Novel Devices and Circuits for Computing
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1 Novel Devices and Circuits for Computing UCSB 594BB Winter 213 Lectures 5 and 6: VCM cell
2 Class Outline VCM = Valence Change Memory General features Forming SET and RESET Heating Switching models Scaling prospects
3 Large choice of materials
4 Typical I V and Switching Mechanism Cartoon for Interface Type Devices Pt/ZrO x /Zr Green = O Purple = Zr in lower valence state Oxygen mobile, Zr is immobile
5 Types of VCM cells (a) AE MIM = AE/MIEC/OE AE = active electrode (low oxygen affinity, high work function, e.g Pt, Ir, TiN) OE = Ohmic electrode (opposite, e.g Ti, Ta) (a) Homogeneous monolayer, e.g. TiO2 x forming is crucial (b) Homogeneous bi layer, e.g. TiO2/TiO2 x or Ta2O5/TaOx (c) Hetergeneous bi layer, e.g. Al2O3/TiO2 x or HfO2/TiO2 x
6 Forming Process ObservationofMagneliphases of intio2 Exp. setup Example of forming in TiN/HfOx/TiOx/TiN X ray diffraction TEM image Forming is thermally assisted and two step process (similar to TCM) lower forming voltage for less resistive films Creates a non stochiometric filament Possibly with morphological changes
7 Oxygen Bubbles with Forming Process Forming to ON and OFF state with different polarity
8 Interface Mechanism Oxygen vacancy profile modulation in disc region Vo is typically a shallow donor Barrier modulation (e.g. that of Schottky) Many indirect experiments supporting this simple model (next slides)
9 Ohmic Interface by Ti Layer Diffusion of Ti and chemical reaction with ihtio2 during annealing = TiO2 x
10 Switching Polarity Dependence on Ti Layer
11 Temperature Dependence for OFF/ON states Simplest model to explain observed behavior
12 Thermometry Experiment
13 Chemical/Thermal/Electrical Mapping J.P. Strachan et al, Nanotechnology 211
14 Heating and Location XRF map infrared M.Janousch et al. Adv.Mat (27)
15 Bulk Mechanism
16 Vacancy Drift Model TiO x Switch Pt TiO 2 TiO 2 x Pt As fabricated, the oxide has a highly resistive TiO2 region and a conductive TiO2-x region that is highly doped with O vacancies, which are positively charged. 3 nm Pt TiO 2 TiO 2 x Pt When a positive bias voltage is applied to electrode 2, the positively charged O vacancies drift to the left, which narrows the tunneling gap. Strukov et al., Nature (28)
17 Model: Carrier Statistics E C, E D eφ(x) eφ n E G = E C E V eφ p E V, E A eφ(x) Shallow Dopants and Acceptors: n = N C F 1/2 [ (eφ n E C + eφ )/(k B T)] N C Exp[ (eφ n E C + eφ )/(k B T)] p = N VF 1/2[ (E V eφ p eφ )/(k BT)] N VExp[ (E V eφ p eφ )/(k BT)] f A = 1 1/(1+Exp[(E D eφ n eφ )/(k B T)] ]/2) 1 f D = 1 1/(1+Exp[(eφ p + eφ E A )/(k B T)] ]/2) 1
18 Defects in TiO 2 x HP s TiO 2 x C y N z devices N, C doping of TiO Calculated DOS 3 ) C concen ntration (cm C ALD 1C 15C 25C sputter Depth (normalized) Measured absorbance N co oncentration (cm -3 ) film thickness: ALD 1C 2 nm; 15C 16 nm 2C 21 nm; 25C 15 nm; sputter 6 nm sputter 25C ALD 1C 15C 2C 1 19 Depth (normalized) 1 ev TiO 2 TiO 2 x N x ev TiO 2 x TiO 2 x C y data from J.Yang Science 293, 269 (21) Science 297, 2243 (22)
19 Equilibrium Profile (v =, N D (x)/ t t = ) semiconductor with uniform N A fixed and N D (x) mobile ions 1 2 )/N D 1 N D Dopant N D (x) N A v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E Length x/l
20 Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge )/N D semiconductor with uniform N A fixed and N D (x) mobile ions N D * /N D = 1 N D Dopant N D (x) 1 2 N A v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E Length x/l
