c# create nested JSON from Model

I am trying to create this nested json string in .NET Core2/C# from model but cant quite wrap my head around it:

{ 
  \"SearchByKeywordRequest\":
   { 
     \"keyword\": \""+transistor+"\", \"records\": 0, \"startingRecord\": 0, \"searchOptions\": \"string\", \"searchWithYourSignUpLanguage\": \"string\" 
   }
 }

I referred to this solution but couldnt get it to format properly for my case

Model

 public class SearchByKeyword
{
    public List<SearchByKeyword> SearchByKeywordRequest { get; set; }
    public string keyword { get; set; }
    public int records { get; set; } = 10;
    public string searchOptions { get; set; } = string.Empty;
    public string searchWithYourSignUpLanguage { get; set; } = string.Empty;
}

Method

public string CreateJson(string transistor) {
        var obj = new SearchByKeyword() {                     
            SearchByKeywordRequest = new List<SearchByKeyword>()
            {
                new SearchByKeyword()
                {
                    keyword = transistor
                }
            }

        };

       return  JsonConvert.SerializeObject(obj);  
    }

this is the string i end up with

"{
  \"SearchByKeywordRequest\":
[ { \"SearchByKeywordRequest\":null, \"keyword\":\"KSA992F\",\"records\":10,\"searchOptions\":\"\",\"searchWithYourSignUpLanguage\":\"\"}],\"keyword\":null,\"records\":10,\"searchOptions\":\"\",\"searchWithYourSignUpLanguage\":\"\"
 }"

Now if I try this in method

    var obj = new List<SearchByKeyword>()
            {
                new SearchByKeyword()
                {
                 keyword = transistor
                }
            };

I get this string

"[{\"SearchByKeywordRequest\":null,\"keyword\":\"KSA992F\",\"records\":10,\"searchOptions\":\"\",\"searchWithYourSignUpLanguage\":\"\"}]"   

Updated Model

    public class SearchByKeyword
{
    [JsonProperty("SearchByKeywordRequest", NullValueHandling = NullValueHandling.Ignore)]
    public SearchByKeyword SearchByKeywordRequest { get; set; }
    public string keyword { get; set; }
    public int records { get; set; } = 10;   
}

Updated Method

       var obj = new
            {
                SearchByKeywordRequest = new SearchByKeyword()
                {
                    keyword = transistor
                }
            };

            string json = JsonConvert.SerializeObject(obj);