RRAM_COMPILER

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This repository includes the Resistive Random Access Memory (RRAM) Compiler which is designed in the context of the research project of Dimitris Antoniadis (PG Taught Student) at Imperial College London

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# Open-Source RRAM COMPILER

Author: 
            
            Dimitrios (Dimitris) Antoniadis

Supervisors:

T. Constandinou
            P. Feng
            A. Mifsud

e-mail: dimitris.antoniadis20@imperial.ac.uk

University: Imperial College London

Research Project: Large-scale mixed-signal array compiler for automatic memory generation

-----------------------
 
* Version 2: RRAM ARRAY GENERATOR (COMPLETED)
* Version 3: RRAM GENERATOR WITH PERIPHERAL CIRCUITS (COMPLETED)
	- Analog Part Schematic - Layout and Verification
	- Digital Part
		- Automatic Synthesis Using Genus for VDD Controller and Decoders
		- Automatic Implementation Innovus
	- Mixed Part
		- Automatic Schematic Generation
		- Automatic LVS clean DRC clean Layout Implementation
		- Automatic Characterisation of Timing Permomance

* Version 4: Future Work: Array of RRAMs

**Research Project Description**: Commercial availability of memory complier is only used for industrial design of static random-access memory (SRAM) or
dynamic random-access memory (DRAM). In academia, a new memory type has been proposed by using memristor based
random-access memory (ReRAM). To design a large-scale ReRAM array is time consuming and tedious to custom design, and
there are not many tools for automating this process. This project aims to develop a script-based compiler that provides a
flexible and portable platform for generating and verifying ReRAM designs across different technologies.
The student will investigate the current memory compiler in terms of architecture and operation to understand the design
process of common memory.

--------------------------------

**Publications**

[Open-Source Memory Compiler for Automatic RRAM Generation and Verification](https://ieeexplore.ieee.org/document/9531908)   presented on MWSCAS 2021

###### Abstract - The lack of open-source memory compilers in academia typically causes significant delays in research and design implementations. This paper presents an open-source memory compiler that is irectly integrated within the Cadence Virtuoso environment using physical verification tools provided by Mentor Graphics (Calibre). It facilitates the entire memory generation process from netlist generation to layout implementation, and physical implementation verification. To the best of our knowledge, this is the first open-source memory compiler that has been developed specifically to automate Resistive Random Access Memory (RRAM) generation. RRAM holds the promise of achieving high speed, high density and non-volatility. A novel RRAM architecture, additionally is proposed, and a number of generated RRAM arrays are evaluated to identify their worst case control line parasitics and worst case settling time across the memristors of their cells. The total capacitance of lines SEL, N and P is 5.83 fF/cell, 3.31 fF/cell and 2.48 fF/cell respectively, while the total calculated resistance for SEL is 1.28 Ohm/cell and 0.14 Ohm/cell for both N and P lines.

[An Open-Source RRAM Compiler](https://arxiv.org/abs/2111.05463) presented in NEWCAS 2022

###### Abstract - Memory compilers are necessary tools to boost the design procedure of digital circuits. However, only a few are available to academia. Resistive Random Access Memory (RRAM) is characterised by high density, high speed, non volatility and is a potential candidate of future digital memories. To the best of the authors' knowledge, this paper presents the first open source RRAM compiler for automatic memory generation including its peripheral circuits, verification and timing characterisation. The RRAM compiler is written with Cadence SKILL programming language and is integrated in Cadence environment. The layout verification procedure takes place in Siemens Mentor Calibre tool. The technology used by the compiler is TSMC 180nm. This paper analyses the novel results of a plethora of M x N RRAMs generated by the compiler, up to M = 128, N = 64 and word size B = 16 bits, for clock frequency equal to 12.5 MHz. Finally, the compiler achieves density of up to 0.024 Mb/mm2.

