Novel Devices and Circuits for Computing UCSB 594BB Winter 213 Lectures 5 and 6: VCM cell
Class Outline VCM = Valence Change Memory General features Forming SET and RESET Heating Switching models Scaling prospects
Large choice of materials
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
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
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
Oxygen Bubbles with Forming Process Forming to ON and OFF state with different polarity
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)
Ohmic Interface by Ti Layer Diffusion of Ti and chemical reaction with ihtio2 during annealing = TiO2 x
Switching Polarity Dependence on Ti Layer
Temperature Dependence for OFF/ON states Simplest model to explain observed behavior
Thermometry Experiment
Chemical/Thermal/Electrical Mapping J.P. Strachan et al, Nanotechnology 211
Heating and Location XRF map infrared M.Janousch et al. Adv.Mat 19 2232 (27)
Bulk Mechanism
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 453 8 (28)
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
Defects in TiO 2 x HP s TiO 2 x C y N z devices N, C doping of TiO 2 1 22 Calculated DOS 3 ) C concen ntration (cm -3 1 21 1 2 2C ALD 1C 15C 25C sputter 1 19 1 Depth (normalized) Measured absorbance N co oncentration (cm -3 ) 1 21 1 2 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 3. 2.5 TiO 2 TiO 2 x N x ev 3. 2.5 TiO 2 x TiO 2 x C y data from J.Yang Science 293, 269 (21) Science 297, 2243 (22)
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) 1 2.1 N A 1 4 2 v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E 2.5 1 Length x/l
Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge )/N D 1 2 1 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 1 4 2 v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E 2.5 1 Length x/l
Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge Dopant N D (x) )/N D 1 2 1 1 2 semiconductor with uniform N A fixed and N D (x) mobile ions N D * /N D = 1.1 N D N A 1 4 2 v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E 2.5 1 Length x/l
Equilibrium Profile (v =, N D (x)/ t t = ) conduction band edge Dopant N D (x) )/N D 1 2 1 1 2 semiconductor with uniform N A fixed and N D (x) mobile ions 1 N D * /N D = 1.1.1 N D N A 1 4 2 v =k BT/e E =v /L N A =8εε E G /(el) 2 Field E/E 2.5 1 Length x/l
Quasi-Equilibrium Profile (v, N D D( (x)/ t t =, N D */N D =.1) v /v nt N D (x)/n DO Dopa 1 1 22 1 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 + 12 4 4 12 12 4 4 al φ/(e G /e) Potenti.5 v.5 1 1 1 1 1 1 1 2 1 3 Length x/l Voltage v/v J Current J/J 1 33 1 6 1 9 J =en D μ e E N A =8εε E G /(el) 2
Quasi-Equilibrium Profile (v, N D D( (x)/ t t =, N D */N D =.1) v /v nt N D (x)/n DO Dopa 1 1 22 1 4 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 + 12 4 4 12 12 4 4 al φ/(e G /e) Potenti.5 v J Current J/J 1 33 1 6 OFF state 1 9 n + p n +.5 1 1 1 1 1 1 1 2 1 3 Length x/l Voltage v/v J =en D μ e E N A =8εε E G /(el) 2
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) 1 1 22 1.5 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 12 4 4 12 12 4 4 v > 1 33 v < 1 6 partial OFF state n + n p n + OFF state n + p n +.5 1 1 1 1 1 1 1 2 1 3 Length x/l Voltage v/v 1 9 J =en D μ e E N A =8εε E G /(el) 2
DO Dopa ant N D (x)/n D 1 11 1 2 1 3 w / L 1 t / t.2 ON OFF (v = +12v ) w N A ON OFF Dynamics ial φ/(e G /e).2 1 4 1 3 1 2 time t/t Potenti t =L 2 /D i Cu urrent J/J 2 2 4 4 Voltage v/v 1 1 3 1 6 1 9 1 1 1 Voltage v/v
DO Dopa ant N D (x)/n D 1 11 1 2 1 3 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.2 2 1 4 1 3 1 2 time t/t t =L 2 /D i 1 1 3 1 6 1 9 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) 4 4 1 1 1 Voltage v/v Voltage v/v
DO Dopa ant N D (x)/n D 1 11 1 2 ON OFF (v = +12v ) OFF ON (v = 12v ) w w N A 1 1 1 N 2 A 1 3 1 3 Potenti ial φ/(e G /e) Cu urrent J/J.2.2 1 4 1 3 1 2 time t/t 1 4 1 3 1 2 time t/t t =L 2 /D i 2 2 1 2 4 4 Voltage v/v 1 3 1 6 1 9 1 1 1 Voltage v/v 2 4 4 Voltage v/v 1 1 3 1 6 1 9 1 1 1 Voltage v/v
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 = 5 1 18 cm 3 E = 5 kv/cm E G = 3 ev N D * = 5 1 19 cm 3 J = 4 A/cm 2 ε = 1 N D = 5 1 2 cm 3 D Case 2: E G = 2eV.2 L= 1 nm N A 5 1 2 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
Dynamics: Memristance 4 v/v = 12 sin[2π(t/t )/.1] Current J/J 2 2 4 f = v t q = J t Sharp boundary Drift by ON electric field Soft boundary condition Charge q/ /q ( 1 3 ) 4 4 1 5 5 Voltage v/v 8.4.2 Flux f/f 1 Asymmetric Memristive
Bulk Resistive Switching: Experiment H.Yang et al. Nature Mat. 8 585 (29) More recent paper from R. Waser group (ask Brian)
Interfacial Switching: 1D model
Dynamics: Concentration Profile Reversal` in Bulk Device OFF ON OFF Pt BST Pt (exp) J J 1 2 1 1 1 1-1 4 12 4 B A 12 C APL 73, 175 (1998) 1-2 v /v = 4 12 4 1-6 1-5 1-4 1-3 1-2 1-1 t t Dopant D(x)/N DO N D 1 1 1 3 B C A Length x/l 1 APL 86, 11284 (1998)
Inversion of Switching Polarity
Experimental Results
3D Model Electronic/Ionic/Thermal Model with Axial Symmetry
Ion drift diffusion: Fourier law: Electronic conductance: Coupled by Poisson eq: Goof paper for presentation
Scaling Prospects
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 1. 1 2. 1..5.2 æ æ æ æ æ æ.3 L= 3 nm H (nm) 1 3 1 L=H.1.1 1 1 I reset,ma Current is at least > 1 μa.1.1.1 1 a D. Strukov, Applied Physics A, 211
Switching Time Scaling STO:Nb/STO/Ti More heating faster switching (with some saturation) Switching energy scales too Possible tradeoff with endurance and variations
Density Prospects Results from IMEC 212