban d (n o n d e g e n er a t e d o p in g)$ $k_{B} : B o l t z mann co n s t an t$
Threshold voltage (cylindrical nanowire body)	$V_{T H} = V_{F B} - \frac{q N _{D} R}{2 C _{o x}} - \frac{q N _{D} R ^{2}}{4 ε _{s i}}$	$C_{o x} = \frac{ε _{o x}}{R l n ( 1 + t _{o x} / R )}$	$R : r a d i u s o f t h e s i l i co n nan o w i r e$ $C_{o x} : o x i d e c a p a c i t an ce p er u ni t a r e a o f t h e s i l i co n s u r f a ce f or a w r a p - a r o u n d g a t e$ $t_{o x}, ε_{o x} : o x i d e t hi c k n ess an d p er mi tt i v i t y$
Gate-induced depletion width	$W_{d e p} (V_{GS}) = \frac{ε _{s i}}{C _{o x}} [1 + \frac{2 C _{o x}^{2} ( V _{F B} - V _{GS} )}{q N _{D} ε _{s i}} - 1]$	$V_{F B} - V_{GS} = \frac{q N _{D} W _{d e p}^{2}}{2 ε _{s i}} + \frac{q N _{D} W _{d e p}}{C _{o x}}$ $W_{d e p} = t_{s i} /2 at V_{GS} = V_{T H}$	$W_{d e p} : d e pl e t i o n w i d t h u n d er e a c h g a t e (v a l i d w hi l e t h e b o d y i s o n l y p a r tl y d e pl e t e d, W_{d e p} < t_{s i} /2)$ $V_{GS} : g a t e - so u r ce v o l t a g e, w i t h V_{GS} < V_{F B}$
Drain current (linear region)	$I_{D} = \frac{q μ _{n} N _{D} Z}{L} (t_{s i} - 2 W_{d e p}) V_{D S}$	$I_{D, ma x} = \frac{q μ _{n} N _{D} Z t _{s i}}{L} V_{D S} (V_{GS} \geq V_{F B})$	$μ_{n} : b u l k - l ik e e l ec t r o n m o bi l i t y a t d o p in g N_{D}$ $Z, L : c hann e l w i d t h an d l e n g t h$ $t_{s i} - 2 W_{d e p} : t hi c k n ess o f t h e n e u t r a l co n d u c t in g l a y er in t h e mi dd l e o f t h e b o d y$ $V_{D S} : d r ain - so u r ce v o l t a g e, s ma l l co m p a r e d w i t h t h e g a t e o v er d r i v e$
Transconductance	$g_{m} = \frac{\partial I _{D}}{\partial V _{GS}} = \frac{2 μ _{n} C _{o x} Z}{L} \frac{V _{D S}}{1 + C _{o x} W _{d e p} / ε _{s i}}$	$1 + \frac{C _{o x} W _{d e p}}{ε _{s i}} = 1 + \frac{2 C _{o x}^{2} ( V _{F B} - V _{GS} )}{q N _{D} ε _{s i}}$	$g_{m} : t r an sco n d u c t an ce in t h e l in e a r r e g i o n$ $C_{o x} W_{d e p} / ε_{s i} : r a t i o o f t h e o x i d e c a p a c i t an ce t o t h e d e pl e t i o n c a p a c i t an ce p er u ni t a r e a$
Normally-off condition	$q N_{D} t_{s i} (\frac{1}{2 C _{o x}} + \frac{t _{s i}}{8 ε _{s i}}) \leq V_{F B}$	$N_{D} t_{s i}^{2} \leq \frac{8 ε _{s i} V _{F B}}{q} (C_{o x} \to \infty)$	$V_{F B} : f l a t - ban d v o l t a g e, se t b y t h e g a t e w or k f u n c t i o n$ $V_{T H} \geq 0 : r e q u i r e d f or t h e d e v i ce t o b e o f f a t V_{GS} = 0$
Threshold sensitivity to thickness and doping	$\frac{\partial V _{T H}}{\partial t _{s i}} = - \frac{q N _{D}}{2 C _{o x}} - \frac{q N _{D} t _{s i}}{4 ε _{s i}}$ $\frac{\partial V _{T H}}{\partial N _{D}} = \frac{k _{B} T}{q N _{D}} - \frac{q t _{s i}}{2 C _{o x}} - \frac{q t _{s i}^{2}}{8 ε _{s i}}$		$\partial V_{T H} / \partial t_{s i} : t h r es h o l d s hi f t p er u ni t c han g e in b o d y t hi c k n ess$ $\partial V_{T H} / \partial N_{D} : t h r es h o l d s hi f t p er u ni t c han g e in d o p in g, in c l u d in g t h e c han g e o f V_{F B}$ $k_{B} : B o l t z mann co n s t an t$
Electrostatic scale length	$ℓ = \frac{ε _{s i} t _{s i} t _{o x}}{2 ε _{o x}}$	$L ≳ 5 ℓ to 6 ℓ (common rule for acceptable short-channel behaviour)$	$ℓ : e l ec t r os t a t i c sc a l e l e n g t h o f t h e d o u b l e - g a t e b o d y, t h e a pp r o x ima t e f or m o f t h e na t u r a l l e n g t h o n t h e D o u b l e - G a t e M O S F E T p a g e (w i t h o u t i t s cor r ec t i o n t er m)$ $t_{o x}, ε_{o x} : o x i d e t hi c k n ess an d p er mi tt i v i t y$
Subthreshold swing	$S = \frac{\partial V _{GS}}{\partial l o g _{10} I _{D}} = m \frac{k _{B} T}{q} ln 10$	$S \geq \frac{k _{B} T}{q} ln 10 \approx 60 mV/dec at 300 K$	$S : s u b t h r es h o l d s w in g$ $m : b o d y f a c t or, m \geq 1, se t b y t h e r a t i o o f t h e b o d y an d in t er f a ce - t r a p c a p a c i t an ce t o t h e o x i d e c a p a c i t an ce (see L o n g C hann e l M O S F E T p a g e)$ $k_{B} : B o l t z mann co n s t an t$
Source/drain access resistance	$R_{a cc} = \frac{L _{a cc}}{q μ _{n} N _{D} Z t _{s i}}$		$R_{a cc} : r es i s t an ce o f o n e u n g a t e d so u r ce or d r ain a ccess r e g i o n, w hi c h ha s t h e s am e d o p in g a s t h e c hann e l$ $L_{a cc} : l e n g t h o f t h e a ccess r e g i o n$