------------------------------------------

**Thesis**

Large-scale Mixed-signal RRAM Array Compiler for Automatic Memory Generation and Verification

###### Abstract - A handful of conventional memory compilers are only available to academia. Conventional memories suffer of volatility issues, high power consumption, high write voltage and low endurance. A number of emerging memory technologies are investigated to tackle the problems. The most promising type of memory is the Resistive Random Access Memory (RRAM). RRAM holds the promise of achieving high speed, high density and non-volatility. This thesis presents an open source RRAM compiler for automatic memory generation and verification. The RRAM compiler is directly integrated within the Cadence Virtuoso and Innovus environment, using physical verification tools provided by Mentor Graphics (Calibre). The compiler automatically generates the RRAM array and its peripheral circuits, verifies its layout and performs timing characterisation of the generated memory. To the best of the authors’ knowledge, this is the first open-source RRAM compiler. Additionally, a novel RRAM architecture is presented and a plethora of square N x N (up to N = 128) RRAM arrays are investigated regarding their worst case control line parasitics and their worst case settling time across the memristors of their cells. A number of various sizes and combinations of M x N RRAMs ,up to M = 128, N = 64 and word size B = 16 bits, are generated and characterised for clock frequencies equal to 25 MHz, 16.66 MHz and 12.5 MHz. The generated RRAMs, including both digital and peripheral circuits, achieve a density of up to 0.024 Mb/mm2 in 180 nm technology.

**Research Project Objectives**

1. to develop an open source array compiler.
2. to design a large-scale ReRAM memory with essential peripheral circuits, such as sense amplifier, address decoder, write
driver, column multiplexer.

The expected outcome of this project is to realize the automatic ReRAM generation from schematic to layout togethering with
physical verification and timing/power characteristics. The deliverable outcome from the student will be a final report showing
Cadence implementation with main compiler components

Abstract RRAM Compiler Flow

------------------------------

**Instructions**

0. Dependencies: This RRAM Compiler is currently using TSMC 180nm technology. The source code is based on the SKILL programming language. Therefore, this compiler needs TSMC PDK 180nm, Cadence Tools and Mentor Calibre tools for verification. Additionally, it needs the basic cellviews 1T1R, SA, WR etc which are used to generate RRAM and its peripheral circuits.

1. The RRAM MEMORY COMPILER files are SKILL code scripts and they have to be placed under folder SKILL in working directory. More specifically, under the working directory, in which the virtuoso command is invoked create a folder named SKILL.

>>mkdir SKILL
>>
>>mkdir RRAM_COMPILER_LOG

2. Under the working directory modify the .cdsinit file to load the corresponding scripts.

>>gedit .cdsinit

3. At the end of the file import the following lines of code.

>>setSkillPath( append( '("./SKILL/RRAM_COMPILER/RRAM_v_3_analog") getSkillPath() ) )		; load path to personal skill scripts
>>
>>load("loadRRAM.il")
>>
>>loadRRAMCompiler()

4. Download RRAM COMPILER Repository and place folder RRAM_COMPILER inside folder SKILL

5. Copy DIGITAL to working directory. Generate folders constraints, tcl, reports, innovus, work if they dont exist.

6. Further TSMC technology Files are needed to run the compiler. After examing which files can be uploaded without violating agreement of use, the repository will be updated.

-----------------------------------

**Function Definition**

createRRAMmixed(		; LIST OF ARGUMENTS
			M		; NUMBER OF COLUMNS b2^X
			N		; NUMBER OF ROWS 2^Y						
			B		; BITS OF A WORD B			
			@optional
			(CLOCK_PS		10000)	; 10ns digital clock
			(LIBRARY "THESIS")
			(VDDW 3.3)
			)		; END OF LIST OF ARGUMENTS

----------------------------------------

**RRAM Memory Cell**

The memory cell of the proposed RRAM consists of 1 memristor 1 transitor. The cellview in the EDA tool does not include the memristor, as it will be placed later on top of the memory cell. The schematic of a memory cell is shown on the next figure.

The RRAM Array is presented on the following image. The SEL lines are shared horizontally and P,N lines are shared vertically.