21 Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge Dopant N D (x) )/N D semiconductor with uniform N A fixed and N D (x) mobile ions N D * /N D = 1.1 N D N A v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E Length x/l
22 Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge Dopant N D (x) )/N D semiconductor with uniform N A fixed and N D (x) mobile ions 1 N D * /N D = N D N A v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E Length x/l
23 Quasi-Equilibrium Profile (v, N D D( (x)/ t t =, N D */N D =.1) v /v nt N D (x)/n DO Dopa semiconductor with uniform N A fixed and N D (x) mobile ions v/v = N D N A 1 ON state tt n + n n al φ/(e G /e) Potenti.5 v Length x/l Voltage v/v J Current J/J J =en D μ e E N A =8εε E G /(el) 2
24 Quasi-Equilibrium Profile (v, N D D( (x)/ t t =, N D */N D =.1) v /v nt N D (x)/n DO Dopa semiconductor with uniform N A fixed and N D (x) mobile ions v/v = N D N A 1 ON state tt n + n n al φ/(e G /e) Potenti.5 v J Current J/J OFF state 1 9 n + p n Length x/l Voltage v/v J =en D μ e E N A =8εε E G /(el) 2
25 Quasi-Equilibrium Profile (v, N D D( (x)/ t t =, N D */N D =.1) nt N D (x)/n DO Dopa Potenti al φ/(e G /e) semiconductor with uniform N A fixed and N D (x) mobile ions 4 4 v/v = N D N A v J Current J/J 1 ON state tt n + n n + v /v v > 1 33 v < 1 6 partial OFF state n + n p n + OFF state n + p n Length x/l Voltage v/v 1 9 J =en D μ e E N A =8εε E G /(el) 2
26 DO Dopa ant N D (x)/n D w / L 1 t / t.2 ON OFF (v = +12v ) w N A ON OFF Dynamics ial φ/(e G /e) time t/t Potenti t =L 2 /D i Cu urrent J/J Voltage v/v Voltage v/v
27 DO Dopa ant N D (x)/n D w / L 1 t / t.2 ON OFF (v = +12v ) w N A ON OFF Dynamics Potenti ial φ/(e G /e) Cu urrent J/J time t/t t =L 2 /D i Fie eld E/E 5 α Length x/l 1 w(t) = L (Av/B) 1/2 Tanh[(ABv) 1/2 t] 2 R ON w/d R OFF (1 w/d) Voltage v/v Voltage v/v
28 DO Dopa ant N D (x)/n D ON OFF (v = +12v ) OFF ON (v = 12v ) w w N A N 2 A Potenti ial φ/(e G /e) Cu urrent J/J time t/t time t/t t =L 2 /D i Voltage v/v Voltage v/v Voltage v/v Voltage v/v
29 Practical Parameters T = 3 K, v = 26 mv (v/v = 12 v = 3V) Case 1: L = 5 nm N A 8εε E G /(el) 2 = cm 3 E = 5 kv/cm E G = 3 ev N D * = cm 3 J = 4 A/cm 2 ε = 1 N D = cm 3 D Case 2: E G = 2eV.2 L= 1 nm N A cm 3 E = 25 kv/cm E G = 3 ev N D * = 1 21 cm 3 J = 2 ka/cm 2 ε = 5 N D = 1 21 cm 3 E max = 5 E, J max = 1 J (v = 3V) 5 5 nm 2 : J max =.2 μa 1 μa
30 Dynamics: Memristance 4 v/v = 12 sin[2π(t/t )/.1] Current J/J f = v t q = J t Sharp boundary Drift by ON electric field Soft boundary condition Charge q/ /q ( 1 3 ) Voltage v/v Flux f/f 1 Asymmetric Memristive
31 Bulk Resistive Switching: Experiment H.Yang et al. Nature Mat (29) More recent paper from R. Waser group (ask Brian)
32 Interfacial Switching: 1D model
33 Dynamics: Concentration Profile Reversal` in Bulk Device OFF ON OFF Pt BST Pt (exp) J J B A 12 C APL 73, 175 (1998) 1-2 v /v = t t Dopant D(x)/N DO N D B C A Length x/l 1 APL 86, (1998)
34 Inversion of Switching Polarity
35 Experimental Results
36 3D Model Electronic/Ionic/Thermal Model with Axial Symmetry
37 Ion drift diffusion: Fourier law: Electronic conductance: Coupled by Poisson eq: Goof paper for presentation
38
39 Scaling Prospects
40 Current Scaling V A z T = T 3 r H L H 1 X K mw rmax 5. k I k M R T = T 3 æ æ æ æ æ Vreset,V V æ æ æ æ æ æ.3 L= 3 nm H (nm) L=H I reset,ma Current is at least > 1 μa a D. Strukov, Applied Physics A, 211
41 Switching Time Scaling STO:Nb/STO/Ti More heating faster switching (with some saturation) Switching energy scales too Possible tradeoff with endurance and variations
42 Density Prospects Results from IMEC 212
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