Important Questions

Ques: Why does a junctionless transistor have no source or drain junction, and what does it replace?

A junctionless transistor is a gated resistor: source, channel and drain share the same heavily doped type, so there is no p-n junction anywhere along the current path. The gate turns the device off by fully depleting a body thin enough that the gate work function can deplete it completely, and turns it on by progressively removing that depletion until the body reaches flat band, where the whole body conducts as a plain resistor. This removes the need for abrupt source/drain doping gradients that become very difficult to make at short gate lengths, since doping diffusion across the junction would otherwise shorten the effective channel. Reference: J.-P. Colinge et al., “Nanowire transistors without junctions,” Nature Nanotechnology 5, 225 (2010).

Ques: Why is the threshold voltage so sensitive to body thickness and doping?

Turning the device off requires the gate to deplete all of the donor charge $q N_{D} t_{s i}$ in the body, so the threshold depends on $N_{D}$ and $t_{s i}$ directly. Differentiating the threshold expression gives the sensitivities in the table: a change of a nanometer in $t_{s i}$ or a small fractional change in $N_{D}$ shifts $V_{T H}$ by an amount that is large compared with a conventional inversion-mode device, whose threshold is set mainly by the work function and a depletion charge limited by the gate. Control of thickness and doping uniformity is therefore the central manufacturing challenge of this device. Reference: J.-P. Colinge, A. Kranti, R. Yan et al., “Junctionless transistors: physics and properties,” in Semiconductor-On-Insulator Materials for Nanoelectronics Applications, Springer, 2011.

Ques: Where does the on-state current flow, and how does that affect mobility compared with an inversion-mode device?

Near flat band the current flows through the neutral volume of the body rather than a thin layer at the oxide interface, so it is less sensitive to surface roughness scattering and to interface traps than an inversion layer is. On the other hand the doping is high, so ionized-impurity scattering lowers the mobility $μ_{n}$ below the low-doped bulk value. The net effect is that mobility degradation with gate voltage is weaker than in an inversion-mode device but the absolute mobility is set by doping. Reference: J.-P. Colinge et al., “Nanowire transistors without junctions,” Nature Nanotechnology 5, 225 (2010).

Quartz 5

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