**RRAM Memory Architecture**

The proposed simplified architecture is show on the image below.

**Version 2 RRAM Compiler Generated 128 x 128 Array**

**Sense Amplifiers**

All sense amplifiers were tested in an equaivalent testbech of 4Mb based on the results presented on 
[Open-Source Memory Compiler for Automatic RRAM Generation and Verification](https://arxiv.org/abs/2104.14885). The outputs of Sense Amplifiers in the testbench had been driving 50.47fF Capacitors. An 100 Monte Carlo Analysis was run on every Sense Amplifier for every possible combination found in the tables below. Even though, 100 Point Monte Carlo Analysis is not enough to estimate the yield of each Sense Amplifier, it provides a clear view about the performance of each Sense Amplifier regarding speed and accuracy. The ratio is the R/R_REF where R_REF is the equivalent resistance of 35kOhm of a nmos transistor which will be used in the architecture as refernece. For the simulation the state was initialised to LRS (HRS) and then altered to HRS (LRS). Both states had to be read correctly for test to be characterised as successful. The read times shown on tables refer to the whole read cycle, the access time occures on the last phase of each cycle, therefore, it is less than the time shown on table. The following Sense Amplifiers have either 1/2 or 2/3 access time of read cycle. As access time, it referred the time that it takes until the correct output is latched.

*Latch Type*

Based on [Design of Sense Amplifiers for Non-Volatile Memory](https://ieeexplore.ieee.org/document/8757026) and [Analysis of sense amplifier circuits in nanometer technologies](https://ieeexplore.ieee.org/abstract/document/8085666). Its schematic is shown below

| R (Ohm) | Ratio | 10n | 20n | 30n | 40n | 50n |
| --- | --- | --- | --- | --- | --- | --- |
| 1000     | 0.028571429 | 0%   |   100% |   100% |   100% |   100% |
| 2387     | 0.0682      | 0%   |   100% |   100% |   100% |   100% |
| 5700     | 0.162857143 | 0%   |   100% |   100% |   100% |   100% |
| 13611    | 0.388885714 | 0%   |   100% |   100% |   100% |   100% |
| 20000    | 0.571428571 | 0%   |   100% |   100% |   100% |   100% |
| 32500    | 0.928571429 | 0%   |   100% |   100% | 97%   | 90%    |
| 40000    | 1.142857143 | 0%   | 0%    | 30%    | 68%    | 86%    |
| 60000    | 1.714285714 | 0%   | 2%      | 100%   |100%    | 100%   |
| 89442    | 2.555485714 | 0%   | 68%    | 100%   |100%    | 100%   |
| 200000   | 5.714285714 | 0%   | 100%   | 100%   |100%    | 100%   |
| 447213   | 12.77751429 | 0%   | 100%   | 100%   |100%    | 100%   |
| 1000000  | 28.57142857 | 0%   | 100%   | 100%   |100%    | 100%   |

*Proposed two stage Sense Amplifier*

Based on [Current-mode techniques for high-speed VLSI circuits with application to current sense amplifier for CMOS SRAM's](https://scholar.google.com/scholar?cluster=17946312173679186529&hl=en&as_sdt=0,5) and [The cross-coupled pair-part ii](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.718.2762&rep=rep1&type=pdf). First and second stages are shown below.

| R(Ohm) | Ratio | 10n | 20n | 30n | 40n | 50n |  
| --- | --- | --- | --- | --- | --- | --- |
| 1000  | 0.028571429 | 0% | 97% | 100% | 100% | 100% |  
| 3191  | 0.091171429 | 0% | 97% | 100% | 100% | 100% |
| 10184 | 0.290971429 | 0% | 97% | 100% | 100% | 100% | 
| 20000 | 0.571428571 | 0% | 97% | 100% | 100% | 100% |  
|32500 | 0.928571429 | 0% | 97% | 100% | 93%  | 84% |                        
|40000 | 1.142857143 | 0% | 88% | 100% | 100% | 99% |                           
| 60000 | 1.714285714 | 0% | 100% | 100% | 100% | 100% | 
| 116960 | 3.341714286 | 0% | 100% | 100% | 100% | 100% | 
| 341000 | 9.742857143 | 0% | 100% | 100% | 100% | 100% | 
| 1000000 | 28.57142857 | 0% | 100% | 100% | 100% | 100% |

*Dimitris proposed 3 stages Sense Amplifier*

This sense amplifier is quite similar to the previous one but it is a current mode only Sense Amplifier. The first stage is a modified version of the previous one and is based on the ideas presented on [Current-mode techniques for high-speed VLSI circuits with application to current sense amplifier for CMOS SRAM's](https://scholar.google.com/scholar?cluster=17946312173679186529&hl=en&as_sdt=0,5), [Precision differential voltage–current convertor](https://digital-library.theiet.org/content/journals/10.1049/el_19730109) and [A high-speed clamped bit-line current-mode sense amplifier](https://ieeexplore.ieee.org/document/75052). The idea is that due to the caprio's quad, the current drawn by lower transistors will be equal, therefore, the difference of bitlines can be extracted by copying the top branch currents. The currents are copied by a CCII- ([CMOS Current Amplifiers](https://www.springer.com/gp/book/9780792384694)) and then they are compared through a regenerative latch based on the idea of [1.5GHz fully differential latched current comparator with 20nA of sensitivity](https://ieeexplore.ieee.org/abstract/document/1689926).

| R       | Ratio       | 10n | 12.5n | 15n  | 20n  | 30n  | 50n   |       
| ---     | ---         | --- | ---   | ---  | ---  | ---  | ---   |
| 1000    | 0.028571429 | 43% | 95%   | 100% | 100% | 100% | 100% |    
| 10000   | 0.285714286 | 16% | 70%   | 96%  | 99%  | 100% | 100% |     
| 20000   | 0.571428571 | 17% | 55%   | 84%  | 94%  | 100% | 100% |    
| 30000   | 0.857142857 | 11% | 56%   | 76%  | 80%  | 94%  | 94%  |                             
| 32500   | 0.928571429 | 11% | 59%   | 78%  | 77%  | 83%  | 79%  |
| 37710   | 1.077428571 | 8%  | 18%   | 63%  | 77%  | 89%  | 90%  |                              
| 40840   | 1.166857143 | 14% | 42%   | 71%  | 86%  | 93%  | 99%  |                              
| 61000   | 1.742857143 | 17% | 65%   | 81%  | 87%  | 100% | 100% |    
| 122000  | 3.485714286 | 30% | 66%   | 80%  | 92%  | 100% | 100% |     
| 1228000 | 35.08571429 | 40% | 74%   | 88%  | 97%  | 100% | 100% |  
  
*Current Sampling Based Sense Amplifier*

This amplifier is presented on [An Offset-Tolerant Fast-Random-Read Current-Sampling-Based Sense Amplifier for Small-Cell-Current Nonvolatile Memory](https://ieeexplore.ieee.org/document/6407149). It is a low power, high accuracy Sense Amplifier. Below, its schematic is shown and Monter Carlo Analysis for various VDD. Multiples VDDs were tested because this Sense Amplifier loads a high voltage compared to VDD on the bitlines that could alter the state of the transistor.

VDD = 1.8V

|R(Ohm)  | Ratio        | 10n | 20n  | 30n  | 40n  | 50n  | 75n  | 100n | 125n | 150n | 
| ---    |       ---    | --- | ---  | ---  | ---  | ---  | ---  | ---  | ---  | ---  |
|100     | 0.028571429  | 0%  | 90%  | 90%  | 91%  | 100% | -    | -    | -    |  -   |                           
|3191    | 0.091171429  | 0%  | 90%  | 90%  | 91%  | 100% |-     |-     |-     |   -  |                          
|10184   | 0.290971429  | 0%  | 0%   | 90%  | 91%  | 100% | -    |-     | -    |   -  |                            
|20000   | 0.571428571  | 0%  | 0%   | 0%   | 79%  | 100% | 100% | 100% | 100% | 100% |
|23513   | 0.6718085714 | -   | -    | -    | -    | 100% | 100% | 100% | 100% | 100% |
|27643   | 0.7898228571 | -   | -    |-     | -    | 100% | 100% | 100% | 100% | 100% |
|32500   | 0.928571429  | 0%  | 0%   | 0%   | 71%  | 100% | 100% | 99%  | 97%  | 96%  |                         
|40000   | 1.142857143  | 0%  | 100% | 100% | 100% | 100% | 100% | 99%  | 96%  | 90%  |                        
|45000   | 1.285714286  |-    |   -  |   -  |  -   | 100% | 100% | 100% | 100% | 100% |
|52000   | 1.485714286  |  -  |  -   |  -   |  -   | 100% | 100% | 100% | 100% | 100% | 
|60000   | 1.714285714  | 0%  | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
|116000  | 3.314285714  | 0%  | 100% | 100% | 100% | 100% |   -  |    - | -    |    - |                          
|341000  | 9.742857143  | 0%  | 100% | 100% | 100% | 100% |   -  | -    |  -   |    - |                        
|1000000 | 28.57142857  | 0%  | 100% | 100% | 100% | 100% |  -   |  -   |   -  |    - |

VDD = 1.5V

|R       | Ratio       | 50n  | 100n | 150n |
|   ---  |   ---       | ---  | ---  | ---  |
|1000    | 0.028571429 | 99%  | 100% | 100% |
|3191    | 0.091171429 | 99   | 100% | 100% |
|10184   | 0.290971429 | 99%  | 100% | 100% |
|20000   | 0.571428571 | 99%  | 100% | 100% |
|32500   | 0.928571429 | 99%  | 99%  | 94%  |
|40000   | 1.142857143 | 100% | 100% | 95%  |
|60000   | 1.714285714 | 100% | 100% | 100% |
|116960  | 3.341714286 | 100% | 100% | 100% |
|341995  | 9.771285714 | 100% | 100% | 100% |
|1000000 | 28.57142857 | 100% | 100% | 100% |

VDD = 1.2V

|R       | Ratio       | 50n  | 100n | 150n |
|   ---  |   ---       | ---  | ---  | ---  |
|1000    | 0.028571429 | 99%  | 100% | 100% |
|3191    | 0.091171429 | 99%  | 100% | 100% |
|10184   | 0.290971429 | 99%  | 100% | 100% |
|20000   | 0.571428571 | 99%  | 100% | 100% |
|32500   | 0.928571429 | 99%  | 99%  | 94%  |
|40000   | 1.142857143 | 100% | 100% | 95%  |
|60000   | 1.714285714 | 100% | 100% | 100% |
|116960  | 3.341714286 | 100% | 100% | 100% |
|341995  | 9.771285714 | 100% | 100% | 100% |
|1000000 | 28.57142857 | 100% | 100% | 100% |

VDD = 0.9V

|R       | Ratio       | 50n  | 100n | 150n |
|   ---  |   ---       | ---  | ---  | ---  |
|1000    | 0.028571429 | 92%  | 100% | 100% |
|3191    | 0.091171429 | 92%  | 100% | 100% |
|10184   | 0.290971429 | 92%  | 100% | 100% |
|20000   | 0.571428571 | 0%   | 100% | 100% |
|32500   | 0.928571429 | 0%   | 100% | 97%  |
|40000   | 1.142857143 | 100% | 100% | 100% |
|60000   | 1.714285714 | 100% | 100% | 100% |
|116960  | 3.341714286 | 100% | 100% | 100% |
|341995  | 9.771285714 | 100% | 100% | 100% |
|1000000 | 28.57142857 | 100% | 100% | 100% |

**Analog Part Simplified Schematic**

The image shown below, shows a simplified version of the Analog Part of the RRAM generated by Version 3. Switches may be nmos switches or transmission gates. This image shows a RRAM Array of 4 x 4. The size of a word is 2 bits. A reference array is on the top right integrated in the RRAM Array schematic. The nmos transistors of the Reference array have resistance in between HRS and LRS of the memristor and facilitate a differential sensing in order to improve the accuracy.

**Proposed Layout Version 3**

The image below shows a simplified version of the layout of the proposed RRAM based on version 3.
<img src="https://github.com/akdimitri/RRAM_COMPILER/blob/main/images/ANALOG_LAYOUT_2.png" width="800">

**Proposed Analog Layout Version 3**

The image below shows a small array of 64 x 64, where the width of a word is 4 bits. This array was chosen so that the circuits location is clear in the image. As the size grows, the smaller relatively to the total area the layout of Write Drivers/Sense Amplifier/IO circuits become. The layout is surrounded on the right and top by power lines which will be later connected on the top level design.

**Proposed RRAM Schematic**

**Proposed RRAM Layout Version 3**

The image below shows a small array of 64 x 64, where the width of a word is 8 bits. This array was chosen so that the circuits location is clear in the image. As the size grows, the smaller relatively to the total area the layout of Write Drivers/Sense Amplifier/IO circuits become. The layout is surrounded by power lines.  The density of memory for this size is around 0.023 Mb/mm2.

**Timing Characterisation**

Timing Characterisation performs 4 tests. Initially, reset signal is received, then a {10...10} is received on IO and write signals at controller. Write signals are for the second to last (horizontally) word on the top row. For this test 1MOhm has been used for resistors, since they cause worst case settling time. Then the complementary value is written. For the read test, initially the last word is set to {10...10} by using values 0.3 * RRef. After this read operation, the resistances are altered and their complementary values are used.

40ns Clock

https://rawcdn.githack.com/akdimitri/RRAM_COMPILER/d65a0a1e8cd08897fe44e501b39ce588698ae23b/raw/64_64_8_CHARACTERIZATION/40_TB_TOP_64_64_8.html

60ns Clock

https://rawcdn.githack.com/akdimitri/RRAM_COMPILER/d65a0a1e8cd08897fe44e501b39ce588698ae23b/raw/64_64_8_CHARACTERIZATION/60_TB_TOP_64_64_8.html

80ns Clock

https://rawcdn.githack.com/akdimitri/RRAM_COMPILER/d65a0a1e8cd08897fe44e501b39ce588698ae23b/raw/64_64_8_CHARACTERIZATION/80_TB_TOP_64_64_8.html

Digital Implementation

Controller

https://rawcdn.githack.com/akdimitri/RRAM_COMPILER/d65a0a1e8cd08897fe44e501b39ce588698ae23b/raw/64_64_8_CHARACTERIZATION/CONTROLLER_5V_64_64_8_innovus_metrics.html#run=0

Low Voltage Controll Signals

https://rawcdn.githack.com/akdimitri/RRAM_COMPILER/d65a0a1e8cd08897fe44e501b39ce588698ae23b/raw/64_64_8_CHARACTERIZATION/SIGNALS_VDDL_64_64_8_innovus_metrics.html

<!---

**Automatically Synthesized Controller in Genus**

The image below shows the schematic of the automatically synthesised based on desired sizes Controller using VDD. This controller is a for a 32 x 32 Array, with 8 bits word.

**Ideal Simulation of a 16 x 16 RRAM with 2 bits word length**

The image below shows the schematic of the testbench for a RRAM of 16x16 with 2 bits word and Latch Type Sense Amplifier. The circuits are based on the architecture presented above. VDDH was set to 5V, VDDW to 3.3V and VDDL to 1.8V. Assuming cordinates (X, Y) where X is a column and Y a row starting counting from 1. The following Resistances have been used:

- R(16,16) = 1M
	- R(15,16) = 1k
	- R(14,16) = 100k
	- R(13,16) = 100k
	
The Reference Resistance for Read Operation is 35k.

Since the RRAM has 16 columns and uses 2 bits words, then multiplexeres needed will be 16 to 2 and they need 2^k=16/2 => k = 3 bits adress word to be controlled. So Column Word Adresses are from 0 to 7, plus 1 to enable reference circuits.
Since the RRAM has 16 rows then  they need 2^k=16 => k = 4 bits word adress. So Ro addresses are from 0 to 15.

The image below shows the write operation at 
	
	-SEL = 16 starting counting from 1 (SEL = 15 starting counting from 0).
	-Columns = [13,14] starting counting from 1 controlled by P_EN[7] starting counting from 1 (Columns = [12,13] 
	starting counting from 0 controlled by P_EN[6] starting counting from 1).
	
	Different counting convention has been used for analog and digital signals.
	
It is shown that after EN, addresses, and Z_WR (I/O port) signals are received, on the next cycle, P and N lines are set either to 3.3V or 0.
Z_WR<1> accounts for the values written on (13,16) and Z_WR<2> for the values written on (14,16). Inittialy, 2'b10
 is written and then 2'b10.
 
<img src="https://github.com/akdimitri/RRAM_COMPILER/blob/main/images/write_16_16_2.png" width="600">

The image below shows the read operation of (15,16) and (16,16) inittially. So when Latch is Enabled the output is 1.8V for R(16,16)>RRef and 0V for (15,16)<RRef. Then the read opeartion is executed for R(13,16)>RRef and R(14,16)?RRef and 1.8V are outputted.

--->

--------------------------------

**Comparison of Versions**

The difference between version 1 and version 2 are in Schematic and Layout Implementation. The following two figures do not include the execution time of DRC, LVS, PEX where the same functions are used. They show the execution time in seconds and the speed up for a RRAM array of SIZExSIZE.

The algorithm complexity is the same for both versions equal to O(n^2) + c(n), where c(n) is the complexity of the Verification Algorithm of Calibre Tool. The second version is much faster on implementation because whole row blocks of RRAM are instantiated. Therefore the instantiaton of cells is of O(n) complexity. The first version instantiates the RRAM cell by cell and the complexity is O(n^2). However, both of them instantiate MR pins pin by pin in each row and line and this is why the second version has also O(n^2) complexity on implementation. Though, the speed up in second version is huge.

The image below shows the execution time including Calibre Verification(DRC, LVS, PEX, Calibre View Setup). It can be shown that Verification occupies the largest portion of execution time. As expected, because of the n^2 complexity of the algorithm, the execution time rises exponentially.

The table below compares the execution times without verification of both versions and the execution time including verification of the second version. The second version achieves better perfomance including verification compared to the first version without including verification. The verification time is the main reason of slowing down the algorithm, since the larger th e size, the longer time it takes for the system to complete the DRC,LVS,PEX and Calibre View Setup. Out of the four verification operations, PEX and Calibre View Setup are the most time consuming. All the measurements are in **seconds**. SIZE refers to an array of size equal to SIZExSIZE.

| SIZE | v1 without verification | v2 without verification | v2 with verification | v2 without verification/ v2 with verification |
| --- | --- | --- | --- | --- |
| 2 | 3.21 | 7.44 | 44.53 | 0.173 |
| 4 | 3.7 | 7.93 | 44.28 | 0.179 |
| 8 | 3.97 | 7.91 | 47.79 | 0.165 |
| 16 | 4.78 | 8.06| 57.61 | 0.139 |
| 32 | 11.66 | 8.4 | 108.61 | 0.077 |
| 64 | 101.76 | 29.51 |302.28 | 0.097 |
| 128 | 1815 | 68.55 | 1096.07 | 0.062 |

The second version creates a fully verified 256x256 RRAM array in 3970.3 seconds, while it takes 22132.72 seconds for a 512x512 array.

The following table presents the timing for every function involved in the RRAM creation and verification. The most time is consumed by PEX. Small variations of same size on different runs may be due to server cpus involved, servers usage etc.

|SIZE | IMPLEMENTATION   | DRC       | LVS       | PEX         | SETUP       | TOTAL       |
|---  | ---              | ---       | ---       | ---         | ---         | ---         |
|2    | 7.50099          | 10.748419 | 8.942634  | 16.239728   | 5.383092    | 48.814863   |
|4    | 7.753175         | 10.596107 | 8.954458  | 16.240825   | 5.384769    | 48.929334   |
|8    | 7.675531         | 10.734499 | 8.663386  | 17.892335   | 6.716267    | 51.682018   |
|16   | 7.774973         | 11.296378 | 9.237844  | 23.56026    | 10.979237   | 62.848692   |
|32   | 8.042589         | 11.955142 | 9.28168   | 53.370914   | 29.845477   | 112.495802  |
|64   | 11.596684        | 13.300558 | 10.088026 | 169.807008  | 102.532625  | 307.324901  |
|128  | 44.291783        | 17.721942 | 11.997517 | 611.663116  | 409.871364  | 1095.545722 |
|256  | 496.515316       | 32.068824 | 19.154827 | 2101.401427 | 1675.637499 | 4324.777893 |
|512  | 7400.911615      | 80.894543 | 51.157234 | 7914.391475 | 7043.145462 | 22490.50033 |

The following image presents the above table. It shows that PEX, Calibre Setup View and Implementation share almost equal time for large arrays. However, the speed up of the second version remains huge. On the contrary, DRC and LVS time is almost negligble for large arrays.

------------------------------------

**Parasitics Extraction**

PEX creates an net.summary under .PEX_Calibre folder inside cellview folder. By using a matlab script the following worst case C+CC (F) were calculated for arrays of SIZExSIZE. As the SIZE gets larger, the worst case C+CC gets larger.

|SIZE | SEL      | P        | N        | MR       | VSS      |
|---  | ---      | ---      | ---      | ---      | ---      |
|2    | 9.80E-15 | 4.74E-15 | 7.03E-15 | 3.18E-15 | 4.62E-15 |
|4    | 2.17E-14 | 9.81E-15 | 1.35E-14 | 3.20E-15 | 1.34E-14 |
|8    | 4.25E-14 | 1.87E-14 | 2.53E-14 | 3.20E-15 | 4.38E-14 |
|16   | 8.42E-14 | 3.65E-14 | 4.90E-14 | 3.20E-15 | 1.56E-13 |
|32   | 1.68E-13 | 7.21E-14 | 9.63E-14 | 3.20E-15 | 5.90E-13 |
|64   | 3.34E-13 | 1.43E-13 | 1.91E-13 | 3.20E-15 | 2.28E-12 |
|128  | 6.68E-13 | 2.86E-13 | 3.80E-13 | 3.20E-15 | 8.99E-12 |
|256  | 1.34E-12 | 5.70E-13 | 7.59E-13 | 3.20E-15 | 3.56E-11 |
|512  | 2.68E-12 | 1.14E-12 | 1.52E-12 | 3.20E-15 | 1.42E-10 |

The following image shows that C+CC rises linearly with regard to the number of cells of a line.

The following image shows that R rises linearly with regard to the number of cells of a line.

**Settling Time**

The worst case settling time for TT model libray occurs for VN=5, VP=0 and R=5MΩ. In general, settling time increases as R increses. The settling time simulations are time consuming. Therefore, the following graph presents results only for arrays with size less than 128x128. It is clear that as array increases exponential, settling time increases too. For the worst case the top right Memristor was chosen. The input pins are placed on the lower left, so the top right Memeristor is expected to have the longest path and as such the worst settling time. The settling interval confidence was set equal to 99%.

The worst case settling time for SS model libray is shown on the next figure. It is the worst possible scenario for settling time across the memristor.

**Known Problems**

Do *not overwrite* a RRAM Cellview. *Delete* and rerun the compiler. If a problem persists try removing potential .cdslck files and *rerun virtuoso*.

RRAM_COMPILER

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